text stringlengths 1.23k 293k | tokens float64 290 66.5k | created stringdate 1-01-01 00:00:00 2024-12-01 00:00:00 | fields listlengths 1 6 |
|---|---|---|---|
SURF-BRISK – Based Image Infilling Method for Terrain Classification of a Legged Robot
Abstract: In this study, we propose adaptive locomotion for an autonomous multilegged walking robot, an image infilling method for terrain classification based on a combination of speeded up robust features, and binary robust invariant scalable keypoints (SURF-BRISK). The terrain classifier is based on the bag-of-words (BoW) model and SURF-BRISK, both of which are fast and accurate. The image infilling method is used for identifying terrain with obstacles and mixed terrain; their features are magnified to help with recognition of different complex terrains. Local image infilling is used to improve low accuracy caused by obstacles and super-pixel image infilling is employed for mixed terrain. A series of experiments including classification of terrain with obstacles and mixed terrain were conducted and the obtained results show that the proposed method can accurately identify all terrain types and achieve adaptive locomotion.
Introduction
Multilegged robot that origniated from reptile bionics has good walking stability and low energy consumption in its stationary state.It maintains good stability in complex environments owing to its redundant limb structure [1].Compared with a wheeled robot, the multilegged robot can cross big obstacles and has many degrees of freedom.Its flexibility and adaptability on complex terrain allow the legged robot to have wide application.Researchers have designed different multilegged robots, such as mine-sweeping [2], volcano-detecting [3], underwater [4], strawberry-picking [5], and transfer robots, in addition to other prototypes.The autonomous mobile ability of multilegged robots is affected by how it perceives its surrounding environment.Multilegged robots mainly work in unstructured environments, so classifying various terrains, detecting obstacles, and localizing and recognizing complex terrain have become primary issues in the field.
For multilegged robots, environment perception is mainly related to accurate terrain identification and obstacle detection.The most normal way is to use image processing methods and classifiers.By extracting information from terrain images, such as spectra [6], color [7], texture [8,9], scale-invariant feature transform (SIFT) features [10], speeded up robust features (SURF) [11], and the DAISY descriptor [11], the terrain can be accurately identified.However, spectral-based methods concentrate on spatial frequencies of texture distributions and color-based methods have poor robustness and are easily affected by light and weather conditions.Among them, local features that are invariant in terms of scale, rotation, brightness, and contrast have been widely used in visual classification.Besides vision, legged robots are often equipped with other sensors, so information from multiple sensors for terrain recognition is also available.Kim [12] used the friction coefficient of different terrains to classify terrains using the Bayes classifier.Ojeda [13] proposed a terrain classification method based on an integration of information from multiple sensors (gyroscopes, accelerometers, encoders).Larson [14] proposed a model based on robot inclination angle obtained from an odometer.Hoepflinger [15] used current values of joint electricity and force sensor data to recognize terrain categories.Jitpakdee [16] proposed a neural network model for terrain classification based on robot body acceleration and angular velocity of the inertial measurement unit (IMU).These kinds of information are quite different from visual information and so special methods are needed.
Most of the existing methods have good classification accuracy on single-type terrain, but few are suitable for mixed terrain, which is common in the natural environment.To solve this problem, Filitchkin [17] used a sliding window technique for heterogeneous terrain images.Liang [18] compiled an algorithm for complex terrain classification based on multisensor fusion.Ugur [19] proposed a learning method to predict the environment by consecutive distance-and shape-related feature extraction.However, most of these methods have poor robustness because they require high-resolution images.Mixed terrain has different features than single-type terrain and sometimes the edges of the terrain cannot be recognized clearly, which makes identification of mixed terrain difficult.In order to enhance the recognition rate of detecting mixed terrain and terrain with obstacles, a systematic classification method for complex terrain is proposed in this paper.The following aspects were studied: Terrain information collected by a Kinect 3D vision sensor.Herein, we established a fast and effective terrain classifier based on speeded up robust features and binary robust invariant scalable key points (SURF-BRISK) features and support vector machine (SVM).A segmentation method for complex terrain images based on super-pixels is proposed, which can effectively segment complex terrain images into single terrain images.An image infilling method for terrain with obstacles and mixed terrain is also proposed.The local features are magnified to help the recognition of different complex terrains.Experiments on classifying terrain with obstacles and mixed terrain are conducted.The proposed system is validated by the multilegged robot.
This paper is organized as follows: In Section 2, the hexapod robot and SURF-BRISK-based image infilling method are introduced.In Section 3, the experimental results are presented and analyzed.Section 4 summarizes and concludes the paper.
Hexapod Walking Robot: SmartHex
In this paper, a six-legged robot with mammalian leg structure named SmartHex is used [20].Each leg has three joints: base joint, hip joint, and knee joint.The robot is suitable for outdoor work due to its low energy consumption and large load characteristics [21].The robot is controlled by a backward control based on a σ-Hopf oscillator with decoupled parameters for smooth locomotion [22].The hardware structure of the robot is shown in Figure 1.BLi, HLi, and KLi (BRi, HRi, and KRi), respectively, indicate the base joint, hip joint, and knee joint of the left (right) leg.LF, LM, and LH (RF, RM, and RH), respectively, indicate the front leg, middle leg, and hind leg of the left (right) side.Each joint consists of a high-reduction-rate gear system and a DC servo motor with an integrated encoder, which is used to detect the position of the joint angle.In order to identify the environment around the robot with a high accuracy, Microsoft's Kinect 3D vision sensor is installed on the robot chassis to collect terrain information.The Kinect's red/green/blue (RGB) camera can collect color images with a resolution of 1920 × 1080 px.A complementary metal-oxide superconductor (CMOS) sensor is responsible for receiving and transmitting infrared signals.Meanwhile, current detection modules (CuSLi and CuSRi) are installed to record the energy consumption of each leg for different gaits.The arrows in Figure 1 indicate the directions of current flow.The robot's posture is monitored by the attitude sensor (AS).The data processed by the wireless module mounted on the control panel are transmitted to the host computer to create instructions [23].
image infilling method are introduced.In Section 3, the experimental results are presented and analyzed.Section 4 summarizes and concludes the paper.
Terrain Classification Methodology
In robot navigation, terrain recognition can essentially be supposed as surface texture recognition.Terrain recognition based on local features is the most popular because of its robustness to illumination and weather and high recognition rate.
The terrain classification system proposed in this paper is depicted in Figure 2. The Kinect is installed on top of the robot to collect information on terrain (color, depth, and infrared images) and an obstacle detection module is established to detect obstacles in the front.If there are no obstacles, the information will be directly transmitted to the terrain classifier.Otherwise, the module will locate obstacles and identify their size.Meanwhile, a color image of the terrain is processed by the image infilling method to decrease the influence of obstacles on terrain identification.After classification, the confidence scores of each terrain are summarized into a pie chart.The analysis of the pie chart shows whether the terrain is mixed or not.If the terrain is mixed, the color image would be subjected to image segmentation and infilling.Then, the processed color image will be classified by the terrain classifier again, which provides an accurate identification of multiple areas of complex terrain.Finally, all terrain types can be predicted accurately, thus good performance by the robot is guaranteed.The function modules are described in detail in the following section.In this paper, a six-legged robot with mammalian leg structure named SmartHex is used [20].Each leg has three joints: base joint, hip joint, and knee joint.The robot is suitable for outdoor work due to its low energy consumption and large load characteristics [21].The robot is controlled by a backward control based on a σ-Hopf oscillator with decoupled parameters for smooth locomotion [22].The hardware structure of the robot is shown in Figure 1.BLi, HLi, and KLi (BRi, HRi, and KRi), respectively, indicate the base joint, hip joint, and knee joint of the left (right) leg.LF, LM, and LH (RF, RM, and RH), respectively, indicate the front leg, middle leg, and hind leg of the left (right) side.Each joint consists of a high-reduction-rate gear system and a DC servo motor with an integrated encoder, which is used to detect the position of the joint angle.In order to identify the environment around the robot with a high accuracy, Microsoft''s Kinect 3D vision sensor is installed on the robot chassis to collect terrain information.The Kinect's red/green/blue (RGB) camera can collect color images with a resolution of 1920 × 1080 px.A complementary metal-oxide superconductor (CMOS) sensor is responsible for receiving and transmitting infrared signals.Meanwhile, current detection modules (CuSLi and CuSRi) are installed to record the energy consumption of each leg for different gaits.The arrows in Figure 1 indicate the directions of current flow.The robot's posture is monitored by the attitude sensor (AS).The data processed by the wireless module mounted on the control panel are transmitted to the host computer to create instructions [23].
Terrain Classification Methodology
In robot navigation, terrain recognition can essentially be supposed as surface texture recognition.Terrain recognition based on local features is the most popular because of its robustness to illumination and weather and high recognition rate.
The terrain classification system proposed in this paper is depicted in Figure 2. The Kinect is installed on top of the robot to collect information on terrain (color, depth, and infrared images) and an obstacle detection module is established to detect obstacles in the front.If there are no obstacles, the information will be directly transmitted to the terrain classifier.Otherwise, the module will locate obstacles and identify their size.Meanwhile, a color image of the terrain is processed by the image infilling method to decrease the influence of obstacles on terrain identification.After classification, the confidence scores of each terrain are summarized into a pie chart.The analysis of the pie chart shows whether the terrain is mixed or not.If the terrain is mixed, the color image would be subjected to image segmentation and infilling.Then, the processed color image will be classified by the terrain classifier again, which provides an accurate identification of multiple areas of complex terrain.Finally, all terrain types can be predicted accurately, thus good performance by the robot is guaranteed.The function modules are described in detail in the following section.
Obstacle Detection Module
Detecting and localizing obstacles are important to realize autonomous motion and path planning.The sensors used for traditional obstacle detection mainly include laser radar sensors, ultrasonic sensors, infrared sensors, visual equipment, etc. [24].In this paper, a fast and accurate detection method based on depth and infrared information is used [25].The image is segmented by
Obstacle Detection Module
Detecting and localizing obstacles are important to realize autonomous motion and path planning.The sensors used for traditional obstacle detection mainly include laser radar sensors, ultrasonic sensors, infrared sensors, visual equipment, etc. [24].In this paper, a fast and accurate detection method based on depth and infrared information is used [25].The image is segmented by the mean-shift algorithm and the pixel gradient of the foreground is calculated.After pretreatment of edge detection Appl.Sci.2019, 9, 1779 4 of 18 and morphological operation, the depth and infrared information are fused.The characteristics of depth and infrared images are used for edge detection.Thus, the false rate of detection is reduced and detection precision is improved.Since depth images cannot be affected by natural sunlight, the influence of light intensity and shadow on obstacle recognition is effectively eliminated and the robustness of the algorithm is improved.This method can accurately identify the position and size of obstacles.In this paper, the results obtained by obstacle detection with this method are used as the input of the terrain image infilling method.
Terrain Classification Module
An online terrain classification system is needed to collect information on terrain through the Kinect sensor and then the key points are extracted from a color image of the terrain.Since the terrain classifier is based on the bag-of-words (BoW) module [26], all extracted features are processed by a clustering algorithm to ensure that the clusters have high similarity.These cluster centers are the visual vocabulary.Then, the terrain images are encoded to form the visual dictionary and a visual vocabulary frequency histogram corresponding to each terrain type.Finally, the information is used to train the support vector machine (SVM) [27] and an optimal hyperplane of each terrain type is divided to classify all terrain types.The algorithm can grasp the key samples and eliminate many redundant samples.
The main structure of the terrain classification system is demonstrated in Figure 3.The system is mainly divided into two steps: training and testing.In the first step, the information of all terrain types is collected and stored in memory and the data flow is presented as shown on the right in Figure 3.Then, local features of images in memory are extracted and extracted features are clustered by the k-means algorithm to generate a certain number of visual words [28].Then, terrain images are encoded using the BoW module to form the visual dictionary and the visual vocabulary frequency histogram corresponding to each terrain type.Then, the information is used to train the SVM.With the aim of validating the terrain classification system established in the training part, the testing part is introduced, shown on the left in Figure 3.The local features from terrain images are extracted in the testing image set and the visual word dictionary is encoded.The images are converted to the frequency histograms that are input in the trained SVM to obtain the terrain label.This part is used by the hexapod robot for terrain recognition.The hexapod robot's gait transform algorithm is guided by terrain identification.
Appl.Sci.2019, 9, x FOR PEER REVIEW 4 of 18 the mean-shift algorithm and the pixel gradient of the foreground is calculated.After pretreatment of edge detection and morphological operation, the depth and infrared information are fused.The characteristics of depth and infrared images are used for edge detection.Thus, the false rate of detection is reduced and detection precision is improved.Since depth images cannot be affected by natural sunlight, the influence of light intensity and shadow on obstacle recognition is effectively eliminated and the robustness of the algorithm is improved.This method can accurately identify the position and size of obstacles.In this paper, the results obtained by obstacle detection with this method are used as the input of the terrain image infilling method.
Terrain Classification Module
An online terrain classification system is needed to collect information on terrain through the Kinect sensor and then the key points are extracted from a color image of the terrain.Since the terrain classifier is based on the bag-of-words (BoW) module [26], all extracted features are processed by a clustering algorithm to ensure that the clusters have high similarity.These cluster centers are the visual vocabulary.Then, the terrain images are encoded to form the visual dictionary and a visual vocabulary frequency histogram corresponding to each terrain type.Finally, the information is used to train the support vector machine (SVM) [27] and an optimal hyperplane of each terrain type is divided to classify all terrain types.The algorithm can grasp the key samples and eliminate many redundant samples.The main structure of the terrain classification system is demonstrated in Figure 3.The system is mainly divided into two steps: training and testing.In the first step, the information of all terrain types is collected and stored in memory and the data flow is presented as shown on the right in Figure 3.Then, local features of images in memory are extracted and extracted features are clustered by the k-means algorithm to generate a certain number of visual words [28].Then, terrain images are In this paper, a dataset was created using six common terrains: grass, asphalt, sand, gravel, tile, and soil.Each terrain image set contained 50 samples, which were acquired by a Kinect camera.A set of samples of terrain images with different illuminations and weather conditions is shown in Figure 4.The K-fold cross-validation was used and K = 5 [29].All images were randomly partitioned into five equally sized groups.Each group was chosen as validation data for testing the classifier and other 4 groups for training set.
frequency histograms that are input in the trained SVM to obtain the terrain label.This part is used by the hexapod robot for terrain recognition.The hexapod robot's gait transform algorithm is guided by terrain identification.
In this paper, a dataset was created using six common terrains: grass, asphalt, sand, gravel, tile, and soil.Each terrain image set contained 50 samples, which were acquired by a Kinect camera.A set of samples of terrain images with different illuminations and weather conditions is shown in Figure 4.The K-fold cross-validation was used and K = 5 [29].All images were randomly partitioned into five equally sized groups.Each group was chosen as validation data for testing the classifier and other 4 groups for training set.
A. Point of Interesting Extracted by SURF
In the aspect of terrain image feature extraction, the SURF algorithm is a commonly used local feature extraction algorithm in image classification.The matching accuracy is high, but the real-time performance is generally poor.In recent years, many excellent algorithms have been proposed.BRISK [30], which combines detection of key points of features from accelerated segment test (FAST) and binary description can enhance the speed of the algorithm, but its classification performance is not ideal.Since the SURF algorithm with many feature points cannot satisfy real-time detection and the BRISK algorithm has fast computation speed but a low matching rate, a method for image matching based on the SURF-BRISK algorithm is proposed.The SURF-BRISK algorithm is established by combining the advantages of both algorithms.Points of interest are detected using the SURF algorithm, descriptors are calculated using the BRISK algorithm, and the Hamming distance is used [31] for similarity measurement, which enables not only high matching rates but also high calculation speed.The algorithm process is described below.In SURF, the criterion of feature points is the determinant of a Hessian matrix of pixel luminance.A pixel u(x, y) is given in image I.In this point, the scale σ of the matrix is defined by: where Lxx(u,σ) is the Gaussian second-order differential ( ) gx convolution of image I at point u, and similarly for Lxy(u,σ) and Lyy(u,σ).In order to facilitate the calculation, the elements of the Hessian matrix are labeled as Dxx, Dyy, Dxy, and the weight of a square area is set to a fixed value.Hence, the approximate value of the Hessian matrix determinant Happrox is defined by:
A. Point of Interesting Extracted by SURF
In the aspect of terrain image feature extraction, the SURF algorithm is a commonly used local feature extraction algorithm in image classification.The matching accuracy is high, but the real-time performance is generally poor.In recent years, many excellent algorithms have been proposed.BRISK [30], which combines detection of key points of features from accelerated segment test (FAST) and binary description can enhance the speed of the algorithm, but its classification performance is not ideal.Since the SURF algorithm with many feature points cannot satisfy real-time detection and the BRISK algorithm has fast computation speed but a low matching rate, a method for image matching based on the SURF-BRISK algorithm is proposed.The SURF-BRISK algorithm is established by combining the advantages of both algorithms.Points of interest are detected using the SURF algorithm, descriptors are calculated using the BRISK algorithm, and the Hamming distance is used [31] for similarity measurement, which enables not only high matching rates but also high calculation speed.The algorithm process is described below.In SURF, the criterion of feature points is the determinant of a Hessian matrix of pixel luminance.A pixel u(x, y) is given in image I.In this point, the scale σ of the matrix is defined by: where L xx (u,σ) is the Gaussian second-order differential ∂ 2 g(σ)/∂x 2 convolution of image I at point u, and similarly for L xy (u,σ) and L yy (u,σ).In order to facilitate the calculation, the elements of the Hessian matrix are labeled as D xx , D yy , D xy , and the weight of a square area is set to a fixed value.Hence, the approximate value of the Hessian matrix determinant H approx is defined by: det where the correlation weight ω of the filter response is utilized to balance the expression of the Hessian determinant.In order to preserve the energy conservation of the Gauss kernel and approximate it, ω is usually set to 0.9.The Hessian matrix is used to calculate the partial derivative, which is usually obtained by a convolution of pixel light intensity and a certain direction of Gauss kernel partial derivative.In order to improve the speed of the SURF algorithm, the approximate box filter is used instead of the Gauss kernel with very little impact on precision.The convolution calculation can be used to optimize the integral image, which greatly improves the efficiency.It is necessary to use three filters to calculate Dxx, Dyy, and Dxy for each point.After filtering, a response graph of the image is obtained.The value of each pixel on the response graph is calculated by the determinant of the original pixel.The image is filtered with different scales and a series of responses of the same image at different scales is obtained.The detection method of feature points is if the value of det (Happrox) of a key point is greater than the value of 26 points in its neighborhood.The number of interest points sampled by SURF is shown in Figure 4.
B. Descriptors by BRISK
The BRISK descriptor adopts the neighborhood sampling model, which takes the feature points as the center of the circle.The points on the concentric circles of several radii are selected as the sampling points.In order to reduce the effect caused by sample image grayscale aliasing, the Gauss function can be used for filtering.The Gauss function of standard deviation sigma is proportional to the distance between the points on each concentric circle.Selecting a pair from the point pairs formed by all sampling points, denoted as (P i , P j ), the gray values after treatment are I(P i , σ i ) and I(P j ,σ j ), respectively.Hence, the gradient between two sampling points is Set A is a collection of all pairs of sampling points, S is a set containing all the short-range sampling pairs, and L is a set containing all the long-distance pairs of sampling points: The general distance thresholds δ max = 9.75 t, δ min = 13.67 t, and t are characteristic point scales.The main direction for each feature point is specified by the gradient direction distribution characteristics of neighboring pixels of the feature point.In general, the BRISK algorithm can be used to solve for the direction g of the overall pattern according to the gradient between two sampling points: In order to achieve rotation and scale invariance, the sampling pattern is sampled again after the rotation angle θ = arctan2 (g y , g x ).The binary descriptor b can be constructed by performing Equation ( 8) on all pairs of points in set S by short-range sampling points.b = 1 0
C. Local Feature Matching
After the feature descriptors extracted by SURF-BRISK are 512-bit binary bit strings consisting of 0 and 1, the Hamming distance is used to measure similarity.Assuming that there are two descriptors of S 1 and S 2 , the Hamming distance is determined as where S 1 = x 1 x 1 . . .x 512 , S 2 = y 1 y 2 . . .y 512 , x, y and the value of x and y is 0 or 1.The smaller the value of D kd , the higher the matching rate, and vice versa.Therefore, the matching point pairs are obtained using the nearest-neighbor Hamming distance in the matching process.
Here, three descriptors, SURF, BRISK, and SURF-BRISK, are compared.Two tile images have been chosen for matching tests to compare the real-time and matching rate of these descriptors, as shown in Table 1 and Figure 5. Obviously, the SURF algorithm has the most matching points, the BRISK algorithm has the fastest matching, and the SURF-BRISK algorithm combines the advantages of both.The algorithm is faster than SURF and gets more matching points than BRISK.
C. Local Feature Matching
After the feature descriptors extracted by SURF-BRISK are 512-bit binary bit strings consisting of 0 and 1, the Hamming distance is used to measure similarity.Assuming that there are two descriptors of S1 and S2, the Hamming distance is determined as ( , ) ( ) where S1 = x1x1 … x512, S2 = y1y2 … y512, x, y and the value of x and y is 0 or 1.The smaller the value of Dkd, the higher the matching rate, and vice versa.Therefore, the matching point pairs are obtained using the nearest-neighbor Hamming distance in the matching process.Here, three descriptors, SURF, BRISK, and SURF-BRISK, are compared.Two tile images have been chosen for matching tests to compare the real-time and matching rate of these descriptors, as shown in Table 1 and Figure 5. Obviously, the SURF algorithm has the most matching points, the BRISK algorithm has the fastest matching, and the SURF-BRISK algorithm combines the advantages of both.The algorithm is faster than SURF and gets more matching points than BRISK.
D．BoW Model and SVM
Li et al. [32] first introduced the image method based on the BoW model.They believed that an image can be analogized to a document and the "words" of an image can be defined as feature vectors.The basic BoW model regards an image as a set of feature vectors and statistics of occurrence frequency of feature vectors, which are used for terrain classification.The BoW model can be set up by a clustering algorithm that is used to obtain the visual dictionary and the steps are as follows.
D. BoW Model and SVM
Li et al. [32] first introduced the image method based on the BoW model.They believed that an image can be analogized to a document and the "words" of an image can be defined as feature vectors.The basic BoW model regards an image as a set of feature vectors and statistics of occurrence frequency of feature vectors, which are used for terrain classification.The BoW model can be set up by a clustering algorithm that is used to obtain the visual dictionary and the steps are as follows.Feature extraction: m images (m ≥ 50) are collected for each terrain type and each image is extracted by SURF-BRISK to obtain n(i) feature vectors.All terrain images form a total sum (n(i)) of feature vectors (words).Generation of dictionary/codebook: The feature vectors obtained from the previous step are clustered (here, the k-means clustering method is used [33]) to get k clustering centers in order to build the codebook.A histogram is generated according to the codebook.The nearest neighbor calculation of each word of the picture is used to find the corresponding words in the codebook in order to form the BoW model.
SVM is an excellent learning algorithm developed on the basis of statistics theory and is widely used in many fields, such as image classification, handwriting recognition, and bioinformatics.The input vector is mapped to a high-dimensional feature space by nonlinear mapping (a kernel function) and an optimal hyperplane is constructed in this space.Compared with the artificial neural network, which suffers from an overfitting problem, the support vector machine has better generalization ability for unknown samples [34].SVM can be divided into three groups: linear separable, nonlinear separable, and kernel function mapping.Linear classifier performance is limited to linear problems, because in nonlinear problems constraints of excessive relaxation can lead to a large number of error samples.At this point, it can be transformed into a linear problem in a high-dimensional space using nonlinear transformation in order to obtain an optimal classification hyperplane.
Complex Terrain Recognition
In the field, terrain is usually complex.The accuracy of terrain with obstacles and mixed terrain, which is composed of two or more terrain types, is greatly reduced if traditional identification methods are used.This scenario affects the normal operation of the robot.Therefore, a systematic method based on image segmentation and infilling for recognition of terrain with obstacles and mixed terrain is introduced in this section.
Image Local Infilling for Terrain with Obstacles
Information on terrain with obstacles collected by Kinect is used as input data for the terrain classifier.It was found that large-volume obstacles cause low accuracy of final identification, because acquired features of terrain information are severely affected, since SURF-BRISK and SURF have the same points of interest.The distributions of points in different terrains with and without obstacles are shown in Figure 6.The obstacles greatly influence local feature extraction.In order to improve the accuracy of recognizing terrain with obstacles, a method of image local infilling (ILI) is presented.The errors for terrain with obstacles in the first round of recognition are shown in Table 2. 2. The first two methods do not improve the accuracy of image recognition, since white and black features do not contribute to the main feature points.However, the background terrain-based image infilling shows satisfactory results.2. The first two methods do not improve the accuracy of image recognition, since white and black features do not contribute to the main feature points.However, the background terrain-based image infilling shows satisfactory results.
Images with Obstacle
hyperplane.
Complex Terrain Recognition
In the field, terrain is usually complex.The accuracy of terrain with obstacles and mixed terrain, which is composed of two or more terrain types, is greatly reduced if traditional identification methods are used.This scenario affects the normal operation of the robot.Therefore, a systematic method based on image segmentation and infilling for recognition of terrain with obstacles and mixed terrain is introduced in this section.Information on terrain with obstacles collected by Kinect is used as input data for the terrain classifier.It was found that large-volume obstacles cause low accuracy of final identification, because acquired features of terrain information are severely affected, since SURF-BRISK and SURF have the same points of interest.The distributions of points in different terrains with and without obstacles are shown in Figure 6.The obstacles greatly influence local feature extraction.In order to improve the accuracy of recognizing terrain with obstacles, a method of image local infilling (ILI) is presented.The errors for terrain with obstacles in the first round of recognition are shown in Table 2. hyperplane.
Complex Terrain Recognition
In the field, terrain is usually complex.The accuracy of terrain with obstacles and mixed terrain, which is composed of two or more terrain types, is greatly reduced if traditional identification methods are used.This scenario affects the normal operation of the robot.Therefore, a systematic method based on image segmentation and infilling for recognition of terrain with obstacles and mixed terrain is introduced in this section.Information on terrain with obstacles collected by Kinect is used as input data for the terrain classifier.It was found that large-volume obstacles cause low accuracy of final identification, because acquired features of terrain information are severely affected, since SURF-BRISK and SURF have the same points of interest.The distributions of points in different terrains with and without obstacles are shown in Figure 6.The obstacles greatly influence local feature extraction.In order to improve the accuracy of recognizing terrain with obstacles, a method of image local infilling (ILI) is presented.The errors for terrain with obstacles in the first round of recognition are shown in Table 2. hyperplane.
Complex Terrain Recognition
In the field, terrain is usually complex.The accuracy of terrain with obstacles and mixed terrain, which is composed of two or more terrain types, is greatly reduced if traditional identification methods are used.This scenario affects the normal operation of the robot.Therefore, a systematic method based on image segmentation and infilling for recognition of terrain with obstacles and mixed terrain is introduced in this section.Information on terrain with obstacles collected by Kinect is used as input data for the terrain classifier.It was found that large-volume obstacles cause low accuracy of final identification, because acquired features of terrain information are severely affected, since SURF-BRISK and SURF have the same points of interest.The distributions of points in different terrains with and without obstacles are shown in Figure 6.The obstacles greatly influence local feature extraction.In order to improve the accuracy of recognizing terrain with obstacles, a method of image local infilling (ILI) is presented.The errors for terrain with obstacles in the first round of recognition are shown in Table 2. hyperplane.
Complex Terrain Recognition
In the field, terrain is usually complex.The accuracy of terrain with obstacles and mixed terrain, which is composed of two or more terrain types, is greatly reduced if traditional identification methods are used.This scenario affects the normal operation of the robot.Therefore, a systematic method based on image segmentation and infilling for recognition of terrain with obstacles and mixed terrain is introduced in this section.Information on terrain with obstacles collected by Kinect is used as input data for the terrain classifier.It was found that large-volume obstacles cause low accuracy of final identification, because acquired features of terrain information are severely affected, since SURF-BRISK and SURF have the same points of interest.The distributions of points in different terrains with and without obstacles are shown in Figure 6.The obstacles greatly influence local feature extraction.In order to improve the accuracy of recognizing terrain with obstacles, a method of image local infilling (ILI) is presented.The errors for terrain with obstacles in the first round of recognition are shown in Table 2. hyperplane.
Complex Terrain Recognition
In the field, terrain is usually complex.The accuracy of terrain with obstacles and mixed terrain, which is composed of two or more terrain types, is greatly reduced if traditional identification methods are used.This scenario affects the normal operation of the robot.Therefore, a systematic method based on image segmentation and infilling for recognition of terrain with obstacles and mixed terrain is introduced in this section.Information on terrain with obstacles collected by Kinect is used as input data for the terrain classifier.It was found that large-volume obstacles cause low accuracy of final identification, because acquired features of terrain information are severely affected, since SURF-BRISK and SURF have the same points of interest.The distributions of points in different terrains with and without obstacles are shown in Figure 6.The obstacles greatly influence local feature extraction.In order to improve the accuracy of recognizing terrain with obstacles, a method of image local infilling (ILI) is presented.The errors for terrain with obstacles in the first round of recognition are shown in Table 2.The obstacle area of pixel matrix I(m, n) is obtained using the obstacle detection method, as are the central pixel coordinates (u, v).Here, three infilling examples are illustrated for comparison.The obstacle area with a pixel value of I = 255 is presented as a white area in Figure 7b.The obstacle area with a pixel value of I = 0 is presented as a black area in Figure 7c.The obstacle area spliced by the no-obstacle sides of the background terrain image is presented in Figure 7d.Due to the use of both left and right sides of the terrain image for infilling, it only needs to compare the abscissa u of the obstacle area center and the abscissa uc of the color image center.At the same time, according to the dimensions of I(m, n), the size and orientation of obstacles are determined.If the width of the obstacle area, i.e., the number n of matrix I(m, n), is too large, the image needs to be processed by multiple infilling.The classification and statistical results of the terrain classifier after ILI are also shown in Table 2.The first two methods do not improve the accuracy of image recognition, since white and black features do not contribute to the main feature points.However, the background terrain-based image infilling shows satisfactory results.
Image Infilling for Mixed Terrain
After the first round of classification, both the terrain label and confidence score of the classified image are obtained.In SVM, the confidence score represents the geometric interval between the classified image and the hyperplane of each terrain type.Therefore, the confidence score needs to be normalized before conducting an analysis.The confidence score is adjusted to the interval [0, 1] to facilitate the comparison.Set Sd contains the confidence scores of all terrain types, and di is the confidence of the test image that corresponds to i terrain class before normalization.Set SD contains confidence scores after normalization and Di is normalized confidence.Therefore, after normalization we get Moreover, a pie chart of confidence scores after normalization can clearly demonstrate the contribution of each terrain type.A pie chart of confidence scores after the first round of classification is shown in Figure 8.In the images of single terrain, the weight of single terrain is much higher than the weights of other terrains.A series of experiments demonstrated that if the highest terrain weight is larger than 30% and more than 10% higher than the second highest weight, the terrain can be considered as a single terrain.Otherwise, it is mixed terrain.For mixed terrain, it is difficult to identify the category from weights in the pie chart.In addition, it is important to note that mixed terrain usually appears at the intersection of different terrains.The traditional methods are not practical for images that contain two or more terrain types, because only one label will be notified.Obviously, some approaches can identify the boundaries of different terrains in an image and then make the decision.Actually, it is difficult to accurately determine terrain boundaries and the algorithm needs to do many computations, which causes poor real-time performance that affects the robot's outdoor walking.In the process of the robot moving in a forward direction, the terrain type is gradually changing.Different types of terrain appear in up and down form in the images.Taking this into consideration, a new method for identification of mixed terrain based on super-pixel image infilling (SPI) is presented.
Image Infilling for Mixed Terrain
After the first round of classification, both the terrain label and confidence score of the classified image are obtained.In SVM, the confidence score represents the geometric interval between the classified image and the hyperplane of each terrain type.Therefore, the confidence score needs to be normalized before conducting an analysis.The confidence score is adjusted to the interval [0, 1] to facilitate the comparison.Set S d contains the confidence scores of all terrain types, and d i is the confidence of the test image that corresponds to i terrain class before normalization.Set S D contains confidence scores after normalization and D i is normalized confidence.Therefore, after normalization we get Moreover, a pie chart of confidence scores after normalization can clearly demonstrate the contribution of each terrain type.A pie chart of confidence scores after the first round of classification is shown in Figure 8.In the images of single terrain, the weight of single terrain is much higher than the weights of other terrains.A series of experiments demonstrated that if the highest terrain weight is larger than 30% and more than 10% higher than the second highest weight, the terrain can be considered as a single terrain.Otherwise, it is mixed terrain.For mixed terrain, it is difficult to identify the category from weights in the pie chart.In addition, it is important to note that mixed terrain usually appears at the intersection of different terrains.The traditional methods are not practical for images that contain two or more terrain types, because only one label will be notified.Obviously, some approaches can identify the boundaries of different terrains in an image and then make the decision.Actually, it is difficult to accurately determine terrain boundaries and the algorithm needs to do many computations, which causes poor real-time performance that affects the robot's outdoor walking.In the process of the robot moving in a forward direction, the terrain type is gradually changing.Different types of terrain appear in up and down form in the images.Taking this into consideration, a new method for identification of mixed terrain based on super-pixel image infilling (SPI) is presented.
not practical for images that contain two or more terrain types, because only one label will be notified.Obviously, some approaches can identify the boundaries of different terrains in an image and then make the decision.Actually, it is difficult to accurately determine terrain boundaries and the algorithm needs to do many computations, which causes poor real-time performance that affects the robot's outdoor walking.In the process of the robot moving in a forward direction, the terrain type is gradually changing.Different types of terrain appear in up and down form in the images.Taking this into consideration, a new method for identification of mixed terrain based on super-pixel image infilling (SPI) is presented.In the field of image segmentation, super-pixel has become a fast-developing image preprocessing technology.Ren et al. [35] first proposed the concept of super-pixels, which quickly divide images into a number of subareas that have image semantics.Compared with the traditional processing method, the extraction and expression of super-pixels are more conducive to collecting local characteristics of the image information.It can greatly reduce the calculation and subsequent processing complexity.Existing segmentation algorithms generally restrict the number of pixels, the compactness, the quality of segmentation, and the practicability of algorithms.Song et al. [36] evaluated the existing super-pixel segmentation algorithms.Their results indicate that the simple linear iterative cluster (SLIC) super-pixel segmentation algorithm has good performance in terms of the controllability of pixel numbers and the close degree of controllability.Aiming at segmentation, the SLIC algorithm is used for mixed terrain regions.The most super-pixels are selected as the target area in a multi-super-pixel area and the boundary pixels of the pixel coordinates of curve fitting are extracted as the terrain boundary segmentation of a complex terrain image.The procedure and results are shown in Figure 9.In the field of image segmentation, super-pixel has become a fast-developing image preprocessing technology.Ren et al. [35] first proposed the concept of super-pixels, which quickly divide images into a number of subareas that have image semantics.Compared with the traditional processing method, the extraction and expression of super-pixels are more conducive to collecting local characteristics of the image information.It can greatly reduce the calculation and subsequent processing complexity.Existing segmentation algorithms generally restrict the number of pixels, the compactness, the quality of segmentation, and the practicability of algorithms.Song et al. [36] evaluated the existing super-pixel segmentation algorithms.Their results indicate that the simple linear iterative cluster (SLIC) super-pixel segmentation algorithm has good performance in terms of the controllability of pixel numbers and the close degree of controllability.Aiming at segmentation, the SLIC algorithm is used for mixed terrain regions.The most super-pixels are selected as the target area in a multi-super-pixel area and the boundary pixels of the pixel coordinates of curve fitting are extracted as the terrain boundary segmentation of a complex terrain image.The procedure and results are shown in Figure 9.
Grass
not practical for images that contain two or more terrain types, because only one label will be notified.Obviously, some approaches can identify the boundaries of different terrains in an image and then make the decision.Actually, it is difficult to accurately determine terrain boundaries and the algorithm needs to do many computations, which causes poor real-time performance that affects the robot's outdoor walking.In the process of the robot moving in a forward direction, the terrain type is gradually changing.Different types of terrain appear in up and down form in the images.Taking this into consideration, a new method for identification of mixed based on super-pixel image infilling (SPI) is presented.In the field of image segmentation, super-pixel has become a fast-developing image preprocessing technology.Ren et al. [35] first proposed the concept of super-pixels, which quickly divide images into a number of subareas that have image semantics.Compared with the traditional processing method, the extraction and expression of super-pixels are more conducive to collecting local characteristics of the image information.It can greatly reduce the calculation and subsequent processing complexity.Existing segmentation algorithms generally restrict the number of pixels, the compactness, the quality of segmentation, and the practicability of algorithms.Song et al. [36] evaluated the existing super-pixel segmentation algorithms.Their results indicate that the simple linear iterative cluster (SLIC) super-pixel segmentation algorithm has good performance in terms of the controllability of pixel numbers and the close degree of controllability.Aiming at segmentation, the SLIC algorithm is used for mixed terrain regions.The most super-pixels are selected as the target area in a multi-super-pixel area and the boundary pixels of the pixel coordinates of curve fitting are extracted as the terrain boundary segmentation of a complex terrain image.The procedure and results are shown in Figure 9. Classification results after image segmentation are shown in Table 3.The output labels do not match actual terrain types.For this mismatch, the number of points of interest extracted from segmented images is shown in Figure 10.Compared with the original terrain image in Figure 4, the number of feature points of segmented images is still related to terrain type but much smaller.Obviously, it is impossible to realize an accurate prediction using the segmentation image, because the feature points are inadequate.Thus, the segmented images are spliced together to enhance the terrain features.Segmented color images would have only some of the pixels of the original color image collected by the Kinect camera and the blank pixels would be infilled by duplication of the segmented image.In the test, the rotation-inversion operation is used for image infilling.The results are shown in Figure 11.Classification results after image segmentation are shown in Table 3.The output labels do not match actual terrain types.For this mismatch, the number of points of interest extracted from segmented images is shown in Figure 10.Compared with the original terrain image in Figure 4, the number of feature points of segmented images is still related to terrain type but much smaller.Obviously, it is impossible to realize an accurate prediction using the segmentation image, because the feature points are inadequate.Thus, the segmented images are spliced together to enhance the terrain features.Segmented color images would have only some of the pixels of the original color image collected by the Kinect camera and the blank pixels would be infilled by duplication of the segmented image.In the test, the rotation-inversion operation is used for image infilling.The results are shown in Figure 11.The number of feature points in Figures 10 and 11 shows that the proposed method can enhance local features of segmented images.The classification results of a spliced image using this approach are shown in Table 3.Using the image infilling approach (rotation-inversion), the error results of the first-round classification can be corrected.It can be seen that confidence scores of the correct terrain type increased after image infilling.On the contrary, confidence scores of wrong terrain types decreased.That means the proposed method can effectively magnify image features for the classifier.Classification results after image segmentation are shown in Table 3.The output labels do not match actual terrain types.For this mismatch, the number of points of interest extracted from segmented images is shown in Figure 10.Compared with the original terrain image in Figure 4, the number of feature points of segmented images is still related to terrain type but much smaller.Obviously, it is impossible to realize an accurate prediction using the segmentation image, because the feature points are inadequate.Thus, the segmented images are spliced together to enhance the terrain features.Segmented color images would have only some of the pixels of the original color image collected by the Kinect camera and the blank pixels would be infilled by duplication of the segmented image.In the test, the rotation-inversion operation is used for image infilling.The results are shown in Figure 11.The number of feature points in Figures 10 and 11 shows that the proposed method can enhance local features of segmented images.The classification results of a spliced image using this approach are shown in Table 3.Using the image infilling approach (rotation-inversion), the error results of the first-round classification can be corrected.It can be seen that confidence scores of the correct terrain type increased after image infilling.On the contrary, confidence scores of wrong terrain types decreased.That means the proposed method can effectively magnify image features for the classifier.Classification results after image segmentation are shown in Table 3.The output labels do not match actual terrain types.For this mismatch, the number of points of interest extracted from segmented images is shown in Figure 10.Compared with the original terrain image in Figure 4, the number of feature points of segmented images is still related to terrain type but much smaller.Obviously, it is impossible to realize an accurate prediction using the segmentation image, because the feature points are inadequate.Thus, the segmented images are spliced together to enhance the terrain features.Segmented color images would have only some of the pixels of the original color image collected by the Kinect camera and the blank pixels would be infilled by duplication of the segmented image.In the test, the rotation-inversion operation is used for image infilling.The results are shown in Figure 11.The number of feature points in Figures 10 and 11 shows that the proposed method can enhance local features of segmented images.The classification results of a spliced image using this approach are shown in Table 3.Using the image infilling approach (rotation-inversion), the error results of the first-round classification can be corrected.It can be seen that confidence scores of the correct terrain type increased after image infilling.On the contrary, confidence scores of wrong terrain types decreased.That means the proposed method can effectively magnify image features for the classifier.Classification results after image segmentation are shown in Table 3.The output labels do not match actual terrain types.For this mismatch, the number of points of interest extracted from segmented images is shown in Figure 10.Compared with the original terrain image in Figure 4, the number of feature points of segmented images is still related to terrain type but much smaller.Obviously, it is impossible to realize an accurate prediction using the segmentation image, because the feature points are inadequate.Thus, the segmented images are spliced together to enhance the terrain features.Segmented color images would have only some of the pixels of the original color image collected by the Kinect camera and the blank pixels would be infilled by duplication of the segmented image.In the test, the rotation-inversion operation is used for image infilling.The results are shown in Figure 11.The number of feature points in Figures 10 and 11 shows that the proposed method can enhance local features of segmented images.The classification results of a spliced image using this approach are shown in Table 3.Using the image infilling approach (rotation-inversion), the error results of the first-round classification can be corrected.It can be seen that confidence scores of the correct terrain type increased after image infilling.On the contrary, confidence scores of wrong terrain types decreased.That means the proposed method can effectively magnify image features for the classifier.Classification results after image segmentation are shown in Table 3.The output labels do not match actual terrain types.For this mismatch, the number of points of interest extracted from segmented images is shown in Figure 10.Compared with the original terrain image in Figure 4, the number of feature points of segmented images is still related to terrain type but much smaller.Obviously, it is impossible to realize an accurate prediction using the segmentation image, because the feature points are inadequate.Thus, the segmented images are spliced together to enhance the terrain features.Segmented color images would have only some of the pixels of the original color image collected by the Kinect camera and the blank pixels would be infilled by duplication of the segmented image.In the test, the rotation-inversion operation is used for image infilling.The results are shown in Figure 11.The number of feature points in Figures 10 and 11 shows that the proposed method can enhance local features of segmented images.The classification results of a spliced image using this approach are shown in Table 3.Using the image infilling approach (rotation-inversion), the error results of the first-round classification can be corrected.It can be seen that confidence scores of the correct terrain type increased after image infilling.On the contrary, confidence scores of wrong terrain types decreased.That means the proposed method can effectively magnify image features for the classifier.the feature points are inadequate.Thus, the segmented images are spliced together to enhance the terrain features.Segmented color images would have only some of the pixels of the original color image collected by the Kinect camera and the blank pixels would be infilled by duplication of the segmented image.In the test, the rotation-inversion operation is used for image infilling.The results are shown in Figure 11.The number of feature points in Figures 10 and 11 shows that the proposed method can enhance local features of segmented images.The classification results of a spliced image using this approach are shown in Table 3.Using the image infilling approach (rotation-inversion), the error results of the first-round classification can be corrected.It can be seen that confidence scores of the correct terrain type increased after image infilling.On the contrary, confidence scores of wrong terrain types decreased.That means the proposed method can effectively magnify image features for the classifier.
Complex Terrain
In the experiments, the hexapod robot walked on six types of terrain without obstacles.Terrain images were collected by a Kinect camera installed on top of the robot.The inclination angle of the Kinect sensor is 40°.Images of terrain with obstacles were collected at different times and in different weather and light conditions.Obstacles mainly included cartons, trash, trees, and so on.There were 50 images collected for each terrain type.The collected images of terrain with obstacles were processed by the ILI method.Then, all images before and after ILI processing were classified The number of feature points in Figures 10 and 11 shows that the proposed method can enhance local features of segmented images.The classification results of a spliced image using this approach are shown in Table 3.Using the image infilling approach (rotation-inversion), the error results of the first-round classification can be corrected.It can be seen that confidence scores of the correct terrain type increased after image infilling.On the contrary, confidence scores of wrong terrain types decreased.That means the proposed method can effectively magnify image features for the classifier.
Complex Terrain
In the experiments, the hexapod robot walked on six types of terrain without obstacles.Terrain images were collected by a Kinect camera installed on top of the robot.The inclination angle of the Kinect sensor is 40 • .Images of terrain with obstacles were collected at different times and in different weather and light conditions.Obstacles mainly included cartons, trash, trees, and so on.There were 50 images collected for each terrain type.The collected images of terrain with obstacles were processed by the ILI method.Then, all images before and after ILI processing were classified by the presented terrain classifier.The recognition results for the two sets are shown in Figure 12a.The recognition rate of terrain with obstacles before ILI processing was relatively low.Since obstacles seriously affect local features of the terrain, error exists in most cases and average recognition accuracy is less than 75%.On the contrary, after the image infilling process, recognition accuracy was improved to above 85%.
Complex Terrain
In the experiments, the hexapod robot walked on six types of terrain without obstacles.Terrain images were collected by a Kinect camera installed on top of the robot.The inclination angle of the Kinect sensor is 40°.Images of terrain with obstacles were collected at different times and in different weather and light conditions.Obstacles mainly included cartons, trash, trees, and so on.There were 50 images collected for each terrain type.The collected images of terrain with obstacles were processed by the ILI method.Then, all images before and after ILI processing were classified by the presented terrain classifier.The recognition results for the two sets are shown in Figure 12a.The recognition rate of terrain with obstacles before ILI processing was relatively low.Since obstacles seriously affect local features of the terrain, error exists in most cases and average recognition accuracy is less than 75%.On the contrary, after the image infilling process, recognition accuracy was improved to above 85%.Usually, mixed terrain appears at the intersection of different terrains.All mixed terrain images were collected at that moment.Specifically, 50 images were collected and processed by the SPI method for terrain recognition.The result is shown in Figure 12b.The classifier shows the labels of two terrain types for different subareas in the image.The average recognition accuracy reached 85% and the results show that the proposed method is effective in recognizing mixed terrain.At the same time, compared with a single label classifier, the SPI method has more practical significance for gait transition of the hexapod robot.
Robot Platform Application
When the robot walks on different terrains, different gaits have different effects on the robot's stability, performance, and energy consumption.The experiment showed that the gait can be changed based on the output of the terrain classifier.In the experiment, the hexapod robot walked for 30 s across three terrain types: asphalt, soil, and grass.The sampling period of the Kinect is 1 s.The gait pattern of the hexapod robot was set according to the output of the terrain classifier.The pseudocode of the gait transition algorithm is depicted in Table 4. Usually, mixed terrain appears at the intersection of different terrains.All mixed terrain images were collected at that moment.Specifically, 50 images were collected and processed by the SPI method for terrain recognition.The result is shown in Figure 12b.The classifier shows the labels of two terrain types for different subareas in the image.The average recognition accuracy reached 85% and the results show that the proposed method is effective in recognizing mixed terrain.At the same time, compared with a single label classifier, the SPI method has more practical significance for gait transition of the hexapod robot.
Robot Platform Application
When the robot walks on different terrains, different gaits have different effects on the robot's stability, performance, and energy consumption.The experiment showed that the gait can be changed based on the output of the terrain classifier.In the experiment, the hexapod robot walked for 30 s across three terrain types: asphalt, soil, and grass.The sampling period of the Kinect is 1 s.The gait pattern of the hexapod robot was set according to the output of the terrain classifier.The pseudocode of the gait transition algorithm is depicted in Table 4.
The value of G has a great influence on the smoothness and efficiency of motion on different terrains.The terrain classification results, including gait value, leg current from robot legs SRL1, and attitude angle, are shown in Figure 13.From 0-5 s, the terrain is supposed to be asphalt.Thus, the robot moves in tripod gait.From 5-6 s, the robot is in transition gait and ready to stride across mixed terrain consisting of asphalt and soil.The value of the terrain curve is nominal, showing that the terrain is complex, e.g., 1.3 means the terrain is changing from type 1 to type 3. From 6-21 s, the robot moves forward with its current gait.Then, from 22-23 s, it changes gait to get ready for another terrain.Finally, from 23-30 s, the terrain is grass and the robot continues to move in a wave gait.than 30%.Therefore, the terrain is supposed to be mixed, and image infilling method is used until the classification result meets recognition reliability requirements.The system outputs the labels of two terrains and causes the robot to make the corresponding gait transitions.
Discussion
This paper describes a terrain classification system for a multilegged robot on complex terrain with obstacles.Several topographic classification methods are summarized in Table 5 [8,11,17,[37][38][39][40][41].With respect to single terrain recognition, several successful single terrain classification methods proved the effectiveness of this kind of methodology via local features, BoW model, and SVM.The common points (also advantages) of these works and our proposed algorithm include the following: Image features are extracted by selecting local features.Unlike color-based and spectra-based methods, local features are invariant to scale, rotation, brightness, and contrast and hence have become popular in image classification.In these methods, the SURF algorithm is used to extract local features of terrain images as input to the BoW model.The performance of SVM in classifying a small number of samples is also excellent.The characteristics of sensor-based information including frequency of leg current [38] and tactile data [40] are also used for terrain recognition.This kind of data is similar in the same terrain and has certain regularity in different terrains.The methods of building the classifier mainly focus on SVM [8,11,17], neural network [37,38,39], and mixtures of Gaussians [40,41].Among them, SVM and neural network are the two
Discussion
This paper describes a terrain classification system for a multilegged robot on complex terrain with obstacles.Several topographic classification methods are summarized in Table 5 [8,11,17,[37][38][39][40][41].With respect to single terrain recognition, several successful single terrain classification methods proved the effectiveness of this kind of methodology via local features, BoW model, and SVM.The common points (also advantages) of these works and our proposed algorithm include the following: Image features are extracted by selecting local features.Unlike color-based and spectra-based methods, local features are invariant to scale, rotation, brightness, and contrast and hence have become popular in image classification.In these methods, the SURF algorithm is used to extract local features of terrain images as input to the BoW model.The performance of SVM in classifying a small number of samples is also excellent.The characteristics of sensor-based information including frequency of leg current [38] and tactile data [40] are also used for terrain recognition.This kind of data is similar in the same terrain and has certain regularity in different terrains.The methods of building the classifier mainly focus on SVM [8,11,17], neural network [37][38][39], and mixtures of Gaussians [40,41].Among them, SVM and neural network are the two main classification models.The application of terrain identification to legged robots is mainly concentrated on gait transition and path planning.For terrain classification with a multilegged robot, the precision requirement is low and a simple SVM is good enough for expected results.Our image infilling algorithm has the effect of magnifying local features of the image, which makes the classification more accurate.We also made an innovation in feature extraction: the SURF-BRISK algorithm is more suitable for real-time classification, its matching speed is much faster than the SURF algorithm alone, and its accuracy is also in line with the SURF algorithm.
Figure 4 .
Figure 4. Different terrains and corresponding numbers of speeded up robust features (SURF) key points.
Figure 4 .
Figure 4. Different terrains and corresponding numbers of speeded up robust features (SURF) key points.
Figure 6 .
Figure 6.Distributions of feature points in terrain with and without obstacles.
Figure 6 .
Figure 6.Distributions of feature points in terrain with and without obstacles.The obstacle area of pixel matrix I(m, n) is obtained using the obstacle detection method, as are the central pixel coordinates (u, v).Here, three infilling examples are illustrated for comparison.The obstacle area with a pixel value of I = 255 is presented as a white area in Figure 7b.The obstacle area with a pixel value of I = 0 is presented as a black area in Figure 7c.The obstacle area spliced by the no-obstacle sides of the background terrain image is presented in Figure 7d.Due to the use of both left and right sides of the terrain image for infilling, it only needs to compare the abscissa u of the obstacle area center and the abscissa u c of the color image center.At the same time, according to the dimensions of I(m, n), the size and orientation of obstacles are determined.If the width of the obstacle area, i.e., the number n of matrix I(m, n), is too large, the image needs to be processed by multiple infilling.The
Figure 9 .
Figure 9. Segmentation result of mixed terrain images: (a) simple linear iterative cluster (SLIC) algorithm; (b) maximum super-pixel extraction; (c) filtering out smaller areas; (d) finding the boundary and fitting the line; (e) results.
Figure 9 .
Figure 9. Segmentation result of mixed terrain images: (a) simple linear iterative cluster (SLIC) algorithm; (b) maximum super-pixel extraction; (c) filtering out smaller areas; (d) finding the boundary and fitting the line; (e) results.
Figure 10 .
Figure 10.Number of feature points in segmented images.
18 Figure 9 .
Figure 9. Segmentation result of mixed terrain images: (a) simple linear iterative cluster (SLIC) algorithm; (b) maximum super-pixel extraction; (c) filtering out smaller areas; (d) finding the boundary and fitting the line; (e) results.
Figure 10 .
Figure 10.Number of feature points in segmented images.
18 Figure 9 .
Figure 9. Segmentation result of mixed terrain images: (a) simple linear iterative cluster (SLIC) algorithm; (b) maximum super-pixel extraction; (c) filtering out smaller areas; (d) finding the boundary and fitting the line; (e) results.
Figure 10 .
Figure 10.Number of feature points in segmented images.
18 Figure 9 .
Figure 9. Segmentation result of mixed terrain images: (a) simple linear iterative cluster algorithm; (b) maximum super-pixel extraction; (c) filtering out smaller areas; (d) finding the boundary and fitting the line; (e) results.
Figure 10 .
Figure 10.Number of feature points in segmented images.
18 Figure 9 .
Figure 9. Segmentation result of mixed terrain images: (a) simple linear iterative cluster (SLIC) algorithm; (b) maximum super-pixel extraction; (c) filtering out smaller areas; (d) finding the boundary and fitting the line; (e) results.
Figure 10 .
Figure 10.Number of feature points in segmented images.
Figure 10 .
Figure 10.Number of feature points in segmented images.Figure 10.Number of feature points in segmented images.
Figure 10 .Figure 11 .
Figure 10.Number of feature points in segmented images.Figure 10.Number of feature points in segmented images.Appl.Sci.2019, 9, x FOR PEER REVIEW 12 of 18
Figure 11 .
Figure 11.Number of feature points in spliced images.
Figure 11 .
Figure 11.Number of feature points in spliced images.
Table 2 .
Classification results of first round and after image local infilling (ILI).
Table 2 .
Classification results of first round and after image local infilling (ILI).
Table 2 .
Classification results of first round and after image local infilling (ILI).
Table 2 .
Classification results of first round and after image local infilling (ILI).
Table 2 .
Classification results of first round and after image local infilling (ILI).
Table 2 .
Classification results of first round and after image local infilling (ILI).
Table 3 .
Image infilling and confidence scores.
Table 3 .
Image infilling and confidence scores.
Table 3 .
Image infilling and confidence scores.
Table 3 .
Image infilling and confidence scores.
Table 3 .
Image infilling and confidence scores.
Table 3 .
Image infilling and confidence scores.
Table 3 .
Image infilling and confidence scores.
Table 5 .
Comparison of recent terrain classification methods. | 15,407 | 2019-04-01T00:00:00.000 | [
"Engineering"
] |
Strong Cosmic Censorship in higher-dimensional Reissner-Nordstr\"{o}m-de Sitter spacetime
It was recently shown that Strong Cosmic Censorship might be violated for near-extremally-charged black holes in 4-dimensional de Sitter space under scalar perturbations. Here, we extend the study of neutral massless scalar perturbations in higher dimensions and discuss the dimensional influence on the validity of Strong Cosmic Censorship hypothesis. By giving an elaborate description of neutral massless scalar perturbations of Reissner-Nordstr\"{o}m-de Sitter black holes in $d=4,5$ and $6$ dimensions we conclude that Strong Cosmic Censorship is violated near extremality.
Introduction
It is well known that the would-be Cauchy horizon (CH) in asymptotically flat black holes (BHs) is a singular boundary [1][2][3]. The remnant fields of gravitational collapse have an inverse power-law decay behavior in the exterior of asymptotically flat BHs [4,5], and will be amplified when propagating along the CH due to the exponential blueshift effect occurring there. The gravitational collapse of matter fields cannot go beyond the CH to the timelike singularity in the eternal asymptotically flat BH, leading to the preservation of the deterministic power of physical laws and the Strong Cosmic Censorship (SCC) hypothesis, proposed by Penrose.
However, for de Sitter (dS) BH spacetimes, due to the change of the boundary conditions, remnant perturbation fields outside de Sitter BHs decay exponentially instead of polynomially [6][7][8][9][10]. The extendibility of the metric at the CH depends delicately on the competition between the exponential decay outside the BH and the exponential blueshift amplification along the CH. In such a scenario, the decay of perturbations could be fast enough such that the CH singularity can be so weak that the spacetime metric will be extendible beyond it as a weak solution to the Einstein field equations [11], meaning that SCC may be violated! Mathematically, it was proven [12][13][14][15][16][17][18][19][20] that SCC will not be respected under massless neutral scalar perturbations if the following condition is satisfied where κ − is the surface gravity of the CH and Im(ω) is the imaginary part of the lowestlying/dominant quasinormal mode (QNM) of the perturbation in the external region of the BH.
In particular, for near-extremal Reissner-Nordstrom-de Sitter (RNdS) BHs, it was shown [20] that neutral massless scalar perturbations are extendible past the CH, since the blueshift amplification along the CH is dwarfed by the exponential decay behavior outside of the dS BH. Such a violation of SCC becomes even more severe in the case of the coupled electromagnetic and gravitational perturbations [21]. Later on, it was shown that the violation of SCC can be alleviated by considering a sufficiently charged scalar field on the exterior of RNdS BHs [22][23][24][25], although there was still a region in the parameter space where SCC may be violated. Similar results have been obtained for Dirac field perturbations [26,27]. On the other hand, the nonlinear evolution of massive neutral scalar fields in RNdS space revealed that SCC might not be saved by such nonlinear effects [28]. In addition, by investigating SCC in lukewarm RNdS and Martnez-Troncoso-Zanelli (MTZ) BH spacetimes, under non-minimally coupled massive scalar perturbations, it was demonstrated that the validity of the hypothesis depends on the characteristics of the scalar field [29]. Besides charged BHs, SCC has been examined in Kerr-de Sitter BH backgrounds and interestingly enough no violation was found for linear scalar and gravitational perturbations [30].
All available studies of SCC in RNdS BH backgrounds are limited in 4 dimensions even though it has been found that in higher dimensions, physics becomes richer. In contrast to the 4-dimensional results, various instabilities have been found in higher-dimensional spacetimes. In a wide class of d ≥ 4 configurations, such as black strings and black branes, the Gregory-Laflamme instability against linear perturbations was discussed in [31,32]. For higher-dimensional BHs in the Einstein-Gauss-Bonnet theory, it was found that instabilities occur for large angular quantum numbers l, while the lowest lying QNMs of the first few angular quantum numbers were found stable [33,34]. In particular, numerical investigations have uncovered the surprising result that RNdS BH backgrounds are unstable for d ≥ 7, if the values of black hole mass and charge are large enough [35], followed by the analytic confirmation of [36]. Moreover, it was argued that the Weak Cosmic Censorship hypothesis could be restored easier in higher dimensions [37] by examining the gravitational collapse of spherically symmetric generalized Vaidya spacetimes. It is, thus, of great interest to generalize the discussion of SCC to higher-dimensional RNdS BHs and explore whether and how they affect the validity of the conjecture.
Scalar fields in higher-dimensional RNdS spacetime
The d-dimensional RNdS spacetime is described by the metric [38] and in which q and m are related to the electric charge Q and the ADM mass M of the BH, and L is the cosmological radius. M and Q are expressed as , (2.4) with ω d being the volume of the unit d-sphere. The causal structure of a sub-extremal ddimensional BH described by (2.2) admits three distinct horizons, where r − < r + < r c are the Cauchy, event and cosmological horizon radius, respectively. We denote the extremal electric charge of the BH as Q max at which the CH and event horizon coincide. The maximal cosmological constant is denoted as Λ max for each dimension, 1 meaning that if Λ > Λ max holds then the spacetime would admit at most one horizon with positive radius, thus rendering our discussion irrelevant. To ensure the existence of three distinct horizons, the cosmological constant must be restricted to Λ < Λ max . The surface gravity of each horizon is then The propagation of a neutral massless scalar field ψ on a fixed d-dimensional RNdS background is described by the Klein-Gordon equation [39]. By expanding our field in terms of spherical harmonics we end up with the master equation where and dr * = dr f (r) the tortoise coordinate. By imposing the boundary conditions we select a discrete set of quasinormal frequencies called QNMs. Due to the similarity of characteristics of (2.8) and the effective potential for odd (Regge-Wheeler [40]) and even (Zerilli [41,42]) gravitational perturbations, the study of massless neutral scalar fields propagating on spherically symmetric backgrounds is a good proxy for more physically relevant gravitational field perturbations.
As shown in Appendix A, for d ≥ 4 the stability of the CH continues to be determined by (1.1). The results shown in the following sections were obtained with the Mathematica package of [43], the asymptotic iteration method (AIM) [44,45], and checked in various cases with a Wentzel-Kramers-Brillouin (WKB) approximation [46] and with a code developed based on the matrix method [47].
Dominant families of modes in higher-dimensional RNdS spacetime
According to [20], the region of interest in 4-dimensional RNdS, where violation of SCC may occur, lies close to extremality. There, the decay rate of perturbations in the exterior becomes comparable with the surface gravity of the CH κ − leading to β > 1/2. We accumulate this result and scan the parameter space of higher-dimensional RNdS spacetimes for near-extremal parameters. By applying our numerics in the region of interest we discover three distinct families of modes.
The photon sphere (PS) is a spherical trapping region of space where gravity is strong enough that photons are forced to travel in unstable circular orbits around a BH. This region has a strong pull in the control of decay of perturbations and the QNMs with large frequencies. For instance, the decay timescale is related to the instability timescale of null geodesics near the photon sphere. For asymptotically dS BHs, we find a family that can be traced back to the photon sphere and refer to them as PS modes. The dominant modes of this family are approached in the eikonal limit, where l → ∞, and can be very well approximated with the WKB method (see Appendix B). For vanishing Λ, Q they asymptote to the Schwarzschild BH QNMs in d ≥ 4 dimensions. We find that l = 10 provides a good approximation of the imaginary parts of the dominant modes which we depict in our plots with solid blue lines.
Our second family of modes, the BH de-Sitter (dS) family, corresponds to purely imaginary modes which can be very well approximated by the pure d-dimensional scalar dS QNMs [10,48]: The dominant mode of this family (n = 0, l = 1) is almost identical to (3.1) which we denote in our figures with red dashed lines. These modes are intriguing, in the sense that they have a surprisingly weak dependence on the BH charge and seem to be described by the surface gravity of d-dimensional dS κ dS of the cosmological horizon of pure d-dimensional dS space, as opposed to that of the cosmological horizon in the RNdS BH under consideration.
Finally, as the CH approaches the event horizon, a new family of modes appears to dominate the dynamics. In the extremal limit of a d-dimensional RNdS BH the dominant (n = l = 0) mode of this family approaches (see Appendix C) where κ − , κ + the surface gravity of the Cauchy and event horizon in d-dimensional RNdS spacetime. We call this family the near-extremal (NE) family of modes. Higher angular numbers l admit larger (in absolute value) imaginary parts, thus rendered subdominant. In the asymptotically flat case, these modes seem to have been described analytically in the eikonal limit [49].
Strong Cosmic Censorship in higher-dimensional RNdS spacetime
In Fig. 1 This perplex picture appears due to the opposite behavior that the dominant PS and dS family possess. As shown in Fig. 1, higher dimensions oblige β PS , as it gets determined by the dominant modes of the PS family (l = 10), to move upwards in the plots, thus becoming subdominant, while β dS , as it gets determined by the dominant modes of the dS family (l = 1), moves downwards. On the other hand, the increment of Λ/Λ max has the opposite effect on these families as expected by [20]. It is easy to realize (see the pattern in Fig. 1) that the inclusion of even higher than 6 dimensions will make the picture of "intermediate" and "large" BHs even richer and much more perplex 3 . The only solid case is the one for "small" BHs. There, β is essentially (for the largest part of the parameter space) determined by the dominant modes of the dS family which will become even more dominant for increasing dimensions if no new families or instabilities occur in d > 6 dimensions. 4 2 Usually we take r+/rc to measure the size of small/big black hole, but in our discussion we compare black holes in different dimensions by fixing Λ/Λmax which has some connection with the size of black holes. It turns out that the value of r+/rc would be notably influenced by Q/Qmax. On the other hand, if Q/Qmax is fixed, one can find that the difference between rc and r+ would increase with the decrease of Λ/Λmax. For these reasons, the "small/large" black holes in this paper are only referred to black holes with small/large Λ/Λmax. To distinguish between "small", "intermediate" and "large" BHs, we scan thoroughly the parameter space of d = 4, 5 and 6-dimensional RNdS BHs to find critical values of Λ/Λ max where different violation configurations are introduced. We find 3 critical values which divide the range of 0 < Λ/Λ max ≤ 1 into 4 regions. In Table 1, we summarize the division of our parameter space into the regions of interest and display the degree of difficulty of SCC violation at each region. We realize that region I corresponds to "large" BHs, regions II and III correspond to "intermediate" BHs and, finally, region IV corresponds to "small" BHs. These regions can be directly seen in Fig. 1 and arise due to the existence and competition between the dominant PS and dS family, as discussed above. In any case, we clearly see that β > 1/2 above some value of the BH charge, no matter the choice of the cosmological constant. This leads to CHs which upon scalar perturbations maintain enough regularity for the scalar field (and thus the metric) to be extendible past it, resulting to a potential violation of SCC. Moreover, if it was up to the PS and dS family, β would always diverge at extremality. However, the dominant modes of the NE family (l = n = 0) will always take over to keep β below 1.
Conclusions and Discussions
The studies of [16,17,19] indicate that the stability of the CH in asymptotically dS spacetimes is governed by β defined in (1.1). Subsequently, the results of [20] indicate a potential failure of determinism in General Relativity when near-extremal 4-dimensional RNdS BHs are considered. Under massless neutral scalar perturbations, the CH might seem singular, due to the blow-up of curvature components, but maintain enough regularity as to allow the field equations to be extended beyond a region where the evolution of gravitation is classically determined in a highly non-unique manner.
Here, we extend our study to higher-dimensional RNdS BHs and find that the same picture occurs when scalar fields are considered. We have proven that (1.1) remains unchanged for d-dimensions. By inferring to d = 4, 5 and 6-dimensional RNdS BHs we realize that the introduction of higher dimensions will fortify SCC for sufficiently "small" BHs (Λ/Λ max 0.135), by the introduction of higher BH charges beyond which β > 1/2. Moreover, we observe that "intermediate" and more complex picture with some dimensions being preferred over others to fortify SCC. This perplexity arises due to the delicate competition of the PS and dS family of modes. Even though for "large" BHs we see that the preferred dimension to fortify SCC, with higher Q/Q max beyond which β > 1/2, is d = 4, we understand that the introduction of even higher than 6 dimensions will eventually change the picture due to the behavior of the dS family demonstrated in Fig. 1, if no instabilities occur in our region of interest [35].
In any case, we can always find a region in the parameter space of the higher-dimensional RNdS BHs in study for which β exceeds 1/2, but still not exceeding unity 5 . This still leaves as with CHs which upon perturbations might seem singular, due to the blow-up of curvature components, but that doesn't imply the breakdown of Einstein's field equations [50] nor the destruction of macroscopic observers [51] at the CH.
It is important to mention that SCC in higher-dimensional RNdS spacetime was also discussed in [52], with a wishful premise that the large l mode always dominates, i.e., the value of β always decreases monotonously with the increase of angular number l. However, this is not the case, as we have seen in Fig. 1, due to the existence of three different families of modes. In fact, the existence of more families highly affects β according to the choice of our cosmological constant and the dimensions of our spacetime, thus rendering the study in [52] incomplete.
Note added: An updated version of [52] was published recently. In the new modified version, their improved results are in agreement with ours, thus confirming our findings.
A The definition of β in higher-dimensional spherically symmetric spacetimes In [23,27] a justification of searching for β > 1/2 was provided, leading to potential violation of SCC in 4-dimensional RNdS BHs under charged scalar and fermionic perturbations. Here, we prove that the same holds for neutral massless scalar perturbations in d-dimensional RNdS spacetime. To determine the regularity of the metric up to the CH we study the regularity of QNMs at the CH. To do so, we change to outgoing Eddington-Finkelstein coordinates which are regular there. The outgoing Eddington-Finkelstein coordinates are obtained by replacing t with u = t − r * in (2.1) to get By expanding the Klein-Gordon equation we get P ψ = 0 where the operator P reads where ∆ Ω d−2 the Laplace-Beltrami operator [39]. By acting on mode solutions of the form ψ ∼ e −iωu φ we obtain It can be shown that the mode solutions of (A.4) are conormal at r = r − , meaning that they grow at the same rate |r − r − | λ . Thus, if φ ∼ |r − r − | λ then the second and last term have higher regularity than the rest, since f ∼ |r − r − | near the CH. This means that these terms can be neglected, which leads to a regular-singular ordinary differential equation near r = r − of the formP φ = f P φ = 0 with the operator It is convenient to use f as a radial coordinate instead of r, so ∂ r = f ∂ f = f (r − )∂ f near the CH modulo irrelevant terms. Moreover, the surface gravity at the CH is It remains to calculate the allowed growth rates λ, i.e. indicial roots of the differential operator (A.6). Acting with |f | λ we get The indicial roots are the roots of the quadratic polynomial (A.7), namely The root λ 1 = 0 corresponds to mode solutions which are approximately constant, i.e. remain smooth at the CH and are irrelevant for SCC, while λ 2 corresponds to asymptotics If we consider QNMs of the form ω = ω R − iω I then The second factor is purely oscillatory, so the only relevant factor for SCC is |r − r − | α κ − with α := −Im(ω) the spectral gap defined in [20]. This function lies in the Sobolev space H s for all s < 1 2 + α κ − . Since we are considering scalar fields, we require locally square integrable gradient of the scalar field at the CH 6 , i.e., the mode solutions should belong to the Sobolev space H 1 loc for the Einstein's field equations to be satisfied weakly at the CH. This justifies our search for β = −Im(ω)/κ − > 1/2.
B WKB approximation of the dominant photon sphere modes
The WKB method can provide accurate approximation of QNMs in the eikonal limit. The QNMs of BHs in the eikonical limit under massless scalar perturbations are related to the Lyapunov exponent λ of the null unstable geodesic, which is inversely-proportional to the instability timescale associated with the geodesic motion of null particles near the photon sphere. For d-dimensions we have [53] ω WKB = l f (r s ) r 2 where r s is the radius of the null circular geodesic, and Ω c the coordinate angular velocity of the geodesic. By focusing on the modes with overtone number n = 0, we have β = |λ| /2κ − for the dominant PS modes at the eikonical limit. In Table 2, we compare the value of β obtained by AIM and the spectral method [43] at l = 10 and the value evaluated by the WKB method at large l for the same BH parameters. We observe that the difference between β WKB , β spectral and β AIM is very small, meaning that the choice of l = 10 in our numerics can be regarded as a good approximation of β WKB of the dominant PS modes at the large l limit.
C Approximation of the dominant near-extremal modes
In [54] it has been proven that long-lived modes (or quasi-bound states) can be supported by a 4-dimensional near-extremal RN BH. In [20] it was realized that this family of modes exist in near-extremal RNdS BHs and is weakly dependent on the choice of Λ. Particularly, for neutral massless scalar fields, these modes can be very well approximated as ω d=4,NE = −i(l + n + 1)κ − = −i(l + n + 1)κ + (C.1) when r − = r + . Motivated by this result, we realize that for any dimension the dominant NE modes should be approximated by Eq. (3.3). For the sake of proving the validity of our approximate results, in Table 3 Table 3. Comparison of β approx derived from (3.3) versus β spectral obtained with a spectral method for a d-dimensional RNdS BH with M = 1, Λ = 0.1 and Q/Q max = 0.999999. | 4,736.2 | 2019-02-05T00:00:00.000 | [
"Physics"
] |
Broadband Signal Amplification Paths for Semiconductor Radiation and Particle Detectors (Review)
This study is devoted to the development of amplifying paths for plasma diagnostics, a significant part of which use semiconductor detectors as sensors that form low-intensity current signals. One feature of these diagnostics is the oscillographic form of registering sensor signals. In tandem with detectors, broadband transimpedance amplifiers that are based on operational amplifiers are used to amplify and normalize sensor signals. The principles of constructing such amplifying paths are considered taking the factors affecting their final noise and frequency characteristics into account. Practical examples of the construction of amplifying paths of corpuscular and neutron plasma diagnostics, as well as the Thomson-scattering diagnostics, that are used at the plasma installations of the Institute of Nuclear Physics (Siberian Branch, Russian Academy of Sciences) are presented.
INTRODUCTION
When conducting research in the field of hightemperature plasma physics and controlled thermonuclear fusion (CTF), diagnostics are widely used that are focused on registering the spatial distributions of the plasma parameters and their temporal dynamics, on the formation of feedback signals that stabilize the plasma-filament position in a magnetic trap, the formation of the necessary radial profiles of its density and temperature, as well as the intensity of fusion reactions. Such diagnostics include microwave, optical, X-ray, corpuscular, and other diagnostics; the key feature of their measuring paths is associated with the need to record sensor signals in an oscillographic form. The actually existing structure of an elementary measuring path includes a sensor, a broadband amplifier, a high-speed analog-to-digital converter (ADC), a digital unit based on a user-programmable gate matrix or a processor that generates measurement results using real-time procedures for digital signal processing, as well as an interface unit that transmits the results to the diagnostic server and/or the corresponding controller. A significant part of the measuring paths that are used in research on plasma physics and CTF, semiconductor diodes are used as detectors that form a low-intensity broadband current signal under the influence of radiation or particles entering their aperture. Such signals are amplified and normalized traditionally using transimpedance amplifiers (TIAs) based on low-noise broadband operational amplifiers (OAs) [1]. The diagram of such a path amplifier is shown in Fig. 1.
CONSTRUCTION OF AN AMPLIFICATION PATH BASED ON A TRANSIMPEDANCE AMPLIFIER
If the characteristics of the basic OA are ideal, the output voltage of the TIA is determined by the values of the feedback resistance and photodiode current: (1) where i sig is the current of the semiconductor detector and R f is the resistance in the feedback circuit (Fig. 1).
For real OAs, this formula is valid only for the lowand medium-frequency regions, in which their gain with the open feedback A( f ) is large and actually constant. As the frequency increases, A( f ) decreases: (2) where f c is the amplifier cutoff frequency. As a consequence, an additional element, the error factor , appears in formula (1) [ where β is the feedback coefficient of the amplifier. Figure 2a presents the amplitude-frequency (frequency response) and phase-frequency characteristics of the amplifier (FR and PFC) at the zero input capacitance. In this case, the feedback coefficient β is represented by a constant, while the loop gain βA( f ) decreases at a rate of 20 dB/decade with increasing frequency, as does the FR of the amplifier. The maximum phase shift of the output signal is 90°. When the input capacitance of the amplifier, which is represented as the sum of three components, (4) differs from zero, where C d is the photodiode capacitance, C in is the input capacitance of the inverting input of the amplifier, and C dif is the differential capacitance between its inputs, the behavior of the FR and PFC changes significantly (Fig. 2b).
This is due to the fact that the feedback coefficient β becomes frequency-dependent: (5) as a result, the loop gain is described by the two-pole function: The appearance of an additional pole at the frequency leads to a decline of A( f )β in the high-frequency region with a rate of 40 dB/decade and an additional phase incursion of 90° (Fig. 2b). The total phase incursion at the moment of intersection of the graphs A( f ) and 1/β becomes close to 180°. Because of this, the transient process acquires an oscillatory character and a resonant peak appears in the graph of the transfer coefficient of the I-to-V transimpedance amplifier. It is possible to prevent the transition of the amplifier to the oscillatory mode by reducing the total phase The frequency-response and phase-frequency characteristics of the amplifier: (а) at and (b) at a nonzero input capacitance; is the frequency of the unity gain of the TIA.
Output incursion via reduction of the R f and С tot values. It is practically impossible to reduce the input capacitance to zero, whose main component is the capacitance of the photodiode. A decrease in the nominal value of the feedback resistance involves a drop of the transfer coefficient, which is undesirable.
The conventional method for stabilizing the operation of a TIA is based on the use of a correcting capacitance C f , which is connected in parallel to the feedback resistor R f (Fig. 1). The correcting capacitance changes the behavior of the feedback coefficient β: which, in the high-frequency region at R f ≫ X f , is described by the expression (8) Figure 3 shows the graph of the amplifier PFC when using the correcting capacitance. Jointly with the feedback resistance, it forms an additional "zero" in the graph βA( f ) at the frequency ; this zero reduces the resulting phase incursion. Figure 4 shows the plots of the FP and PFC at a fixed R f and different C f ratings. In Fig. 4а, the gain 1/β reaches a plateau at a level of approximately much earlier than the point of intersection with the FR A( f ) of the amplifier, which corresponds to the condition f p ≪ f 0 . As a consequence, the phase margin at their intersection point that corresponds to the frequency f 0 has a value that exceeds 45°. In this case, the graph A( f )β changes the decay rate from 40 to 20 dB/decade in the interval f 0 -f p . A resonance peak in the transfer-coefficient curve I sig -to-V is absent or has a small value. When the gain 1/β reaches a plateau at the moment of intersection with the graph А( f )β at f p = f 0 (Fig. 4b), the phase margin is 45°. A pronounced resonant peak that corresponds to a partial phase compensation appears on the I sig -to-V transfer-coefficient curve. At f p > f 0 (Fig. 4c), there is almost no phase compensation, the phase margin is less than 45°, and the amplitude of the resonant peak actually coincides with its amplitude in the absence of a corrective capacitance.
In essence, C f stabilizes the operation of the TIA due to the narrowing of its operating frequency band. The optimal value of the correcting capacitor that cor- 3. The phase-frequency response when using a corrective capacitance. Noises of the photodiode and TIA are factors that directly affect the resulting dynamic amplitude range of the detector. Due to the relatively small energy gap width of semiconductor photodiodes (units of volts) and the high energy of photons and other particles detected by them (tens of kiloelectronvolts-units/tens of megaelectronvolts), the number of charge carriers generated in the region of the p-n junction usually is large, thus determining a high value of the signal-todark current ratio. Therefore, the noise of the dark current of semiconductor photodiodes in most applications that are significant for plasma physics and CTF is not a factor limiting the operating dynamic range of the detector. The determining contribution to this limitation is made by amplifier noises. Figure 5 shows an equivalent circuit of the frequency-compensated TIA with all noise sources. The frequency dependence of its output voltage is defined as where is the signal current, is the transfer coefficient of the TIA, and is the signal noise component at its output: In this expression, is the root-mean square (RMS) value of the voltage noise component at the feedback resistor R f , is the noise determined by the noise component of the amplifier input current I B that flows through the feedback resistor R f , and is RMS value of the remaining noise components reduced to the TIA input. The first component in expression (11) is shot noise, while the second is thermal noise. Both of these components can be described as "white" noise. In the case where the loop gain is , the bandwidth of these components is limited by a low-pass filter, which is formed by the capacitance C f and the feedback resistor R f , with the cutoff frequency f p = . If the input capacitance С tot is large, the shot and thermal noises are then also frequency dependent [3]. The noise voltage reduced to the amplifier input is determined through the spectral density e amp and the gain A noise : , and is the unity-gain frequency of the TIA. In Fig. 6, a solid line marks the graph of the noise gain A noise ; the dashed and dashed-dotted lines are the graphs of the transfer coefficient of the amplifier with the open feedback loop A( f ) and the feedback coefficient of the amplifier 1/β, respectively. The noise gain is small and constant in region 1; therefore, we are mainly interested is the regions 2-4. In the frequency range from to , the noise gain increases with a rate of 20 dB/decade. In the region 4 where А noise = A(f), the noise gain decreases with a rate of 20 dB/decade down to . In the region 3, it reaches a plateau and becomes equal to . This allows us to consider the RMS noise voltage in the range from f z to f 0 or from f p to as (14) When the TIA operates with large-area photodiodes, the predominant contribution to is made by the diode capacitance C d . As C d increases, the noise gain increases as well. In the high-frequency region, beginning with ( . noise that is caused by the input noise voltage of the OA dominates in the TIA. Relationship (15) unambiguously indicates that for confident detection of broadband signals it is necessary to use photodiodes with the lowest possible capacitance C d , as well as broadband OAs with , which have the noise voltage e amp and the input capacitance C tot with extremely low values reduced to the input. The resistor R f in the feedback circuit sets the value of the TIA transfer coefficient in the region of low and medium frequencies. It usually has a large nominal value and, therefore, has almost no significant effect on the amplifier noise characteristics. It is not always possible to fulfill the key condition, that is, to minimize the value of the parasitic capacitance that is connected to the amplifier input. The exceptions include detectors based on p-i-n and avalanche photodiodes with a small active-zone area and broadband OAs.
CONSTRUCTION OF THE AMPLIFICATION PATH FOR DETECTORS WITH A SMALL
JUNCTION CAPACITANCE However, even for detectors with a small junction capacitance, it is extremely difficult to achieve the operating frequency band that is necessary for numerous applications, with an acceptable signal-to-noise ratio (SNR) at the amplifier output. This is explained by the characteristics of modern broadband OAs and the complexity of taking parasitic factors into account when designing TIAs based on them. In this regard, single-chip analogues of TIAs that have recently appeared and include OAs, feedback-loop elements, and correction circuits in their composition look more attractive. One example is the OPA857 amplifier (Texas Instruments), which, with a feedback resistor with a resistance of 20 kΩ and an input capacitance of 1.5 pF, provides the signal amplification in the operating frequency band from 0 to 105 MHz [4]. At the same time, the value of the noise current, which is reduced to the amplifier input, taking the component in the form into account, does not exceed 15 nA (RMS). The OPA857 is intended to operate with avalanche or p-i-n photodiodes that have a relatively small area of the active zone and a corresponding value of the junction capacitance C d of up to 4.7 pF. It is important that in the specified range of capacitance variation this amplifier is stable and its FR with the closed feedback loop remains almost flat. Only the value of the upper cutoff frequency of the bandwidth (from 105 to 80 MHz) and, in a relatively small range (from 15 to 23 nA), the value of the noise current reduced to the amplifier input change. The unique combination of these parameters makes it possible to use the OPA857 as part of broadband radiation detec- tors, e.g., those typical for diagnostics of Thomson scattering, which is intended to measure the density and temperature of the electron component of plasma in magnetic traps [5].
The key features of the Thomson-scattering diagnostics are as follows: the short duration of the probing pulse (1-20 ns) with the ratio of the probing and scattered radiation powers at a level of 10 -15 , the presence of powerful background plasma radiation, as well as laser radiation reflected from the walls of the vacuum chamber, which enter the detector aperture. In this case, it is possible to select a useful signal only when the measuring paths are operating in the oscillographic mode.
In particular, in the diagnostics of Thomson scattering on an axially symmetric magnetic gas-dynamic trap (GDT) of the Institute of Nuclear Physics (Siberian Branch, Russian Academy of Sciences) [6], a neodymium laser that generates a pulse with an energy of 1.7 J and a duration of ~10 ns is used as the radiation source. The laser operates in a pulse-periodic mode with a pulse repetition rate of up to 10 Hz. The optical diagnostic system is focused on measuring the plasma temperature at six spatial points. Each point has its own measuring path that includes a spectrometer with six photodetectors. The number of photons in a pulse of plasma-scattered probing radiation at each spatial point is approximately (2-3) × 10 4 , which corresponds to approximately 5 × 10 3 photons that enter the detector aperture. The value of the signal current of the detector, which uses an S11519-15 avalanche photodiode (Hamamatsu), is defined as where M is the avalanche gain (25), η is the quantum efficiency of the photodetector at the laser wavelength (1.06 μm), e is the electron charge, t is the laser-pulse duration, and n PH is the number of photons. Using these parameters, we can estimate the RMS value of the photodiode noise current: where I d is the dark current of the avalanche photodiode (it equals ~9 nA), and f apd is the cutoff frequency of its transfer coefficient (~100 MHz). Figure 7 shows a diagram of the amplification path of the Thomson-scattering diagnostic detector. It has three stages. The first amplification stage is based on an OPA857 TIA. The capacitance of the avalanchephotodiode junction that is connected to its input has a value of ~3 pF. Due to it, as well as the parasitic capacitances of the inverting input of the amplifier (C tot ), the noise current (RMS) reduced to this input does not exceed 18 nA in the entire operating frequency band (0-100 MHz). The value of the current noise component reduced to the OPA857 input, taking the noise component of the photodiode current into account, is equal to (18) It can be seen that the main contribution to i det is made by the noise component of the avalanche-photodiode current i apd . It also determines the value of the resulting ratio of the signal amplitude to the RMS noise value, which characterizes the resolution of the detector unit: This result is acceptable but not impressive. It should be noted that it corresponds to the operating frequency band of the detector (0-100 MHz) that is redundant from the physical point of view in the Thomson-scattering diagnostics. The fact is that in order to determine the plasma temperature in this diagnostics it is necessary to know the broadening of the spectral line of probing radiation, which is determined by its scattering by energetic electrons. There are two ways to solve this problem: by reconstructing the shape of the spectral line of scattered radiation from the amplitudes of the scattering signals, which are registered by detectors in a set of neighboring spectrometer windows, or from the integral values of these signals. Obviously, from the metrological viewpoint, the second method should be preferred, since within its framework the high-frequency components of noise and interference that are superimposed on the scattering signals are efficiently suppressed. From the radio-engineering point of view, the integration operation is equivalent to the procedure of filtering the high-frequency signal components; in our case, it is equivalent to reducing the upper cutoff frequency of the amplification-path bandwidth to an acceptable level. This operation is performed in all stages of the amplification path: in the TIA and the intermediate amplification stage, using corrective capacitances in the feedback circuits; in the output stage, due to its construction on the basis of an active two-pole filter. The cutoff frequencies of the FR of these links and elements are identical and equal to 60 MHz, thus providing the slope of the decline of the FR amplification path in the high-frequency region at a level of 80 dB/decade. In this case, the signal bandwidth is limited from above (at a level of -3 dB) to a frequency of 26 MHz, while the noise amplification frequency band is limited to a frequency of 29.5 MHz. These values are almost four times lower than the values of similar cutoff frequencies of the elements of the amplification path without correcting and filtering circuits. Due to this, the resulting SNR at the amplifier output is almost doubled: from 30 to 60. The subsequent procedures for processing detector signals are performed using their digitization and digital filtering paths. Figure 8 shows the output signals of the Thomson-scattering diagnostic detectors that were obtained in a real experiment with a probing-radiation pulse duration of ~50 ns. The time shift of signals relative to each other is due to the design of the spectrometer. When trying to use a photodiode with a larger junction area in the detector and, accordingly, with a larger parasitic capacitance , the characteristics of the amplification paths constructed on the basis of TIAs deteriorate sharply. First, in proportion to the value of this capacitance, the amplitude of the output-signal noise component begins to increase; when this capacitance exceeds a certain critical value the amplifier loses stability and ceases to perform its functions. Therefore, it is possible to expand the bandwidth of the amplification path that operates in tandem with a photodiode with a relatively large junction capacitance only by changing the circuitry of this path, e.g., using a "cascode" connection of its design (Fig. 9), in which the functions of the photocurrent receiver are performed by a transistor connected according to a common-base circuit. The relatively low input impedance of this transistor together with the photodiode capacitance form a pole with the cutoff frequency f c = in the FR of the amplification path, where r e is the dynamic resistance of the emitter junction. The collector circuit of the transistor, whose load is the inverting input of the TIA, has a signal-current transfer coefficient that is close to unity and efficiently isolates this input from the photodiode capacitance.
In essence, in a cascode circuit, the photodiode capacitance at the input of a classical TIA is replaced by the collector-base junction capacitance of the transistor, which may have a value of fractions of pico- Here, F is the upper cutoff frequency of the signal path bandwidth. The latter expression does not take the effect of the transistor-base resistance on the noise value into account, since its contribution at I 0 ≪ 1 mA is negligibly small. The values of the transistor noise current I n and its quiescent current I 0 are interrelated via the simple dependence: where C d is the value of the photodiode capacitance in picofarads. It follows from this ratio that with a photodiode capacitance of 10 pF and an RMS value of the transistor noise current comparable with the TIA noise current (15 nA) the I 0 value must not exceed 36 μA. In this case, due to the relatively large value of the transistor input resistance ( ≈ 700 Ω), the upper cutoff frequency of the input-path bandwidth is limited to 23 MHz. At the cost of increasing the quiescent current of the transistor to 100 μA, it can be increased to 64 MHz with a simultaneous increase in both the noise current component of the input stage (up to 45 nA) and the resulting value of the noise current (RMS) (reduced to the amplifier input) to 47 nA. With an amplitude of the photodiode signal current of 10 μA, the resulting SNR reaches approximately 212, which is already acceptable for many applications. Thus, the cascode amplification circuit is efficient when working with photodiodes with a capacitance of 10 pF. The possibility of using it with photodiodes with a larger junction capacitance is still questionable. Let us try to modify this scheme so as to provide the solution of the formulated task. It is obvious that in order to reduce the influence of the photodiode capacitance on the characteristics of the amplifier, it is necessary to get rid of this very capacitance at least partially if not completely. This can be done by prohibiting its recharging with a signal current. To do this, it is sufficient to stabilize the voltage at the photodiode with the help of auxiliary elements, e.g., with the help of a voltage follower and a signal-level offset circuit that maintain the equality of the voltage drops at both its terminals (Fig. 10).
Such a solution was considered in [7]. It is based on the transfer of the voltage change from the emitter of the input transistor, to which the signal output of the photodiode is connected, to its second output. For this purpose, an emitter voltage follower based on the Q 2 transistor and an R 3 , R 4 , C 2 resistive-capacitive circuit for biasing the level of its output signal are used. These elements prevent a charge exchange of the parasitic capacitance C d of the photodiode in the frequency range in which the value of the Q 2 transistor output resistance is much lower than the reactance of this capacitance: r e . Therefore, with a fixed value of the photodiode capacitance, it is possible to expand the operating frequency band of the modified cascode amplification circuit only by reducing the value of r e , d C X which is equivalent to an increase in the quiescent current of the Q 2 transistor. It should be taken into account that an increase in the quiescent current inevitably leads to an increase in the base current of the Q 2 transistor, which, because of the necessity of stabilizing the value of the input-stage noise component at a level of , must be much smaller than the quiescent current of the input stage. This contradiction is resolved when constructing a follower based on a bipolar microwave transistor with a high current gain or on a low-noise high-frequency fieldeffect transistor (FET) with a high slope, e.g., ATF55143. In the case of a bipolar transistor, the operating frequency band of an amplifier based on the modified cascode circuit increases by a factor of / in comparison to its previous version with preservation of the spectral density of the noise component at a level close to up to the frequency F = . Starting from this frequency, the quiescent current of the Q 2 transistor will begins to make a decisive contribution to the current noise component reduced to the TIA input. Similar relationships, when replacing with 1/s, where s is the slope of the transfer characteristic, are also valid in the case of a signal follower based on a FET. A modified cascode photocurrent amplification circuit was used at the GDT installation in the diagnosis of the intensity of the proton flux generated in a nuclear reaction: MeV. The corpuscular diagnostics of plasma is based on determining the flow intensity of particles that are produced during the interaction of plasma with beams of neutral atoms injected into it. The specific feature of the GDT installation is that the concentration of trapped particles in the central probkotron is relatively small; however, their density increases significantly in the region of the magnetic mirrors. As a consequence, the intensity of particles that are detected by the diagnostics may vary in a wide range, which implies the necessity of operation of the measuring paths both in the counting mode (at a low plasma density) and in the oscillographic mode (at a high plasma density), in which the behavior of the flow intensity of particles that leave plasma is recorded in time.
In the corpuscular diagnostics in the GDT installation, protons are detected by a D1A silicon diode manufactured by SNIIP-PLYuS (Moscow, Russia) with a surface area of 100 mm 2 , which has a capacitance of the reversely biased junction of ~100 pF at a bias voltage of 40 V. Due to the intense interaction of protons with the residual gas, which forms a "coat" of the plasma filament, and with the material of the walls of the vacuum chamber, the diode is located together with the collimator in the vacuum volume. The diode is connected to the amplifier-shaper (Fig. 11), which is placed outside of this volume in a shielded box, using a vacuum-tight connector and connecting wires with a length of up to several centimeters.
At an energy of formation of an electron-hole pair of 3.66 eV, each proton that is formed in plasma within the framework of the D-D reaction generates a charge of approximately 100 fC in a silicon diode. Such a small value of this charge, a relatively large capacitance of the diode, and its severe operating conditions are the key factors that determine the amplifiershaper circuitry.
This amplifier consists of two series-connected components: a modified cascode amplifier (Fig. 12) and an output amplifier-shaper A out based on an OA with differential inputs and outputs. The upper cutoff frequency of the LMH3401 with a parasitic input capacitance at a level of ~1.5 pF and an equivalent feedback resistance of 20 kΩ reaches 250 MHz. In this frequency band, the noise current (RMS) reduced to its input does not exceed 49 nA. The input stage of the cascode amplifier is based on a BUF740 low-noise microwave transistor (Q 1 ) with the quiescent current I 0Q1 = 25 μA; the stage for stabilizing the photodiode voltage is based on a high-frequency BC847 transistor (Q 2 ) with an emitter current of 1 mA.
The operating frequency band of the cascode amplifier, in which the spectral density of the current noise component reduced to the input is constant and is determined by the value of the current I 0 , is limited from above by the value (21) In this frequency band, the value of the input-current noise component for the entire amplifier, taking the above estimates for each stage into account, does not exceed 27 nA (RMS), which corresponds to a SNR at a level of 370. The problem is that the operating frequency band of the stage with a common base and the TIA is much wider. Therefore, in order to obtain the desired result and exclude the influence of the quiescent current of the emitter follower and the high-frequency components of the input-transistor and TIA noise current on the resulting SNR, the operating frequency band of the amplification path is limited using an auxiliary filter. The role of the filter is performed by an output shaper that is based on a differential amplifier. Like an active filter of the detector LMH3401 of the Thomson-scattering diagnostics, it restricts the bandwidth of the operating frequencies of the amplification path from above to the cutoff frequency F and increases the transfer coefficient of the latter by 5 times. The specified cutoff frequency is set by the resistive-capacitive elements of the feedback circuits of the amplifier-shaper output stage. Figure 13 shows a signal response of the described amplifier to a particle with an energy of ~5 MeV that enters the detector aperture. The figure also shows an oscillogram of the signal response to the arrival of the same α particle at a detector with a similar amplifiershaper and a D4.5A silicon diode, which has a fourfold active-region area and, thus, the corresponding value of the parasitic capacitance C d of the junction.
CONSTRUCTION OF AN AMPLIFYING PATH
FOR DETECTORS LOCATED REMOTELY Unlike silicon detectors, artificial-diamond-based detectors are radiation-resistant and operate at high bias voltages (hundreds of volts); due to the high mobility of carriers and the small width of the p-n junction, they have subnanosecond durations of signal responses and an energy resolution acceptable for thermonuclear applications (at a level of percent or less). Carbon atoms of the diamond detector have a relatively large cross section of the interaction with high-energy neutrons. Due to their design features, detectors based on them are characterized by a much smaller interaction cross section with energetic γ quanta. Because of this, diamond detectors are used to register neutron events on the installations characterized by severe radiation conditions and, accordingly, intense thermonuclear neutron fluxes. WEST (France, Cadarache), JET (UK, Culham), and ITER (France, Cadarache) are examples of such installations. Together with collimators and electromagnetic protection elements, the detectors are placed in close proximity to the experimental complex and are interfaced with preamplifiers-shapers, which are placed behind the biological-shield elements, and lines based on a radiation-resistant cable with a length of up to several tens of meters (Fig. 14).
The bias voltage is fed along the same lines to the detectors from the corresponding power sources through ballast resistors. The inputs of the preamplifiers are isolated from the cable lines and DC bias-voltage sources via decoupling capacitances [8].
The total charge that is generated by a thermonuclear neutron (14 MeV) as a result of nuclear reactions in a diamond detector is relatively small, slightly larger than 100 fC. When passing through a long cable communication line, the initial subnanosecond signal response of the detector is transformed due to dispersion into a current pulse with a duration of 10-15 ns, which determines the possibility of its operation with neutron fluxes of rather high intensity (≥10 7 events/s). This option is realized if the integration time constant τ of the amplifier-shaper is comparable with the characteristic current-pulse duration at the output of the cable line and its input resistance r is equal to the characteristic impedance of this line. These conditions determine not only the high cutoff frequency of the preamplifier FR but also the need to eliminate reflections in the signal path and, as a consequence, a relatively large value of the spectral density of the noise current generated by the matching resistor or its equivalent at the receiving end of the cable communication line. When the line is matched using a 50-Ω resistor, the spectral density of the noise current has a large value, . On an integration ≈ = 4 18 pA/ Hz kT i R Fig. 13. A signal response to an arrival of an α particle at the detector aperture. interval whose duration is comparable with the typical pulse duration at the cable-line output (15 ns), it forms a noise charge of ~2.6 fC, which is only 35-40 times smaller than the charge formed by a thermonuclear neutron when it hits the diamond detector. As a consequence, the energy resolution of the signal path turns out to be poor. The situation can be somewhat improved by replacing the resistive matching line of the cable with its less noisy counterpart. The functions of the latter can be performed by the dynamic resistance r e of the base-emitter junction of the transistor connected according to the common-base circuit (Fig. 15). Due to the dependence of the dynamic resistance of the transistor emitter-base junction r e on the emitter current I e (r e = ϕ/I e , where ϕ is the temperature potential), this matching at the transistor emitter current I e = 0.5 mA allows the noise determined by resistive matching to be reduced by a factor of . It can be seen that the cascode circuit of the signal amplifierformer in tandem with the diamond detector has certain advantages, as in previous cases. It reduces the level of the noise component reduced to the input of the amplifier-shaper, but does not ensure the inputresistance stability. This is due to the fact that the dynamic resistance of the emitter-base junction of the transistor is modulated by the signal current of the diamond detector. As a consequence, the level of its reflection at the receiving end of the cable line changes as well, depending on the signal amplitude. In view of the random nature of signals that are generated by the diamond detector, it can be concluded that the level of reflections directly affects the resulting SNR, thus leveling the gain obtained via changes in the cable-line matching scheme. Thus, the task of minimizing the modulation level of its input resistance by the signal current becomes urgent in the signal amplifier-shaper of the diamond detector. The input stage based on transistors of different conductivities Q 1 and Q 2 that are connected according to the circuit with a common base allows this problem to be solved (Fig. 16).
A signal from the cable line is fed to the emitterbase junctions of these transistors through decoupling capacitances that isolate them from the bias-voltage 2 source. These junctions are connected in parallel with respect to the signal source. The dynamic resistance of each junction with a value of 100 Ω is observed at a quiescent current of the emitter of I 0 = 0.25 mA. Changes in the signal current in the emitter circuit of the transistors are the same and equal to I s /2 but are opposite in sign. Therefore, the resistances of the emitter-base junctions of the transistors change under the influence of a signal current by almost the same value but in the opposite directions. In the transistor in which the signal current is added to the quiescent current this resistance decreases; in the second one, where the signal current is subtracted from the quiescent current, this resistance increases. Since the transistor base-emitter junctions are connected in parallel with respect to each other, these changes in their dynamic resistances actually compensate for each other. As a consequence, the modulation of the amplification-path input resistance by the signal current is efficiently suppressed. The value of the SNR remains unchanged. This is due to the fact that half the quiescent currents in a two-transistor matching circuit together form the same noise current as the quiescent current of its single-transistor analogue. A relatively low SNR at the input and large fluctuations in the position of the zero line of signals at the amplificationpath output, which depend on the detector loading, are the key factors that affect the resulting energy resolution of the neutron diagnostics. It is possible to reduce the influence of the first factor, as noted earlier, by filtering the high-frequency components of the amplification-path output signal and the second one by eliminating the "averaged" component from this signal on the interval of its registration. The latter operation is equivalent to eliminating the low-frequency spectral components of the signal from it. An obvious conclusion suggests itself: it is desirable to Fig. 15. The use of the r e resistance as the matching resistance. Fig. 16. The modified circuit for matching to the cable line. perform the basic procedures for processing the output signal of the amplification path of neutron diagnostics with its digital equivalent, which is represented in a spectral or amplitude-frequency form, which is essentially the same. Let us return to the amplification path. In order for the above processing procedures to become real, the path must generate an output signal with the maximum possible SNR, which is suitable for digitization by a high-speed ADC. Since the result of the neutron diagnostics is represented in the form of an energy spectrum of particles or the flux intensity of neutrons with a certain energy that fall within the detector aperture, two key factors have a decisive influence on the resulting characteristics of the amplification path. These are the maximum permissible load of the detector and the maximum possible duration of its output signal, which excludes a sharp increase in the dead diagnostic time due to overlapping events. When the detector load is several million events per second, which is typical of the neutron diagnostics of many plasma facilities, the characteristic duration of an output signal of the detector amplification path lies in the range of 20-70 ns (FWHM). Wider signals are preferred because the bandwidth limitation of the amplification path that is necessary for their formation in the high-frequency region is transformed into an increase in the resulting SNR. In addition, in the case of "long" signals, the requirements for the performance of ADCs that convert the current amplitude values of these signals into a digital equivalent are considerably attenuated.
The circuit of the amplification path of the neutron diagnostics, with the exception of the input stage, reproduces the circuit of the Thomson-scattering diagnostic amplifier (see Fig. 17). Its main amplification stage is based on an LMH32401 TIA, which, with a feedback resistor of 20 kΩ in the frequency band from 0 to 250 MHz, has a spectral noise-current den-sity reduced to the input I n = . It is much smaller in magnitude than the spectral noise-current density of the matching cascade and therefore has almost no effect on the resulting SNR of the amplifier-shaper (of course, provided that its bandwidth is limited from above by the aforementioned cutoff frequency). The output stage of the amplifier-shaper that is based on an ADA4938 OA with differential inputs solves this problem. The bandwidth of the signal path is limited at a given level by corrective capacitances in its feedback circuits.
The resulting duration of the output signal and the SNR depend on the ratings of the corrective capacitances. Figure 18 shows a characteristic waveform of the output signal of the amplification path of the neutron diagnostics.
CONCLUSIONS
The task of constructing the amplification paths for semiconductor detectors of plasma diagnostics is not trivial despite its apparent simplicity. The final signal/noise characteristic of the amplification path and its frequency characteristics are significantly influenced by the parameters of the TIA (the input current, input voltage, bandwidth, etc.), as well as the input capacitance of the detector, the differential capacitance, and the input capacitance at the noninverting amplifier input. The methods for solving this problem strongly depend on the goals that the developer seeks to achieve: an increase in the bandwidth or an increase in the SNR. In most cases, it is necessary to come to a compromise between the allowable bandwidth in a particular task and the corresponding SNR value. | 9,233 | 2022-02-01T00:00:00.000 | [
"Physics",
"Engineering"
] |
Selective activation of cellular stress response pathways by fumaric acid esters
The cellular response to oxidants or xenobiotics comprises two key pathways, resulting in modulation of NRF2 and FOXO transcription factors, respectively. Both mount a cytoprotective response, and their activation relies on crucial protein thiol moieties. Using fumaric acid esters (FAEs), known thiol‐reactive compounds, we tested for activation of NRF2 and FOXO pathways in cultured human hepatoma cells by dimethyl/diethyl as well as monomethyl/monoethyl fumarate. Whereas only the diesters caused acute glutathione depletion and activation of the stress kinase p38MAPK, all four FAEs stimulated NRF2 stabilization and upregulation of NRF2 target genes. However, no significant FAE‐induced activation of FOXO‐dependent target gene expression was observed. Therefore, while both NRF2 and FOXO pathways are responsive to oxidants and xenobiotics, FAEs selectively activate NRF2 signaling.
The cellular response to oxidants or xenobiotics comprises two key pathways, resulting in modulation of NRF2 and FOXO transcription factors, respectively.Both mount a cytoprotective response, and their activation relies on crucial protein thiol moieties.Using fumaric acid esters (FAEs), known thiol-reactive compounds, we tested for activation of NRF2 and FOXO pathways in cultured human hepatoma cells by dimethyl/diethyl as well as monomethyl/monoethyl fumarate.Whereas only the diesters caused acute glutathione depletion and activation of the stress kinase p38 MAPK , all four FAEs stimulated NRF2 stabilization and upregulation of NRF2 target genes.However, no significant FAE-induced activation of FOXO-dependent target gene expression was observed.Therefore, while both NRF2 and FOXO pathways are responsive to oxidants and xenobiotics, FAEs selectively activate NRF2 signaling.
Cellular responses to stressful stimuli, including reactive oxygen species (ROS) and xenobiotics, frequently overlap, with both oxidative stress and xenobiotics eliciting acute and delayed cellular adaptations, the latter usually being at the level of transcriptional regulation.There are, however, also a few intracellular molecules and pathways modulated in parallel by both oxidative stress and xenobiotics.Among the shared cytoprotective pathways are those that lead to activation of NRF2 (NFE2-like bZIP transcription factor 2, NFE2L2) and FOXO (forkhead box, class O) transcription factors [1].At a molecular level, crucial thiol moieties contribute to these processes, as they may not only be oxidized but also form adducts with electrophilic xenobiotics.In the case of NRF2 signaling, cysteine thiols of kelch-like ECH associated protein 1 (KEAP1) render it a target protein that controls the activity of NRF2 by mediating its proteasomal degradation under non-stressed conditions.Oxidation or alkylation of KEAP1 interrupts this regulatory circuit, resulting in stabilization and nuclear translocation of NRF2 as well as induction of NRF2 target genes, including genes encoding ROS-detoxifying (antioxidant) enzymes as well as enzymes required for biosynthesis of the reducing equivalents glutathione (cGlu-Cys-Gly, GSH) and nicotinamide adenine dinucleotide phosphate (NADPH) [2,3].Similar to the KEAP1/ NRF2 system, transcription factors of the FOXO family (as well as proteins upstream in the cascade, modulating FOXO activity) contain cysteine residues that are involved in their redox regulation [4,5].FOXO signaling, accordingly, is affected by xenobiotics and oxidants [6][7][8].FOXOs, in turn, control the expression of genes encoding several antioxidant enzymes [9].
There are reports indicating that the redox-sensitive NRF2-and FOXO transcriptional regulatory systems may be connected, for example through transcriptional regulation of antioxidant enzymes by FOXOs and the consecutive modulation of steady-state levels of ROS such as hydrogen peroxide, which, in turn, affects the activity of KEAP1/NRF2 (for review, see ref. [1]).Moreover, several flavonoids were shown to stimulate both NRF2-and FOXO-dependent signaling in cultured human cells [10].In this regard, exposure of the model organism Caenorhabditis elegans (C.elegans) to the electrophilic and adduct-forming compound diethylmaleate (DEM) caused glutathione depletion and, at lower levels of exposure, a significant lifespan extension.Both the FOXO and the NRF2 orthologs in the worms (DAF-16 and SKN-1, respectively) were involved in the DEM-mediated increase in lifespan [11].
The course of events and the mode of the potential collaboration between these two redox-sensitive transcriptional regulatory pathways are ill-defined.For example, if both pathways react to thiol-modulating agents and to oxidative stress, does one of the pathways predominate the cellular response, or do both collaborate?Can one pathway be stimulated independently of the other?
Here, we begin to address these questions by making use of fumaric acid esters (FAEs) as a group of electrophilic substances with different membrane permeation properties: the uncharged diesters, diethyl fumarate (DEF) and dimethyl fumarate (DMF), as compared to the monoesters, monoethyl fumarate (MEF) and monomethyl fumarate (MEF), that are ionized at physiological pH (Fig. 1A).FAEs were chosen as compounds to analyze activation of both NRF2 and FOXO pathways for two reasons.(a) Esters of both fumaric acid as well as maleic acid (including the above-mentioned DEM) were found to stimulate the expression of genes encoding GSH S-transferases (GSTs) and NAD(P)H:quinone oxidoreductase 1 (NQO1), now known as genes regulated by NRF2, already in 1990 [12].(b) FAEs are being employed pharmacologically and are, therefore, of rather general interest: DMF is approved for the treatment of a form of multiple sclerosis (MS), relapsing-remitting MS [13,14].It is also used in the treatment of psoriasis, another inflammatory disease, often in combination with other FAEs, such as MEF [14][15][16][17].The exact mechanism of action has not been resolved entirely, but both immunomodulatory and antioxidant effects (through stimulation of signaling cascades) were proposed to contribute to the efficacy of FAEs.
Cultured HepG2 human hepatoma cells were chosen as a model to investigate the effects of FAEs as they (a) have been characterized previously in our laboratory regarding their harboring both NRF2 and FOXO signaling cascades [18,19] and (b) physiologically, liver -although not the ultimate target tissue of FAEswould be expected to be exposed to systemically applied FAEs via portal blood in vivo.(c) Moreover, psoriasis has been found to be associated with an increased risk to develop liver injuries such as non-alcoholic fatty liver disease (NAFLD), and systemic use of FAEs may elicit both hepatoprotective and hepatotoxic effects [20].
We found that all of the tested FAEs, independent of their acute thiol-depleting effects, stabilized NRF2 and upregulated the expression of NRF2 target genes.In contrast, despite, in part, affecting FOXO cytoplasmic/nuclear shuttling, FAEs did not affect the expression of FOXO target genes.In summary, while both NRF2 and FOXO pathways are generally responsive to oxidants and xenobiotics, FAEs selectively activate NRF2 signaling.
Materials
Chemicals were purchased from Merck/Sigma (Darmstadt, Germany) or Carl Roth GmbH (Karlsruhe, Germany), Fig. 1.Effects of fumaric acid esters (FAEs) on viability and glutathione levels in HepG2 cells.(A) Structures of FAEs and of diethylmaleate (DEM): monomethylfumarate (MMF), monoethylfumarate (MEF), dimethylfumarate (DMF), diethylfumarate (DEF).(B) Dose-dependent cytotoxicity of FAEs.HepG2 cells were exposed to FAEs at the indicated concentrations or to DMSO (solvent control) in serum-free medium for 24 h.Cell viability was assessed using a neutral red assay.Relative values were calculated by setting the viability of cells exposed to solvent control to 100%.Data are given as means of four independent experiments +SD/ÀSD.(C) Glutathione (0.5 GSSG + GSH) levels and redox ratio (0.5 GSSG/GSH) in HepG2 cells exposed to FAEs, DEM (as positive control) or DMSO ("0 mM"; solvent control) at the indicated concentrations for 60 min in serum-free medium.Data are means of three independent experiments AE SD.Data were normalized against control conditions (DMSO; "0 mM"), which were set to 1.Under these conditions, glutathione and glutathione disulfide concentrations were as follows (mean AE SD): [GSH] = 55. 1
Determination of intracellular glutathione concentrations
Glutathione and glutathione disulfide concentrations were determined by HPLC following derivatization of thiols in cell lysates with orthophthaldialdehyde (OPA) as described [21], with minor modifications.In brief, cells were collected in 0.01 N HCl, followed by sonication on ice and precipitation of proteins by the addition of 2 N perchloric acid to a final concentration of 0.67 N. Following neutralization of the supernatant using 0.5 mM sodium phosphate buffer (pH 7.0), thiols were derivatized with OPA (final concentration: 0.065 M) at room temperature in the dark for 60 min.OPA adducts of GSH were analyzed using HPLC on a Nucleodur C18 Pyramid 5 l RP column (4 9 250 mm; Macherey-Nagel, D€ uren, Germany) and gradient elution with (A) 98% of 50 mM sodium acetate (pH 7.0)/2% acetonitrile and (B) 80% acetonitrile/20% 50 mM sodium acetate (pH 7.0) as eluents.Detection of adducts was by fluorescence (Ex: 350/Em: 420 nm).
For analysis of GSSG content, all GSH was alkylated by the addition of N-ethylmaleimide (NEM, final conc.9.1 mM) to the deproteinized supernatants.Excess NEM was removed by addition of N-acetyl cysteine (final conc.8.3 mM).Subsequently, GSSG was reduced to GSH using dithiothreitol (DTT; final conc.7.7 mM), followed by detection of GSH by OPA-derivatization as above.
Analysis of FOXO1 subcellular localization
HepG2 cells were grown for 28-30 h to approx.60% confluence on 6-channel-microscopy slides with a coverslip bottom ("l-Slides VI 0.4"; ibidi, Cat# 80606).Cells were transiently transfected with 2 lg of plasmid DNA encoding an EGFP-coupled form of FOXO1 [21] and 6 lL GenJet transfection reagent (tebu-bio, Offenbach, Germany) for 16-18 h.Following a preincubation with serum-free medium for 4-5 h, cells were exposed to bovine insulin (100 nM; Merck/Sigma, Cat# I0516) and/or DMF, DEF (or the respective solvent controls) while being observed under the microscope.The microscopy slides were then placed in an incubator box (Okolab, Ottaviano, Italy), held at 37 °C/5% CO 2 and analyzed.Fluorescence microscopic images were taken at multiple time points (Nikon Eclipse Ti fluorescence microscope).Transfected cells (as judged by their green fluorescence) were grouped into three categories with respect to the predominant subcellular localization of the EGFP signal ("cytoplasmic", "cytoplasmic/nuclear" or "nuclear").
Quantitative RT-PCR (qRT-PCR)
HepG2 cells were seeded in 6-well plates and were starved for 18 h in DMEM supplemented with 100 UÁmL À1 penicillin, 100 lgÁmL À1 streptomycin and 1% (v/v) non-essential amino acids.Afterwards, they were exposed to different concentrations of FAEs (MMF, MEF, DMF, DEF) or DEM and/or 100 nM insulin or 0.1% (v/v) DMSO as solvent control diluted in serum-free DMEM.Exposure was for 4 or 16 h, respectively, followed by lysis of cells and isolation of total RNA using the RNeasy Mini kit (Qiagen, Hilden, Germany) according to the manufacturer's instructions.
1 lg of total RNA was converted to cDNA using RevertAid reverse transcriptase (Thermo Scientific) according to the manufacturer's instructions, and subjected to qPCR analysis on a CFX Connect cycler (Bio-Rad Laboratories AG, Munich, Germany) using SsoAdvanced Universal SYBR Green Supermix (Bio-Rad).The housekeeping gene HPRT1 transcript was used for normalization of mRNA levels.Sequences of primers used are listed in Table 1.
Statistical analysis
Means were calculated from at least three independent experiments, and error bars represent standard deviation (SD).Statistical analyses were performed using GRAPHPAD PRISM software, version 8 and above (GraphPad Software, San Diego, CA).Statistically significant differences were determined using a one-way ANOVA with Dunnett's post-hoc test.Values of P < 0.05 were considered statistically significant and denoted as follows: *P < 0.05, **P < 0.01, ***P < 0.001, ****P < 0.0001.
Results
Fumaric acid diesters, but not monoesters, elicit acute depletion of glutathione and activation of the stress kinase p38 MAPK HepG2 cells were exposed to various concentrations of any of four FAEs (see Fig. 1A), mono-or dimethylfumarate (MMF, DMF) or mono-or diethylfumarate (MEF, DEF), followed by analysis of cell viability (Fig. 1B) and two parameters reflecting the capability of eliciting an acute stress response, depletion of glutathione (Fig. 1C), e.g. through a reaction depicted in Fig. 1D, and activation of p38 MAPK (Fig. 2).FAE cytotoxicity was assessed after a 24 h-incubation period and was highest with the diesters, DEF and DMF (Fig. 1B), likely owing to their higher lipophilicity and better membrane permeation [22].The highest final concentration achievable with DMF in our hands was 0.3 mM, which was less toxic than the same concentration of DEF, but more so than MMF or MEF (Fig. 1B).
Only DMF and DEF caused statistically significant glutathione depletion in exposed cells (Fig. 1C).Moreover, only DEF at 1 mM elicited oxidation of reduced glutathione (GSH) to form GSSG and result in a significantly elevated GSSG/GSH ratio, indicative of an impaired redox homeostasis (Fig. 1C); overall, this suggests that the glutathione depletion observed was largely due to alkylation.More rapid access to the intracellular milieu is likely to contribute to the higher acute glutathione depletion by the fumaric acid diesters as well as interaction with cellular protein thiols, resulting in a cellular stress response (Fig. 1D).This FAE reactivity pattern is also reflected at a cellular signaling level: only DMF and DEF elicited statistically significant phosphorylation (activation) of the kinase p38 MAPK , which is known to respond to a variety of stress-inducing stimuli (Fig. 2).
The cis-isomer of DEF, DEM (Fig. 1A), was used as a positive control for several parameters in this study, based on previous work on its effects in HepG2 cells [18,21].Similar to the fumaric acid diesters, DEM induced rapid glutathione depletion and p38 MAPK phosphorylation (Figs 1C and 2).
All FAEs stimulate NRF2 stabilization and signaling but differ with respect to active concentrations and the time courses of upregulation of NRF2 target genes In contrast to the stark differences between mono-and diesters of fumaric acid in acute glutathione depletion and p38 MAPK activation, all tested FAEs were capable
As reported before [18], NRF2 protein levels were very low in non-stressed (mock-treated) HepG2 cells (Fig. 3, white bars).An increase in NRF2 levels is indicative of its stabilization due to KEAP1 inactivation and was elicited in a concentration-dependent manner by MMF and MEF, with induction observed after 60 min of exposure to less than 1 mM of these FAEs (Fig 3A,B).The diesters were even stronger NRF2 activators that required 10-(DEF) to 100-fold (DMF) lower concentrations (Fig 3D , C, respectively), as compared to the monoesters.In the case of DEF, the effect elicited at 0.1 mM even appears to constitute a maximum, as less effect was observed with higher concentrations (Fig. 3D).DEM served as positive control, and induced NRF2 stabilization at the applied concentration of 1 mM (Fig. 3).Further downstream, the expression of NRF2 target genes was stimulated by FAEs (Fig. 4).Known target genes include those encoding heme oxygenase-1 (HMOX1), GCLC (glutamate-cysteine ligase, catalytic subunit), the enzyme catalyzing the rate-limiting step in GSH biosynthesis, the quinone-reducing (and thereby antioxidant) enzyme NAD(P)H:quinone oxidoreductase-1 (NQO1) and glucose 6-phosphate dehydrogenase (G6PD), the first enzyme in the pentose phosphate pathway, also providing NADPH.Of the tested target genes, HMOX1 appeared to be the most sensitive toward exposure to FAEs, with highly significant induction observed upon exposure to DEF (like DEM) and DMF already after 4 h.Similarly, a fast and pronounced DEM-induced upregulation of HMOX1 mRNA levels in HepG2 cells
1237
has been reported before [18].After 16 h of exposure, signals elicited with diesters still persisted, and strong, highly significant HMOX1 expression elicited by the monoesters, MMF, MEF, was now observed as well (Fig. 4A).As with NRF2 protein levels (Fig. 3), an apparent maximum active concentration was again observed with DEF at 0.3 mM.GCLC gene expression appeared to be slightly elevated over control already at 4 h and at low FAE concentrations, whereas after 16 h DEF was the most strongly stimulating FAEagain with a maximum at 0.3 mM (Fig. 4B).Except for DEF, the observed stimulation of GCLC expression remained just below the level of significance.Rather minute, yet (in part highly) significant, effects on gene expression were observed with NQO1 and (for the diesters) also G6PD (Fig 4C, D) after 16 h of exposure, with no more than a two-fold increase in the respective mRNA levels.
Fumaric acid diesters stimulate nuclear accumulation of EGFP-FOXO1
Shuttling between cytoplasm and nucleus contributes to the regulation of FOXO1 transcriptional activity.Therefore, in order to test for effects of FAEs on FOXO signaling, we first analyzed FOXO1 subcellular localization following exposure of HepG2 cells to FAEs.To that end, we transfected HepG2 cells with a plasmid encoding EGFP-tagged FOXO1, followed by treatment with insulin and/or FAEs and subsequent detection of the overexpressed EGFP-FOXO1 by fluorescence microscopy.Treatment of the cells with insulin prior to exposure to FAEs occurred in order to elicit nuclear exclusion of FOXO1, which would then enable us to observe any potential activating effects of FAEs in analogy to DEM, which we had previously identified as a stimulator of FOXO nuclear accumulation [21].As demonstrated in Fig. 5A,B, insulin treatment (different from control treatment, Ctrl) in fact strongly stimulated nuclear exclusion, as nuclei appear as darker spheres in EGFP-positive cells after 30 min of insulin treatment.
We then tested for the effects of the fumaric acid diesters, DMF and DEF, with respect to EGFP-FOXO1 nuclear accumulation.DEF, like its isomer DEM [21], elicited strong nuclear accumulation, even following insulin-induced nuclear exclusion.DEF, therefore, appears to override the effects of insulin.The effect was strong enough to be detectable also in cells not pre-treated with insulin (Fig. 5A).The response to DMF exposure was less pronounced, but nevertheless following the same trend: DMF supported nuclear accumulation of EGFP-FOXO1 (Fig 5A ,B).
The relatively weak DMF effect may be attributed to the lower achievable concentrations that were used.On the other hand, these lower concentrations also elicited effects on parameters such as GSH depletion (Fig. 1C) or p38 MAPK activation (Fig 2C,D) and NRF2 stabilization (Fig 3C,D) that are similar in extent to those of higher DEF concentrations.Another reason for a difference in effect intensity of FAEs may be the reactivity toward protein substrates that are involved in regulating upstream signaling, resulting in FOXO1 modulation.Therefore, we next tested for signaling events up-and downstream of FOXO1 nuclear accumulation.
FAE-induced nuclear accumulation of FOXO1 is independent of modulation of AKT/FOXO1 signaling
In the insulin signaling cascade, the Ser/Thr kinase AKT is immediately upstream of FOXO1.AKT activation (through phosphorylation at Thr-308 and Ser-473) is elicited by exposure of cells to growth factors, such as insulin [23].AKT, once activated, phosphorylates FOXO proteins, resulting in their inactivation and (in the case of isoforms FOXO1, FOXO3 and FOXO4) nuclear exclusion [9].
In order to test whether the observed nuclear accumulation elicited by exposure of HepG2 cells to FAEs (Fig. 5) corresponds with AKT inactivation (dephosphorylation) and suppression of AKT-dependent FOXO1 phosphorylation, we exposed cells to FAEs accordingly, in part following a pre-stimulation by insulin.Insulin treatment was intended to elevate AKT/FOXO1 phosphorylation levels to allow for better observation of a potential dephosphorylation following FAE exposure.Insulin treatment indeed elicited a strong phosphorylation of AKT (Ser-473) (Fig. 6), as well as FOXO1 (at the AKT substrate site Thr-24) (Fig. 7).FAEs, however, did not cause a loss of AKT phosphorylationneither of basal nor of insulin-induced phosphorylation (Fig. 6).On the contrary, a slight increase of insulin-induced AKT activation was observed in cells exposed to the diesters, DMF, DEF and DEM.DEF, at 3 mM, even stimulated AKT phosphorylation in the absence of insulin and enhanced insulin-induced activation.
No major changes of basal or insulin-induced FOXO1 phosphorylation at Thr-24 were observed in cells exposed to FAEs, except for DEF (Fig. 7).DEF treatment dose-dependently suppressed FOXO1 phosphorylation.This is in sharp contrast to DEF-induced AKT activation (Fig. 6), which would be expected to
FAEs tend to attenuate rather than stimulate FOXO-dependent gene expression
In order to test for consequences of FOXO1 nuclear accumulation for gene expression, mRNA levels of two FOXO target genes, G6PC [24] and SELENOP [25] were analyzed in cells exposed to FAEs for up to 16 h.Insulin was used as positive control, provoking AKT-induced FOXO inactivation and, consequently, downregulation of FOXO target gene expression.This was most obvious with G6PC (Fig. 8A), both at 4 and 16 h of insulin treatment.SELENOP mRNA levels were also downregulated by insulin, but only transiently, at 4 h, and not as strongly as those of G6PC (Fig. 8B).
No clear long-term changes in expression of G6PC or SELENOP were observed following exposure to FAEs.A transient (i.e., detected at 4 h, but not 16 h) downregulation of G6PC expression was observed with the diesters, DMF, DEF, and a similar trend with DEM (Fig. 8A).This is in contrast to expectations, as a DEF-induced decrease in FOXO phosphorylation and enhanced nuclear accumulation of FOXO would be predicted to result in a stimulation, rather than attenuation, of target gene expression.
Therefore, FAEs may cause FOXO1 nuclear accumulation, but nuclear FOXO1 is not productive in terms of stimulating target gene expression.
Discussion
All FAEs tested in this study, both mono-and diesters, increased NRF2 protein levels and induced NRF2-dependent signaling in HepG2 human hepatoma cells.Besides hydroxy-carboxylic acid receptor 2 (HCAR2) and glyceraldehyde-3-phosphate dehydrogenase (GAPDH), KEAP1 was listed as one of the key target proteins considered relevant for the mode of action of DMF in a recent edition of an encyclopedia of molecular pharmacology [26].Considering the reactivity as a,b-unsaturated carbonyl compounds (see Fig. 1D) that suggest pleiotropic action of FAEs, however, this list is unlikely to be exhaustive.In line with this, FAE target molecules include the major lowmolecular-mass thiol, glutathione, which is a crucial contributor to cellular antioxidant defense systems as well as to xenobiotic metabolism [27].Therefore, as alkylating properties are generally accepted as contributing to NRF2 activation by FAEs, we tested for acute depletion of cellular glutathione as a measure of alkylation.No effect was observed with the fumaric acid monoesters MMF and MEF whereas the diesters DMF and DEF (as well as the positive control DEM) caused a glutathione depletion.Despite these differences between fumaric acid mono-and diesters, the monoesters were also capable of inducing a stabilization of NRF2, leading to stimulation of NRF2 target gene expression.Induction of expression of the most sensitive target gene, HMOX1, was delayed upon exposure to monoesters relative to diesters, suggesting that diesters are more potent stimulators of NRF2 signaling.
Based on in vitro [28,29] and in vivo [30] data suggesting hydrolysis of DMF under physiological conditions, it was proposed that the active form of DMF is MMF.MMF reaches the systemic circulation following oral administration of DMF, whereas DMF does not even appear to show up in portal blood (for a comprehensive review of pharmacokinetic data, see ref. [22]).This would imply that DMF is mainly a prodrug.For example, DMF-induced activation of the G protein-coupled HCAR2, which is linked to immunomodulatory NF-jB-dependent signaling [14], is through MMF: HCAR2 is bound and activated by MMF, but not DMF [31], and was demonstrated to mediate therapeutic effects of DMF in a mouse model of MS [32].It remains to be elucidated whether, and to what extent, DMF has activities distinct from those of MMF.For example, DMF permeates membranes better than MMF and is much more active as a Michael reagent [33], alkylating cysteines of target proteins, such as KEAP1 [34] and GAPDH [35].On the other hand, MMF was demonstrated to also target Fig. 5. Effects of fumaric acid diesters on subcellular localization of EGFP-labeled FOXO1.HepG2 cells were transfected with an expression plasmid coding for EGFP-FOXO1.Prior to exposure of cells to FAEs, cells were pre-incubated with serum-free medium for 4-5 h, followed by addition of insulin (Ins., 100 nM) or solvent control for 30 min.Medium was then replaced by serum-free medium containing FAEs.(A) Cells were exposed to DMF or DEF for 60 min prior to analysis of EGFP-FOXO1 subcellular localization.Subcellular distribution of EGFP-FOXO1 in cells was assessed by counting cells with a detectable GFP signal and categorizing them as cells with predominantly nuclear EGFP-FOXO1 (N), with EGFP-FOXO1 predominantly in the cytoplasm (C) or cells with EGFP-FOXO1 equally distributed between the compartments (N/C).The resulting numbers were used to calculate percentages of cells in each category.Data were calculated from three independent experiments.On average, 142 (min: 93, max: 184) cells were categorized per condition in three independent experiments each.Data are given as means AE SD. (B) Cells were prepared as above followed by exposure to insulin (at 100 nM) or control for 30 min and, thereafter, DMF or DEF (or DMSO as control, "0 mM") for up to 2 h.Scale bars (white) indicate 20 lm.cysteine residues of proteins, including GAPDH [36] (Fig. 1D).
Considering the observed differences in acute glutathione depletion upon exposure to FAEs (Fig. 1C), and the reported capability of monoesters to alkylate protein thiols, it is proposed that both mono-and diesters are capable, in principle, of alkylating thiols in vivo, but that this is affected by their general differences in avidity to undergo alkylation and by their different membrane permeation properties.The KEAP1/NRF2 system is a major xenosensor involved in the regulation of cellular antioxidative and stress response and adaptation [2].Accordingly, NRF2 signaling is widely accepted as a crucial component of therapeutic and beneficial actions of FAEs [15,22].Similarly, FOXO transcription factors are involved in a multitude of cellular processes, including the regulation of apoptosis, cell cycle, fuel metabolism, and stress response.Again, there is ample evidence for redox regulation of FOXO signaling, including the role of protein thiols in the signaling cascades affecting FOXO activity (for review, see ref. [4,9]).A multitude of stimuli were identified that affect both NRF2 and also FOXO (or upstream) signaling, including reactive oxygen species such as H 2 O 2 [8,37] or peroxynitrite [38][39][40], lipid peroxidation products such as 4hydroxynonenal [41,42], flavonoids [8,10], transition metal ions and metalloids, such as Cu [6,43,44], Zn [45,46] or As [19,37,47].
Why, then, do FAEs not significantly affect FOXO signaling in HepG2 cells, while clearly stimulating NRF2-dependent gene expression?Several distinctive features of FOXO-and KEAP1/NRF2 signaling can be delineated in the context of an exposure to FAEs: i KEAP1/NRF2 appears to be generally more sensitive to FAEs than the signaling cascade(s) leading to modulation of FOXO activity.While we are not aware of an indication that KEAP1 cysteines are more easily oxidized than sensitive protein thiols in pathways affecting FOXOs, there may be a selectivity with respect to thiol alkylation.In fact, of all KEAP1 cysteines, only specific Cys residues (predominantly Cys151) were identified to be alkylated by fumarates [48], implying that not all Cys thiols are equally prone to be attacked by fumaric acid esters.Importantly, however, there is indication of an additional mode of interaction of FAEs (as demonstrated for DMF and MMF) with KEAP1, as they may also bind to KEAP1 noncovalently, additionally interfering with KEAP1/NRF2 interaction [49].No such noncovalent interaction of FAEs has been demonstrated with components of FOXO-modulating pathways.ii Although the same stress-activated kinases, including ERK MAPK , JNK MAPK , and p38 MAPK (see Fig. 2) as well as AKT (Fig. 6) modulate both FOXO and NRF2 activity, the outcome of an activation of these kinases appears to be mostly stimulating with respect to NRF2, but highly variable with respect to FOXO activity.For example, stressinduced activation of ERK MAPK , JNK MAPK and p38 MAPK may cause their cooperative stimulation of NRF2 [50], whereas their effect on FOXO activity varies with FOXO isoform, site phosphorylated and cell type [9].Similarly, AKT activation causes phosphorylation of FOXOs, resulting in their nuclear exclusion and inactivation.NRF2 activity, however, is stimulated: AKT phosphorylates and thereby inactivates glycogen synthase kinase 3 (GSK3), thereby attenuating NRF2 phosphorylation by GSK3, which results in an attenuation of NRF2 degradation (and thereby its activation) [51].Hence, AKT activation may differentially affect transcriptional regulation by FOXO (which is inactivated) and NRF2 (which is activated).In the present study, however, such an effect of AKT is unlikely, as no basal AKT activation was observed with FAEsexcept for the highest concentration of DEF (Fig. 6).iii In addition to KEAP1 alkylation and noncovalent binding to KEAP1, impairment of a repressor of NRF2 signaling, BACH1, was proposed to contribute to FAE-induced NRF2 activation: both DMF and MMF were shown in a cell culture model (human M17 neuroblastoma cells) to elicit nuclear export of BACH1, with DMF effects being more pronounced [52].DMF was also demonstrated to non-specifically alkylate overexpressed BACH1 in cultured Cos-7 cells [53].It is unclear whether such alkylation contributes to BACH1 nuclear exclusion.In contrast to these reports for BACH1, nuclear export of FOXO1 was previously hypothesized to be impaired by the cis-isomer of DEF, DEM [21].
Based on reports that DEM interferes with nuclear export mediated by exportin CRM1 [54], which is a known mediator of FOXO1 nuclear exclusion [21], one would have to hypothesize that nuclear export impairment by FAEs is selective rather than general.
In summary, despite the similarities in NRF2 and FOXO signaling with respect to their being modulated by similar stressful stimuli and with respect to their stimulating the expression of genes encoding antioxidant enzymes, only NRF2 signaling was activated by FAEs in HepG2 cells.Both mono-and diesters were capable of eliciting a NRF2 response, thus activating NRF2-dependent expression of potentially hepatoprotective factors.FOXO1, however, despite nuclear accumulation upon exposure of cells to FAEs, was not activated under conditions that lead to NRF2 activation.
Fig. 2 .
Fig. 2. Phosphorylation of p38 MAPK in HepG2 cells exposed to FAEs for 60 min.(A) Monomethylfumarate, (B) Monoethylfumarate, (C) Dimethylfumarate, (D) Diethylfumarate.Diethylmaleate (DEM) was used as positive control in all experiments.Blots are representative of at least three independent experiments.Positions of protein markers closest to the detected band are indicated on the left (in kDa).Bar graphs represent densitometric analyses of the blots, means AE SD.Statistically significant differences from control (white bars) were determined by one-way ANOVA with Dunnett's post-hoc test.**P < 0.01, ***P < 0.001, ****P < 0.0001.
Fig. 3 .
Fig. 3. NRF2 protein levels in HepG2 cells exposed to FAEs for 60 min.(A, B) Monomethyl-and monoethylfumarate, (C, D) Dimethyl-and Diethylfumarate.Diethylmaleate (DEM) was used as positive control in all cases.Blots are representative of at least three independent experiments.Positions of protein markers closest to the detected band are indicated on the left (in kDa).Bar graphs represent densitometric analyses of all experiments, means AE SD.Statistically significant differences from control (white bars) were determined by one-way ANOVA with Dunnett's post-hoc test.*P < 0.05, **P < 0.01, ****P < 0.0001.
Fig. 6 .
Fig. 6.Phosphorylation of AKT in HepG2 cells exposed to FAEs for 60 min.(A, B) Monomethyl-and monoethylfumarate, (C, D) dimethyland diethylfumarate.HepG2 cells were pre-incubated with serum-free medium for 16 h, followed by exchange of medium for fresh serumfree medium containing insulin (100 nM) or a buffer control for 30 min.Insulin was used as a positive control for AKT activation.Cells were washed with serum-free medium and exposed to fresh serum-free medium containing monomethyl-or monoethylfumarate, dimethyl-or diethylfumarate or DEM at the indicated final concentrations for 60 min.Cells were washed twice with cold PBS, lysed, and tested for AKT activation using an antibody detecting Ser-473 phosphorylation.Blots are representative of three (MEF, DEF), four (DMF), or five (MMF) independent experiments (biological replicates).SDS/PAGE/western Blot were performed twice (two technical replicates) for all experiments (except MMF).Two different replicates are shown for all experiments (one with GAPDH, the other with AKT detected as loading control).Positions of protein markers closest to the detected band are indicated on the left (in kDa).Bar graphs represent densitometric analyses of all experiments (means AE SD).Statistically significant differences were determined by one-way ANOVA with Dunnett's post-hoc test.*P < 0.05, **P < 0.01, ***P < 0.001.
Fig. 7 .
Fig. 7. Phosphorylation of FOXO1 in HepG2 cells exposed to FAEs for 60 min.(A, B) Monomethyl-and monoethylfumarate, (C, D) dimethyland diethylfumarate.HepG2 cells were treated as described in the legend to Fig. 6.Insulin was used as a positive control for stimulation of phosphorylation of FOXO1.Following treatments, cells were washed twice with cold PBS, lysed, and tested for FOXO1 inactivation by detecting phosphorylation of a known AKT substrate site, Thr-24.Phosphorylation of FOXO1 at Thr-24 was determined by immunoblotting and subsequent densitometric analysis of the blots, with normalization against Ponceau S-stained protein bands.For each experiment, two different replicates are shown (one with GAPDH, the other with total FOXO1 detected as loading control).Positions of protein markers closest to the detected band are indicated on the left (in kDa).A minimum of three independent experiments was performed for each of the tested compounds; bar graphs represent means AE SD.Statistically significant differences were determined by one-way ANOVA with Dunnett's post-hoc test.*P < 0.05.
Table 1 .
Sequences of primers used for qPCR.
FEBS Open Bio 14 (2024) 1230-1246 ª 2024 The Author(s).FEBS Open Bio published by John Wiley & Sons Ltd on behalf of Federation of European Biochemical Societies. | 7,336 | 2024-05-24T00:00:00.000 | [
"Chemistry",
"Medicine"
] |
Genealogical approaches to the temporal origins of the Central American gap : Speciation and divergence in Pacific Chthamalus ( Sessilia : Chthamalidae )
A large section of the tropical Eastern Pacific coastline is nearly devoid of reef or consolidated habitat, and is known as the Central American Gap as it is associated with a biogeographic transition in fish and invertebrate species. We analyze phylogeographic data for intertidal barnacles (Chthamalus) to identify relevant temporal patterns that describe the origins of this biogeographic transition (the Mexican-Panamic Transition Zone). These contrasts of populations on either side of the transition zone include two pairs of closely related species (C. panamensis and C. hedgecocki; C. southwardorum and a Southern form of C. southwardorum), as well as gene flow data within one species (C. panamensis) that currently is found on both sides of the boundary between provinces. Using sequence data from a prior phylogenetic study, we used traditional (net nucleotide divergence) measures as well as coalescent analyses that incorporate the isolation-migration model to identify the likely time of separation between Northern and Southern taxa in two species pairs. A total of 67 individuals were sequenced at two mitochondrial (cytochrome c oxidase i, 16S) and one nuclear (elongation factor 1-alpha) gene regions. Our analyses indicate that the regional isolation of these intertidal barnacles occurred approximately 315-400kya, with subsequent expansion of C. panamensis from the Southern region into the North much more recently. There are insufficient survey data to conclusively document the absence of species from this group within the Central American Gap region near the Gulf of Tehuantepec. However, appropriate habitat is quite sparse in this region and other environmental factors, including upwelling and water temperature, are likely to be associated with isolation of many species in the Mexican and Panamic provinces sensu stricto. Some taxa may maintain gene flow across this region, but very few genetic studies have been completed on such taxa. Until further work is done, distinguishing between prior hypotheses of a faunal gap, or a faunal transition zone, is somewhat speculative. Additional taxonomic revision will be necessary in Chthamalus but is beyond the scope of this paper. Rev. Biol. Trop. 61 (1): 75-88. Epub 2013 March 01.
The conundrum of marine speciation has become a common subject of investigation in recent years.The long dispersal potential of many marine organisms and the paucity of absolute physical barriers would suggest the existence of a small number of widespread species, and yet in actuality marine systems are incredibly diverse, with high levels of endemism (Palumbi 1994).What we have come to recognize is the dynamic nature of habitat and species distributions through time.Histories of allopatry, expansion, and habitat loss are not always readily apparent from contemporary species distributions (McGovern et al. 2010).it is of interest to characterize these historical events when they appear to have influenced large numbers of taxa. in particular, what ancient and contemporary forces separate particular marine provinces, and ecoregions within provinces (Spalding et al. 2007)?The origins of biogeographic transition zones may be environmental in nature (associated with habitat) or may be caused by ancient events that are no longer concordant with environmental patterns.
One such transition zone is found along the Mexican coast of the Tropical Eastern Pacific (TEP) ocean between roughly 13-15°N latitude.Called the "Central American Gap" (CAG) by some (Hastings 2000, Pitombo & Burton 2007) and the Mexican-Panamic transition zone (MPTZ) in other sources (Laguna 1990), this region separates the Mexican and Panamic sensu stricto marine provinces with a "stretch of coastline over 1 200km in length dominated by sandy/muddy shores and mangrove-lined lagoons" (Hastings 2000).This region is known to influence the distribution of rocky shore and reef fish, as well as invertebrates, and is a likely factor in the separation of cryptic species in the region.
The widespread barnacle genus Chthamalus has been the subject of several biogeographic studies in the TEP (Laguna 1990, Wares 2001, Pitombo & Burton 2007, Wares et al. 2009).Very low levels of morphological variation have made determining species distributions difficult, and until recently many species in the 'fissus group' (defined by two minute but verified synapomorphies) were considered a single species or species complex (Dando 1987).Recent phylogenetic studies have indicated that cryptic diversity is yet to be fully explored in this group, with fine-scale morphological variation and DNA barcoding being used to fully describe two new species, C. hedgecocki and C. southwardorum (Pitombo & Burton 2007).Based on morphology alone, the latter is reported to be distributed from Bahio Kino, Mexico, to Puerto Chicama, Perú, but molecular data were previously only available from the Northernmost samples.Pitombo & Burton (2007) predicted that a sibling species group may still exist in this widespread species range, which crosses the CAG; this prediction was founded in part on allozyme data presented by Dando & Southward (1980), but no formal revision or analysis has been completed to date.
To evaluate both the potential for further cryptic diversity and the insights this diversity can provide for understanding the temporal habitat dynamics of the CAG, we have analyzed previously sampled populations of C. southwardorum from sites North and South of this faunal transition and use mitochondrial and nuclear sequence-based markers to measure genetic differentiation among these sites.The same methods are applied to a closely related species pair, C. hedgecocki and C. panamensis, that are found in more wave-exposed coastal habitats.We use analytical approaches based on coalescent theory that allow the co-estimation of divergence times among populations and the migration rates among them (the isolation-migration model; Hey & Nielsen 2004).This approach enables us to separate the effects of ancestral polymorphism and gene flow at loci where alleles are shared between the two regions.Using substitution rates generated from a phylogenetic analysis of the genus (Wares et al. 2009), we have also evaluated the likely time frame at which these regional populations could have become isolated from one another.
Study system:
The taxonomy of this species complex has been confused in the literature for nearly 30 years.This has been in part because although data were available to indicate there were two pairs of Chthamalus along this coast (Northern and Southern pairs of wave-exposed habitat and wave-sheltered habitat species), the taxonomy was only partially updated by Pitombo & Burton (2007), after a series of intervening papers that applied unofficial and inconsistent nomenclature.The four species evaluated here, with an attempt at taxonomic history for each, are: C. panamensis Pilsbry -though its exact distribution has been in question given the difficulty in field identification of this species, panamensis has been consistently used for this taxon.Found in wave-exposed coastal habitats, this species resides primarily in Southern locations in the TEP.Pitombo & Burton (2007) indicated that it may range as far North as 20°N.
C. hedgecocki Pitombo & Burton -originally part of the C. fissus (Darwin) species complex (Hedgecock 1979), this species was distinguished from the rest of the complex using phenotypic and electrophoretic data by Dando & Southward (1980) and unofficially called C. "mexicanus".The same name was also used by Laguna (1990), but this species was officially described as C. hedgecocki in Pitombo & Burton (2007).it is found in waveexposed coastal habitats, primarily at Northern locations in this region.
C. southwardorum Pitombo & Burtonas with C. hedgecocki, this was originally distinguished as a separate taxon by Dando & Southward (1980) and unofficially called C. "cortesianus" (Laguna 1990).Formally described as C. southwardorum in Pitombo & Burton (2007), it can be found in wavesheltered coastal habitats, solely at Northern locations in this region.
C. southwardorum "Farfan" form -named for the putative type locality in Panama (at which 100% of individuals were of this form in 1978, P. Dando pers. comm.), populations of this form were identified as distinct by Dando & Southward (1980) but with no formal description.it has been confused in the literature with C. southwardorum sensu stricto, which may influence our understanding of regional biogeography.The "Farfan" form is found in wave-sheltered coastal habitats, solely at Southern locations in this region.Recent data further suggest a difference between the forms (Wares et al. 2009), though the nomenclature of the C. southwardorum A and B clades is inconsistent in that source.
Note that other congeneric species, including C. fissus and C. anisopoma, may be sympatric with these taxa in the Gulf of California or along the Baja California peninsula, but are more readily distinguished from this complex.
Chthamalus individuals were collected in 2005-2006 from seven primary locations in the TEP (Fig. 1, Table 1) as part of a global phylogeny of the group (Wares et al. 2009).Species in this complex are largely indistinguishable in the field based on external morphology (Pitombo & Burton 2007; P. Dando, pers. comm.).Thus, it was not possible to sample directly for particular species, but rather the available specimens were defined using standard DNA barcoding approaches with the mitochondrial cytochrome oxidase i (COi) locus (Wares et al. 2009).Specimens of C. southwardorum were found in five locations (Table 1, Fig. 1), with three locations North of the CAG and two locations to the South.Specimens of C. hedgecocki and C. panamensis were identified from three additional locations (Table 1).Molecular PCR and sequencing techniques are described in Wares et al. (2009).Two sequences at the 16S locus from the previous study, one each from C. panamensis and C. southwardorum, were excluded from analysis after being identified as either erroneously labeled or product of contamination.Removal of these two sequences results in the reciprocal monophyly of C. southwardorum and the clade containing C. hedgecocki and C. panamensis (Wares et al. 2009).
Phylogenetic analysis:
Here we use previously reported (Wares et al. 2009) aligned sequence data for two mitochondrial gene regions (COi and 16S rDNA) and one nuclear locus (elongation factor 1-alpha, EF1) from the locations indicated in table 1 and figure 1.Additional nuclear sequence data are available for these specimens, but provide little phylogenetic signal at this level and considerable homoplasy (Wares et al. 2009).The separation of locations by the CAG is used for all a priori structuring of data in subsequent analysis.Due to difficulty in amplifying some loci from some individuals, not all locations/individuals/loci are equally represented (Table 1).
Sequence data at the EF1 nuclear locus were directly sequenced and polymorphism within sequences was recoded as ambiguity, Fig. 1.Sampled locations for genetic data in this study, and sample locations from the TEPE 1978 survey.Sites at which the "Farfan" form of Chthamalus southwardorum were identified using phenotypic and allozyme data are indicated.The Gulf of Tehuantepec is the approximate boundary between "Southern" and "Northern" populations in this study, and the demarcation of the Mexican-Panamic transition zone as well as the "Central American Gap" discussed in the text.either unknown "N" in mitochondrial data or appropriate iUPAC ambiguity codes for nuclear data.Phylogenetic reconstructions were performed on the concatenated data using MrBayes v3.1.2(Ronquist & Huelsenbeck 2003) with model estimation unlinked across loci.Bayesian estimation followed 5x10 6 generations of four MCMC chains, with a burn-in fraction of 25%.Data from the EF1 locus were analyzed with ambiguity represented as heterozygous sites for phylogenetic analysis.
Coalescent analysis:
We analyzed the data as multilocus observations from the Northern and Southern sites using the program iMa2 (Hey & Nielsen 2004), which applies the isolation-migration model for estimation of the relative importance of migration and time since divergence.The iMa2 program uses a Markov Chain Monte Carlo method for assessing posterior probability densities of six model parameters: time of divergence, migration from North to South, migration from South to North, and effective population sizes for the two regional populations as well as their ancestral source population.Substitution rate estimates for each locus (Wares et al. 2009) were included to allow the time since divergence to be estimated from the coalescent model.These rates, in units of substitutions per locus/year, are: mtCOi (1.83x10 -5 ); mt16S (7.65x10 -6 ); nEF1 (1.86x10 -6 ).The nEF1 data were separated into haplotypes for coalescent analysis using the PHASE algorithm (Stephens et al. 2001) as implemented in DNAsp (Librado & Rozas 2009).This analysis was repeated for the taxon pair C. hedgecocki -C.panamensis, and for Northern and Southern populations of C. panamensis.Priors allowed for population mutation rates ranging from 10-100 (most likely estimate based on π of 15 was used for final calculations with a maximal range of 30, see below), migration parameter from 0-5, and separation time of four coalescent units.A burn-in period of 10 000 steps was used, followed by a run duration of 10 8 steps with 20 geometrically heated chains.
Given the potential for spatial and temporal concordance of separation between the Northern and Southern species pairs, temporal association was tested using the msBayes pipeline (Hickerson et al. 2006).This approach uses approximate Bayesian computation (ABC) simulation approaches to evaluate the most likely isolation scenarios associated with empirical data; in our case we used 10 6 simulated data sets and an upper prior on ancestral effective size equal to the upper prior on current effective size (otherwise default parameters for analysis).
RESULTS
Phylogenetic analysis: Data from C. southwardorum, C. panamensis, and C. hedgecocki used in this study are as in Wares et al. (2009) but with more focused analysis of genealogical relationships.Genbank voucher numbers for all sequence data are provided in Wares et al. (2009).Bayesian phylogenies for each taxon pair are shown in figures 2 and 3; similar results were obtained from likelihood bootstrap analysis and parsimony analysis (results not shown).Net nucleotide divergence (Nei & Li 1979) between the Northern and Southern populations of C. southwardorum was 0.0288±0.0043for COi, 0.0047±0.0019for 16S, and 0.0019±0.0013for EF1 (0.0044±0.0016 after haplotype phase calculated).Given the substitution rates indicated above, these d A values would suggest divergence times of approximately 5.11x10 5 , 1.69x10 5 , and 5.32x10 5 years, respectively (mean 4.04x10 5 ).
Coalescent analysis: Homogeneity of populations in the Northern and Southern regions for each taxon was indicated from Hudson's (2000) Snn statistic (p>0.05 in all cases).Coalescent analysis of the nEF1 locus produced similar results for C. southwardorum whether using phased or unphased sequences (results not shown); each supported negligible migration between populations of C. southwardorum, though the age estimation based on the nEF1 locus alone is relatively uninformative as there is considerably less polymorphism.Overall, the iMa2 analyses ran sufficiently long to reach good convergence as determined by effective sample size (ESS) values and very similar likelihood distributions (Fig. 4).Effective size estimates were consistent between runs, with the ancestral effective population size 9.27-9.54x10 4 , and current effective population sizes of 1.45-1.47x10 5(Northern) and 2.36x10 5 (Southern).Migration rate estimates between the two regional populations were consistently negligible (≤0.0001 migrants per 1 000 generations in either direction).Posterior probability distributions of divergence time estimates peaked approximately 340kya in all runs, with minimum 95% limits at around 220kya (Fig. 4).High 95% limits are not reported because the distributions have fat tails and thus these maximum (and mean) values are conditioned on the prior.Our time distribution range was set to correspond with the time since the rise of the isthmus of Panama (~three million years ago).
An identical analysis performed on the C. panamensis -C.hedgecocki species pair was consistent with the above results.Migration rate estimates between the two taxa were consistently negligible (≤0.001 migrants per 1 000 generations in either direction).However, the Full analysis of the C. panamensis data in iMa2 indicated maximal population sizes in current Northern and Southern regions (e.g.limited only by the prior, as discussed here prior maximum on theta is 30; see Discussion).The ancestral population substitution rate estimate was approximately what would be predicted from π (13.9; 95% range 8.26-24.38).Migration rate 2Nm from the South to the North was estimated at (mean) 2.46 (0.16, 4.84) and from North to South at 1.48 (0.03, 4.58).Plots of migration rates between the two regions are substantially different, with a maximal posterior probability from South to North of 2.36 and from North to South of 0.003 (Fig. 5).The time of separation of the Northern and Southern populations, coestimated with migration, is approximately 166 830 years given our substitution rate estimates (95% range of 47 400-922 000).
Analysis in msBayes of the coalescentbased divergence times of the two species pairs indicated high probability that separation of the two lineages of C. southwardorum, and C. panamensis and C. hedgecocki, was temporally concordant.With local multinomial logit regression, the posterior probability for a single divergence time between the two pairs was 0.929, with remaining probability allowed for two distinct divergence times.The estimated time of simultaneous divergence using this approach, with the calculations of Huang et al. (2011), is 315 000 years (assuming a generation time of one year and the substitution rates noted above).
DiSCUSSiON
Our results suggest a temporal pattern of increasing isolation among TEP chthamalid barnacles; the deepest separation of the four species evaluated suggests that the shelteredexposed species pairs were separated approximately one million years ago, based on net Estimation of gene flow between these two taxon pairs (treating the Southern populations of C. southwardorum as a distinct taxon, or at least separate population) indicates negligible gene flow between the Northern and Southern forms of both the wave-sheltered (C.southwardorum) and wave-exposed (C.hedgecocki, C. panamensis) taxa.However, additional analysis of the one taxon for which we have samples spanning the region, C. panamensis, indicates that a more recent (~160kya) expansion from the Southern populations to the North is likely to be the cause of the current distribution, both geographic and in terms of genetic diversity.All of these results are also supported by the inclusion of data from one additional nuclear locus, though sample sizes were too small to provide sufficient additional information (results not shown).
Conclusions from our analyses must be tempered by the sparse samples available for this study.Most of the sequence data are from a single mitochondrial locus, sequenced at two distinct regions (mtCOi and mt16S).it should be emphasized that the data obtained were initially part of a separate phylogenetic analysis in which cryptic species were distinguished, without reference to external morphology in field collections.Samples of C. southwardorum were not recovered from sites immediately North of the CAG, nor were any chthamalids identified within the CAG during the NSF-funded Tropical Eastern Pacific Expedition of Newman in 1978 (W.Newman, P. Dando, E. Southward, pers. comm.).Thus, the opportunistic sample size reflects both the sampling effort and PCR success in these samples.Considering the reciprocal monophyly of regional samples at mitochondrial gene regions and extensive lineage sorting at nuclear gene regions, the results appear to be robust to sample size (Rosenberg 2007).One problematic result of the coalescent analyses was the estimate of Ne in populations of C. panamensis being predicated on the maximum of the prior distribution.This is often the case when the data are limiting, and may be associated with the signal of expansion noted above.Briggs (1974) and Brusca & Wallerstein (1979) first indicated that a zoogeographic break in the marine fauna existed at approximately 15° N (roughly the Gulf of Tehuantepec).There are a number of strong environmental shifts associated with this coastal region (Udvardy 1975, Hayden & Dolan 1976).There are significant sea surface temperature and wind stresses associated with the Gulf of Tehuantepec (Sun & Yu 2006), generating strong upwelling in the Gulf and offshore movement of surface waters (Kessler 2006, Barton et al. 2009).Upwelling patterns alone have previously been associated with divergence of regional barnacle populations (Dando & Southward 1981).The coast in this region is predominantly sandy (Robertson & Cramer 2009, W. A. Newman, pers. comm.), with little consolidated habitat for barnacles or reef organisms to persist.A remaining concern is whether this region represents a true faunal 'gap' or transition zone, a question that requires integration across more taxa (Audzijonyte & Vrijenhoek 2010).
While certain groups of species that require consolidated habitat have reduced diversity or abundance in this region, indicating a gap, the patterns of distribution in most taxa may still be consistent with an overlap zone between two biogeographic provinces.Reid (2002) provides such data for littorinid snails, and Laguna (1990) illustrates this in the distribution of barnacles along the tropical Eastern Pacific coast.Notably, there is a clear demarcation between the Mexican and Panamic provinces sensu stricto, but there are a number of barnacle species defined by Laguna (1990) as being of the Panamic province sensu lato that do broadly overlap this transition zone and the CAG.
The present study makes it apparent that at least one of these species (called C. "mexicanus" at the time, but presently C. southwardorum) does not readily cross this region.Though the samples in the present study are sparse, it is consistent with information from the TEPE survey, with no representatives of C. southwardorum (or the "Farfan" form) collected between 9°54' N and 21°30' N. Based on allozyme data from the earlier survey, what is now C. southwardorum was found in high abundance in the Northern Gulf of California (and 100% of our Chthamalus from Bahia Kino are C. southwardorum), but collections between Bahia Chamela (19°30' N), Salina Cruz (16° N) and at isla Sacrificios (15°42' N) recovered only C. hedgecocki (P.Dando, W. Newman, pers. comm.). in the Southern range, as far North as Murciélagos, Costa Rica (10°48' N) only C. panamensis were recovered at the time.Certainly, even when multiple species are present, one may be extremely rare or microhabitat specific.it is an open question whether genetic analysis of other species in this region (group iV in Laguna 1990) would indicate a population genetic pattern consistent with the divergence of C. southwardorum.
The generality of results presented here to the broader faunal distribution patterns of the Tropical Eastern Pacific remains ambiguous.it is clear that for some taxa that require (or form) consolidated substrate or reef habitat, the lack of such habitat in this region (the Central American Gap) is a significant demarcation in diversity along this coast (Hastings 2000, Díaz-Jaimes et al. 2006, Vargas et al. 2008).Studies that have focused only on the apparent distribution of species suggest, however, that the effect of these habitat gaps on marine diversity is minimal and the association of transition zones with gaps like the CAG is possibly stochastic (Robertson & Cramer 2009).Robertson & Cramer (2009) note that because the appearance of the CAG as a "distinctive entity" in their analysis is in part because of an absence of data, rather than information on the potential for migration or gene flow across the region, additional range-wide genetic analysis of fish and other taxa is warranted.The small number of population genetic studies that span this region suggest there are many cryptic populations along the TEP coast (Hellberg 1998, Arnaud et al. 2000, Díaz-Jaimes et al. 2006, Wares et al. 2009, Saarman et al. 2010), and in many cases the break in diversity could be spatially associated with the CAG (Díaz-Jaimes et al. 2006, Hurtado et al. 2007, Pitombo & Burton 2007). in the intertidal snail Nerita, two species are known to span this region; one exhibits a strong break while the other does not (Hurtado et al. 2007), suggesting that knowledge of both habitat and interactions between life history, behavior, and physical oceanography may be necessary to predict the effect of this habitat break on coastal diversity.Robertson & Cramer (2009) noted that the CAG may have formed recently relative to the origins of many taxa in their study, and that more work must be done to assess intraspecific genetic variation among populations of TEP fish taxa on either side of the CAG.Although they argue that the distribution of species suggests gene flow has the potential to be quite high even across this substantial habitat gap -placing the emphasis on other forms of environmental variation for driving the diversity patterns of this coast -we show that for species with long (2-3 weeks; Miller et al. 1989) effective larval dispersal, gene flow is negligible.On recent time scales, the CAG may be promoting intraspecific diversification.it is important to note that the CAG may have distinct effects on different groups of organisms; the delimitation based on absence of reef fishes (Robertson & Cramer 2009) is quite narrow (15-16° N). it may be that more vagile organisms like pelagic fish are less sensitive to such barriers (Lessios & Robertson 2006), while benthic invertebrates or demersal fish have less opportunity to complete such a journey and successfully recruit (Waters et al. 2007).For intertidal invertebrates, and in particular the Cirripedia, this region is certainly an area of faunal transition (Laguna 1990), separating the Mexican and Panamic provinces.The mechanism for diversification may be more than simply habitat availability, as Laguna (1990;also W. A. Newman, P. Dando, pers. comm.) points to earlier work that suggests local currents and upwelling could act as dispersal barriers in this depositional shoreline region.Eventually, with addition of more locational information and microhabitat environmental data, there may be more explicit ways to evaluate the mechanism by which these species have been separated (Glor & Warren 2011).A more thorough spatial survey will be necessary to fully generate models that are useful for microhabitat identification (Lozier et al. 2009).
Assuming an average age of the isolating event between these Northern and Southern lineages of around 400kya (Fig. 4), it is not clear what model of isolation best fits these data.The analytical approaches used here are necessarily indirect (Slatkin 1985) and can have their limitations (Wares & Cunningham 2005), but the concordant results between two distinct estimators suggests our temporal estimate is robust.Hickerson & Meyer (2008) developed a method for comparing the likelihood of "soft" vicariance (in which an effectively panmictic species then becomes isolated across some stretch of its geographic range because of habitat or climate change) versus peripatric events in which a colonization from one side of the boundary establishes a new lineage on the other side.However, these methods require data from a larger number of taxa.Separating the influences of temporal isolation and recurrent gene flow is often critical in assessing alternate historical scenarios that could produce patterns of extant diversity (McGovern et al. 2010).
The question of whether the two subgroups, Northern and Southern, of C. southwardorum merit taxonomic revision is a question that has been addressed but only informally.The regional populations were considered likely to represent separate taxa based on the relative mobilities of Ald and Pgk allozymes, and some coloration differences between exposed-shore populations and sheltered populations in the Mexican (now C. hedgecocki and C. southwardorum) and Panamic (now C. panamensis and the Southern group of C. southwardorum) provinces (Dando & Southward 1980), and tergal groove morphology separating the two Panamic species.The exposed coast forms have orange tergal-scutal tissue flaps (with two pale spots on the flap in C. hedgecocki), and the sheltered coast forms are brown or "orange-brown" for the same tissues (P.Dando, pers. comm.).Pitombo & Burton (2007) also note that C. southwardorum could consist of two sibling species, but this was untested in that study.At present it is simply referred to as the "Farfan" form to avoid any further taxonomic confusion in this group; full taxonomic designation will require integration of phenotypic and genetic identifiers, and will be handled separately.What may be of most general interest about these results -particularly in designing future studies of taxa that apparently cross this coastal region -is that for Chthamalus, the speciation of inshore (sheltered) and outer coast (exposed) forms clearly happened first (Wares et al. 2009), followed by the latitudinal divergence associated here with the CAG.The generality of this result should be examined further.
ACKNOWLEDGMENTS
The authors would like to express their appreciation first and foremost to Bill Newman, Eve Southward, and Paul Dando, who dug into their files to recover historical surveys of the chthamalid fauna to assist our study.We certainly appreciate the decades of work these scientists and the late Alan Southward put into study of the Cirripedia, and these species in particular.Fabio Pitombo, Liza Gomez Daglio, and John Binford contributed significantly to early data collection efforts in this project.Carolyn Embach provided technical editing services.This work was partially supported by the National Science Foundation (OCE-1029526 to JPW) and the U.S.-israel Binational Science Foundation (grant # 2004/239 to JPW).
Fig. 2 .
Fig. 2. Bayesian multilocus gene tree for the data from C. southwardorum.The two clades are separated with a posterior probability of 1.0.The type sequence for mitochondrial COi is included and labeled Pitombo FP185; the other clade represents the "Farfan" form of this species.Width of line indicates posterior probability of branch.
Fig. 3 .
Fig. 3. Bayesian multilocus gene tree for the data from C. hedgecocki and C. panamensis.The two clades are separated with a posterior probability of 0.79.The type sequence for mitochondrial COi (from Pitombo & Burton 2007) is included and labeled for each species.Width of line indicates posterior probability of branch.'N' and 'S' in the C. panamensis clade indicate individuals sampled from North and South of the CAG, respectively.
Fig. 4 .Fig. 5 .
Fig. 4.Posterior distributions of divergence time estimates (horizontal axis) for Northern and Southern populations of C. southwardorum using iMa for the mtCOi, mt16S, and nEF1 gene regions combined.Analyses were run two times with identical inputs except random number seeds.Distributions peaked (probability distribution indicated by vertical axis) at 342 400 years ago in run 1 and 339 700 years ago in run 2, with the low 95% credibility intervals at 222 500 and 219 800 years ago respectively.(High 95% credibility intervals are not reported because distributions never reach zero and thus values are conditioned on the prior; only first 2mya are shown, distribution remains level through remainder).Migration estimates were ≤0.01 in both directions. | 6,813.8 | 2013-03-01T00:00:00.000 | [
"Biology",
"Environmental Science"
] |
Dead time optimization method for power converter
This paper introduces a method for dead time optimization in variable speed motor drive systems. The aim of this method is to reduce the conduction time of the freewheeling diode to a minimum without generation of cross conduction. This results in lower losses, improved EMC, and less overshooting of the phase voltage. The principle of the method is to detect beginning cross currents without adding additional components in the half bridge like resistors or inductances. Only the wave shape of the phase voltage needs to be monitored during switching. This is illustrated by an application of the method to a real power converter.
Introduction
Power converter systems are used today in many applications.In particular, in the context of battery supplied vehicles and similar areas the improvement of Electromagnetic Compatibility (EMC) and the reduction of power losses become increasingly important.One approach to improve power converter systems in this respect is to reduce the dead time during switching.To illustrate the concept of dead time, the following Fig. 1 shows a typical half bridge, which is used in power converter systems: In the operation of the half bridge the Highside-and Lowside-MOSFET are mutually switched.The dead time is here defined as the time delay between the falling edge of the control signal of one MOSFET and the rising edge of the control signal of the opposite MOSFET.
With the reduction of the dead time, the time in which the freewheeling diode conducts and the stored charge in this diode, which is responsible for the Reverse Recovery Effect (Polenov et al., 2009), can be reduced.This effect increases switching losses (Polenov et al., 2009;Reiter et al., 2010) and the snap off of the reverse current results in overvoltage and oscillation of the phase voltage (Semikron, 1998, p. 166).In this context an optimal dead time can prevent the diode from conducting without generating a cross current in the half bridge.
Several methods already have been introduced to reduce the dead time.Many are especially for DC/DC converter systems.For example Reiter et al. (2010) describes an approach which reduces the dead time in one phase and compares after every step the efficiency to a reference phase.An increasing efficiency in one phase will result in an increase of its current.A current balancing controller compensates the resulting deviation of the phase currents.This information can be used for the dead time optimization.As a result, this method uses the existing current balancing controller of a multiphase DC/DC-converter, which does not exist in power converters.
In Yousefzadeh and Maksimović (2005) a method that applies to DC/DC-converters is described which changes the dead time until the duty-cycle command is minimized, corresponding to maximized converter efficiency.This method uses the integrated voltage controller which doesn't exist in that form in a power converter.
Another approach measures the voltage drop across the freewheeling diode (Mappus, 2003).The dead time is reduced until this voltage drop no longer reaches the diodes forward voltage.But measuring this voltage drop is difficult during current commutation because of the influence of induced voltages in the parasitic inductances (Rose et al., 2009).
In addition to these approaches there are several methods which use Zero Voltage Switching (ZVS), compare (Trescaes et al., 2004;Acker et al., 1995;Lau and Sanders, 1997).Most of these methods involve measuring the voltage drop across the switching transistor and the gate-source voltage which is compared to the threshold voltage.However, these approaches can only be used in conjunction with ZVS.In contrast to this, the method described in this paper is focused on a hard switching converter.
Beside the approaches above, there are further methods which apply to hard switching three phase power converters.In Huselstein et al. (1993) an inductance is introduced in the half bridge.This allows detecting an occurring cross current from the change of voltage drop across this inductance: This change can be measured and then the dead time is reduced until a cross current occurs.Here, the main problem is the inclusion of the inductance into the half bridge which can result in a worsening of the switching behavior.An additional method described in Rose et al. (2009) measures the threshold voltage of the MOSFETs involved.The beginning and the end of the current commutation is detected by means of a small inductance introduced in the half bridge.Since the complexity of this method is relatively high, a new designed gate driver is used to reduce the dead time according to this information.This can be disadvantageous because often a simpler and more flexible method is desired which does not require a special Integrated Circuit (IC).Also an additional inductance is needed and it can be assumed that the measurement of the threshold voltage has to be very exact to prevent cross conduction.
In this paper a method is presented which does not require additional components in the half bridge.Only the wave shape of the phase voltage during switching has to be monitored.When a cross conduction occurs, this wave form changes, as it is also stated in (Yousefzadeh and Maksimović, 2005) in view of DC/DC converter systems.These changes have been verified by means of simulation of a half-bridge and measurement in an existing power converter.This power converter is designed for low voltage applications, such that Power-MOSFETs can be used.A measuring circuit has been designed to detect this variation without the need of special or extremely fast components.The measured phase voltage (Baliga, 2008).The supply voltage is denoted by U 0 .
is the basic for the proposed dead time optimization process which successively reduces the dead time until the changes in the wave shape of the phase voltage, that are due to the cross current, are detected.
The structure of the remainder of this paper is as follows: the origin of variation of the phase voltage, which is the basis for the proposed method, is discussed in the following Sect.2, where also the measuring circuit is introduced and important results of simulations and measurements are presented.In Sect. 3 an actual implementation of the dead time optimization process is described and followed by a conclusion in Sect. 4.
Reverse Recovery Effect
When the MOSFET takes over the load current from the freewheeling diode of the opposite MOSFET during switch-on, the Reverse Recovery Effect occurs when this diode blocks.The following illustration shows typical current and voltage waveforms during the blocking of the freewheeling diode.
First, the MOSFET starts to take over the load current from the diode during switch-on.Eventually, the MOSFET also has to carry a reverse current of the diode because the stored charge of the diode has to be degraded before it blocks.This results in higher losses in this MOSFET (Baliga, 2008, p. 245).Once the stored charge is degraded the freewheeling diode blocks and the reverse current quickly reduces to zero.This current change induces a voltage in the parasitic inductances of the half bridge (Semikron, 1998, p. 166).If the Reverse Recovery Effect occurs at the transition low-high this voltage results in an overshoot of the phase voltage.The corresponding additional contribution U L σ to the phase voltage can be characterized by the equation Here, the internal inductances of the MOSFETs and of the junction lines are combined in L σ .The fast current change can also induce oscillations which have a negative impact on EMC (Rose et al., 2009;Semikron, 1998, p. 166).
Influence of reduced dead time on the Reverse Recovery Effect
The charge Q R stored in the freewheeling diode can be reduced by decreasing the dead time because this leads to a decreased conducting time of the freewheeling diode (Polenov et al., 2009).The peak I RM of the reverse current depends on this charge (Wang et al., 2004).
where S is the softness factor of the diode.With a reduced peak, the slope of the reduction of the reverse current, i.e. the term di D dt R , can be decreased as well (Baliga, 2008, p. 251).According to (1) this results in a lower voltage overshoot.It is also mentioned that the losses in the MOSFET during switch-on are reduced due to the lower reverse current and faster switching (Polenov et al., 2009).
Influence of the cross current on the phase voltage
In the same way as the decrease of the reverse current induces an overshoot of the phase voltage, the cross current can initiate an overshoot of the phase voltage, too.Particularly, the reduction of the cross current is directed in a way such that the voltage induced in the parasitic inductances adds to the phase voltage.
To investigate this behavior, a half bridge was simulated with the main parasitic inductances and resistors included.An existing power converter served as basis for the simulations and also was used for subsequent measurements described below.Figure 3 shows the simulated wave shape of the phase voltage at a dead time where a cross current occurs.
In Fig. 3, the second maximum is due to a decrease of the cross current, as has been confirmed by both simulation and measurement.The width of the peak that is associated to this second maximum depends on the magnitude of the cross current: a larger magnitude implies a larger width and vice versa.This effect can be used to detect the cross current, as described next.
Setup of the measurement circuit for detecting cross currents
The effect described in the previous paragraph also appears at the transition from the Highside-to the Lowside-MOSFET.The sign of the induced voltage is such that it results in an additional decrease of the phase voltage.This leads to a second undershoot.As a consequence two measurement circuits are necessary: one for detecting the overshoots of the phase voltage and one for detecting the undershoots at the other transition.In Fig. 4 a possible design of these circuits is shown.
First the circuit for detecting the voltage overshoot is described.When the phase voltage becomes larger than the supply voltage plus the forward bias of the diode D1, this diode starts to conduct and the capacitor C1 is charged.To discharge the capacitor for detecting a smaller overshoot after a larger one has occurred, the resistor R1 is connected in parallel.R1 and C1 have to be dimensioned in a way such that the first voltage overshoot is charging the capacitor only to a small fraction and, as a consequence, the second voltage overshoot still can charge the capacitor as well.The voltage measured at the capacitor will be characterized by a charging and discharging process and thus approximately have a triangular shape.Then a possibility is to measure only the peak value of this voltage.An option to realize this is to use a capacitor with a diode put in series.This peak detecting capacitor then will be loaded until the maximum voltage will be reached.To discharge this capacitor, a MOSFET put in parallel can be used.This MOSFET can be controlled by the microprocessor that realizes the dead time optimization.
It must be noted that the reference potential of the voltage across the capacitor C1 is given by the phase voltage while the microprocessor who measures this voltage has in most cases a ground reference potential.However, for converting the voltage across the capacitor C1, special ICs can be used, which are e.g.designed for current measurement with a resistor.The peak detection circuit can be set at the output of this IC such that the microprocessor can directly control the discharging MOSFET and measure the voltage over the peak detecting capacitor.
The circuit for detecting undervoltage behaves in the same way.In this case the measurement capacitor is charged when the voltage is below the ground potential plus the forward bias voltage of the diode D2.Here the usage of a peak detection circuit in combination with a voltage transferring IC is also reasonable.
Influence of the dead time on the measured signal
To investigate the behavior of the measurement circuit of Fig. 4 it is integrated in the half bridge of an actual power converter, which can switch currents up to 400 A. With a successively reduced dead time, the ground referenced voltage across the capacitor for peak detection, as described in the previous section, is measured.
Starting from a large dead time of 750 ns, the absolute value of this voltage decreases because of the reduced Reverse Recovery Effect of the freewheeling diode which leads, according to Eq. ( 1), to a decreased overvoltage.It is then observed that at a dead time of approximately 350 ns the voltage starts to increase.At this dead time a beginning cross current was detected in several measurements and simulations.Also, beginning from this dead time, increasing losses were measured due to the developing cross current.
At dead times around 350 ns the amplitude of the first overvoltage is strongly reduced in comparison to the larger dead time of 750 ns.But as the simulation result of Fig. 3 shows, the second overshoot becomes larger with increasing cross current.This change of wave shape can also be measured at the half bridge with decreasing dead time.Due to this wider second overshoot the measurement capacitor is stronger charged, which results in the increasing voltage drop.This rise can be detected by a dead time optimization method which is described in the following section.
Process of the dead time optimization method
In general the dead time optimization process only has to be started once at the beginning of the drive.But in some cases it might be useful to repeat this process, e.g.due to an increased temperature of the converter.This has to be analyzed for a given power converter system.
The PWM-controlling microprocessor has to measure the voltage over the peak detecting capacitors.These signals can directly be transmitted to the AD-converter.It is necessary that the microprocessor can influence the dead time, which is often the case.The dead time is now gradually decreased and after every step the actual voltage over a peak detecting capacitor has to be measured.As an initial condition of this process it is necessary that the capacitor is discharged via the MOSFET which is also controlled by this microprocessor.The discharge has to last until the capacitor C1 or C2 has adapted the new value, which usually takes about 200 µs to 400 µs.After this period, the peak detecting capacitor has to attain the peak voltage.This time depends on the IC used for the voltage transfer.For the cases considered, this time turned out to be about 200 µs.
In the actual process, first the measured peak voltage will decrease as it can be seen in Fig. 5.When the dead time approaches the range where a cross current occurs an increase will be detectable.Figure 6 exemplifies this process.
This process has been integrated in the control of an actual half bridge.For exemplification a voltage was generated via a DA-converter which was chosen to be proportional to the dead time.In Fig. 7 a screenshot of the measured voltages illustrates this process.
First a reduction of the dead time leads to a decrease of the measured voltage.After every dead time reduction, which here is about 50 ns, the peak detection capacitor is discharged until the measurement capacitor C1 has reached the new value.After the fourth step it is seen that the measured voltage starts to increase.This is detected by the controller which then stops the dead time reduction.Since after the fourth step a small cross current exists, the controller increases the dead time about one step.As a result an optimal dead time is found to be about 380 ns.
Setting of the optimal dead time
Basically four switching transitions have to be distinguished, which are illustrated in Fig. 8.
When the load current is directed out of the half-bridge the Reverse Recovery Effect can be monitored at the transition low-high and in case that the load current runs in the halfbridge the Reverse Recovery Effect can be monitored at the transition high-low.For these two transitions a dead time optimization is useful, as described above, to reduce losses and to improve EMC.The dead time at the other transitions can be chosen relatively high such that no cross current occurs.
But it has to be mentioned that the described effect of second overshoot also appears at these transitions.Here it can also be useful to find the optimal, lowest dead time to increase the dynamic range of modulation.
To summarize, four different dead times have been determined.These are, depending on the direction of the load current, two dead times for each switching transition.Therefore the dead times have to be adjusted at each switching tran- Switching transitions in a half-bridge, indicated by curved arrows, as adapted from stein et al., 1993).
the load current is directed out of the half-bridge the Reverse Recovery Effect can be red at the transition low-high and in case that the load current runs in the half-bridge verse Recovery Effect can be monitored at the transition high-low.For these two ons a dead time optimization is useful, as described above, to reduce losses and to e EMC.The dead time at the other transitions can be chosen relatively high such that ss current occurs.But it has to be mentioned that the described effect of second oot also appears at these transitions.Here it can also be useful to find the optimal, dead time to increase the dynamic range of modulation.
marize, four different dead times have been determined.These are, depending on the n of the load current, two dead times for each switching transition.Therefore the dead ave to be adjusted at each switching transition in the zero-crossing of the load current.
y applications the controlling microprocessor measures or calculates the actual current n, such that this adjustment can easily be achieved.nclusion resented dead time optimization method provides a new alternative to existing ches.In contrast to the majority of these methods this approach does not need nal components in the main current tracks of the half bridge, which would produce nal losses.A suitable measurement circuit has been proposed to detect the changes in sition in the zero-crossing of the load current.In many applications the controlling microprocessor measures or calculates the actual current direction, such that this adjustment can easily be achieved.
Conclusions
The presented dead time optimization method provides a new alternative to existing approaches.In contrast to the majority of these methods this approach does not need additional components in the main current tracks of the half bridge, which would produce additional losses.A suitable measurement circuit has been proposed to detect the changes in the wave shape of the phase voltage when a cross current occurs.This measured value is the basic variable of the dead time optimization process.The proposed method also has been successfully tested in an actual half-bridge.With this dead time reduction both the overshoot of the phase voltage and the switching losses are reduced.Also a considerable improvement in the EMC of the power converter has been observed.
So far this method has only been tested with MOSFETs but it should also be applicable to transistors such as IGBTs.Also the application in other contexts, such as the optimization of DC/DC-converters, is conceivable.
Fig. 2 .
Fig.2.Typical waveforms of the diode current i D and the voltage drop over the diode u D of a blocking diode, as adapted from(Baliga, 2008).The supply voltage is denoted by U 0 .
Fig. 3 .
Fig. 3. Waveform of the phase voltage at a comparatively short dead time where a cross current occurs.
Fig. 4 .
Fig. 4. Measurement circuits for detecting the over-and undershoot of the phase voltage.
Fig. 6 .
Fig. 6.Principle of the dead time optimization process.The variable AD corresponds to the measured peak voltage.
Fig. 7 .
Fig. 7. Dead time optimization process.Curve 1: output of the DA-converter, proportional to dead time: an increase of the DA output voltage corresponds to a decrease of the dead time.Curve 2: measured voltage over the peak detection capacitor C3. | 4,580.8 | 2013-07-04T00:00:00.000 | [
"Engineering"
] |
Continuous Casting Continuous Casting
Continuous casting is a process whereby molten metal is solidified into a semi-finished billet, bloom, or slab for subsequent rolling in finishing mills; it is the most frequently used process to cast not only steel, but also aluminum and copper alloys [...]
Introduction and Scope
Continuous casting is a process whereby molten metal is solidified into a semi-finished billet, bloom, or slab for subsequent rolling in finishing mills; it is the most frequently used process to cast not only steel, but also aluminum and copper alloys. Since its widespread introduction for steel in the 1950s, it has evolved to achieve improved yield, quality, productivity, and cost efficiency. It allows lower-cost production of metal sections with better quality, due to the inherently lower costs of continuous, standardized production of a product, as well as providing increased control over the process through automation. Nevertheless, challenges remain and new ones appear, as methods are sought to minimize casting defects and to cast alloys that could originally only be cast via other means. This Special Issue covers a wide scope in the research field of continuous casting.
Contributions
Fourteen research articles have been published in this Special Issue of Metals. Twelve of these [1][2][3][4][5][6][7][8][9][10][11][12] relate to the continuous casting of steel, a general schematic for which is shown in Figure 1. As is evident from this figure, the overall process consists of a ladle and a tundish through which molten steel passes, a cooling mould region where solidification starts and at which electromagnetic stirring (EMS) may be applied, secondary cooling regions where water is sprayed on the solidified steel, a socalled strand electromagnetic stirrer, a further region at which final EMS is applied, and withdrawal rollers, by which point the steel has completely solidified. In addition, Figure 2 shows which stage of the continuous casting process each of the articles has focused on. Commencing from the start of the process and working downwards [2,5,7], it is important to consider flow in the tundish. Huang et al. [2] use particle image velocimetry (PIV) and numerical simulation to investigate the flow characteristics for a two-strand tundish in continuous slab casting. On the other hand, Ni et al. [5] present a numerical study on the influence of a swirling flow tundish on multiphase flow and heat transfer in the mould, whereas Qin et al. [7] conduct a simulation study on the flow behavior of liquid steel in a tundish with annular argon blowing in the upper nozzle. Su et al. [9] use machine-learning techniques for mold-level prediction by means of variational mode decomposition and support vector regression (VMD-SVR), whereas Cho and Thomas [1] review the literature on electromagnetic forces in continuous casting of steel slabs. Yin et al. [10] consider modelling on inclusion motion and entrapment during full solidification in a curved billet caster, while Long et al. [4] develop a combined hybrid 3-D/2-D model for flow and solidification prediction during slab continuous casting. Qin et al. [6] perform an analysis of the influence of segmented rollers on slab bulge deformation, while Lei and Su [3] use machine learning in the research and application of a rolling gap prediction model. Zhang et al. [11] devise a laboratory experimental setup and consider heat transfer characteristics during secondary cooling, whereas Ren et al. [8] carry out numerical simulations of the electromagnetic field in round bloom continuous casting with final electromagnetic stirring. Zhou et al. [12] consider control of upstream austenite grain coarsening during the thin-slab cast direct-rolling (TSCDR) process, after complete solidification has occurred.
Aside from all of the above, Yang et al. [13] simulate crack initiation and propagation in the crystals of a continuously-cast beam blank, whereas Vynnycky [14] gives a review of applied mathematical modelling of continuous casting; this considers a hybrid of analytical and numerical modelling with an emphasis on the use of asymptotic techniques, and gives examples of problems not only in the continuous casting of steel, but also that of copper and aluminum alloys.
Conclusions and Outlook
A variety of topics have composed this Special Issue, presenting recent developments in continuous casting. Nevertheless, there are still many challenges to overcome in this research field and applications still need to be more widespread. As a Guest Editor, I hope that all of the scientific results in this Special Issue contribute to the advancement and future developments of research on continuous casting.
Finally, I would like to thank all reviewers for their invaluable efforts to improve the academic quality of published research in this Special Issue. I would also like to give special thanks to all staff at the Metals Editorial Office, especially to Toliver Guo, Assistant Editor, who managed and facilitated the publication process. Commencing from the start of the process and working downwards [2,5,7], it is important to consider flow in the tundish. Huang et al. [2] use particle image velocimetry (PIV) and numerical simulation to investigate the flow characteristics for a two-strand tundish in continuous slab casting. On the other hand, Ni et al. [5] present a numerical study on the influence of a swirling flow tundish on multiphase flow and heat transfer in the mould, whereas Qin et al. [7] conduct a simulation study on the flow behavior of liquid steel in a tundish with annular argon blowing in the upper nozzle. Su et al. [9] use machine-learning techniques for mold-level prediction by means of variational mode decomposition and support vector regression (VMD-SVR), whereas Cho and Thomas [1] review the literature on electromagnetic forces in continuous casting of steel slabs. Yin et al. [10] consider modelling on inclusion motion and entrapment during full solidification in a curved billet caster, while Long et al. [4] develop a combined hybrid 3-D/2-D model for flow and solidification prediction during slab continuous casting. Qin et al. [6] perform an analysis of the influence of segmented rollers on slab bulge deformation, while Lei and Su [3] use machine learning in the research and application of a rolling gap prediction model. Zhang et al. [11] devise a laboratory experimental setup and consider heat transfer characteristics during secondary cooling, whereas Ren et al. [8] carry out numerical simulations of the electromagnetic field in round bloom continuous casting with final electromagnetic stirring. Zhou et al. [12] consider control of upstream austenite grain coarsening during the thin-slab cast direct-rolling (TSCDR) process, after complete solidification has occurred.
Aside from all of the above, Yang et al. [13] simulate crack initiation and propagation in the crystals of a continuously-cast beam blank, whereas Vynnycky [14] gives a review of applied mathematical modelling of continuous casting; this considers a hybrid of analytical and numerical modelling with an emphasis on the use of asymptotic techniques, and gives examples of problems not only in the continuous casting of steel, but also that of copper and aluminum alloys.
Conclusions and Outlook
A variety of topics have composed this Special Issue, presenting recent developments in continuous casting. Nevertheless, there are still many challenges to overcome in this research field and applications still need to be more widespread. As a Guest Editor, I hope that all of the scientific results in this Special Issue contribute to the advancement and future developments of research on continuous casting.
Finally, I would like to thank all reviewers for their invaluable efforts to improve the academic quality of published research in this Special Issue. I would also like to give special thanks to all staff at the Metals Editorial Office, especially to Toliver Guo, Assistant Editor, who managed and facilitated the publication process. | 1,754.2 | 2019-06-03T00:00:00.000 | [
"Materials Science"
] |
Journal of Biomedical Informatics: X
A
Introduction
The biomedical sciences are pioneers for open-access publication, with the PubMed database alone indexing over 27 million journal articles. Given the rich knowledge contained in these articles, obtaining insights from the publications can be used to address a variety of biomedical problems. The sheer volume of unannotated text dwarfs that of the annotated documents and hence it is imperative to utilize unsupervised machine learning models to capture the semantic meaning of words and phrases from such large corpus which in turn can be used for various downstream biomedical tasks.
For many Natural Language Processing (NLP) tasks based on vector space models, the text is transformed into meaningful vector representations to help improve performance. Recent efforts have introduced new neural network models that can induce semantically meaningful word representations (or embeddings) from large corpora [1,27,36,3]. Dense, low-dimensional vector representation of words are learned such that similar words are close in space. The ability to preserve semantic and syntactic similarities between words been shown to be very useful in a variety of NLP tasks including information retrieval [12], part-of-speech (POS) tagging [9], text summarization [39,46], sentiment analysis [13,24], named entity recognition (NER) [23,42], synonym extraction [18] and relation extraction [19]. Moreover, several biomedical domain word representations have been created from biomedical literature [21,38] and the impact of training word vectors on corpus from various domains for downstream biomedical tasks is explored by [43,33].
Although word embeddings have achieved great success in wordoriented tasks such as NER and POS tagging, they perform poorly on phrases-oriented tasks such as Semantic Role Labeling [8]. The common approach to train state-of-the-art embeddings such as Word2Vec [25], GloVe [36], and FastText [3] is to learn the vector representation for each individual word. Phrase representations are then constructed using compositional approaches of the unigram vectors [45,47,22]. However, the compositional approaches (e.g., sums and products of the word vectors) are often order-insensitive and fail to capture the semantic meaning of the phrase [28]. Unfortunately, in the biomedical domain, many key concepts are often expressed as multi-word phrases [20] and thus are critical for capturing lexical semantics. Furthermore, biomedical phrases may only be weakly compositional, or unlikely to be expressed only based on the meaning of its part. As motivating examples, the phrases 'Glasgow Coma scale', 'open reading frame', and 'nuclear magnetic resonance', may not be well-expressed as a composition of the individual words. Therefore, it is important to build a distributed representation that not only captures single words but multi-word phrases as well.
Learning a distributed phrase and word embeddings have been shown to be effective on a general, non-domain specific corpus [26]. Yet, one of the key challenges is to identify useful phrases. While this task is well-studied, many of the existing works require annotation or extensive computation to achieve good performance [4,10,35,37,44]. A new unsupervised method has been proposed to collect over 700,000 common phrases that may be useful for biomedical NLP from PubMed articles [20]. Unfortunately, including all possible phrases into the https://doi.org/10.1016/j.yjbinx.2019.100047 embedding model significantly impacts the computational complexity and negatively impacts the learned representations.
We propose PMCVec, an unsupervised method that generates useful phrases from the corpus and builds a distributed representation that contains both single words and multi-word phrases by treating both as a single term (or unit). In this paper, we consider a phrase to be a continuous sequence of two or more words with no stopwords or punctuation marks except for a hyphen. We used a standard NLTK 1 stopword list. For example, our method obtains similar representations for the pairs 'hypertension' and 'high blood pressure' as well as 'myocardial infarction' and 'heart attack'. We introduce a new criterion to rank the generated phrases that balance phrase frequency, phrase length, and the frequency of the individual words within the phrase. This step allows us to select only the k-most useful phrases, where k is a hyperparameter that can be learned as well.
We compared our method against several existing embeddings: two general word embedding models and two biomedical domain word representations. Using five benchmark datasets for biomedical semantic similarity, we show that PMCVec achieves significant improvement over other models. We show that our distributed representation not only captures the semantic meaning of the phrases better than compositional methods, but it also does not significantly degrade the singleword representations.
This paper is organized as follows. First, we describe the various steps in the PMCVec process including preparing the text data; generating, ranking and filtering phrases; and learning the term embeddings. We then describe experimental results on several biomedical term-similarity evaluation datasets. We conclude with a discussion of how our method compares to other similar techniques and what can be done to improve further.
Methods
In this section, we present our framework for computing the distributed phrase representations. PMCVec consists of multiple steps: (1) preprocessing the articles, (2) generating phrases from the articles based on chunking, (3) ranking and filtering the phrases, and (4) tagging the phrases and building the distributed phrase representation. Fig. 1 depicts the entire workflow.
Preprocessing
We used titles and abstracts from all the 27 million documents in PubMed. The National Library of Medicine produces the citation records (in XML format) for PubMed [29]. The XML files are parsed to collect titles and abstracts. These are merged into a single large document. We then cleaned the document by removing terms that consisted only of numbers or special characters. For example, in the sentence "in 29 (69%) patients, the cancer cells showed a strong immunoreactivity for PCNA" the number 29 and (69%) would be removed.
Phrase generation
The next step in the process is to identify phrases from the corpus. Traditional techniques focus on identifying noun phrases since most meaningful phrases are of this form. These methods use predefined parts of speech (POS) rules or learn those rules from annotated documents to chunk the text [4,44,37]. However, such rule-based methods usually suffer in domain adaptation and will miss out on meaningful non-noun phrases including 'multilocus sequence typing', 'calcitonin gene related peptide', 'electrophoretic mobility shift assay', 'zollinger ellison syndrome', and 'diffusion tensor imaging'. Other generic phrase generation techniques leverage frequency statistics in document collections by extracting all possible n-grams from the text and retaining the most popular concepts [35,10]. However, this result enumerates all the possible n-grams and does not scale well for a large corpus. Instead, we use a conceptually simpler and more generic approach. Potential phrase boundaries are identified using stop words and punctuation [41]. Although this eliminates the possibility of stop words occurring in a phrase, it provides a more systematic methodology for generating variable n-gram phrases without having to specify ahead of time the maximum number of terms and enumerating all the possibilities. Thus, with the last example sentence in Fig. 1, the potential phrases from our chunking process are 'patients', 'cancer cells showed', and 'strong immunoreactivity', and 'PCNA'. Since our interest is to generate meaningful phrases, we remove any single word occurrences.
Rank and filter
The third step in our workflow is to rank and filter the potential phrases. This is a necessary step as there is no guarantee that all the phrases generated in the previous step are meaningful. Moreover, incorporating all the phrases impacts the learning process in terms of computational and memory complexity, and may degrade the distributed word representations. Thus, it is important to rank the phrases using a metric and filtering out those that do not meet certain criteria. Prior to ranking, we perform an initial filtering step that removes any phrases that do not appear sufficiently in the corpus. While we set the minimum corpus frequency to be 100, this number can be increased to further improve the speed of the ranking process. Thus, in our example in Fig. 1, 'paraffin-embedded bladder cancer section' did not occur frequently enough and was filtered out in this initial stage.
After the initial filtering step, we rank the multi-word phrases to identify meaningful phrases based on their likelihood to occur in PubMed literature as coherent units. Although there are several common phrase ranking criteria [6,17], we found they offered a poor trade-off between phrase frequency, constituent word frequency, and phrase length. Thus, we propose our own ranking criteria "Information Frequency (Info_Freq)" that provides a good balance. As an example, we filter out the phrase "cancer cells showed" in the filtering step of Fig. 1 since it has a low rank according to our criteria. Below, we describe Info_Freq and four of the commonly used phrase ranking metrics as well as discuss the benefits and limitations of each of them.
1. Raw Frequency: A measure of the number of times the phrase appears in the entire corpus. With the removal of stop words, most of the phrases that occur very frequently are likely to be good phrases. However, the simple nature of this metric punishes meaningful phrases that do not appear often and predominately favors 2word phrases. Phrases like 'results suggest' and 'present study' which occur in most documents are ranked high but other important phrases like 'epithelial tissue' and 'acute respiratory failure' do not occur as frequently and subsequently have a low rank. 2. Point-wise Mutual Information (PMI) [7]: A measure of how much information is gained about a particular word if you also know the value of a neighboring word. It is defined as: where p x ( ) is the probability of the word x occurring in a document, and p x y ( , ) is the probability of the co-occurrence of both words x y , occurring in the same document. For a three-word phrase, we adapt the above formula as: PMI is often used to find good collocation pairs as high PMI occurs when the probability of the co-occurrence is either higher or slightly 1 https://www.nltk.org/.
lower than the probabilities of the occurrence of each word. Conversely, phrases that contain frequently occurring words will have small PMI scores even if the phrase is good. As an example, 'blood cells' should be an important and meaningful phrase. Unfortunately, the constituent words 'blood' and 'cells' occur frequently in the corpus. As a result, the phrase is ranked very low. 3. Jaccard's Coefficient (JC) [40]: A measure of the similarity and diversity of the entire phrase set. It is defined as the frequency of a phrase divided by the total number of phrases that contain at least one term in the phrase: where * x freq( , ) denotes the frequency of any phrase that contains the term x but not y. For a three-word phrase, we adapt JC as: ( , , ) freq( , , ) freq( , , ) freq( , ) freq( , ) freq( , ) , Although Jaccard index accounts for the diversity of the phrase, longer phrases are punished as there is a higher likelihood of at least one word appearing in a phrase. Thus, longer phrases like 'reverse transcription polymerase chain reaction' and 'cervical squamous cell carcinoma' will be ranked low even though they are meaningful phrases. 4. Word2Phrase: This is a method proposed by [26]. It is a datadriven approach where phrases are formed based on unigram and bigram counts.
σ is used as a discounting coefficient to prevent too many phrases with infrequent words to be formed. This technique is applied in multiple passes to find longer phrases. For example, the phrase "blood cells" occurs 7000 times while "tagging snps" occurs only 350 times but the latter will have a higher score since the constituent words "tagging" and "snps" are infrequent compared to the more frequently occurring words "blood" and "cells" in the first phrase. The discounting coefficient takes off a constant number so that phrases with much less frequency but higher scores due to infrequent constituent words will be penalized more. We provide an empirical example in the supplementary file. 5. Info_Freq: Our proposed measure of the association between words in the phrase that accounts for the phrase frequency, the constituent words frequency, and the length of the phrase. For a two word phrase "x,y", we calculate the info_freq as: For a three-word phrase, we adapt the above formula as: = * x y z p x y z Info Freq x y p z x y z Info_Freq( , , ) log ( , , ) _ ( , ) ( ) log(freq( , , )).
In the above equation, we assume the two-word-phrase (x,y) occurs more frequently than (y,z). Scores are calculated in increasing size of phrase length. All two-word-phrase scores will be calculated before any three-word phrases and so on. For instance, to calculate the info_freq of the phrase "high blood pressure", we first calculate the score for the shorter phrase "blood pressure" and use this to get the score for the longer phrase. This is applied for phrases with more than three words as well. For the four-word phrase "chronic obstructive pulmonary disease", we calculate the score for "pulmonary disease", then for "obstructive pulmonary disease" and finally for "chronic obstructive pulmonary disease". In the attached supplementary file, we provide detailed examples of how the scores are calculated for longer phrases. Table 1 shows the top 10 phrases from all 27 million PubMed abstracts based on each of the five above criteria. Both the frequency and JC metrics only contain 2-word phrases. Moreover, the top-ranked phrases by frequency are not medically meaningful. PMI and Word2-Phrase are also biased towards short phrases mostly consisting 2 words. On the other hand, the top 10 phrases using Info_Freq contain a good mix of long and short phrases that are biomedical-relevant terms. We get 2-word, 3-word, 4-word and 5-word phrases using Info_Freq. Since our goal is to minimize the number of phrases to embed while keeping the most important ones, Info_Freq allows us to extract quality phrases The text data is preprocessed and chunked to obtain candidate phrases. The phrases are ranked using our proposed Information Frequency criteria, and then filtered. The resulting phrases are tagged to form a single unit and the tagged text is passed into a standard word embedding model. Each term is then represented using a dense vector that maintains semantic similarity and relatedness.
with different number of words.
Tag and build embeddings
The final step in our workflow is to tag the selected phrases as a single term and then build the distributed word embeddings. The tagging process reformats the original phrase by joining the constituent words using the '_' symbol. This is to ensure the phrase is considered a single term (or unit) in the embedding process. For example, 'proliferating cell nuclear antigen' is tagged as 'pro-liferating_cell_nuclear_antigen' in the original corpus.
Once the tagging process is complete, we train a word embedding model on the entire tagged corpus. Under the word embedding model, terms are represented as dense vectors that capture the meaning of the words and retain the semantic and syntactic relationship between words. We use Word2Vec, the most widely used embedding method [27], which trains a shallow neural network to learn the word vectors. Word2Vec consists of two different architectures, the continuous bag of words (CBOW) and Skipgram. In CBOW, each word is trained using its surrounding context wordsgiven this set of context words, what is the word that is most likely to appear? For example, in Fig. 2a, using the context of six words, what is the word that is most likely to appear between them? On the other hand, Skipgram (Fig. 2b) trains the context based on the target wordgiven the word, what are the other words that are likely to appear? We assessed the impact of the two different architectures (Fig. 2) on the quality of the resulting embeddings. We used an existing work to guide the hyperparameter searches for CBOW and Skipgram to achieve optimal performances on both architectures [5]. While our framework can leverage other word embedding models such as Glove [36] and FastText [3], we achieved the best performance with the Word2Vec model. We assessed our model on five different evaluation datasets and performed several experiments to study the impact of the number of phrases, embedding architecture, and phrase generation. We also evaluated PMCVec with several other publicly available word embeddings.
Evaluation datasets
We evaluated the performance of the final models on five popular medical term similarity and relatedness datasets. • miniMayo: This is a subset of the 'Mayo' dataset and consists of 30 term pairs on which a higher inter-annotator agreement was achieved. Out of a total of 60 term pairs, 31 are unigrams, 22 are 2grams and 7 are 3-gram or more.
• AH [16]: This is a set of 36 medical concepts extracted from the MeSH repository by Hliaoutakis. The similarity between word pairs was assessed by 8 medical experts. This dataset contains 41 unigram terms, 20 2-gram terms, and 11 terms which are 3-gram or more.
• UMNSRS [32]: This is a dataset of 566 UMLS concept pairs that have been ranked by eight medical residents for similarity on a continuous scale. All the 1132 terms are unigrams.
• UMNSRS_R [32]: This is a dataset of 587 UMLS concept pairs that have been ranked by eight medical residents for relatedness. All of the 1174 terms are unigrams.
Two of the datasets (UMNSRS and UMNSRS_R) consist of only singleword term pairs only. The other three (Mayo, miniMayo, and AH) contains both single and multi-word term pairs.
Evaluation metric
The comparison on the semantic similarity and relatedness datasets is based on the Spearman rank order correlation coefficient (ρ). The coefficient is computed by comparing the ranking from the model (r i ) to the expert judged ranking (r i ): Since the benchmark models only support single words, we use a compositional approach of vector averaging wherever there are multiword similarity comparisons. For instance, when comparing the semantic similarity of the two phrases "Kidney Failure" and "Renal Failure", our model represents both terms as single entities and learns a vector representation for each phrase. The baseline models, however, learn embeddings for each word in the phrase and average those vectors to represent the phrase.
Impact of phrase generation
Our first experiment assesses the impact of our phrase generation step. A qualitative comparison can be seen in Table 1, which contains the top phrases generated by different phrase generation criteria. In this section, we quantify the performance of the metrics on the evaluation datasets. Table 2 shows the comparative scores based on similarity and relatedness for each metric, with the word2vec hyperparameters selected that achieved the highest score with 18,000 phrases used as this gave the best performance across the board. The full table with exhaustive parameters is attached in the supplementary file for further comparison. We see that Info_freq gets the best scores in the three mixed datasets (both single and multi-word phrases) and performs similarly in the single word datasets too. Moreover, Info_Freq is robust across a wide range of hyperparameter settings for the embedding models.
We also compared the quality of our phrases to PubMed Phrases, a collection of common phrases that were generated for biomedical NLP [20]. Each phrase comes with a precalculated score based on the p value of the hypergeometric test the authors performed on segments of consecutive terms that are likely to appear together in PubMed. To compare the phrase generation method, we tagged the PubMed Phrases in the PubMed abstracts and re-trained a new CBOW model. Longest phrases are tagged first to avoid conflict with substring phrases. Any substring phrases of longer phrases will be tagged only if they appear as stand-alone not as sub-phrase of longer phrase. Fig. 3 shows the average similarity scores using all five test datasets using the PubMed phrases [20] and PMCVec. We include two models for PubMed Phrases, the first is using the top n phrases as scored by the authors and the second (exist in chunk) is also using the authors scores but only tagging phrases if the phrase exists in our preprocessed chunks. The PMCVec-based models consistently outperform the PubMed phrases at all the ranges of phrases. This showcases the effectiveness of our phrase generation technique.
Impact of number of phrases and embedding techniques
Our second experiment assesses the quality of the PMCVec-embeddings based on the number of tagged phrases and the two Word2Vec architectures. Fig. 4a depicts how the number of phrases affects the quality of the learned model with respect to the five test datasets (CBOW model is used). For the two datasets (UMNSRS and UMNSRS_R) with only single word pairs, the quality of the embedding monotonically decreases as we include more phrases. As more phrases are tagged, fewer unigrams are available to learn the word embeddings. For the combined test sets (miniMayo, mayo and AH), the quality of the embeddings increases and then decreases or stalls thereafter. Thus, for optimal performance we need to cap the number of phrases so that our model learns quality vectors both for single and multi-word terms.
We also assessed the quality of the word vectors using the two different Word2Vec architectures. Fig. 4b shows the average similarity scores on all five datasets for both the CBOW and Skipgram architecture. CBOW is better when there are fewer phrases. As the number of phrases increases, the Skipgram model slightly outperforms CBOW. Based on the figure, the best performance is achieved by CBOW using 18 K tagged phrases. The hyperparameters associated with this model are a negative sample size of 10, sub-sampling of 1e−5, a minimum count of 1, vector dimension of 200, context window size of 10, and a learning rate of 0.025.
Baseline methods comparison
We benchmarked PMCVec with four other word-embedding models, all pre-trained on different corpora. For our model, we used hyperparameters associated with the best performance as described above.
• Google news [15]: A Word2Vec model that is trained on a general non-biomedical corpus. This is widely used as state-of-the-art embedding model as it is trained on part of Google News dataset (about 100 billion words). The model contains 300-dimensional vectors for 3 million terms.
• Glove [14]: A GloVE model that is trained on a general non-biomedical corpus. Training is performed on aggregated global wordword co-occurrence statistics from a corpus of Wikipedia and Gigaword 5 (6 Billion tokens). It is a 300-dimensional vector representation for 400k words. The best scores for each evaluation dataset are shown in bold. The performance of PMCVec and the baseline models on the five datasets is shown in Fig. 5. The two models trained on general corpora (Google news and Glove) have the lowest scores on all the datasets. On the contrary, the other two baseline models trained on biomedical corpora perform significantly better. This is consistent with prior results outlining the importance of the training corpus [31]. PMCVec outperforms the baseline models on all the datasets. The improvement is noticeable in the Mayo dataset, where the task is harder due to the lower inter-annotator agreement. We also note that our model performs better on both of the single-word pair datasets (UMNRS and UMNRS_R), which shows that incorporating phrases into the embedding process does not significantly compromise the quality of the single word vectors.
To quantify the performance of PMCVec on the single words and multi-words separately, we extract unigrams from the "AH" and "Mayo" datasets. Since "MiniMayo" is a subset of the "Mayo" dataset, all terms are already included in the extracted set. The remaining two datasets (UMNSRS and UMNSRS_R) are all single words and the performance of the models on these datasets are shown in Fig. 5. We depict how all the aforementioned models compare when using only unigrams and multi-word phrases in Fig. 6. We observe that the performance gain from PMCVec is noticeable for both single words and multi-words compared to the baseline methods.
The inclusion of multi-word phrases not only improves the semantic similarity performance but is also qualitatively better. Fig. 7 shows the cluster of terms that are semantically similar to the word 'hypertension'. In the two scenarios where no phrases are tagged (Fig. 7a) and the PubMed phrases are tagged (Fig. 7b), the closest terms to hypertension are the same which are 'hypertensive' and 'hypertensions' and the third closest are 'hypertensives' and 'prehypertensive' respectively. Moreover, only two multi-word phrases ('arterial hypertension associated' and 'uncomplicated essential renovascular') appear when using the PubMed phrases. Using PMCVec, 'high blood pressure', 'elevated blood pressure', and 'essential hypertension' are the closest and all three are semantically similar to hypertension.
Additional examples of similar terms are shown in Table 3 for different disorders, symptoms, and medications. In all 6 cases, PMCVec is able to return relevant multi-word synonyms in the top 5 closest words. 'diabetes mellitus' is a semantically similar to 'diabetes' whereas the other two methods contain the top word 'mellitus'. Similarly for symptoms, 'joint pains' is returned for aches whereas the other two embeddings do not have this term. The same holds true for drugs; for 'aspirin', single words returns 'clopidogrel' and PubMed phrases gets 'dipyridamoleasprin' as the most sematically similar term. These are drugs commonly administered with aspirin. With PMCVec, the top term is 'acetylsalicylic acid' which is another name for aspirin. In general, the PMCVec-based embeddings produce more accurate vector representations for phrases. Biomedical text is rich with multi-word concepts and terminologies, and as such representing these terms appropriately as single units to learn their vector representations is an important step in biomedical text processing.
Limitations
Our model focused on obtaining a good distributed term representation by combining multi-word phrases and single-words. Unfortunately, training GloVe and FastText models took considerably more time to train in large dimensions. Due to computational time and Fig. 7. Word cloud for semantically similar terms to 'hypertension'. The size of the term is proportional to how semantically close it is to the word 'hypertension' with the largest denoting the most similar. memory limitations, we were not able to train these models with large dimensions and window sizes. The GloVe and FastText models we trained performed much worse than the other two Word2Vec models in smaller dimensions (100-dimension and 200-dimension results are in the supplementary table) which is consistent with the work of Fan et al. [11] on clinical notes. The method we used for phrase generation did not consider terms and phrases containing only digits or stop words. Even though it is common to remove stop words in the form of subsampling for word embedding generation since they occur much more frequently and inflate the vocabulary size and training time [26], it may not be desired for biomedical phrase generation. We believe that this may result in the exclusion of meaningful phrases. However, incorporating these aspects into the phrase generation process would significantly lengthen the computation time. We plan to experiment in the future to determine the viability of including phrases with digits and stop words.
Conclusion
Learning quality vector embeddings that incorporate both single word and multi-word phrases can be quite challenging. Although compositional approaches to combine unigram vectors to obtain a phrase representation has worked well in some domains, this does not capture the meaning of key biomedical concepts. Moreover, incorporating all the existing identified biomedical phrase can negatively impact the quality of the embeddings. To address these issues, we introduced PMCVec, an unsupervised method that bridges the gap in learning quality vector embeddings for multi-word phrases which are a staple in biomedical literature. Our method not only generates useful phrases from the corpus, but it also introduces a new criterion to rank the generated phrases to avoid incorporating all the phrases and achieve a better embedding for both single words and multi-word phrases. We showed that the learned phrase embeddings result in better performance than compositional approaches using several benchmark datasets. As an example, a search result for the term 'colitis' should include multi-word expressions like 'inflammatory bowel disease'. The learning of vectors for both these terms allows easy association of the concepts, which are very similar terms but will not be learned as such with just single-word embeddings. We believe that PMCVec-learned representations will be widely useful for a variety of biomedical NLP tasks.
Data availability
The PubMed dataset used in this study is publicly available for download at https://www.nlm.nih.gov/databases/download/pubmed_ medline.html. The resources we used and the final model are available for download at https://github.com/ZelalemGero/PMCvec. | 6,598.2 | 2019-07-20T00:00:00.000 | [
"Computer Science",
"Medicine"
] |
The Role of Context Definition in Choice Experiments: a Methodological Proposal Based on Customized Scenarios
. One of the most critical points for the validity of Discrete Choice Experiments lies in their capability to render the experiment as close to actual market conditions as possible. In particular, when dealing with products characterized by a large number of attributes, the construction of the experiment poses the issue of how to express the choice question providing sufficient information. Our study verifies the role of scenario definition in choice experiments and proposes a methodology to build customized scenarios by eliciting responses from interviewees on the main choice criteria, which makes it possible to render the conditions of the experiment more realistic. This methodology is applied to the case study of wine and is introduced by a systematic review of the Discrete Choice Experiments conducted on wine. The findings show that customized scenarios result in different preference estimates compared to the conventional approach. In particular, we found a significant decline in the importance of the price attribute, which could be attributed to a better definition of the product being evaluated. Moreover, the methodology is capable of gathering information on the decision-making process that would otherwise remain unobserved and that can be used for a better segmentation analysis.
The DCEs are conducted by means of interviews that seek to reproduce a choice situation as close as possible to that of a real purchasing decision (Ben-Akiva et al., 2019). The interviewee is presented with several product alternatives that differ by the different levels of the attributes considered. The choice of these attributes and levels is a crucial point in carrying out the DCE. This issue becomes particularly important when dealing with complex products (such as wine, beer, motor vehicles, and property), the valuation of which is subject to a large number of stimuli. In fact, while considering many elements of value to describe the products can, on one hand, render the experiment more realistic, on the other hand, a large number of attributes and levels makes the experimental design difficult to manage (Hoyos, 2010), increases the variance of the error term, and entails a cognitive effort for the respondent that can become an error of evaluation (Arentze et al., 2003;Caussade et al., 2005). Moreover, it is also fundamental to not omit the attributes that are important for the majority of consumers, so as to avoid overestimating the importance of the attributes included in the choice task (Boncinelli et al., 2017;Casini et al., 2009;Corduas et al., 2013), and to avoid respondents making inferences about omitted attributes without the researcher being able to have information about them (Lancsar and Louviere, 2008). In this regard, Ben-Akiva et al. (2019) point out that the presentation of incomplete product profiles in the DCEs is a widespread issue among scholars. The same authors claim that the resulting fill-in problem puts the interviewees in the condition of making unrealistic and heterogeneous assumptions about missing attributes.
Many studies have tackled this issue defining in greater detail the context of reference where the actual choice is made. In this manner, the attributes considered important, but that are not included in the experiment, are described in context by the researcher, and therefore represent a scenario shared by all choices and all respondents. This solution presents some difficulties, however. In fact, when dealing with complex products, an excessively detailed description of the scenario can lead to high rates of no-choice, as excessively specific products are proposed that may not prove interesting to many consumers. Furthermore, scenarios with too many details would lead to creating an experiment that would be valid only for specific cases, and therefore, incapable of assuming a general value.
In order to make the experiment as realistic as possible, Ben-Akiva et al. (2019) recommend building it so as to maintain the same complexity of the real market in defining the products, possibly also incorporating the filtering heuristics in the choice of the product.
Indeed, as pointed out by Swait and Adamowicz (2001), in a real market where goods comprise many attributes, consumers often adopt filtering heuristics that consists of screening out products that fail to pass thresholds on selected attributes.
In view of making a contribution to these issues, our study proposes a methodology to build the choice experiment in which defining the scenario is based on what each interviewee states about the attributes and levels considered for the choice of the product being analyzed, according to a procedure analogous to that of filtering heuristics. It is thereby possible to obtain a choice scenario tailored to respondents' behavior. In literature, the studies that have attempted to adapt the experiment to the respondents have modified the attributes of the choice sets, applying the Adaptive Choice Experiments or Menu Choice methodologies Liechty et al., 2001;Toubia et al., 2004;Yu et al., 2011). In the ambit of environmental economics, the personalization of the experiment concerned the statusquo option (see, as example, Ahtiainen et al., 2015). To our knowledge, however, there are no studies that have worked on personalizing the choice scenario, which makes our proposal the first contribution in this sense.
The article illustrates this proposal of methodology applied to the case study of wine. The choice of wine derives from the consideration that it is a complex product whose preferences depend on an abundance of extrinsic and intrinsic attributes (Charters and Pettigrew, 2007;Contini et al., 2015;Oczkowski and Doucouliagos 2015;Schmit et al., 2013). The literature review presented in the following section illustrates the way these attributes were used in building the choice experiments on wine.
In our DCE, besides the attributes used in the choice sets, the scenario was described leaving the interviewees free to choose the attributes they felt were most important from among the principal attributes of literature. Using a mixed logit model, the results of this approach are compared with those obtained by applying the conventional methodology in which the researcher chooses a priori the elements to define the scenario. Moreover, the information collected on the choice criteria of the interviewees can be utilized for further analyses on consumer behavior. In our case, for example, this information was used to obtain a more meaningful segmentation by a latent class analysis. In the discussions section, a critical analysis is performed on the methodology and several suggestions are made for a further development of studies. We conducted a systematic review of the articles published on the study of wine preferences from 1998 to 2019 by applying DCEs. Relevant articles were identified and gathered from two scientific article databases (Scopus, Web of Science) and a web search engine (Google Scholar) by means of using the following keywords: "choice experiment" AND "wine", "choice modeling" AND "wine", "discrete choice" AND "wine". We selected only articles published in journals indexed in WOS and Scopus, excluding conference proceedings.
We found a total of 35 studies. The various attributes that appeared in the selected articles were reclassified in the following 15 categories: "alcohol content"; "awards" includes awards and mentions in guidebooks; "brand" includes the indication of the producer, bottler, and brand notoriety; "format" includes characteristics like bottle capacity and shape; "functional properties" concerns the presence of information on health benefits; "price"; "production methods" conveys information on the production process, including various certifications of an environmental nature, such as organic; "promotion" states whether a discount is offered; "protected geographical indication" includes the geographic indications of different countries and regions like, for example, the DOCGs in Italy or the AOCs in France; "region of production"; "sulfites" i.e. the absence of added sulfites; "taste", such as, for example, fruity, sweet, tannic, and full-flavored; "typology" includes the typologies red/ white, still/sparkling, the grape variety, and the name that identifies the wines, such as, for example, Chianti or Champagne; "winery distinctiveness" includes information about the producer, such as company history, label graphics, and company web site; "consumption advice" includes advice to enhance the consumption experience by means of pairings with particular dishes, and indications on the best modalities for enjoying the wine, such as, for example, the serving temperature.
In addition to these elements, we also examined the "occasion", which is to say the special or usual situation of consumption, at home or with friends, insomuch as the preference for the attributes evaluated in the DCEs also depends on the situational variables connected with the social and physical environment in which the wine is consumed .
The experiments reviewed utilized the aforesaid categories either to describe the choice context, which is to say the scenario defined by the researcher and shared by all of the choice sets, or as attributes that characterize the alternatives in the choice set. The different use in the choice experiment is synthetically illustrated in Table 1, where "C" means that the element is used in describing the context, and "A" indicates that the attribute describes the choice option.
In addition to price, the review shows that the category most utilized in the literature is wine "typology", which is found in experiments both as a choice attribute (17 articles) and as a context (13 articles). To be more exact, the information on color and style (still or sparkling) is used in defining the context, while the information on grape variety or wine name are among the choice set attributes.
Next in line for frequency of use is the "region of production" (21 articles), which was always used in the DCEs as a choice attribute. Conversely, the "format" was almost always considered as a context variable (18 times out of 19). "Brand", "designation of origin", "production methods", "alcohol content", "taste", "winery distinctiveness", "acknowledgements", and "consumption advice" are less studied in the literature and are mostly treated as choice attributes. In particular, to date, no studies have used awards and the evaluation in specialized guidebooks as a context, which is to say that none have formulated a DCE in which the preference for awardwinning wines is evaluated. Finally, only a limited number of studies have used choice attributes like absence of added sulfites (2 articles), nutraceutical characteristics (2 articles), and offer of discounts (2 articles). Defining the "occasion" is used as a context variable and is found in 22 articles out of 35. This description shows that almost all of the 15 categories of attributes considered are found in a consistent number of studies, thus confirming that the choice process of wine takes numerous attributes into account. The difficulty of implementing DCEs with all of the important attributes, however, has led researchers to select only a few attributes in making the experiments, inevitably reducing the realistic nature of the choice. In particular, in building the choice sets, an average of 4 categories are employed (each of which almost always represented by a single attribute), while the definition of the scenario involves, on the average, 1-2 categories more.
Our study proposes to surpass these limits by defining a methodology to create the DCE that makes it possible to take account of most of the attributes of the complex product that are considered important, guaranteeing sufficient effectiveness in developing the experiment.
METHODOLOGY
This section opens with a presentation of the procedure applied in our experiment; it then presents the
Experimental procedure
Our experiment was conducted in January 2018 by administering an on-line questionnaire to a sample of 600 Italian wine consumers. A company specialized in market research (Toluna Inc.) handled recruiting participants and collecting data. In particular, the experiment consisted of a DCE divided into two treatments. Following a betweensubject approach, each respondent was randomly assigned to only one of the treatments. In this manner, two subsamples of 300 respondents each were formed.
We called the first treatment "limited information". It is tantamount to a conventional unlabeled DCE in which the description of the scenario conveys the information that the experiment concerned a 0.75-liter bottle of red wine for an occasion of everyday home consumption. In the second treatment, which we called "full information", every single respondent received the same information as the first treatment, plus a description of the scenario that was more detailed and consistent with his purchasing habits. The description of the scenario was based on questions asked prior to the choice experiment.
The procedure of the second treatment can be divided into 3 steps. In the first step, respondents were asked to select, from a list we drew up based on the literature review, the criteria that they normally use in choosing wine. The criteria they could select from were: the wine's region of origin, the grape variety, the brand, alcohol content, and mention in guidebooks. In the second step, for each criterion selected, the participant was asked to select their preferred option from a dropdown menu containing the principal possible alternatives (Table 2). For example, if the interviewee indicated grape variety as a choice criterion, then he was asked to select the one he habitually preferred from a list of 20 grape varieties. In the third step, the respondents participated in a DCE where the choice scenario was defined on the basis of the information collected in phases 1 and 2. In other words, the respondents received a choice scenario "personalized" to their purchasing habits. In this manner, we were able to work around the problem that each respondent could make inferences about the attributes important for them but not included in the choice experiment and that the researcher could therefore not survey.
By way of example, the respondent who selected Tuscan wines produced from the Sangiovese grape variety and with an alcohol content of 13° performed the choice experiment reported in Fig. 1.
The attributes included in the choice tasks, identical for the two treatments, number 4 ( Table 3). The first attribute concerns the organic production method with two levels: conventional (the product does not have an organic certification) and organic (the product carries the European logo concerning organic certification). The second attribute concerns sulfites with two levels: contains sulfites, no sulfites added. The third attribute considered concerns the geographical indications (GI). The levels of GI are those regulated by the Italian classification system of GI wine (Italian Law 238/2016). The levels utilized for the GIs are: DOCG (Designation of Imagine you need to purchase a 0.75-litre bottle of red wine from Tuscany, made from the Sangiovese grape variety and with an alcohol content of 13% for everyday consumption (which is to say not tied to special occasions). In each choice set, from among the alternatives proposed, choose the one you would purchase. In the event that none of the alternatives is to your liking, you can select the no-choice option Controlled and Guaranteed Origin), DOC (Designation of Controlled Origin), and IGT (Typical Geographical Indication). The DOCG wines are subjected to stricter regulations than the DOC wines. The DOC wines instead respect stricter regulations than the IGT wines. Finally, the fourth attribute is price with 4 levels: € 2, € 6, € 10, € 14.
Each respondent was required to answer 8 choice questions, indicating in each choice task their preferred wine between two product alternatives that differed by attribute levels. Each choice task also included a no-buy option. The experimental design was done by means of the Ngene software version 1.1.2, applying an orthogonal fractional design.
Econometric model
DCEs have their theoretical foundations in Lancaster's consumer theory (1966), which postulates that the utility deriving from the consumption of a certain good is a function of the same good's characteristics. We can therefore model the product's utility in function of the attributes included in the choice tasks and handle the information collected with the DCE by means of a mixed logit model (Train, 2009) that takes account of the unobserved heterogeneity across the sample.
The utility function of the individual i obtained from the choice alternative j in the choice task t is as follows: where ASC is an alternative-specific constant that represents the no-buy option; α is the marginal utility of the price; PRICE represents the price levels offered to the respondent to purchase a bottle of wine; β i is the vector of utility parameters for participant i; x ijt is the vector of the wine's attributes and their levels with respect to alternative j, individual i and choice task t. Finally, ε ijt is an unobserved random term. In the specification of our model, PRICE and ASC have been estimated as fixed coefficients, while the coefficients of the other attri-butes (organic certification, sulfites, and GI) have been assumed as independently distributed following a normal distribution. Therefore, in addition to the median effect, for each attribute, a standard deviation was estimated for each of the random components. The model has been estimated by STATA 15.1. We used the mixed logit model to compare the results of our approach with those obtained by applying the conventional methodology in which the researcher chooses a priori the elements to define the scenario. We then created a latent class model (LCM) in order to provide an example of how the information obtained with our proposed procedure can be used to obtain a more meaningful segmentation. The LCM represents the semi-parametric version of a mixed model inasmuch as heterogeneity has a discrete distribution with C mass points, where C represents the number of classes with which the model is estimated (Greene and Hensher, 2003;Hynes and Greene, 2016). The LCM considers that every single individual belongs to a specific latent class c, where c = 1, ..., C; where all of the individuals belonging to that class have homogeneous preferences but are heterogeneous with respect to the individuals belonging to other classes. We can therefore write that following Greene and Hensher (2003), the probability that individual i in the choice task t chooses the alternative j among the J alternatives is: (2) where β c is the vector of utility parameters of class c. The model estimates the parameters of the attributes for each class, as well as the probability of each individual π ic to belong to a specific class c. This process too, can be modeled as a multinomial logit (Greene and Hensher, 2003;Ouma et al., 2007;Wu et al., 2019): where z i is the vector of the respondent's observed individual characteristics and γ c is the parameter vector for consumers in class c. In our case, z i represents the criteria that respondents stated they normally use in choosing wine, which is to say the information collected in the first step of the experimental procedure with the full information group.
The sample
Six hundred Italian respondents filled in the questionnaire, 300 for each treatment. All participants were screened to ensure they were over 18 years of age and had consumed wine in the previous months. The overall sample consists of approximately 48% men and 52% women. The different age categories are well represented and most of the respondents have a secondary education. However, the consumers with a university degree are slightly over-represented. The two sub-samples have the same socio-demographic make-up as shown by the Chi-squared test (Table 4).
RESULTS
This section presents the choice criteria selected in the first step of the experiment, the results of the mixed logit models and the latent class analysis. Table 5 reports the frequencies with which respondents chose criteria in the course of the first step of the experiment. The information most used is origin, indicated by 77% of the respondents, followed by brand, selected by approximately 69% of the interviewees. Guidebooks are utilized by just over one-fifth of the sample and represent the criterion used less frequently.
Choice criteria
As interviewees were given the possibility to choose one or more criteria, an overall 30 combinations were chosen, the first 10 of which represent 73% of all of the respondents (Fig. 2). The combination of origin and brand is the most numerous, and is utilized by almost 14% of respondents. The successive combinations add to these two criteria, alcohol content and grape variety.
The group of respondents that utilizes all 5 criteria (8.7%) is quite consistent, while the groups that use a single criterion are few. Among these, the most conspicuous is in fact the group that only considers origin, which represents only 4% of respondents.
The results of this first explorative analysis confirm that the choice of wine is very complex, that there are large differences between consumers, and that defining the product in creating the choice experiment can therefore be critical.
Likelihood ratio tests for pooled models
To test whether the coefficients between the two models are equal, we used the likelihood ratio (LR) test. The LR test is calculated as: where LL lim_info is the log-likelihood of the model applied to the sub-sample with limited information, LL fullinfo is that of the model for the group that received the treatment with full information, while LL pooled is the log-likelihood pertaining to the pooled model. The LR test has a Chi squared distribution with a number of degrees of freedom equal to the difference of the number of parameters. Table 6 reports the results of the LR test calculated both with a model specified in the utility space and with a model specified in the WTP space. The latter model serves to make sure that the results are the same in both of the specifications and to take into account the scale heterogeneity between the two subsamples. For both of the models, the LR statistics do not significantly exceed the critical values. Based on this outcome, we can affirm that the results between the two sub-samples are different. Table 7 reports the results of the mixed logit models for the limited information scenario, the full information scenario, and the pooled model.
Parameter estimates
In both scenarios, the parameters of the attributes are 99% significant and bear the expected signs. With the exception of that of the IGT with limited information, the coefficients associated with the standard deviations are also all significant, which indicates a substantial heterogeneity in consumer preferences with respect to the attributes considered in the model. Specifically, the coefficient of the no-buy option is negative in both models, which indicates that the consumers receive a greater utility from choosing at least one of the options presented compared to the no-choice option. As expected, the coefficient of price is negative for both of the scenarios, indicating that the increase in price corresponds to a decrease in consumer utility. For this parameter, the magnitude is substantially different in the two scenarios, -0.10 for the limited information scenario compared to -0.05 for the full information scenario, indicating the lesser role of the price attribute in the utility function in the latter case.
The parameters of the other attributes' levels all prove to be positive in both of the scenarios, thus indicating that the consumers prefer wines without added sulfites, with geographical indication, and organic. In particular, the absence of added sulfites is the parameter with the greatest magnitude and thus constitutes the characteristic that on a par with other conditions confers greater utility to wine.
From the analysis of the confidence intervals, we can also note that the two models substantially differ only by the parameter of price. Indeed, as we have already pointed out, the coefficient of price for the full information scenario is about half that of the limited information scenario, and the confidence intervals in the two models do not overlap.
To further verify the determinants of the differences between the two sub-samples, a new model was performed on the pooled sample, inserting variables of interaction between the treatment (full information) and the attributes specified in equation 1. The results of this different specification indicate that all of the interaction variables are not statistically significant except for the interaction variable between treatment and price (Table 8). This confirms that the full information treatment affects the parameter of price, determining a significant reduction of its importance.
Random parameters in utility functions
Notably, the interaction between the no-buy option and treatment is also not significant, which indicates that the treatment has not affected the no-choice rate during the choice experiment. Providing the respondent with a more definite scenario by means of the proposed methodology therefore does not modify the no-choice rate.
In order to test whether the treatment also had an effect on the willingness to pay, we applied a Poe (2005) test. The results reported in table 9 show that the willingness to pay of the two sub-samples differ by the attributes No sulfites added, IGT and DOCG. The difference for the willingness to pay for the DOC attribute is significant only for 10%, while the willingness to pay for the organic certification does not differ in the two treatments.
Latent class results
The segmentation analysis was conducted by means of a LCM with a specification of the model with respect to the same utility function as that of equation 1 and utilizing the choice criteria of each respondent as class membership variables. We have chosen the 5-class model based on the Bayesian Information Criterion (BIC), which shows an inversion between the models with 5 and 6 classes ( Table 10).
The results of the LCM (Table 11) show a marked heterogeneity in consumer preferences indicated by the strong differences between classes as per significance, magnitude, and sign of the utility function parameters.
For example, the price coefficient is negative and significant for classes 1 and 3, positive and significant for classes 4 and 5, and not significantly different from zero for class 2. Organic certification is instead significant only for class 5, where it represents one of the attributes with the greatest positive impact on consumer utility. The absence of added sulfites is perhaps the most homogeneous parameter among the classes; it is indeed always significant with a positive sign even when it presents a Notes: Asterisks indicate the following significance levels: *= 10%; **= 5%; ***= 1%. conspicuous variability of magnitude, passing from 0.33 for class 1 to 4.74 for class 5. The GI parameters always have a positive sign, but are not always significant. For example, they are all significant for classes 3 and 5, while for class 2, no indication of origin is significant. Class 1, which has the most consistent class size, has a significant preference only for DOCG wines, the top-tier certification.
The coefficients of class membership indicate the role of the different criteria in determining the probability of belonging to each class with respect to class 1. The Wald test of joint difference of parameters between classes indicates that the main predictors among the classes are origin (Wald = 9.77; p-value = 0.044) and mention in guidebooks (Wald = 16.75; p-value = 0.0022). In particular, the probability of belonging to class 2 and 4 (40% of respondents) depends significantly on the choice of origin. While respondents belonging to class 3 are consumers who, more than those of other classes, are more likely to disregard the judgement of guidebooks as a choice criteria of wine. The coefficients concerning alcohol content, grape variety, and brand are instead not statistically significant.
CONCLUSIONS
DCEs are a widely utilized methodology to evaluate the market potentials of new attributes of products. One of the main challenges in applying them is represented by the capability to reproduce the decision-making context in the most realistic manner possible (Ben-Akiva et al., 2019). This issue is particularly important when dealing with complex products. Their evaluation necessitates considering a great number of stimuli, and also involves a filtering heuristic, progressively screening out products that fail to pass thresholds on a selected attribute.
In the literature, creating DCEs for complex products has frequently implied the use of a large number of attributes and levels in the experimental design without, however, always succeeding in adequately reproducing the actual choice situation. Moreover, the use of a large number of attributes and levels entails important criticalities in terms of experimental design complexity and the difficulty of interviewees to reply. An enhancement of the realistic nature of the experiment can also be obtained by means of a better definition of the context in which the choice is made, but in this case, excessive detail can determine the undesired effect of a high no-reply rate, considering the fact that the product described in this manner might not prove interesting to a sufficient number of consumers.
The solution proposed here confronts this problem by means of a methodology of building the choice experiment that takes into account the actual behavior of the consumer in choosing wine. For this product, as for others with similar characteristics of complexity, the final choice derives from a filtering heuristic of the many alternative products available on the market (Swait and Adamowitcz, 2001). For example, first we choose the Notes: Asterisks indicate the following significance levels: *= 10%; **= 5%; ***= 1%.
59
The Role of Context Definition in Choice Experiments: a Methodological Proposal Based on Customized Scenarios color, then the grape variety, then we consider the price, and so on until we complete the range of attributes that each consumer considers important. In attempting to make the choice experiment as realistic as possible, we therefore developed a procedure to define the scenario of reference which includes all the attributes that each interviewee considers important in their decision-making process. In greater detail, in the first phase, the respondents were asked what attributes were important for them in choosing wine. Then for each attribute selected, the main alternatives were proposed, and they were asked to select the one they preferred. The mix of options indicated in this manner was then used to define the choice scenario of each interviewee. It was thereby possible to obtain a more realistic choice situation, maintain the design within acceptable limits of complexity, and also observe the specific characteristics of the product that each interviewee referred to in his choice. The capability to identify the specific preferences that the decision-making process of wine develops along constitutes an important improvement compared to traditional procedures. Furthermore, we found significant differences in the choice criteria for wine, as far as the nature and number of attributes to consider are concerned.
Applying the procedure of tailoring the scenario of reference to the individual respondent has shown that defining the choice scenario is not neutral with respect to the choices elicited in the experiment. In fact, our approach has shown preference estimates that are significantly different from those of the conventional approach, as pointed out by the LR test. These differences proved substantial for the parameter of price, indicating that a better description of wine in the scenario of reference gave rise to a reduction in the importance of the price attribute, which can plausibly be explained by the fact that the consumer is less uncertain about the definition of the two alternatives of wine to evaluate. Our outcomes are coherent with general economic theory and with earlier consumer studies which indicate that price sensitivity is a function of available information. In this regard, Alba et al. (1997) find that having more information on quality attributes reduces price sensitivity, while Nagle and Müller (2017) suggest that consumers show lower price sensitivity when they perceive specific quality features of the product. These results call for further research on the role that the specification of the choice scenario has on preference estimates. In fact, in various case studies, an issue might arise on how detailed the product definition should be, and the adopted solution might not be neutral with respect to the results, especially in terms of WTP.
Furthermore, our results point out that the use of the "region of origin" and "mention in guidebooks" criteria, in particular, contribute to defining specific segments of consumers. It is worth mentioning that the information acquired through the methodology proposed is greater than the information used in this paper. The numerousness of the choice options utilized by respondents, however, was such that given the size of the sample, it did not permit more in-depth segmentation analyses.
The type of approach utilized does not allow us to identify econometric indicators that define whether the procedure we propose has greater statistical properties than the traditional procedure. From the practical point of view, however, the possibility to avail ourselves of individual information on the choice criteria and on the preferred options for each choice criterion represents an important element for a better understanding of the decision-making process, and can also be used for further segmentation analyses, as proposed in the article.
In conclusion, this article represents a first contribution to achieving a more realistic decision-making context by improving the choice scenario definition in DCEs. Overall, the proposed solution offers various advantages over the traditional approaches, even though its application in different contexts and on different products could certainly make for further improvements in the phase of eliciting preferences. | 7,644 | 2020-11-23T00:00:00.000 | [
"Business",
"Economics"
] |
Understanding Translationese in Multi-view Embedding Spaces
Recent studies use a combination of lexical and syntactic features to show that footprints of the source language remain visible in translations, to the extent that it is possible to predict the original source language from the translation. In this paper, we focus on embedding-based semantic spaces, exploiting departures from isomorphism between spaces built from original target language and translations into this target language to predict relations between languages in an unsupervised way. We use different views of the data — words, parts of speech, semantic tags and synsets — to track translationese. Our analysis shows that (i) semantic distances between original target language and translations into this target language can be detected using the notion of isomorphism, (ii) language family ties with characteristics similar to linguistically motivated phylogenetic trees can be inferred from the distances and (iii) with delexicalised embeddings exhibiting source-language interference most significantly, other levels of abstraction display the same tendency, indicating the lexicalised results to be not “just” due to possible topic differences between original and translated texts. To the best of our knowledge, this is the first time departures from isomorphism between embedding spaces are used to track translationese.
Introduction
The term "translationese" refers to systematic differences between translations and text originally authored in the target language of the translation, in the same genre and style (Gellerstam, 1986;Baker and others, 1993;Baroni and Bernardini, 2005;Volansky et al., 2015). Characteristics such as simplification, over-adherence to conventions of the target language, and explicitation can occur as a communicative process itself. This is contrasted with "interference" or "shining-through" (Teich, 2003), described as "phenomena pertaining to the make-up of the source text tend to be transferred to the target text" (Toury, 2012). Prominent evidence for shining-through as a translationese effect is found in the work of Rabinovich et al. (2017), who show that footprints of the source language remain visible in translations, to the extent that it is possible to predict the original source language from the translation. In the similar vein, a significant amount of work has gone into training classifiers to distinguish between translations and originally authored text and then investigating the contributions of individual features to the result of the classification (Baroni and Bernardini, 2005;Koppel and Ordan, 2011;Volansky et al., 2015;Avner et al., 2016). Features that contribute strongly to classification are interpreted as indicating important dimensions of translationese.
In contrast, in this work, we leverage departures from isomorphism between embedding-based semantic spaces to detect translationese. We construct embedding spaces from original English (O) data and translations into English (T ) from comparable data in a number of languages. We hypothesize that the closer the source language is to English, the more isomorphic the embedding spaces are. In other words, departure from isomorphism is an indicator of language distance. We use eigenvector similarity (Søgaard et al., 2018) to quantify departure from isomorphism. If our hypothesis is correct, we should be able to reconstruct phylogentic trees from measures of departure from isomorphism. We show that this is indeed the case and compare our embedding-based results with previous results of reconstructing phylogenetic trees (Serva and Petroni, 2008). In order to show that our outcomes are not the result of topic divergences between O and T data, we explore delexicalised views 1 of our data, using embeddings based on parts of speech (PoS), semantic tags (ST), and synsets (SS), rather than word tokens (Raw). We show that our results are robust under delexicalisation.
Our paper is structured as follows: Section 2 discusses related work and inference of phylogenetic trees. Section 3 introduces our experimental setup. The distance measure is described in Section 4. We present our results and analysis in Section 5, followed by conclusions in Section 6.
Phylogenetics and Shining-through
Historical comparative linguistics determines genetic relationships between languages using concept lists of words that share a common origin, similar meaning and pronunciation across multiple languages (Swadesh, 1952;Dyen et al., 1992). By contrast, computational analysis methods aim to reconstruct language phylogeny based on measurable linguistic patterns (Rabinovich et al., 2017;Bjerva et al., 2019). Rabinovich et al. (2017) showed that source language interference is visible in translation. Specifically, they leverage interference (PoS trigrams and function words) and translation universal features (cohesive markers) to construct phylogenetic trees. Agglomerative clustering with variance minimisation (Ward Jr, 1963) is used as linkage procedure to cluster the data. The result is compared to the pruned gold tree of Serva and Petroni (2008) (henceforth referred to as SP08) used as the linguistic phylogenetic gold standard tree. Their comparison metric, which is based on the L2 norm, is basically the sum of squared deviations between each pair's gold-tree distance g and computed distance P : (1) SP08 was constructed by computing the Levenshtein (edit) distance between words from an open cross-lingual list (Dyen et al., 1992) to compare linguistic divergence through time and thus partially encodes lexical similarity of languages (Oncevay et al., 2020). Rabinovich et al. (2017) also acknowledges that SP08 has been disputed and researchers have not yet agreed on a commonly accepted tree of the Indo-European languages (Ringe et al., 2002). More recently, Bjerva et al. (2019) built on this work and compared different languages based on distance metrics computed on phrase structure trees and dependency relations. They claimed that such language representations correlate better with structural family distances between languages than genetic similarities. These examples show that phylogenetic reconstruction approaches and in particular, the evaluation of generated trees remains a highly debated topic in the history of linguistics and is beyond the scope of this study.
Experimental Settings
Data. We use the comparable portion of Europarl (Koehn, 2005) with translations from 21 European Union languages into English to minimise the impact of domain difference. The amount of tokens per language varies, ranging from 67 k tokens for Maltese to 7.2 M for German. We refer to the multiple translations into English as L j 's, where j = 1, 2, ..., n; and to originally written text in English as L e . We select the subset of translations from 16 languages covering three language families: Romance (French, Italian, Spanish, Romanian, Portuguese), Germanic (Dutch, German, Swedish, Danish) and Balto-Slavic (Latvian, Lithuanian, Czech, Slovak, Slovenian, Polish and Bulgarian) into English and English original text.
Abstractions. In addition to using raw word tokens, we create multiple views of the data at the morphological (PoS), lexical semantic (ST) and conceptual-semantic (SS) levels. We use the spaCy tagger (Honnibal and Johnson, 2015) with the OntoNotes 5 version (Weischedel et al., 2013) of the Penn Treebank PoS tag set. For ST (Bjerva et al., 2016;Abzianidze et al., 2017), we use the best model of Brants (2000) which works directly on the words as input, and determines formal lexical semantics. Their implementation achieves around 95% accuracy, when evaluated on short Parallel Meaning Bank sentences. For SS, we follow España-Bonet and van Genabith (2018) to retrieve synsets according to the PoS of a token using the knowledge base of WordNet (Miller, 1998). We only select a subset of PoS tags, namely NN, ADV, ADJ and VB and consider the first synset for each word/tag combination. Table 1 presents an overview and examples of each type of annotation used in this study.
Vector Spaces. For each view, we induce a separate monolingual word embedding space (both L e and L j 's) by treating each token or tag as a word using fastText (Bojanowski et al., 2017). Embeddings have 300 dimensions and only words with more than 5 occurrences are retained for training. We use skip-gram with negative sampling (Mikolov et al., 2013) and standard hyper-parameters.
Measuring Isomorphism
An empirical measure of semantic proximity between two languages is often computed using the degree of isomorphism, that is, how similar the structures of two languages are in topological space (Søgaard et al., 2018). Research in cross-lingual transfer tasks shows that linguistic differences across languages often make spaces depart from isomorphism (Nakashole and Flauger, 2018;Søgaard et al., 2018;Patra et al., 2019;Vulić et al., 2020). While this degrades the quality of bilingual embeddings, it is a desired characteristic in our case: since our task involves processing of (multi-view) representations of monolingual text, departures from isomorphism indicate diversity in the source that generates them.
To quantify isomorphism, we compute embeddings on a corpus in language L. Embeddings reflect distributional properties in the data: words in similar contexts have similar meanings (Harris, 1954) and should be close in embedding space. We then view the points representing words or tags in the resulting hyperdimensional embedding space as a graph and compare different spaces (e.g. for data from different languages, or originals and translations into the language of the originals) in terms of how similar or dissimilar the corresponding graphs are. This is measured in terms of a well established metric, the eigenvector similarity.
Eigenvector Similiarity (EV). Søgaard et al. (2018) proposed this spectral metric based on Laplacian eigenvalues (Shigehalli and Shettar, 2011) to estimate the extent to which nearest neighbor graphs are isomorphic. We use the same idea to model differences between two spaces: original X and translationese Y for the single target language translations from different source languages. First, we compute the nearest neighbour graphs G i of the two embedding spaces for the most frequent overlapping vocabulary. 2 We then compute the eigenvector similarity of the Laplacians of the nearest neighbor graphs, L(X ) and L(Y) in original and translationese respectively. The degree of graph similarity is given by the distance among the eigenvectors λ of the Laplacian of G: Following Søgaard et al. (2018), we find the smallest k 1 in Equation 2 such that the sum of its k 1 largest eigenvalues k 1 i=1 λ 1i is at least 90% of the sum of all its eigenvalues. Analogously, we find k 2 Table 3: Correlations between similarities (SPO8 and EV) on the different views of linguistic representations (the higher the better).
and set k = min(k 1 , k 2 ). The graph similarity metric returns a value in the half-open interval [0, ∞), where values (∆) closer to zero indicate more isomorphic embedding spaces.
To control the impact of data size for different L j 's, we choose the size of common overlapping vocabulary list corresponding to the range of the most resource-poor language in each view (see last column of Table 1) and run EV on this size for the rest of L j−1 .
Results and Analysis
To analyse the computed distances between original English and English target translations on different levels of linguistic analysis, in a first step, we calculate the sum of the normalised EV scores per language family (i.e., Germanic, Romance, Balto-Slavic) shown in Table 2. Translations from Germanic languages are the closest ones to original English (itself a Germanic language) regardless of the level of linguistic representation, followed by translations from Romance and finally from Balto-Slavic source languages. This shows that language distance in vector space is higher for etymologically distant language pairs in translation providing evidence that languages with similar topological semantic structure exhibit less interference. The fact that deviation from isomorphism between multi-view semantic spaces of translation into English and original English changes with respect to source language shows that source language interference is a strong characteristic of translated texts, adding new semantic space based support for the findings in Rabinovich et al. (2017).
Footprints of the source language into the translation product allow us to construct phylogenetic trees. Figure 1 shows the result of clustering the distance scores using agglomerative clustering with variance minimisation (Ward Jr, 1963) for four views considered in this study. Consistent results across all the trees demonstrate strong presence of the shining-through. We identify some of the well known language-language relationships in all four trees, such as for example, English is grouped with Germanic and Romance languages while Balto-Slavic languages are always put together. Some interesting divergences, with respect to Balkan Sprachbund (BS) are visible as well. The geographical location of Romanian opens it to cross-pollination with the other languages of the BS area and the figures provide some evidence for that. Table 3 shows the Kendall τ correlation coefficients between how close languages are in SP08 and in our difference-from-isomorphism based reconstructions. Our results show that both lexicalised and delexicalised structures correlate reasonably well (τ ∈ [0.37, 0.55]) with the linguistically motivated phylogenetic tree, indicating that the lexicalised results are not "just" due to possible differences in topic between original and translated texts. In fact, the delexicalised representations (PoS and ST) which are less influenced by topic and have fewer types show more functional similarities with SP08 than the fine-grained semantic representations.
Conclusion
We presented an investigation of translationese effects in a single language sourced from multiple translations based on the topology of their multi-view embedding spaces. We explored embedding spaces constructed from word level (Raw), morphological (PoS), lexical semantic (ST) and conceptual-semantic (SS) views of the data. To the best of our knowledge, our study is the first to track translationese using isomorphism in semantic space.
Our translationese-based results can infer phylogenetic language family relations based on divergence from isomorphism between embedding spaces from translations and originally authored text. We find that language distances correlate with the divergence from isomorphism in embedding space. Our analysis demonstrates that while all embedding views exhibit source-language interference, delexicalised embeddings do so most significantly. In turn, this allows us to conclude that the lexicalised results are not just due to possible topic differences between original and translated texts.
Unlike supervised lexicostatistic approaches relying on aligned multilingual cognate lists, our isomorphism analysis is unsupervised and still able to detect important language differences related to linguistic typology. In a sense, and compared to some previous approaches, departure from isomorphism in embedding spaces lets "the data speak more for itself".
As future work, we intend to extend our experiments to capture geometric properties of the embedding features and work on isolated languages. Since we see that spaces with less tags, i.e., a smaller vocabulary, are better predictor of genetic relationships, more thorough robustness tests on the quality of the embeddings that might have an effect in skewing the results will be applied as well. | 3,311 | 2020-12-01T00:00:00.000 | [
"Computer Science",
"Linguistics"
] |
Exploring Effectiveness of Relationship Marketing on Artificial Intelligence Adopting Intention
The major contribution of present study is to revisit how consumer obtain high adoption intention of artificial intelligence (AI)’s production/service based on symmetric and asymmetric thinking in data analysis. In recent years, technology involving AI has become key technology for success worldwide and has received prominence among academics and practitioners. Accordingly, it is necessary to identify the relationships among relationship marketing, AI perceived usefulness, perceived ease of use, perceived risk, and adoption intention. The main contribution of the symmetric approach (i.e., SEM, structure equation modeling) is to test the research hypothesis to determine the net effect between the variables, and asymmetric approach (i.e., fsQCA, fuzzy set qualitative comparative analysis) contributes to the identification of sufficient conditions leading to high level adoption intention in the concept of fuzzy sets. With symmetric approach, results of path analysis of SEM indicate that impacts of trust are greater than that of commitment. Similarly, perceived usefulness of AI has a greater impact on the adoption intention. Furthermore, AI perceived risk is negative associate with adoption intention. With asymmetric approach, intermediate solutions from fsQCA show that there are three sufficient conditions for high adoption intention of AI. For instance, one of configurations or sufficient conditions is trust, commitment, and AI perceived usefulness present but perceived ease of use absent. Plain Language Summary Revisiting AI adopt intention The major contribution of present study is to revisit how consumer obtain high adoption intention of artificial intelligence (AI)’s production/service based on symmetric and asymmetric thinking in data analysis. The main contribution of the symmetric approach (i.e., SEM, structure equation modeling) is to test the research hypothesis to determine the net effect between the variables, and asymmetric approach (i.e., fsQCA, fuzzy set qualitative comparative analysis) contributes to the identification of sufficient conditions leading to high level adoption intention in the concept of fuzzy sets. With symmetric approach, results of path analysis of SEM indicate that impacts of trust are greater than that of commitment. Similarly, perceived usefulness of AI has a greater impact on the adoption intention. Furthermore, AI perceived risk is negative associate with adoption intention. With asymmetric approach, intermediate solutions from fsQCA show that there are three sufficient conditions for high adoption intention of AI. For instance, one of configurations or sufficient conditions is trust, commitment, and AI perceived usefulness present but perceived ease of use absent.
Introduction
For nearly a 100 years, technological innovation has continuously improved human life.In the digital age, AI can be used to enhance perception and expand our sense of reality in many ways (Al Halbusi, 2023).However, will human intelligence prefer to use products or services based on artificial intelligence technology?What factors influence adoption intention?Are their effects different?Are there sufficient conditions that would surely lead to a high level of adoption intention?To answer these questions, this study contributes to extend knowledge of relationship marketing and technology acceptance model (TAM) to measurement of adoption intention in AI market based on perspectives of symmetric (i.e., exploring the difference in impact) and asymmetric (i.e., exploring the sufficient condition of high level of adoption intention) thinking in data analysis.
In recent years, AI-related technologies has received prominence among academics and practitioners (e.g., Adel et al., 2022;Boaventura et al., 2022;Colombo et al., 2019;Gursoy et al., 2019;Khan et al., 2021;van Esch et al., 2019).The development of AI is becoming more and more important globally (Suh & Ahn, 2022).AI-related technology is a key strategic element on a global market.AI technology has the potential to reduce the workload of laborers (Yunjiu et al., 2022).The use of AI devices to replace human existence has always been a controversial topic, so that most consumers do not have a firm stand on whether to accept or reject AI devices and robots (Gursoy et al., 2019).Jarrahi (2018) proposes that AI has penetrated many organizational processes, and it is necessary to understand complementarity of humans and AI.Human-computer communication has not yet been popularized, and the rules of humancomputer interaction need to be explored urgently.Accordingly, the present study focuses on AI and proposes that managers must understand customer behavior in AI-related marketing strategy to enhance competition of business activities.To evaluate or explore consumer behaviors of new technology, several study of social sciences or consumer behaviors are paying much attention to technology acceptance model (TAM), theory of planned behavior (TPB) (e.g., Baby & Kannammal, 2020;Boley et al., 2018;Chuah et al., 2021;Singh & Verma, 2017), or their extentions, such as interactive technology acceptance model (iTAM) (e.g., Go et al., 2020), TAM2 (e.g., Wang et al., 2022), or technologyorganizational-environment (TOE) (e.g., Chatterjee et al., 2021).Although these are well-known adoption models, this study focuses on analyzing the consumer behavior related to AI products or services based on symmetric and asymmetric approaches.Accordingly, the present study contributes to revisit relationships among relevant antecedents of adoption intention based on TPB and TAM.TPB has been used extensively to predict engagement in behaviors and understand why do individuals engage in certain behaviors (Boley et al., 2018).Based on TPB, the present study investigatges the antecedents of AI adoption intentions.Based on TAM, several research point out that PU (perceived usefulness) and PEOU (perceived ease of use) are the main factors affecting willingness to adopt new technologies (e.g., Ben-Mansour, 2016;Chen & Lu, 2016;Cormick, 2019;Haile & Altmann, 2016).Accordingly, the present study attemps to explore effectiveness of PU and PEOU on adoption intention of AI.
Although TAM's knowledge has been provided valuable contributions by many studies, AI adoption intention can also be influenced by other factors.In the field of customer relationship management (CRM), many scholars believe that relationship marketing strategy is one of the hidden influential factors (e.g., Guerola-Navarro et al., 2021;Hanaysha & Al-Shaikh, 2022;Li & Xu, 2022;San-Martı´n et al., 2016;Youn & Jin, 2021).For instance, Li and Xu (2022) proposes that CRM is a powerful strategy that focuses on long-term consumer relations.Youn and Jin (2021) indicates that customer relationship management is the basis of marketing, and trust is one of the key elements of customer relationship management.Guerola-Navarro et al. (2021) shows that CRM is one of the most powerful modern tools for managing the business reality of customer relationships and should focus on long-term trust and commitment.
As the competition among business activities becomes more prevalent, practitioners and academia are paying more and more attention to the effectiveness of relationship marketing strategies, and several studies focus on trust and commitment to explore relationship marketing (e.g., Akrout & Nagy, 2018;Armstrong & Kotler, 2009;Brown et al., 2019;Salem, 2021).Relationship marketing strategies can be regarded as necessary for companies to survive in a fiercely competitive market (Armstrong & Kotler, 2009).For the market where AI technology is applied, relationship marketing can effectively maintain and develop existing customer bases, and at the same time develop new customer bases or markets.Accordingly, relationship marketing (i.e., trust and commitment) has become the main method to adapt to a dynamic competitive environment.For instance, Alalwan et al. (2021) proposes that the rapid development of information technology has changed the interaction relationship, and the trust-commitment theory of relationship marketing has become the key driving source of most research concerns.
According to the users' prospective, they may ask themselves: Who or what that can I trust?Is it worthwhile to adopt?Does it involve risks?Bonnin (2020) suggests that customer's evaluation of the undesirable consequences and uncertainty of purchasing or using services or products can be usually defined as perceived risk and become a focal issue for both academics and practitioners.According to these regards, the present study further explores the effectiveness of perceived risk on AI adoption intention.
While several studies have provided valuable contributions to the knowledges of adoption intention, most of these studies focused on applying multiple regression analysis (MRA) or structure equation modeling (SEM) to explore the net effects estimation approach.However, several problems in social science can be considered verbal and can be formulated in terms of sets and set relations, and social science theorists have developed a large number of concepts and methods for asymmetric relations (Ragin, 2017).The net effects estimation approach appears to be more difficult to assess the sufficiency of a high degree of AI adoption intention.To fill this gap, this study further using fsQCA that focus on treat configurations for testing social science theories rather than net effects estimation approach to combine relevant antecedents (i.e., relationship marketing, AI PU, PEOU, and risk) into various causal recipes to explore the configurations for achieving high AI adoption intention.In sum, adoption intention plays a critical role in AI consumer behavior that it can be regarded as the main determinant of the success of artificial intelligence companies, and this study focuses on exploring adoption intention of AI by integrating the perspectives of relationship marketing, AIPU, PEOU, and risk from both symmetric thinking (i.e., SEM) and asymmetric thinking (i.e., fsQCA) in data analysis.
Theory of Planned Behavior (TPB) and Technology Acceptance Model (TAM)
In the field of customer behavior research, several researchers apply TAM or TPB and have shown great interest in the interrelationships among PU, PEOU, and adoption or purchase intention (e.g., Bediako et al., 2018;Dong et al., 2022;Han et al., 2019).TPB is an extension of theory of reasoned actions that aims to understand the impact of norms, attitudes, and behavioral perspectives on behavioral changes (Abdelfattah et al., 2022), and it has been used extensively to predict engagement in behaviors and understand why individuals engage in certain behaviors (Boley et al., 2018).According to TPB, intention to perform behavior, such as purchase intention or adoption intention, plays a critical role in investigating actually consumer behavior.Behavioral intention focuses on individual strength to perform a specific action based on perceptions of response and desired outcome (Chi, 2018).
To understanding of the antecedents of AI adoption intention, the technology acceptance model is powerful model that developed by Davis et al. (1989).Technology acceptance model takes into account the parametric attributes of behavior relevant components of attitudes, and specifies how external components are casually linked to attributes (Baby & Kannammal, 2020).Based on technology acceptance model, several studies focus on exploring impacts of perceived usefulness and perceived ease of use on intention to adopt new technology (e.g., Ben-Mansour, 2016;Chen & Lu, 2016;Chuah et al., 2021;Haile & Altmann, 2016;Liu et al., 2022).For instance, Liu et al. (2022) shows that TAM is suitable for explaining users' AI service robots adopt intentions.The technology acceptance model appears to be the most widely accepted among new technology researchers, and it addresses two constructs, that is, perceived usefulness and perceived ease of use, that affect the acceptance of technical innovations (Ben-Mansour, 2016;Chen & Lu, 2016).Based on these regards, AI PU, PEOU, and adoption intention are applied in the conceptual framework of this study based on TPB and TAM.
Relationship Marketing and AI PU/PEOU
As artificial intelligence is one of new technologies that created the third industrial revolution, it is indeed necessary to understand the relationship among marketing strategy, PU, and PEOU associate with AI.Existing literature in the fields of marketing has express a strong interest in relationship marketing that is major weapon for developing long-term win-win relationship in the highly competitive marketplace (e.g., Brown et al., 2019;Casais et al., 2020;Gilboa et al., 2019;S ˇeric´et al., 2020;Youn & Jin, 2017).In practice, more and more companies use AI-related technology (such as chatbots) to improve the effectiveness of relationship marketing through digital media (such as facebook, line, IG, twitter or blogs).For example, APPLEFANS can generate stronger cohesion, and continue to attract and care for new members.In the era of rapid growth of AI-related technologies, most researchers believe that trust and commitment are key constructs of relationship marketing (e.g., Alalwan et al., 2021;Brown et al., 2019;Casais et al., 2020;Gilboa et al., 2019).New technologies used to overcome trust issues tend to strengthen co-creation processes and enhance effectiveness of relationships marketing (Casais et al., 2020).Many companies enhance trust and commitment by employing advanced technologies to manage the customer experience based on virtual, non-human interactions with customers (Gilboa et al., 2019).Relationship marketing could be considered as a process and emphasized developing and continuing the relationships with the customers.Armstrong and Kotler (2009) believes that maintaining a win-win marketing relationship between the company and the customer will help improve the customer's positive evaluation or performance They further suggest that long-term customer value is the key to the success of relationship marketing.Scholars in the field of marketing generally believe that keeping customers happy throughout the shopping period is an important issue that companies should pay attention because positive emotions affect the ability to maintain effective public ratings and satisfaction levels (e.g., Armstrong & Kotler, 2009;Youn & Jin, 2017).The ultimate value of relationship marketing is usually to effectively strengthen or improve long-term customer performance and evaluation, and continue to provide customers with high satisfaction (Armstrong & Kotler, 2009).Yu and Tung (2013) suggests that escellent relationship marketing will reduce the cost of cultivating new customers when establishing long-term mutually beneficial relationships, and generate satisfied customers and create a good reputation.
The major purpose of relationship marketing is to gain customer value and cultivate customer loyalty by establishing long-term mutually beneficial relationships.In general, marketing needs to focus on customer needs to help its customers create value in the process based on relationship marketing.Trust influence relationship outcomes in relationship marketing literature.Hirshberg and Shoham (2017) suggests that trust is the most common construct investigated and plays central role in the relationship marketing paradigm.Guo et al. (2017) further shows that from the perspective of relationship marketing, trust or emotional commitment is usually related to social exchange, and calculative commitment has been associated with an economic exchange based on perceived benefits.According to existing literature in the field of relationship marketing, trust is the general expectation that consumers can rely on the AI provider, and commitment is the degree of emotional attachment and identification of consumers to the AI provider in this study.Therefore, firm's managers need focus on improve the degree of trust and commitment to enhance positive evaluations of their customers.
In AI marketing, the technology acceptance model is powerful model to understanding customer behavior or evaluation, and mostly researches focus on explore causal conditions or consequences of PU and PEOU (e.g., Alalwan et al., 2018;Rafique et al., 2020).Based on these regards, AI provider focuses on developing relationship marketing associate with trust or commitment may enhance customer's positive evaluation, including PU (i.e., customers think that using specific AI products or services will improve their outcomes) and PEOU (i.e., customers think that using specific AI products or services will be free of effort).Although both commitment and trust may positively influence AI PU and PEOU, trust seems more associate with customer's confidence or belief, but commitment more refers affective condition of customer that emotionally attached to and identify with the AI provider.Trust can be seen as user confidence and is a key factor in usage and acceptance (Al Halbusi et al., 2022).
Several empirical results indicate that trust may be more influential than commitment in relationship marketing efforts (e.g., Akrout & Nagy, 2018;Gilboa et al., 2019;S ˇeric´et al., 2020).For instance, Akrout and Nagy (2018) shows that influence of trust on relationship quality is greater than influence of commitment on relationship quality.Gilboa et al. (2019) proposes that although both trust and commitment in relationship marketing may positively influence word-of-mouth or customer loyalty, but trust has more positively linked to communication or treatment benefits, and commitment is more associate with social benefits.Accordingly, effectiveness of trust may differ with commitment on AI PU and PEOU.Therefore, this study develops H 1 and H 2 to explore relationships among trust, commitment, AI PU, and PEOU.
H 1 : The impact of trust on AI PU is greater than commitment on AI PU.H 2 : The impact of trust on AI PEOU is greater than commitment on AI PEOU.
Relationship Marketing and AI PR
In general, trust and confidence play an important role in the risk assessment process (Al Halbusi et al., 2021).Effectiveness of trust may also differ with commitment on AI PR. S ˇeric´et al. (2020) further proposes that brand trust will have a positive impact on affective brand commitment.Though both trust and commitment may influence the degree of perceived risks, trust is a more complex and multifunctional effects.Trust is the subjective view of someone acting in a certain way based on an implicit or explicit promise (Casais et al., 2020).Akrout and Nagy (2018) highlights the positive effects of economic and hedonic benefits on trust.Gilboa et al. (2019) proposes trust is major factor that leads to relationship development and reduce uncertainty.In other words, trust can reduce more uncertainties or unknown situations that require more information or experience.Moreover, productive efficiency and costs may moderate the positive effect of commitment on perceived risk.Accordingly, this study develops H 3 to explore relationships among trust, commitment, and AI PR.
H 3 : The impact of trust on AI PR is greater than commitment on AI PR.
AI PU/PEOU and Adoption Intention
Typically, behavior intention is defined as the intention to certain behaviors (Ghazali et al., 2023).Both TPB and TAM suggest that intention for a specific action is based on an assessment of the consequences of taking that action.More recent studies have extended and validated TAM and found positive relationships among PU, PEOU, and behavioral intention.For example, Alalwan et al. (2018) shows that PU, enjoyment, trust and innovation will have a significant impact on customers' willingness to adopt mobile Internet.PU and PEOU are major sources that can positive influence intention to use new technology at the inner level, and then in turn enhance actual use of new technology based on technology acceptance model.Chen and Lu (2016) applies TAM to explore using intention of green transportation and proposes that both green PU and PEOU can positively influence their using intentions.Baby and Kannammal (2020) uses TAM to explore PU and PEOU which deals toward the attitude toward using a technology.PEOU is a critical effective factor for the mobile ticketing service adoption intentions and most studies have further pointed out that PEOU has a positive impact on the intentions of technology users (Ben-Mansour, 2016).Haile and Altmann (2016) shows that the use intention simply means that if the technology is used based on utility theory, the utility will increase, and PU has been found to be a powerful predictor of technology use intention.Ben-Mansour (2016) further indicates that PU is the main and direct factor affecting behavioral intention, and influence of PEOU on intentions mainly through PU based on TAM.
In generally, consumers' rational pre-assessment of the usefulness of the innovation will help them to use the innovation.Manis and Choi (2019) proposes that PU had PU usually has a direct impact on usage attitude and usage behavior intention, and PEOU can inference PU and attitude toward using.Both PU and PEOU will affect consumers' attitudes toward using new technologies, and PEOU can further enhances PU of information technology.Rafique et al. (2020) proposes that PEOU will have a significant positive impact on PU.Consumers also need to be able to use technology according to their level of ability, and consider that PEOU is the determinant of consumers' adoption of technological innovation (Armstrong & Kotler, 2009).Based on these regards, though both AI PU and PEOU may influence the degree of adoption intention, PEOU will produce a more complex and more functional effect.In particular, AI PU may positively influence on customer's adoption intention, but it may differ with the impact of PEOU on customer's adoption intention.Based on these regards, we developed the following hypothesis: H 4 : The impact of AI PU on adoption intention is greater than AI PEOU on adoption intention.
AI PR and Adoption Intention
For most people, risk barriers usually have a negative effect on the user's intentions and behavior (Alshallaqi et al., 2022).Perceived risk is one of the important concepts for adopting or not adopting new and intangible products/services for adoption or non-adoption of a new and intangible product/service (e.g., Ma et al., 2020;Qiu et al., 2020).Individuals may not consider risky situation in decision making.In general, perceived risk is a powerful indicator commonly used to predict fear or an important barrier for consumers who were considering whether to make a purchase, and then it plays a key role in the decision-making process (Hussain et al., 2017).In-depth understanding of risk perception is an important factor in risk decision analysis Lopes et al. (2020) proposes that perceived risk should be used as the main predictor of consumer behavioral intentions.Perceived risk can usually be used to predict personal fears, and then to predict their possible avoidance behaviors.Hussain et al. (2017) proposes that perceived risk may affect the extent to which information is adopted through the quality of the argument.Han et al. (2019) focuses on electric airplane and suggests that reducing customers' perceived risk is critical to a positive attitude toward electric aircraft, which has significantly stimulated their adoption and willingness to pay.Based on these regards, higher level of perceived risks may reduce the AI consumer's overall adoption intention.Accordingly, we developed the following hypothesis: H 5 : AI PR is negative associate with adoption intention.
Empirical Research
To capture the nature of consumer behavior in AI market, the major purpose of this research is to evaluate the willingness to adopt artificial intelligence through the perspectives of integrated relationship marketing, artificial intelligence perceived usefulness, ease of use and risk.
The development of the questionnaire project is divided into the following stages.First of all, integrate previous research and theories to formulate key components related to artificial intelligence adoption intentions In order to integrate the structure of relationship marketing strategies in the artificial intelligence market, this research uses trust, commitment, PU, PEOU, PR, and adoption intention as the research structures.The previous research related to the research structure was reviewed to formulate the empirical measures for this research.Secondly, this research invited professors who are proficient in marketing research related issues and experts such as well-known corporate managers to participate in the selection of suitable projects.The questionnaire items have been revised based on the results of the pilot study before it is finally formed.Hair et al. (2019) proposes that items with factor loading less than 0.5 can be considered for removal.Accordingly results of pilot study, two items (i.e., AIPR03 and AIAI01) were deleted based on the principle of low factor loading.Then, participants asked to rate the relevance of each item to the research structure on the Likert seven-point scale, based on ''strongly disagree'' to ''strongly agree.''Regarding trust and commitment in relationship marketing, this study defines trust as the general expectation that consumers can rely on artificial intelligence providers, and commitment is defined as the degree of consumer's emotional attachment and identification with artificial intelligence providers.To measure trust and commitment in relationship marketing, this study mainly uses Akrout and Nagy (2018) and Hirshberg and Shoham (2017).Eight questions to determine trust and commitment with relationship marketing, such as I trust the product or service quality of AI.In addition, this research focuses on the artificial intelligence market and defines PU as the degree to which customers believe that the use of specific artificial intelligence will improve their performance, and PEOU is the degree to which customers believe that using artificial intelligence does not require effort.Eight items for PU and PEOU were adopted from Ben-Mansour (2016), such as I believe that using AI's production/service can improve my working effectiveness.According to previous research relating to the constructs of perceived risk (Han et al., 2019), this study defines perceived risk as an evaluation function of potentially uncertain negative outcomes of AI, and the sample item of questionnaire as: It is probable that AI's production/service would not be worth its cost.Based on TPB and TAM, the present study defines AI adoption intention as the degree of willing to adopt AI's production.Four items assessing were adopted from Bediako et al. (2018) and Singh and Verma (2017) to measure AI adoption intention.The sample questionnaire item as follows: I am willing to adopt AI's production/service.This study focuses on investigating the relationship among trust, commitment, PU, PEOU, risk, and adoption intention in AI market.AI has been widely used in multiple markets as a powerful technical tool.All the questionnaire items were translated from English to Chinese using a back-translation procedure suggested by Brislin (1980) with two bilingual professionals.
The population of this study are customers with AI's production/service consumption experience.Specifically, this study employs purposive sampling and uses an Internet-based questionnaires surveys (i.e., Google forms) based on anonymous approach and collect primary data in evaluating the applicability of this conceptual model.First of all, we send a link to the online questionnaire through an online platform (such as Line or facebook) to participants with experience (such as those who have used automatic driving systems, chat robots, AI voice assistants or smart homes, etc.) are asked to fill in the questionnaire anonymously.Second, the present research sends a reminder 3 weeks later, and then 1 month after the recipient agrees to participate.The present study firstly evaluate the characteristics of the respondents.In order to verify the dimensionality and reliability of the research structure, this study carried out a purification process, including factor analysis and internal consistency analysis (i.e., Cronbach a) have been conducted in this study.The main purpose of this research is to reveal the relationship between trust, commitment, PU, PEOU, PR, and willingness to adopt.
To evaluate the structure of the model, this study uses path analysis.For path analysis, this study uses the AMOS 22.0 system to evaluate the conceptual research model as a structural equation model (SEM).SEM is indeed one of the great and popular statistical analysis tools, and covariance-based SEM (i.e., CB-SEM) and variance-based partial lease squares (i.e., PLS-SEM) are the most widely used types.PLS-SEM is indeed an excellent and popular statistical analysis tool.However, several studies propose that compared to PLS-SEM, CB-SEM is better at providing model fit indices and unbiased estimation and is more suitable for factor-based models or for confirmation of established theory (Dash & Paul, 2021;Hair et al., 2017;S ˇisˇka, 2017).In order to discover the relationships within the whole research model of this study, covariance based SEM has be used.The AMOS 22.0 package software analyzes the relationships within the entire research model to discover the relationships among variables, such as trust, commitment, perceived usefulness, ease of use, risk, and adoption intention.The model fit indices have been adopted for this study including the CMIN/DF (Minimum value of discrepancy, C, divided by its degrees of freedom) is less than 3, goodness of fit index (GFI .0.9), the adjusted goodness of fit index (AGFI .0.9), the normed fit index (NFI .0.9), and the root mean square error of approximation (RMSEA \ 0.08) based on Hair et al. (2019).According to the results of path analysis, each hypothesis has been tested.
fsQCA has been generally accepted as a normative model of set theory connections, and has been widely used as a powerful analytical tool for the analysis of social science theories.According to user's guide of fsQCA (Ragin, 2017), this study explore the configurations for achieving high adoption intention of AI step by step, including transform ordinary data into fuzzy sets, conduct true table, recognize configurations, and interpresentation (see Figure 1).The first step is to transform ordinary data into fuzzy sets based on Ragin (2017).In order to transform antecedents (i.e., trust, commitment, PU, and PEOU) and adoption intention into fuzzy variables, it is necessary to calibrate these constructs.In this study, participants asked to rate the relevance of each item to the research structure on the Likert seven-point scale, and then sets original values of 1, 4, 7 from Likert seven-point scale to correspond to full non-membership (5%), cross-over anchors (50%), and full membership (95%), respectively.The second step is to identify a valid truth table by specifying the consistent cutoff value as 0.85 and the case number threshold as 1.Specify analysis and standard analysis are two for fsQCA, and Ragin (2017) recommended recommended that standard analysis is better than specify analysis, because standard analysis can generate ''intermediate'' solution.
Based on user's guide of fsQCA (Ragin, 2017), each standard analysis can generate parsimonious solution, intermediate solution, and complex solution.However, intermediate solution keep valid logical remainder and will not allow removal of necessary conditions.In other words, intermediate solution is better than complex solution and parsimonious solution.Based on these regards, this study provides the intermediate solution in the third step to identify causal configurations or sufficient conditions of adoption intention in AI market.
Results
To capture the nature of consumer behavior in AI market, this study contribute to explore relationships among relationship marketing, AI PU, PEOU, PR, and adoption intention of AI.This study employs Internet-based questionnaires surveys based on anonymous approach and collect primary data, and 235 valid samples were obtained from respondents with AI's production/service consumption experience between January 2021 and December 2021.For the main sample structure, most of the respondents are male (i.e., approximately 66%), married (i.e., than 73%), 36 to 45 years old (i.e., more than 65%), and had college education (i.e., more than 53%).The reliabilities and validities for the constructs are shown in Table 1.
Results of fsQCA indicate that there are three acceptable sufficient conditions (i.e., solution coverage .0.1 and solution consistency .0.6) that can lead to high adoption intention of AI (see Table 2).According to user's guide of fsQCA (Ragin, 2017), values of solution coverage and solution consistency in this study are 0.826 (more than 0.1) and 0.935 (more than 0.6), and these results identify these causal configurations explain a large proportion of adoption intention of AI.Path 1 signals a logical statement ''Trust*Commitment*AIPU*;AIPEOU'' (e.g., trust, commitment, AI perceived usefulness present but perceived ease of use and risk absent), and this sufficient condition shows that it can achieve high adoption intention of AI when the values of trust, commitment, and AI perceived usefulness are high with lower value of AI perceived ease of use (see Figure 2).Path 2 shows that trust and AI perceived usefulness present but commitment and perceived risk absent, and this sufficient condition indicates that when the values of trust, AI perceived usefulness are high with lower values of commitment and perceived risk, it can achieve high adoption intention of AI.Path 3 identifies that it can achieve high adoption intention of AI when the values of trust, AI PU, and AI PEOU are high with lower value of PR.
Discussion
This study contributions to identify relationships among relationship marketing, AI PU, PEOU, PR, and AI adoption intention from both symmetric thinking (i.e., SEM) and asymmetric thinking (i.e., fsQCA) in data analysis.With symmetric thinking approach, the present study uses SEM for path analysis, and then the impacts or interrelationships among research variables have be compared, and all five hypotheses are supported by path analysis of SEM.Both trust and commitments can enhance AIPU and AIPEOU, trust can further reduce AIPR, and then improve AI adoption intention.In particular, impacts of trust are greater than that of commitment, the impact of AIPU on adoption intention is greater than AIPEOU on adoption intention, and AIPR is negative associate with adoption intention.The majority of participants in this study were married males with 36 to 45 years old and had college degree.They may place greater emphasis on trust, perceived usefulness, and perceived risk due to social and economic conditions (i.e., culture of the country, economic situations, working conditions).Although most studies have been conducted on knowledge building of relationship marketing, theory of planned behavior (TPB) and technology acceptance model (TAM), almost rare of them have comparative effectiveness of trust, commitment, AIPU, and AIPEOU.Therefore, the contribution of this study is to extend knowledge by confirming that trust and AIPU are more influential than commitment and AIPEOU.With asymmetric thinking approach, this study focuses on using trust, commitment, AI PU, PEOU, PR as antecedents into causal recipes for achieving high adoption intention of AI.The sufficient conditions for fsQCA to produce results mainly based on the concept of Boolean algebra (Ragin, 2017).Accordingly, the present study further contributes to revisit sufficient conditions for high adoption intention of AI from intermediate solution of fsQCA.When there are k causal conditions, there will be have multidimensional vector space with 2 k rows representing logically possible combinations of causal conditions.Therefore, the initial truth table in this study has 32 (i.e., 2 5 ) rows in this study, and intermediate solutions can identify three sufficient conditions found to be sufficient for high adoption intention of AI.These results can provide decision makers with different strategic thinking.For instance, several studies in the fields of relationship marketing, TPB, or TAM highlight that low level commitment or AIPEOU may lead to negative consumer evaluation.However, path 1 shows that even if the company cannot improve AIPEOU in the short term, there is still a chance to enhance adoption intention of AI.Similarly, path 2 proposes that even if the company cannot improve commitment in the short term, as long as it can improve trust, AIPU, and reduce AIPR at the same time, it can still achieve a high degree of adoption intention of AI.These contributions extend the knowledge of relationship marketing, PTB, and TAM.
Conclusions
AI can be regarded as one of the important engines driving the progress of the times, and AI has been widely used as a powerful technical tool for developing products or services.Accordingly, the present study contributes to extend knowledge of relationship marketing to measurement of adoption intention via intermediary variables in AI market based on perspectives of symmetric and asymmetric in data analysis to derive several contributions.Specifically, results of SEM identify that impacts of trust on AIPU, AIPEOU, and AIPR are greater than commitment, impact of AIPU is also greater than AIPEOU on adoption intention of AI, and AIPR is negative associate with adoption intention.Accordingly, In the AI market, it seems that trust and AI perceived usefulness are more important.Furthermore, results of fsQCA can revist the three determinants of high AI adoption intention.Path 1 shows that even if the company cannot effectively improve AI perceived ease of use in the short term, it can also improve adoption intention of AI by strengthening trust, commitment, and AI perceived usefulness.Path 2 shows that improve trust, AI perceived usefulness, and reduce perceived risk can increase adoption intention of AI when level of commitment is not high.Path 3 identifies that whether the level of commitment is high or low, it can achieve high adoption intention of AI when the values of trust, AI PU, and PEOU are high with lower value of PR.
Theoretical Implications
The present study has made several contributions to the existing literature related to relationship marketing, TPB, and TAM.Firstly, the existing literature have focus on impacts of trust, commitment, PU, or PEOU on consumer behavior.Thus, the present study advances research that explore the effectiveness of trust, commitment, PU, or PEOU by comparing the impacts of them.As far as we know, fewer studies have explored these comparative relationships.Therefore, our findings support this relationship in a previously unstudied context when comparing effects between variables.Secondary, most of current researches generally only focused on the net effects among variables.The net effects estimation approach appears to be more difficult to identify the sufficient conditions of high level AI adoption intention.To fill this gap, this study further contributions to the knowledge of AI adoption intention by using asymmetric thinking in data analysis (i.e., fsQCA) to combine relevant antecedents (i.e., trust, commitment, AIPU, AIPEOU, and AIPR) into various causal recipes to identify three configurations for achieving high AI adoption intention.Set-based approach can further propose the effectiveness of trust, commitment, AIPU, AIPEOU, and AIPR, and provides opportunities or solutions when the dilemma (i.e., low levels of AIPEOU or commitment) cannot be changed in the short term.
Practical Implications
This research also makes some practical contributions to management practice, which can provide AI product or service providers with reference when making decisions.Firstly, trust and AIPU are more influential than commitment and AIPEOU, so managers or decision makers should focus more on developing strategies to strengthen trust and AIPU.For example, managers can consider establishing a quality assurance mechanism for AI products or services or provide more specific AI information to consumers.In addition, because lowering the AIPR can improve the AI adoption intention, managers can also provide subsidies or compensation programs when the production/service of artificial intelligence does not work properly.
Third, results of fsQCA provide opportunities for managers to comprehensively consider relevant antecedents (i.e., trust, commitment, AIPU, AIPEOU, and AIPR) into various causal recipes at the same time and explore solutions to dilemmas.Path 1 shows that it can also improve adoption intention of AI by strengthening trust, commitment, and AI perceived usefulness even if AIPR cannot effectively improved in the short term.For example, managers can consider simultaneous improvement in AI product or service quality, provide long-term assurance, or demonstrate effective improvement in performance.Path 2 imply that the solution to solve commitment is not high is to improve trust, AIPU, and AIPR at the same time.Accordingly, managers can consider to provide credible information, consumer experience, and establishing assurance mechanisms.Path 3 suggests that managers need to pay attention to trust, AIPU, AIPEOU, and AIPR at the same time.For instance, manager can consider to provide credible information, consumer experience, easy to use method, and establishing assurance mechanisms.
Limitations and Future Research
There are five major limitations in this study.The first limitation is the sampling process and period.The present study uses purposive sampling to collect empirical data through online questionnaires, and the questionnaire collection period is from January 2021 to December 2021.Based on this limitation, future research may be considered for conducting a couple years or longer period to analyze the effects of time series.International readers and organizational scientists may focus on effects over time or across cultures.Second, this study focused on understanding how consumer can achieve high adoption intention of artificial intelligence's production/service based on symmetric and asymmetric thinking in data analysis.Accordingly, future research may consider other causal conditions (e.g., innovation, brand, technology application ability, culture of the country, economic situations, working conditions, or other dimensions of CRM, etc.) or outcome variables (e.g., performance, loyalty, or repurchase intention).Third, AI PU, PEOU, and adoption intention are applied in the conceptual framework of this study based on TPB and TAM.Therefore, future research may use other will-known adoption models such as technologyorganizational-environment (TOE) or TAM2.Forth limitation of this study is that the method of collecting primary data is the application of online questionnaires.Accordingly, future research can consider using other methods to collect primary data or use secondary data.Finally, this study focused on using symmetric thinking (i.e., SEM) and asymmetric thinking (i.e., fsQCA) in data analysis, and future research can consider other methods of multivariate analysis (e.g., regression analysis or ANOVA) or qualitative research methods (such as the interview or the Delphi method).
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Figure 2 .
Figure 2. The sufficient conditions for high adoption intention of AI.
Table 1 .
Results of Factor, Reliability Analyses, and SEM.
Table 2 .
The Causal Configurations for High Adoption Intention of AI.Note.Black circles '''' indicate the presence of causal conditions (i.e., antecedents).White circles ''s'' indicate the absence or negation of causal conditions.The blank cells represent ''don't care'' conditions. | 9,070.6 | 2023-10-01T00:00:00.000 | [
"Business",
"Computer Science"
] |
A Beam-Specific Optimization Target Volume for Stereotactic Proton Pencil Beam Scanning Therapy for Locally Advanced Pancreatic Cancer
Purpose We investigate two margin-based schemes for optimization target volumes (OTV), both isotropic expansion (2 mm) and beam-specific OTV, to account for uncertainties due to the setup errors and range uncertainties in pancreatic stereotactic pencil beam scanning (PBS) proton therapy. Also, as 2-mm being one of the extreme sizes of margin, we also study whether the plan quality of 2-mm uniform expansion could be comparable to other plan schemes. Methods and Materials We developed 2 schemes for OTV: (1) a uniform expansion of 2 mm (OTV2mm) for setup uncertainty and (2) a water equivalent thickness–based, beam-specific expansion (OTVWET) on beam direction and 2 mm expansion laterally. Six LAPC patients were planned with a prescribed dose of 33 Gy (RBE) in 5 fractions. Robustness optimization (RO) plans on gross tumor volumes, with setup uncertainties of 2 mm and range uncertainties of 3.5%, were implemented as a benchmark. Results All 3 optimization schemes achieved decent target coverage with no significant difference. The OTV2mm plans show superior organ at risk (OAR) sparing, especially for proximal duodenum. However, OTV2mm plans demonstrate severe susceptibility to range and setup uncertainties with a passing rate of 19% of the plans meeting the goal of 95% volume covered by the prescribed dose. The proposed dose spread function analysis shows no significant difference. Conclusions The use of OTVWET mimics a union volume for all scenarios in robust optimization but saves optimization time noticeably. The beam-specific margin can be attractive to online adaptive stereotactic body proton therapy owing to the efficiency of the plan optimization.
Introduction
Pancreatic adenocarcinoma is one of the most lethal cancers and has a 5-year survival rate of less than 10%. 1 To improve the overall survival, there is increasing interest in exploring the hypofractionated regime of radiation therapy in treating local advanced pancreatic cancer.
Stereotactic body radiation therapy (SBRT) is one of the techniques allowing delivery of higher dose to target and steeper dose falloff to normal tissues in 3 to 5 fractions, thereby maximizing the therapeutic ratio. The alternative treatment options are to deliver an ablative dose in 15 to 28 fractions 2 for better local control. 2 Proton therapy has the clinical advantage of depositing the entire prescription dose to the target and yielding no exit dose. Therefore, proton therapy can potentially reduce the dose to normal tissues, resulting in ameliorated local control and decreased toxicities. The study by Thompson et al 3 shows that compared with conventional photon therapy, proton plans could significantly decrease the low and intermediate dose to critical organs (ie, duodenum, stomach and liver, etc), while maintaining the dose levels to target. Craneet al 2 show that proton therapy can reduce exposure to normal tissue compared with intensity-modulated radiation therapy with 10 -15 mm margin size from GTV to PTV for pancreatic head cancer. Bouchard et al 4 confirm this finding and claim it is feasible to boost the therapeutic ratio. Recently, Jethwa et al 5 implemented a dosimetric analysis between intensity modulated proton therapy (IMPT) plans and volumetric modulated arc therapy plans for localized intact pancreatic cancer, showing IMPT offers superiority to intensity-modulated radiation therapy in reduction of dose to OARs.
Combining the techniques of SBRT with proton therapy as an emerging novel technique is believed to further boost the gain of local control and minimize toxicity. 6 Sio et al 7 provided a systematic quantitative comparison between photon stereotactic body radiation therapy (SBRT) and proton stereotactic body proton therapy (SBPT), and the results suggest comparable organs at risk (OAR) sparing in the high-dose region and improved dosimetric sparing for low-and medium-dose regions.
To accurately deliver the prescribed proton dose to the target, one must incorporate setup and range uncertainties. Owing to the inherent uncertainty of conversion of computed tomography (CT) image to stopping power, a range uncertainty of 3.5% is often considered in treatment planning. 8−10 For instance, for margin-based treatment planning, a target volume used for optimization target volumes (OTV) iscreated from expansion from clinical target volume or gross tumor volumes (GTVs) . Sio et al 7 compared the plan quality of 3 mm, 5 mm, and 7 mm expansions for SBPT in pancreatic cancer. Thompson et al 3 used the expansion of 5 mm as photon therapy to produce OTV for proton pencil beam scanning (PBS). A beam-specific margins tehcnique is proposed to account for proton beam range uncertainties explicitly for by Park et al. 11 They tested this technique on prostate cases to demonstrate its superiority to the geometric margin used by Thompson et al 3 and Sio et al 7 for target coverage. However, the efficacy and robustness of this method on the abdominal case remain to be investigated.
Other than designing margins explicitly to account for uncertainties in proton therapy, a novel way of treatment planning that incorporates the uncertainty into the process of optimization was recently introduced, 12 namely robustness optimization (RO). It aims to achieve a robust dose distribution that is insensitive to setup and range uncertainties. The input parameters are determined based on the scenarios of estimated setup and range margins. For example, during the optimization process, to account for range uncertainties, the optimizer automatically expands the margin implicitly without specifying the OTV. 5,9 If an OAR is adjacent to the target, instead of placing the margins directly, the optimizer will place dose falloff to shape the dose distribution. 9 Although robust optimization outperforms margin-based methods in the robustness of target coverage, 13 a large number of error scenarios impose a huge computation burden on clinical implementation of robust optimizations.
The amount of setup-uncertainty margins used in margin-based planning or robustness optimization planning are often derived from imaging guidance (ie, stereoscopic, kilovoltage, 2-dimensional x-ray imaging). 5 With the help of 3-dimensional imaging guidance and surrogate fiducials implanted close to the lesion, the setup uncertainties can be further reduced. It is yet known how the reduction of setup margin can benefit the robustness optimization process of proton treatment planning for abdominal targets. To battle with the duodenum toxicity, a novel, absorbable iodinated polyethylene glycol−based hydrogel for tissue marking and spacing was studied to further increase the separation between panceas and duodenum. 14,15 The feasibility of incorporating this spacer into proton planning has not systematically investigated. As a first step, if the mere uncertaines other than range uncertainty are studied, it remains unclear whether the spacer can behave a "buffer" to help to reduce the duodenum toxicity, as in photon therapy.
We also investigated 2 margin-based optimization schemes, isotropic expansion and beam-specific OTV, to account for uncertainties associated with setup errors and range uncertainties in pancreatic stereotactic PBS proton therapy. The size of the expansion is inferred from the tolerance of the 3-dimensional cone-beam CT imaging guidance device used in our center. The robustness, target dose coverage, and OAR sparing of the plans generated by the 2 margin-based optimization schemes are quantitatively compared with plans using robustness optimization.
Methods and Materials
Six patients with clinically diagnosed, localized, advanced pancreatic adenocarcinoma who underwent SBRT active breath control technique were chosen in this planning study. All patients were positioned in supine with arms above the head under breath hold during the simulation.
The GTV, OAR, i.e. duodenum, small bowel, etc were contoured by physicians. GTV volumes ranged from 7.6 mL to 82.2 mL. The OARs, including duodenum, small intestine, stomach, kidneys, and spinal cord, were delineated. The CT images and structures were imported into Raystation 9A (RaySearch Laboratories AB, Stockholm, Sweden) for PBS proton treatment planning.
All patients were prescribed with a total dose of 33 Gy (RBE) in a treatment course of 5 fractions. The nominal goal of dose coverage of the GTVs should be 98% of volume receiving at least 100% of the prescribed dose (D98). More details can be found below for each optimization scheme. The OAR constraints include the volume of receiving 100% prescribed dose V 33Gy(RBE) < 1 cm 3 ; V 20 Gy(RBE) < 20 cm 3 and V 15 Gy (RBE) < 15 cm 3 in compliance with our institutional guidelines.
Beam configuration
The plans were designed to be delivered via PBS using the Hitachi Probeat-CR system equipped with volumetric imaging guidance of the cone-beam computed tomography system. Two posterior oblique fields at gantry of 210 and 150 degrees were used in the treatment planning for all patients except one, who was planned with a posterior (180) and posterior oblique beam (150) to reduce dose to the right kidney. The spot scanning pattern is set hexagonal. The spot size is decided by the optimization algorithm. The use of range shifter is determined on a patient-specific basis.
OTV definitions
Two OTV schemes were investigated. The first scheme is the OTV 2mm , which was designed in a fashion of geometric uniform 2-mm expansion around the GTV. With the help of cone-beam computed tomography and implanted fiducial markers, a tolerance of 2 mm was then used in the treatment planning process for the setup uncertainty. The second scheme is a patient-specific scheme (OTV WET ), proposed by Park et al 11 and based on water-equivalent thicknesses (WETs). Along the beam direction, distal and proximal WETs were determined based on the stoichiometric calibration method and converted to geometric margins by multiplying 3.5% added to GTV as the OTV WET . On the beam's eye-view directions, an expansion of 2 mm was used to account for lateral setup uncertainty.
Plan optimization
The OTV 2mm and OTV WET were used for the target dose coverages in the plan optimization. The homogeneous dose objectives (minimum, maximum, and uniform doses) were applied to the whole OTV 2mm, and 2 beam-specific OTV WET with equal dose weight. The OTV-optimized plans were compared with the robustness optimization (RO) method, which incorporates the setup and range uncertainties. In this study, a setup uncertainty of 2 mm and a range uncertainty of 3.5% on GTV were used in the RO optimization process. A total of 42 scenarios have to be computed to account for all possible uncertainties, including isocenter with no shifts, and shifted toward patient's anterior, posterior, right, left inferior directions, and diagonal directions (14 scenarios), each of which is with 3 scenarios of À3.5%, 0, +3.5% scaling of WET. The singlefield optimization was used for all plans to have the uniform dose distribution in target volumes from each field.
Plan evaluation
The target (GTV) dose coverage of the target volume (GTV) and the dose sparing of OARs were compared among 3 schemes for 6 patients. A Bonferroni-corrected t test was used to evaluate the statistical significance.
There is an agreement that plan robustness as a plan quality metric should be included. 16 Although there is no consensus on what exact scenarios should be included in the evaluation for robustness evaluation, 16 a separate exam of setup and range uncertainties were used. To evaluate the dose coverage of target under the various conditions of uncertainties, simultaneously 14 setup errors (in both parallel and diagonal directions) and 3 range uncertainties (including a nominal plan with no range uncertainty) with 42 totality of scenarios are examined. All plans aim to achieve at least 95% of the volume of the GTV receiving 100% of the prescribed dose.
The plan robustness could also be evaluated using the dose-volume histogram (DVH) deviation, "bandwidth," due to the perturbations of isocenter shift and range uncertainties for target and duodenum. A separate independent of 6 setup errors and 3.5% for an under and over range were analyzed. Of all the 8 scenarios, the bandwidth of DVH is defined as the standard deviation at specified dose parameters.
Because one of the most main critical structures duodenum, abuts tumor target, a quantity, termed as dose spread function, was proposed to describe dose falloff in the abutment region. In Fig. 1a, the spatial relationship between a typical 100% iso-dose line and duodenum is shown. A line dose profile can be sampled and shown in Fig. 1b. The dose profile can be obtained by fitting the sampled line dose. By differentiating the fitting line dose, the dose spread function (DSF) can be analytically obtained. Mathematically, this can be expressed as follows: Here r is the distance from either end of the dose line. LD refers to the line dose profile. Via DSF, the steepness of the dose falloff gradient, can be described quantitatively. For example, on Figure 1c, the FWHM is referring to the width needed to reduce 100% dose to 50%, whereas FW20M presents the width for the dose to drop from 100% to 20%. To show the practical use of DSF, the line dose, representing dose dropping from 100%, is chosen to cross the abutment region between 100% isodose to duodenum structure. The dose distribution, DVH and line dose profile were exported from Raystation TPS and analyzed by using in-house MATLAB tools.
Results
The derived OTV WET has a more substantial expansion: >2 mm from GTV due to targets being deep-seated in general. It is estimated that the geometric distance from the beam entrance to GTV distal is about 16 to 19 cm. Not like uniform expansion, OTV WET has less conformality to target due to the expansion for range uncertainties. This can be observed from one of the patients shown in Figure 2. The more expansion in the beam direction, the more degradation of dose conformality can be seen in Figure E1 a of the Supplementary Materials. Figure 3 a exemplifies the DVH similarities for target coverage among 3 plans for one of the patients. Table E1 in the Supplementary Materials summarizes the results of the planning comparison. DVHs of the GTV show that for D98, D max and D mean , these 3 plans have very similar coverage. As expected, no statistically significant differences among the plans were found for GTVs, except D98 for RO and OTV WET plans. A slightly larger D max can be found for the plan using robust optimization (RO plan). Figure 3b shows an example of dose sparing for critical OARs achieved by 3 plans. Due to a smaller margin than OTV WET , the OTV 2mm yields the best dose avoidance for duodenum in the high, medium, and low dose regions. In addition to the setup uncertainties of 2 mm, the RO plan also considers the range uncertainties explicitly, leading to the performance of dose sparing similar to the plan of OTV WET . However, in this case, the plan of OTV WET is the worst of sparing small bowel compared with the other 2. According to Table E1 in the Supplementary Materials, OTV 2mm plans show statistically significant in dose sparing of the duodenum and small bowel over OTV WET due to the smaller margin in OTV 2mm . The plans of OTV 2mm also outperform the RO plans in high dose region sparing for small bowel and stomach.
Among all the plans, the response of the nominal plans to perturbations may be plan scheme specific. For example, for target coverage in Figure 4, the compactness or bandwidth of D98 and D50 on DVH shows the least for RO plans. It demonstrates that the RO plans are more forgivable to the setup and range uncertainties as expected. The bandwidths of OTV 2mm and OTV WET are similar, mainly, for D50, the widths are 3.80% and 3.84% for OTV 2mm and OTV WET , respectively. In other words, the worst resultant target dose could be under-or overdose around 4%. The bandwidths at D98 for OTV 2mm and RO 4.8% and 2.8%, respectively. For this case, the loss of the plan quality due to the perturbation could be up to around 5% for OTV 2mm , while for RO plan, such loss could be around 3%. According to our plan objectives, the goal of the target coverage could be maintained.
The average passing rate of target coverage for all patient with the goal of 95% target covered by 100% prescribed dose is only 19% in OTV 2mm compared to 100% for OTV WET and RO. This result shows that OTV 2mm is not robust enough to offset the perturbation to the dose coverage. One example can be found in Figure 5, where an intentional isocenter shift posteriorly 2 mm and overranged by 3.5% are introduced. In this case, the target dose coverage (D95) can dramatically drop to 70%, leading to huge plan quality degradation.
The impact of perturbation on OAR (i.e. duodenum) could be revealed in the example case of Figure 6. The OTV WET (b) plan has the most significant bandwidth of medium-dose V 20Gy(RBE) among the 3 plans. In the high dose region, the use of OTV 2mm (a) has more advantages compared with the other plans in response to perturbation scenarios. Again, this is due to a smaller margin of plans of OTV 2mm . For the low dose region, 3 plans show similar performance. Table E2 in the Supplementary Materials summarizes the statistical significance of the resultant impact on the duodenum. For V 20Gy(RBE) , OTV 2mm plan shows the difference from the RO plans. No other significant difference was found among the 3 plans.
The DSF from the RO plan in Figure E2 in the Supplementary Materials shows slightly larger than the other 2, indicating that RO has a more gradual dose falloff region on this particular dose plane. In Table E3 in the Supplementary Materials OTV 2mm shows the fastest dose-off among all the patients and plans. For FW20M, the RO plans need about more than 2 mm space to reduce the dose to 20% of the prescribed.
Discussion
Designing an appropriate margin for treatment plan optimization in proton therapy is quite challenging. 9,10,16 Although accurate in delivery of high dose to target, the
Advances in Radiation Oncology: XX 2021
Optimization Target Volume for Proton Therapy proton beam is also sensitive to any variation along the beam path. Such variation could be due to change of anatomy, setup, and range uncertainties. 17 Thus, image guidance in proton therapy plays a crucial role in clinical to achieve the intended treatment plan dose distribution. The plan quality of OTV 2mm shows it not suitable for clinical use. Our motivation to attempt an aggressive 2 mm margin size in this study is rooted in 3 aspects. First, during the SBRT planning, a higher dose to the tumor while a relatively lower dose to the OARS is highly desired. SBRT is ideally suitable for tumors in parallel organs. The pancreas, however, is in close promity to serially functioning OARs (ie, duodenum, small bowel). The ablative BED dose around 106 Gy with current fractionation scheme to these OARs can produce impairment in the organ function. As such, limiting the OAR dose in LAPC SBPT has become increasingly crucial to the improvements in oncological endpoints. 18 A more aggressive reduction of margin size is an alternative approach to sparing more OARs dose.
Second, it is worth noting that OTV 2mm plan is sensitive to range uncertainties owing to its sufficient margin size to cover the uncertainty along the beam direction. One way to improve the robustness and maintain the low toxicity OTV 2mm to duodenum is to place hydrogel not only in the space between duodenum and pancreas, but also along the beam direction by any means. In other words, the function of hydrogel in proton therapy could be viewed as 2-folds: to reduce the toxicity and uncertainties.
Third, the geometric limit of combing fiducial markers and a developed real-time gated floruoscopy at our institution could be within 2 to 3 mm. 18−20 Therefore, as a motion management strategy, OTV 2mm as the extreme case of margin design is investigated, whereas this aggressive margin size is not realistic in current proton community.
In line with tolerance allowed by the 2-dimensional imaging device, various sizes of margins up to 5 mm or more expansions from clinical target volume or GTV for pancreas proton therapy have been implemented. 3,5,7,21 As for comparison with OTV 2mm , we implemented OTV 5mm plan study as well. The summary of all OTV 5mm plans is updated in Table E1 in Supplementary Materials. One of the patient plans has been shown in Figure 7.
It can be seen that target coverage (D98) is similar to Figure 4, but the overdose of duodenum could be up to 5 times compared with OTV 2mm . The evaluation of the Figure 5 Target dose of OTV 2mm (optimization target volume) from one of the patients shows vulnerability to simulated setup and range uncertainties. For one of the cases above, the D95 coverage of gross target volume has been degraded to <5% if simultaneous setup errors and range uncertainties exist, and 2 mm expansion fails to compensate the total errors. robustness shows that using a 5-mm margin size is immune to the perturbations of 2-mm setup errors and 3.5% range uncertainties. In this study, it is our expectation that with larger margin size, we are sacrificing OAR sparing for robustness. The robustness evaluation for OTV 5mm plans shows resiliency of the plans to the setup error of 2 mm and range uncertainties with passing rate close to 100%.
Owing to the combined uncertainties of both patient positioning and proton range, the construction of a beamspecific OTV is more appropriate. 22 In addition to the margin-based a priori method OTV WET , a robustness optimization that considers the range uncertainties and setup error without specifying the margins for optimization was proposed and implemented. 9,12 By minimizing the maximum of objective function for scenarios accounting for setup and range uncertanities, robustness optimization could yield plans that are resilient to the perturbation within the specification. Comparing the plans between OTV WET and RO in DSF, it was found that RO plans have less dose gradient in the beam direction. For the case shown herein, the dose falloff is roughly steeper for RO plan than OTV WET . As a result, when beams overshoot or undershoot, the dose distribution can be only moderately affected by shifting dose distribution as shown in Figure 8. In other words, RO plan can automatically extend the irradiated region distally along the beam direction to compensate the dosimetric perturbations introduced by range uncertainties. Meanwhile, RO plans can reshape the dose distribution accordingly. 9 The OTV WET plans predefine the margin with priori knowledge of range uncertainties and shift the dose distribution. 22 In the Figure 8c, this is demonstrated by a bare coverage of prescribed dose to GTV.
However, one disadvantage of this method is that it requires computation of all the scenarios to determine the maximum of the objective function. In other words, it could be rather time-consuming to minimize or optimize the objective function for a plan. For instances, using Monte Carlo optimization with the running time about 2 hours, while using beam-specfic OTVwet method, the computation time can be decreased to within a half hour. In the pipeline of online adaptive proton therapy, robustness optimization becomes clinically challenging. 23 Robustness optimization and margin-based plans achieve a similar target dose coverage in D98, D mean . In terms of OAR dose sparing of the duodenum, OTV 2mm outperforms the other types of plans owing to its smaller expansion. On the other hand, OTV WET plans show inferior to other plans owing to the relatively large expansion. However, the RO plans are robust to setup and range uncertainties without sacrificing the quality of the plans too much. The OTV 2mm plans fail most of the scenarios in the robustness evaluation owing to the plans that are extremely sensitive to the perturbations from range uncertainties. The OTV WET plans are insensitive to setup errors and range uncertainties for the beam arrangements used in the pancreatic patients. The dose spread function proposed in the study reveals that RO plans have less gradient of dose falloff at the specified location, indicating that more room between critical structure and 100% isodose line is needed to spare the duodenum in general. The OTV 2mm and OTV WET plans have only one scenario to compute, while the RO scheme has 21 scenarios. If the Monte Carlo dose engine was used, it is anticipated that the RO process would take even longer. 24 In summary, the quality of OTV WET plans falls in the category between OTV 2mm and RO; it has similar target dose coverage compared with the other 2 but has the inferior normal tissue sparing compared with OTV 2mm .
The OTV WET plan explicitly accounts for setup and range uncertainties; it is less susceptible to dosimetric perturbation. As indicated in the results, OTV WET plans have the degradation of quality in robustness evaluation, although the light computation is maintained. In general, the plan quality of OTV WET is closer to RO plans than that of OTV 2mm plans.
The proposed quantity DSF can correlate the spatial information of anatomical structure and dose distribution. The edge spread function (ie, dose profile) is used to quantify the dose-response at the edge of the critical structure. At the same time, DSF indicates the rate of dose falloff on the selected image with spatial and directional information. There are other useful tools to quantify the dose falloff behavior, 25 which may only focus on the distance between the isodose lines, not on the simultaneous effect of the anatomic specific and dosimetric performance. It is noted that recent studies from Rao et al 14,15,26−29 showcased a novel biodegradable hydrogel material injected at head-of-duodenum interface that can limit the dose to the duodenum. However, it is necessary to correlate the amount of injected hydrogel with the dosimetric consequence for each patient. By combining the information from DSF in a volumetric format on a patient-specific basis, the injection of the hydrogel can be optimized more accurately. This will remain in our future studies. In this study, the WET calculation is based on the stochiometric conversion from single-energy CT images, which is believed to introduce 3.5% uncertainties. 8,30 To further improve the dose sparing, a possible method is to incorporate dual-energy CT images into this study. It is accepted that the DECT technique can decrease the range uncertainty from 3.5% to 2%. 31−37 To the authors' best knowledge, this study is the first one to compare the 2 types of proton treatment planning techniques for pancreas cancer: margin-based versus robustness optimization. However, this study has several limitations. First, the optimization of beam angle selection is not implemented, as it shows an essential role in the quality of the plans. 22 Second, the dose falloff region of interest is selected at the abutment of 100% isodose line and duodenum. The choice of this region could be optimized in future investigation. 38
Conclusions
We evaluated the plan quality among 3 optimization schemes using uniform expandsion OTV 2mm , beam-specific OTV WET , and robustness optimization on GTV. Although the margin-based method (OTV 2mm ) provides superiority in fast computation and low toxicity, the quality of plans fails to match the ones from robustness optimization in the evaluation of susceptibility to perturbation. A beam-specific margin also remains further investigations for online adaptive stereotactic body proton therapy owing to the efficiency of the plan optimization. | 6,342 | 2021-07-29T00:00:00.000 | [
"Medicine",
"Physics"
] |
GIT proteins, A novel family of phosphatidylinositol 3,4, 5-trisphosphate-stimulated GTPase-activating proteins for ARF6.
ADP-ribosylation factor (ARF) proteins are key players in numerous vesicular trafficking events ranging from the formation and fusion of vesicles in the Golgi apparatus to exocytosis and endocytosis. To complete their GTPase cycle, ARFs require a guanine nucleotide-exchange protein to catalyze replacement of GDP by GTP and a GTPase-activating protein (GAP) to accelerate hydrolysis of bound GTP. Recently numerous guanine nucleotide-exchange proteins and GAP proteins have been identified and partially characterized. Every ARF GAP protein identified to date contains a characteristic zinc finger motif. GIT1 and GIT2, two members of a new family of G protein-coupled receptor kinase-interacting proteins, also contain a putative zinc finger motif and display ARF GAP activity. Truncation of the amino-terminal region containing the zinc finger motif prevented GAP activity of GIT1. One zinc molecule was found associated per molecule of purified recombinant ARF-GAP1, GIT1, and GIT2 proteins, suggesting the zinc finger motifs of ARF GAPs are functional and should play an important role in their GAP activity. Unlike ARF-GAP1, GIT1 and GIT2 stimulate hydrolysis of GTP bound to ARF6. Accordingly we found that the phospholipid dependence of the GAP activity of ARF-GAP1 and GIT proteins was quite different, as the GIT proteins are stimulated by phosphatidylinositol 3,4, 5-trisphosphate whereas ARF-GAP1 is stimulated by phosphatidylinositol 4,5-bisphosphate and diacylglycerol. These results suggest that although the mechanism of GTP hydrolysis is probably very similar in these two families of ARF GAPs, GIT proteins might specifically regulate the activity of ARF6 in cells in coordination with phosphatidylinositol 3-kinase signaling pathways.
ankyrin repeats, and a carboxyl-terminal GRK interaction domain. One major splice variant of GIT2, termed GIT2-short, lacks the carboxyl-terminal GRK interaction domain (35). Overexpression of GIT1 leads to reduced  2 -adrenergic receptor signaling and increased receptor phosphorylation, which appear to result from reduced receptor internalization and resensitization (11). These cellular effects of GIT1 require an intact ARF GAP activity, suggesting a critical role of the coupling of GIT1 and ARF in  2 -adrenergic receptor endocytosis.
Both ASAP1/DEF-1 and PAP/KIAA0400 were identified through interactions with known proteins, the Src and Pyk2 kinases, respectively (13,14). They share a similar organization, with a PH domain, central ARF GAP-like putative zinc finger domain, multiple ankyrin repeats, and a carboxyl-terminal SH3 domain. Both were active as GAPs for ARF1 and ARF5, but poor GAPs for ARF6, and both were activated by PIP 2 (13,14). PAP was localized to the Golgi complex and the plasma membrane and shown to prevent the ARF-dependent generation of post-Golgi vesicles, in vitro (14), whereas ASAP1/ DEF-1 promoted the differentiation of fibroblasts into adipocytes (15). To understand the similarities and differences among ARF GAP proteins, we compared the zinc binding, ARF GAP activity, ARF family specificity, and lipid regulation of GIT1 and GIT2 to those of ARF-GAP1.
EXPERIMENTAL PROCEDURES
Materials-TLC plates were purchased from VWR Scientific and lipids from Sigma. Sources of other materials have been published (11, 16 -18).
Preparation of Recombinant ARF Proteins-For large-scale production of recombinant ARF proteins, 10 ml of overnight culture of the appropriate transformed bacteria were added to a flask with 500 ml of LB broth and ampicillin, 50 g/ml, followed by incubation at 37°C with shaking. When the culture reached an A 600 of 0.6, 250 l of 1 M isopropyl--D-thiogalactopyranoside was added (0.5 mM isopropyl--D-thiogalactopyranoside final concentration). After incubation for an additional 3 h, bacteria were collected by centrifugation (Sorvall GSA, 6000 rpm, 4°C, 10 min), and stored at Ϫ20°C. Bacterial pellets were dispersed in 5 ml of cold phosphate-buffered saline, pH 7.4, with trypsin inhibitor (20 g/ml), leupeptin and aprotinin (each 5 g/ml), and 0.5 mM phenylmethylsulfonyl fluoride. Lysozyme (10 mg in 5 ml) was added. After 30 min at 4°C, cells were disrupted by sonication and centrifuged (Sorvall SS34, 16,000 rpm, 4°C, 20 min). The supernatant was applied to a column (2.5 ϫ 100 cm) of Ultrogel AcA 54 equilibrated and eluted with TENDS buffer (20 mM Tris-HCl, pH 8.0, 1 mM EDTA, 100 mM NaCl, 2 mM DTT, 250 mM sucrose, 5 mM MgCl 2 , 1 mM NaN 3 ). Fractions that had both high ARF activity and high purity were pooled and further purified on a column (1.5 ϫ 40 cm) of DEAE, eluted with a linear gradient of 50 to 500 mM NaCl (0.6-ml fractions), and by gel filtration on Ultrogel AcA 34 (1.5 ϫ 30 cm) before storage in small portions at Ϫ20°C. For large-scale production of recombinant myristoylated ARF proteins, expression was induced in bacteria containing the N-myristoyltransferase gene, in the presence of 0.5 M myristic acid and 0.06 M bovine serum albumin as described by Franco et al. (19). Myristoylated ARF6 was purified by hydrophobic interaction HPLC on a TSKgel Phenyl-5PW column (Supelco, Belfonte, PA) using the method described by Randazzo (4). A single protein peak eluted in the decreasing salt gradient and was shown to stimulate cholera toxin-catalyzed ADP-ribosylation.
Construction and Expression of GAP Proteins-Rat GIT1/6xHis, ⌬45GIT1/6xHis were purified from baculovirus-infected Sf9 cells as described previously (11), using nickel affinity and ion exchange chromatography. The human GIT2-short/6xHis (35) was transferred into the pVL1393 shuttle vector, and used to prepare recombinant baculoviruses by recombination in Sf9 cells with Baculo-Gold virus DNA (Pharmingen). The GIT2-short/6xHis protein was purified from infected Sf9 cells using ProBond metal chelate resin (Invitrogen) batchwise, followed by chromatography on a HiTrap-Q column (Amersham Pharmacia Biotech), as described for GIT1/6xHis (11). Full-length rat ARF- and myristoylated ARF6 (lane 9) were purified from Escherichia coli containing a plasmid coding for the N-myristoyl transferase. Five g of each GAP and 2.5 g of each deleted GAP or ARF was separated by SDS-polyacrylamide gel electrophoresis in a 10% gel and stained with Coomassie Blue. Position of molecular size markers is on the left. A doublet pattern for purified GIT2-short and ARF-GAP1 is often seen and likely reflects post-translational modification. GAP1 cDNA (5) was amplified from a rat brain cDNA library and subcloned into a modified pBK-CMV vector (Stratagene) using EcoRI and XhoI. The entire cDNA was then re-amplified using an antisense primer that inserted a 6xHis tag immediately before the stop codon, and subcloned as before into pBK-CMV. The pBK-⌬45ARF-GAP1 construct was prepared by amplification using a 5Ј-primer that adds an initiator Met codon immediately before codon 46. All constructs were sequenced on both strands from specific primers by using automated dye terminator chemistry with AmpliTaq FS reagents (Applied Biosystems) and an ABI 377 instrument. The ARF-GAP1/6xHis and ⌬45ARF-GAP1/ 6xHis cDNAs were subcloned into the EcoRI and XhoI sites of the pVL1392 recombination vector (Pharmingen), which was used to prepare a recombinant baculovirus using Baculo-Gold virus DNA (Pharmingen). The ARF-GAP1/6xHis and ⌬45ARF-GAP1/6xHis proteins were purified from the soluble extract of infected Sf9 cells using nickel affinity and ion exchange chromatography, essentially as described for GIT1/6xHis (11).
Assay of GTPase Activity-The indicated amounts of ARF were incubated for 30 min at 30°C in 20 mM Tris, pH 8.0, 10 mM DTT, 2.5 mM EDTA with bovine serum albumin, 0.3 mg/ml, and phosphatidylserine (PS), 30 g/ml (160 M), with 0.5 M [␣-32 P]GTP (3000 Ci/mmol) and 10 mM MgCl 2 . 10-l samples were incubated at 30°C for 5 to 30 min, with the indicated amounts of GAP protein or an equal volume of buffer (total volume 50 l), in the presence of the indicated phospholipids ( Fig. 3), before proteins with bound nucleotides were collected on nitrocellulose by vacuum filtration (18). Bound nucleotides were eluted in 250 l of 2 M formic acid, of which 3-4-l samples were analyzed by TLC on polyethyleneimine-cellulose plates developed with 1 M formic acid, 1 M LiCl. TLC plates were subjected to autoradiography at Ϫ80°C for 18 -36 h. The remaining solution was used to quantify the total amount of nucleotide bound in the assay (GDP plus GTP) by scintillation counting. The absolute quantities of GTP and GDP, with or without incubation with GAP protein, were calculated by multiplying the total bound nucleotide by the fraction determined to be GTP or GDP by TLC. As shown previously (4,10,20), in most assays the concentration of ARF-GTP was much less than the K m . Under these conditions, substrate is consumed at a first-order rate equal to V max /K m . This rate was meas-
RESULTS AND DISCUSSION
We have previously shown that GIT1 and GIT2, of which both exhibit the conserved putative zinc finger motif found in the ARF-GAP1 protein, stimulated hydrolysis of GTP bound to ARF1, without themselves binding GTP or acting as a nucleotide releaser for ARF1 (11,35). ARF-GAP1 is to date the best characterized GAP for ARFs. We compared the respective activities of purified recombinant, 6xHis-tagged ARF-GAP1, GIT1, and GIT2-short proteins (Fig. 1). Confirming our previous observations (11,35), GIT1 and GIT2 stimulated GTP hydrolysis by ARF1. The rate of hydrolysis of GTP bound to ARF1 induced by GIT1 and GIT2 was comparable to the rate of hydrolysis induced by ARF-GAP1 (Fig. 2A). The activities of , or amino-terminal deleted ARF GAPs for 10 min at 30°C before stimulation of cholera toxin-catalyzed ADP-ribosylagmatine formation was assayed for 60 min at 30°C. ARF activity is the difference between CTA-catalyzed formation of [ 14 C]ADPribosylagmatine without and with ARF1 protein (nanomole/h). Data are mean Ϯ one-half the range of values quadruplicate assays. These findings were replicated twice with two independent preparations of proteins. GIT1, GIT2, and ARF-GAP1 were constant for at least 20 min before slightly slowing down ( Fig. 2A), so for further assays we used 10-min incubations. In addition, the assays appeared linear until nearly 50% of the added GTP-bound ARF substrate was converted to GDP-bound ARF. GIT1, GIT2, and ARF-GAP1 stimulated hydrolysis of GTP bound to ARF1 in a concentration-dependent manner (Fig. 2, B and C). GIT1 was slightly more potent than ARF-GAP1 and GIT2-short was the least potent GAP (Fig. 2C). These results suggest that the intrinsic GAP activity of GIT1, GIT2, and ARF-GAP1 is very similar in the absence of additional cofactors.
Phospholipids seem to play a critical role in the control of ARF activities by ARF regulatory proteins. It was concluded that the effect of phospholipids on ARF GAP activity was to increase the GAP concentration at the membrane where GTPbound ARF resides (8). Investigations with ARF-GAP1 have shown that it is indeed stimulated by PIP 2 and dioleylglycerol (4,8), but the phospholipid dependence of GIT proteins has not been explored. We compared the effects of PIP, PIP 2 , and PIP 3 on the GAP activity of GIT1, GIT2-short, and ARF-GAP1. Confirming previous observations (4,5,20), 200 M PIP 2 dramatically stimulated the GAP activity of ARF-GAP1 from 0.64 to 2.46 nmol/min/mg, but not that of GIT1 (from 0.88 to 0.91 nmol/min/mg) or GIT2 (0.56 to 0.65 nmol/min/mg) (Fig. 3). On the other hand, 200 M PIP 3 significantly increased the hydrolysis of GTP bound to ARF1 induced by GIT1 (0.82 to 2.56 nmol/min/mg) and GIT2 (0.56 to 1.01 nmol/min/mg) but not by ARF-GAP1 (0.64 to 0.87 nmol/min/mg) (Fig. 3). PIP did not increase GTP hydrolysis by any of the ARF GAPs tested here (Fig. 3). Because dioleylglycerol, produced mainly from phos-phatidylcholine hydrolysis by phospholipase D (an effector of ARF), dramatically increased the activity of a recombinant fragment of ARF-GAP1, it was suggested that phospholipase D activity could be a major regulator of ARF GAPs (8). Dioleylglycerol had similar effects on Gcs1, an analogous ARF GAP from yeast (9). We confirm that DAG (C18:1-(3)C18:1) stimulated the GTPase activity of ARF-GAP1, but no effect on the activity of GIT1 or GIT2 was found (Fig. 3). The ARF GAPs that are activated by PIP 2 or other phosphoinositides are presumably subject to diverse kinds of regulation. From these results it seems plausible that GIT proteins and ARF-GAP1 are involved in distinct signaling pathways, which is also suggested by their distinct cellular localization. Centaurin-␣ has been described to be a potential PIP 3 -binding protein with similarity to ARF GAPs that could complement a yeast strain deficient in the yeast ARF GAP Gcs1 (21), suggesting that several ARF GAPs could be regulated by PIP 3 . In many cell types, the agonist-stimulated PI 3-kinase utilizes predominantly PIP 2 as a substrate to generate PIP 3 (22,23). The ratio of PIP 2 and PIP 3 seems to play a critical role in many aspects of vesicular trafficking (24). It will now be of particular interest to know if signaling pathways involving PI 3-kinases or other enzymes involved in the synthesis or hydrolysis of PIP 3 may contribute to intracellular regulation of GIT proteins.
It was demonstrated that the amino-terminal GATA-like zinc finger motif of ARF-GAP1 (5) and ARD1, an ARF-related protein that has an amino-terminal GAP domain (18), are critical for GTP hydrolysis. In the presence of GTP or a nonhydrolyzable analogue, all members of the ARF family serve as allosteric activators of cholera toxin (CTA) ADP-ribosyltransferase (25). As expected, addition of ARF-GAP1 and GIT1 reduced the ability of ARF1 to activate CTA in the presence of GTP, but not GTP␥S (Fig. 4). This result confirms that GIT1, like ARF-GAP1, influences the biological activity of ARF1 by promoting GTP hydrolysis. Deletion of 45 amino acids from the amino terminus of GIT1 or ARF-GAP1 (containing the conserved zinc finger motif) completely prevented inhibition of ARF-induced CTA activation (Fig. 4), suggesting that the zinc finger motif is required for GAP activity of both proteins. We can exclude that this loss of activity results from complete misfolding of the ⌬45GIT1 protein, because several additional GIT interacting proteins (GRK2, PIX, paxillin) do bind normally to ⌬45-GIT1 in co-immunoprecipitation assays.
TABLE I Zinc content of ARF GAPs assessed by inductively-coupled plasma emission spectroscopy
The indicated amounts of Hi-Trap-Q chromatography purified Histagged ARF-GAP1 (GAP1), GIT1, and GIT2-short proteins were analyzed for metal ions by inductively-coupled plasma emission spectroscopy. The detection limit for zinc was 0.1 g/ml. No significant amounts of the other metal ions were found in any samples, except for Na ϩ from the buffer and Ca 2ϩ in single samples of ARF-GAP1 and GIT2-short. Members of the ARF GAP family identified to date share a conserved domain containing a CX 2 CX 16 CX 2 C putative zinc finger (5,11,13,14). To investigate whether ARF GAP proteins actually bind to a metal through this domain, we subjected three purified ARF GAP proteins to plasma emission spectroscopy, a sensitive technique that allows for the simultaneous detection of over 20 metal ions (Table I). For each of the three ARF GAP proteins analyzed, the only metal ions detected over background were zinc and sodium (from the NaCl buffer), except for one instance, when significant calcium was also detected in ARF-GAP1/6xHis and GIT2-short/6xHis. The nanomole of zinc detected was similar to the nanomole of protein analyzed for each ARF GAP, consistent with a near one-to-one complex of zinc with protein. Recent publication of the crystal structure of the ARF-GAP1 protein amino-terminal domain bound to ARF1 reveals that one zinc ion is indeed bound by the four conserved cysteine residues of the ARF GAP domain (26). Interestingly, the metal ion does not contact the ARF protein, but appears to play a role in determining the overall structure of the GAP domain (26). Mutation of single cysteine residues within this zinc finger abrogated GAP activity of ARF-GAP1 (5) and ARD1 (18), presumably because such mutants could not bind zinc. As GIT1 and GIT2 also appear to bind zinc, we predict that zinc chelation by this CX 2 CX 16 CX 2 C motif is a common feature of ARF GAP proteins. The effect of removing the zinc to form the cognate apoproteins, or of replacing it with similar metal ions, remains unexplored. It is now well established that RasGAPs and RhoGAPs share a common mechanism of the GTPase-rate enhancement involving a critical arginine residue (27,28). A putative arginine finger motif has also been postulated within the zinc finger region in ARF-GAP1 (29) and this specific arginine residue is present also in GIT1 and GIT2. Recently, data from the crystal structure of the ARF1⅐ARF-GAP1 complex suggested that the postulated arginine in ARF-GAP1 did not make contact with the active site of the GTPase (26). The function of this conserved arginine residue in ARF GAPs remains to be established.
We tested further the GAP activities of GIT1, GIT2-short, and ARF-GAP1 on different members of the ARF family. ARF-GAP1 stimulated hydrolysis of GTP bound to ARF1, ARF2, ARF3, and ARF5, but not to ARF6 (Fig. 5A), confirming previous observations that this GAP affects the class I and class II, but not class III ARFs (4). On the other hand, GIT1 and GIT2 promoted GTP hydrolysis by all five ARFs tested (Fig. 5A). Neither ARL1 nor ARL2, members of the ARF-like family, nor ARD1, the ARF-related protein with its intrinsic GAP domain, were substrates of GIT1, GIT2, or ARF-GAP1 (Fig. 5A). Over a range of GAP concentrations where the two GIT proteins were quite active, ARF-GAP1 failed to accelerate the GTPase activity of ARF6 (Fig. 5B). These results suggest that ARF-GAP1 and GIT proteins are indeed specific GAPs for ARF proteins. More importantly, they indicate that unlike ARF-GAP1, both GIT1 and GIT2 can stimulate the efficient hydrolysis of GTP bound to ARF6.
Native ARF proteins in the cell are myristoylated on their amino termini, while the bacterially expressed recombinant ARF proteins used in the preceding assays in this study are not. The effect of myristoylation of ARF on the GAP activity of GIT1, GIT2-short, and ARF-GAP1 was also tested. No significant difference in GAP activities was detected whether or not ARF1 or ARF6 were myristoylated (Fig. 6A). These results are in agreement with previous observations made with a different ARF GAP activity purified from rat spleen (10). It is notable that myristoylated ARF6, the form found in cells, was a particularly good substrate for GIT1 and GIT2 compared with ARF-GAP1 (Fig. 6B).
Of all ARF GAP proteins characterized to date, the GIT proteins appear to be the best GAPs for ARF6, a type III ARF with several unusual features including a predominantly plasma membrane localization. ARF6 also has been localized on endosomes (30,31) and on secretory granules (32), where it is believed to participate in endocytotic and exocytotic trafficking events. Interestingly, GIT proteins were identified in a yeast two-hybrid screen through their ability to interact with GRK2. Overexpression of GIT1 leads to increased receptor phosphorylation and reduced  2 -adrenergic signaling, resulting from attenuated receptor internalization and resensitization (11). These cellular effects do not reflect regulation of GRK kinase activity, but require an intact amino terminus, suggesting a function for ARF in regulating  2 -adrenergic receptor endocytosis (11). The involvement of ARF6 in this specific recycling pathway will now have to be investigated.
In addition to their role as ARF GAPs, GIT proteins also appear to have other important cellular functions. A two-hybrid screen with GIT1 identified an interaction with -PIX, a putative rac1/cdc42 guanine nucleotide-exchange factor that binds the rac1/cdc42-activated PAK kinases (35). Both GIT1 and GIT2 interact with ␣and -PIX proteins, in a multiprotein complex which also contains p21-activated kinase (PAK) (35). Bagrodia et al. (33), starting with PAK kinase, recently identified the GIT⅐PIX⅐PAK complex, as did Turner et al. (34), who additionally discovered the interaction of a distinct third GIT family member (p95-PKL) with paxillin. Together, these studies document a role for GIT proteins in anchoring the PIX-PAK complex, via paxillin, in cellular focal adhesions. These results suggest that the multidomain proteins of the GIT family could be at the cross-roads of several signal transduction pathways involving multiple small GTPases in vesicular trafficking and cytoskeletal remodeling. | 4,569.6 | 2000-05-05T00:00:00.000 | [
"Biology",
"Computer Science"
] |
An approach for reducing the air conditioning costs in office buildings in Vietnam
. According to statistics from the Ho Chi Minh Energy Saving Center, the electricity costs of the air conditioning system for office buildings are about 70% of the electricity costs. There are many solutions that have been proposed to reduce the operating costs of the air conditioning systems, this article discusses a method of accumulating cold to reduce the cost of electricity for the air conditioning system of an office building.
Introduction
Nowadays, the consumption of electricity for an air conditioning system in an office building is one of the most important issues not only for the owners but also for the electricity suppliers. The cooling needs of the building are not constant, and the price of electricity at different times of the day also has a different value. There is a lot of research on saving electricity costs by different methods. One approach to reducing air conditioning costs is to reduce energy consumption by applying the active cooling method [1]. Another approach is the accumulation of cold. The accumulation of cold is used not only to save on electricity costs but is also used for other purposes. According to the research of D. Shlichkov [2], a chilling system with a storage tank, in which the ice freezes on the outer surface of the heat exchange tubes of the evaporator, leads to a significant reduction in electricity costs for air conditioning systems. The combined method between cold accumulators and cryocoolers has been considered by Arkhipov et al [3] in order to increase the life of the cryogenic cooling system. According to R. Sekret et al [4], the cold accumulator is applied by using the latent heat of a phase-change material in a layer of capsules with diameters of 80 mm, 70 mm, and 60 mm, the optimal working conditions according to the study are when using capsules with a diameter of 70 mm and a mass flow rate of 0.084 kg/s. In Vietnam, a study by Nguyen The Bao [5] also mentioned the melting of ice outside the pipes used in the cold storage battery in air conditioning systems.
In Vietnam, as in other countries, consumption in the national electricity grid for one day is not stable (Figure 1), so the Vietnamese Electricity Company (EVN) sets three prices to stimulate the reduction of electricity consumption during the main peak periods and to encourage the use of electricity in the low hours. According to EVN, the price of electricity at the peak hours is 4,586 VND/kWh (19.80 $cent/kWh), in normal hours the price is 2,666 VND/kWh (11.51 $cent/kWh) and in the low hours the price is 1,662 VND/kWh (7.18 $cent/kWh). The peak hours are during the intervals 10:00 ÷ 12:00 and 17:00 ÷ 20:00. The normal hours are in the intervals 4:00 ÷ 10:00, 12:00 ÷ 17:00 and 20:00 ÷ 22:00. The low hours are in 22:00 ÷ 4:00.
An opportunity for savings arises if at night, when the price of electricity is lowest, the cooling system works and the produced cold accumulates, and in other periods, when the price is higher, this accumulated cold is used to cool a building. The accumulation of cold not only reduces the electricity costs of the air conditioning system but also stabilizes the national electricity grid. Ho Chi Minh City is an economic and commercial centre not only in Vietnam but also in Southeast Asia and is known for its large number of large office buildings. These buildings do not work at night (when the price of electricity is lowest), which is why an office building was chosen as the subject of this study.
Modelling office building and conditioning system
The pilot building is an office building, located in Ho Chi Minh City. It has 3 basements for parking, 22 floors for offices and total area of 19,800 m 2 . The mode of operation of the building is only on weekdays, from 7:00 to 17:00. The air conditioning system is designed according to Vietnamese norms. The designed indoor temperature and relative humidity are t = 26 o C, = 65%.
The cooling load of the building is calculated by the Carrier method, according to which the total heat load is calculated by: 11 21 22 23 31 32 where: • : Total sensible heat load of the building, kW; • : Total latent heat load of the building, kW; • Q 11 : Heat from solar radiation through the transparent area, kW; • Q 21 , Q 23 : Heat transfer through the roof and through the floor, kW; • Q 22 : Heat transfer through the walls, doors and windows, kW; • Q 31 , Q 32 : Heat from lighting systems and from equipment, kW; • Q 4h , Q 4a : Sensible and latent heat of people, kW; • Q Nh , Q Na : Sensible and latent heat of fresh air, kW; • Q 5h , Q 5a : Sensible and latent heat of infiltration air, kW. The cooling load of the building is Q o = 3128 kW (894 tons of refrigeration). The air conditioning system is designed with 3 chillers Model RTHD -D2G2G1 (RTHD 300 -350 Tons -built for Industrial and Commercial Application), with Refrigerant R134a.
The cold accumulation systems
Currently, there are many cold accumulation technologies and schemes, divided of two groups: -Sensible cold accumulation storage; -Latent cold accumulation storage (ice cold storage, eutectic salt cold storage and etc.).
In this study, Christopia's technology was chosen to represent the second group. Cristopia technology offers the accumulation of cold in phase-change materials. The phase change temperature (-33°C → 27°C) can be selected according to the user's needs (Table 1).
Cristopia's technology
With this technology, the phase change material is contained in nodules with structure ( Figure 2) as follows: -A sphere one millimetre thick, obtained by blow moldings of a blend of polyolefins. This material is neutral towards the heat transfer fluids; -Phase Change Material (PCM) [9]. It could be organic (paraffin and fatty acids for example) or inorganic (hydrated salts), depending on temperature; -Air pocket for expansion, the effect is a low stress on the nodule shell; -Plug. The cold accumulation tank (STL -le stockage latent in French [10], or STorage of Latent heat) is made of steel or concrete and is well thermally insulated. The heat exchange between the spherical nodules and the system is by a liquid, in this case water. The tank can be horizontal or vertical (Figure 3).
Principle of operation of the cold accumulation system
The principle of operation can be represented by five operating modes of the system.
-STL charging: At hours when the price of electricity is the lowest and there is no cooling load, the chillers work and the produced cold accumulates as the energy of the phase change (from liquid to solid phase) of the substance in spherical nodules (Figure 4.a).
-The chillers work for building's cooling needs: In off-peak hours, the chillers work for air conditioning system and there is no flow through the STL (Figure 4.b). -STL discharging: At peak hours, when the price of electricity is highest, the chillers do not work and the air conditioning system uses accumulated cold from STL ( Figure 5.a).
-In case of overload of the air conditioning system or some of chillers are damaged: STL can also be used when the air conditioning system is overloaded or some of chillers are damaged, to share cooling power ( Figure 5.b). -The chillers work for cooling needs and charge the STL (Figure 6).
Analysis of the options for cold accumulation
Principle of operation: The STL system accumulates a sufficient amount of cold in hours when the price of electricity is the lowest. This accumulated cold will satisfy 100% of the required cold at peak hours and part of the required cold at normal hours.
Three steps to determine electricity costs: -Step 1: Calculation of the cooling load of the building for each hour according to the Carrier method with the climatic data of Ho Chi Minh City. The climatic data includes the hourly values of temperature, relative humidity and solar radiation on horizontal and 8 vertical surfaces [11]. The temperature and relative humidity could be seen below ( Figure 7). where: • Q 0 -Cooling capacity of chiller, kW; • N 1 -Electric power of chiller, kW; • N 2 -Electric power of the pump for the first circulation circuit, kW; • N 3 -Electric power of the pump for the second circulation circuit, kW; • N 4 -Electric power of the cooling tower fans, kW; • N 5 -Electric power of fans in AHU and FCU, kW; • N 6 -Electric power of fresh air fans, kW.
-Step 3: According to the calculated electricity consumption for each hour of a typical day of the month from January to December, the annual saved electricity costs can be calculated using the following options: Option 1: The accumulated cold in STL is used only during the peak hours. In other periods, the cooling load is provided by the chiller system. Option 2÷7: The total consumption of cold at peak hours and 10% to 60% of the cooling demand at normal hours are provided by STL. The calculation for Option 1 for January is shown below in Table 2, the same calculations are made for each month. Summarizing the results for all months leads to a result for the whole year.
In option 1, the distribution of cooling power for a typical day in January is shown in Figure 8. At peak hours (10:00 ÷ 12:00), when the price is highest, the demand for cooling of the building is satisfied by the accumulated cold in the STL tank. This accumulated cold is produced in the low hours (22:00 ÷ 4:00) when the price is the lowest. The saved electricity costs for a typical day of the month are calculated using the electricity costs for systems with and without STL as shown below.
-Calculation of electricity costs for a chilling system without STL: Based on the hourly climate data, the required cooling capacity for each hour is calculated. Therefore, the electricity consumption and electricity costs of the chilling system for each hour can be calculated. -Calculation of electricity costs for the chilling system with STL: The required chiller capacity for each hour, electricity consumption, and electricity costs of the chilling system in normal hours (7:30÷10:00, 12:00÷17:00) are calculated as without STL. Electricity consumption from the chilling system and electricity costs in peak hours are calculated at the lowest price of electricity ( Table 2). The difference between the total amount of daily electricity costs without STL (717.73 USD) and the total amount of electricity costs with STL (571.13 USD) is the savings for one day: 146.60 USD. Based on the saved electricity costs for a typical day of January and the number of working days per month, the saved electricity costs for one month are calculated. The same calculations are made for other months. Summarizing the results for all months, the saved electricity costs for the whole year are calculated.
To calculate the effectiveness of each option, it is necessary to calculate the investment. Based on the summary of the accumulated cold (kWh) each month for the option, the volume of the STL tank is calculated from the data in Table 1 (kWh/m 3 ). So the investment for the option is also calculated. The result of option 1 is shown in Table 3. Options 2 to 7 explore the greater potential for cold accumulation. This inevitably leads to larger investments, which must be assessed through technical and economic analysis. Figure 9 shows the distribution of cooling power in January for option 4 when the total cold consumption at peak hours and 30% of the cold consumption at normal hours are used by STL. Compared to option 1, the accumulated cold (kWh) is larger, so the volume of STL is larger and therefore the investment is also larger. Fig. 9. Distribution of the cooling power of January (Option 4, peak hours + 30% normal hours).
Technical and economic analysis was made for all seven considered options. Nominal interest rate (8% for Vietnam) and inflation (3% last year) are taken into account. The economic life for all options is 15 years. The results of the analysis are shown in Table 4. Table 4. Summary results for all options (calculated using the software ENSI Economy).
The analysis shows that option 1 has the best: Pay-off, Internal rate of return and Net present value quotient. Another advantage of this option is the lowest space required to install facilities. | 2,963.8 | 2021-01-01T00:00:00.000 | [
"Engineering",
"Environmental Science"
] |
Evaluation of the X-Ray Absorption by Gold Nanoparticles Solutions
The increase in the X-ray absorption due to gold nanoparticles was investigated by using aqueous solutions containing gold (Au) nanoparticles. A sample with 15 nm in size nanoparticles and 0.5mg/mL gold concentration and a distilled water sample were used. Transmitted X-ray beams through the samples were registered with a CdTe detector and with an ionization chamber. Results show an enhancement in the X-ray absorption in the range 20%–6% for beams generated from 20 kV to 120 kV tube voltages, respectively. Results show that the use of gold nanoparticles, even at low concentrations, should result in a significant contrast enhancement for low-energy X-ray beams.
Introduction
X-ray radiography procedures are one of the most useful tools adopted in the early diagnosis of cancer in both time and cost related to the process of image acquisition [1].The efficacy of these techniques relies on the image quality which depends on the X-ray absorption by the tissues that are being exposed [1].In some of these radiological procedures, such as X-ray computed tomography, a contrast agent is injected directly into the blood stream followed by immediate imaging.The contrast agent leads to increased X-ray attenuation by the targeted tissue resulting in an enhanced image contrast [1,2].Currently, contrast agents used in clinical routine procedures are mainly based on iodine-containing molecules.However, such iodine-based compounds present a shortimaging time which results from its rapid renal clearance [3,4].In this way, biocompatible nanostructured materials are being investigated in order to improve the image contrast and to enhance the image acquisition time [3][4][5][6][7].
Gold nanoparticles (GNPs) have been the subject of numerous theoretical and experimental studies related to its applications as contrast agents in the X-ray imaging field [3,5,8].The use of these particles in computed tomography has attractive properties such as high atomic number (Z = 79) and density ( = 19.3g/cm 3 ), high X-ray attenuation coefficients, and enhanced time of blood circulation providing imaging contrast for longer time periods [5,9].
As the radiographic image contrast depends on the radiation absorption by the target materials, the effect of gold nanoparticles in the X-ray image could be evaluated by means of X-ray spectroscopy.In this work we report the spectral changes on X-ray beams transmitted through a gold nanoparticle aqueous solution registered with a Xray spectrometer.We chose this detector due to its good performance in the diagnostic energy range [10][11][12].Results presented here account for the effect of gold nanoparticles at a low concentration on the X-ray attenuation compared to distilled water for broad beam spectra.The effects on the airkerma and subject contrast by the gold nanoparticle solution relative to water are also evaluated.
Nanoparticles Samples.
In this work we used aqueous solutions of highly monodispersed gold nanoparticles with 15 nm diameter (Nanoprobes).The sample was composed of 0.5 mg/mL gold concentration (0.05% wt) in distilled water.A pure sample of distilled water was also used for comparison.Both samples were placed into a plastic container with rectangular base shape and internal thickness of 2 cm.
X-Ray Spectroscopy.
The knowledge of the X-ray spectra is an important tool for investigations of the dose delivered to the patient and the image quality [1].In this work, the X-ray spectra were generated by a Philips equipment MG 450 model, equipped with a tungsten anode tube with a Be window with 2.2 mm thickness.The anode angle is of 22 ∘ .A XR-100T-CdTe detector (Amptek Inc., Bedford, MA, USA) with 9 mm 2 nominal active area and 1 mm nominal thickness was used to detect the radiation beam.The detector has a 100 m Be window and is cooled by Peltier cells.Output pulses were processed by a Digital Pulse Processor (DPP) PX4.
Transmitted spectra through the above-mentioned solutions have been recorded with the detector positioned in the center of the radiation field at 520 cm from the focal spot as illustrated in Figure 1.A lead collimator with aperture of 8 mm was positioned at the window of the X-ray tube and before the sample.An EXVC tungsten collimator housing and a collimator with 1000 m aperture and 2 mm thickness was used in front of the detector.Alignment between the focal spot and CdTe detector was performed with a laser device.Rise Time Discriminator (RTD) was switched off in the DPP system.Pile-up was maintained less than 2% in all the acquisitions.The transmitted X-ray spectra were registered for beams generated in the voltage range between 20 and 120 kV.Energy calibration of the X-ray spectra was performed with the gamma and X-rays emitted by 241 Am, 133 Ba, and 152 Eu radioactive sources.The air kerma produced by the spectra transmitted through the samples was also measured with an ionization chamber.The experimental setup used in the measurements of the air kerma was the same as showed in Figure 1.In this case, the CdTe detector with its tungsten collimator was replaced by the ionization chamber.The ionization chamber used in this work was a Radcal 6cc (model 9015).
Spectrum Correction.
The raw photon distribution measured with the CdTe detector were corrected in this work in order to obtain the true X-ray spectra.The raw X-ray spectra were corrected for the energy dependence of the detection peak efficiency and escape of fluorescent X-rays by means of the analysis of the X and gamma rays emitted from 241 Am, 133 Ba, and 152 Eu radioactive sources [13].Photon mass attenuation coefficients were obtained from data provided by NIST [14].The corrected X-ray spectra were used to calculate the air kerma and the mean energy for each X-ray spectra [15].
The relative air kerma was calculated as follows: where Kerma Au is the air kerma produced by the beams transmitted through the gold nanoparticle solution and Kerma to those produced by the beams transmitted through the water sample.Total signal due to the beams transmitted through the samples was calculated by integrating the photon fluence spectra over all the energy range as follows: ( The subject contrast () was evaluated according to the following relation: where Φ is the photon fluence (photons/cm 2 ) transmitted through the water sample and Φ Au is the photon fluence calculated from the spectra transmitted through the gold nanoparticle solution sample.The value of is a number between 0.0 and 1.0 [2].We attempt to constrain the firstorder behavior of the data performing a nonlinear least squares fitting of an exponential function of the type = − + with a Levenberg-Marquardt algorithm [16].Grayscale intensity images were generated by considering the photon fluence spectra transmitted through water and through the gold nanoparticle solution for 20 kV and 25 kV tube voltage X-ray beams.The images were built up with the aid of a computational code based on the Gnuplot graphing utility.
Results and Discussion
Measured transmitted X-ray spectra through a sample of distilled water and a gold solution containing nanoparticles with 15 nm are illustrated in Figure 2.
The X-ray beams transmitted through pure distilled water were normalized to the unity at the maximum of the spectra.As stated in Section 2.1, both samples have 20 mm thickness, and the gold concentration in the solution was 0.5 mg/mL (0.05% wt).According to Figure 2, it is possible to observe that the X-ray absorption is clearly higher for the gold nanoparticles solution mainly for the 20 kV and 25 kV X-ray beams.The air kerma values calculated from these beams transmitted through the pure water sample are about 17% higher than those calculated for the beams transmitted through the 0.05% gold nanoparticle solution for 20 kV.For the 25 kV X-ray beams, this difference was 13%.In the case of beams measured at 80 and 100 kV tube voltages, the difference in the X-ray absorption is about 7% and 6%, respectively.
Figure 3 shows the air kerma values produced by the beams transmitted through the sample of 15 nm nanoparticles with 0.05% Au concentration and through the water sample.In this figure, the air kerma values are presented as a ratio of the values measured for the beams transmitted through the gold nanoparticle solution and those measured for the beams transmitted through the water sample.The values presented in this figure are due to measurements performed with an ionization chamber and calculated from the corrected Xray beams.In both cases the beams were generated in the range from 20 kV to 120 kV tube voltages.A good agreement among the air kerma values measured with the ionization chamber and calculated from the corrected X-ray spectra is observed over all the energy range.Results based on the ionization chamber measurements show that for the 20 kV beam the X-ray absorption is about 20% higher than for the beam transmitted through the gold nanoparticle solution when compared to that transmitted through the pure distilled water sample.For the 25 kV beam the absorption by the nanoparticle solution was about 13% higher than that relative to distilled water.In the case of the 30 and 35 kV X-ray beams, this difference was 10% and 9%, respectively.For beams generated with tube voltages from 50 kV to 120 kV, this difference varies from 10% to 4%.
Figure 4 brings the grayscale images produced with the beams transmitted through the distilled water sample and the gold nanoparticles solution presented in Figure 3 The upper and the bottom parts of Figure 4 concern in the beam transmitted through the water sample while the middle part refers to the beams transmitted through the gold nanoparticles solution.The ticks on the intensity axis in Figure 4 indicate the boundary between the gray intensity produced by the beams transmitted through water and those transmitted through the gold nanoparticles solution.These figures show that the maximum contrast occurs in the ranges of 16 to 18 keV for the 20 kV beams and 18 to 22 keV for the 25 kV X-ray beams.Figure 5 brings the subject contrast calculated from the photon fluence of the beams transmitted through the solution containing nanoparticles and the water sample.Results show that the subject contrast enhancement due to the gold nanoparticles varies from about 17% to 2% for beams with a mean energy ranging from 17 keV to 63 keV.
Conclusion
X-ray absorptions by samples of gold nanoparticles solutions and distilled water were investigated in this work.A solution with 0.5 mg/mL gold nanoparticle concentration and a water sample were used in order to evaluate the X-ray absorption and its effect on the air kerma values and subject contrast.We conclude, based on the experimental results, that the Xray absorption for a solution with 0.05% gold nanoparticle concentration increases from 20% to 6% for beams generated between 20 kV and 120 kV, respectively.Also, a significative subject contrast enhancement was observed for low-energy beams.Effectively, targeted tissues with these electron-dense nanoparticles, even at a very low concentration, are able to display significant enhanced X-ray absorption resulting in a higher image contrast or absorbed dose.
Figure 1 :
Figure1: Experimental setup used in the measurements of the transmitted spectra of X-ray through the materials.X-ray tube was a Philips MG 450.
Figure 2 :
Figure2: Comparison of the experimental X-ray spectra transmitted through a solution of gold nanoparticles with 0.05% wt Au concentration and a pure water sample.The data were registered for gold nanoparticles with 15 nm in size and X-ray beams generated at 20, 25, 80, and 100 kV tube voltages.
Figure 3 :
Figure 3: Comparison of the relative air kerma values measured with an ionization chamber and calculated from the corrected x-ray spectra.The data were registered for beams generated in the voltage range from 20 to 120 kV.
Figure 5 :
Figure 5: Subject contrast calculated for beams transmitted through the water sample and through the gold nanoparticle solution for beams generated in the 20 kV to 120 kV tube voltage range. | 2,702 | 2013-03-11T00:00:00.000 | [
"Physics",
"Materials Science"
] |
Bioethical Perspective of Charlie Gard Case
This short commentary is about the ethical, rather bioethical, issues of the Charlie Gard case in the United Kingdom. The commentary tries to analyse the case from bioethical perspective and outlines some of the pertinent bioethical issues.
Introduction
On 28 July 2017, Charles Matthew William Gard, popularly known as Charlie Gard, breathed his last at the innocent age of 11 months 24 days in London, England.Charlie, however, did not face the death naturally.His terminal life support system was withdrawn, amidst several agreements and disagreements, to usher him to permanent rest on 27 July 2017.Charlie succumbed to his conditions almost 24 hours after withdrawal of his mechanical ventilation triggering several bioethical issues.In this commentary, some of those bioethical issues would be discussed with the implications for the greater concern.
The Medical and Legal Issues
Charles "Charlie" Matthew William Gard was born at full term and normal weight on 4 August 2016 in London.Although born as a normal baby, Charlie, however, failed to gain weight even after regular breast-feeding and was unable to lift his head even after days of birth.In October 2016, a cranial MRI (Magnetic Resonance Imaging) scan was performed, an ECG (Electrocardiogram) was carried out to detect the source of problem and a nasogastric tube was inserted to help him to increase his weight.On 11 October 2016, baby Charlie was taken to Great Ormond Street Hospital (GOSH), a 389 bed children's hospital funded by the National Health Service (NHS), England.Charlie, because of his shallow breathing, was admitted to GOSH to be put on a mechanical ventilator but the intervention of tracheostomy was thought to be unnecessary at this stage.By November, Charlie was suspected to have mitochondrial DNA depletion syndrome (MDDS), a set of rare diseases caused by mutations in genes.In mid-November, a genetic test confirmed that Charlie had two mutated versions of the gene coding for the RRM2B protein because of which Charlie had the potential threat of suffering brain damage, muscle weakness, organ failure, and even death during infancy.Charlie's parents contacted Dr. Michio Hirano, a New York based neurologist working on an experimental treatment based on nucleoside supplementation with human MDDS patients.Dr. Hirano and GOSH together agreed to proceed with the treatment for Charlie's interest with funding from the NHS England.
Dr. Hirano and GOSH team came to the decision to work collaboratively for Charlie after checking that Charlie does not have any structural damage to the brain and agreeing that there is only a "theoretical possibility" that the treatment would provide some benefit to Charlie.From mid-December, however, Charlie's brain function deteriorated and he began having persistent seizures (BBC, 2017).He suffered deafness, gradual failures of heart and kidneys, and was unable to breathe or move independently.By first week of January 2017, Charlie began having epileptic seizures, which continued until end of the month.These were deemed likely considered to be the consequences of epileptic encephalopathy (brain damage).Meanwhile, on 9 January 2017, GOSH team intended to attempt the nucleoside treatment in the next few weeks with the ap-proval from hospital's ethics committee which was scheduled to meet to discuss the issues and the case on 13 January.And Charlie was provisionally scheduled for a tracheostomy on 16 January (Garrison, 2017;Bailii, 2017).In the meantime, GOSH also invited Dr. Hirano to examine Charlie in January, but he could only physically examine him in July when the legal tension between GOSH and Charlie's parents had reached the second hearing.(Boseley, 2017).On 13 January the GOSH doctors informed Charlie's parents that the benefits of the experimental treatment were futile because of the brain damage and it is better to withdraw the life support to minimize Charlie's sufferings.
As this appeal of GOSH went against the interest of Charlie's parents, they decided to transfer Charlie to try the experimental treatment in the United States and started raising funds for hospital transfer to New York.As the parents continued to go against the GOSH's decision to terminate the treatment, on 24 February 2017, GOSH sought help of the England and Wales High Court (Family Divisions) to give the orders in support of GOSH considering the following aspects; "That Charlie, by reason of his minority, lacks capacity to make decisions regarding his medical treatment; it is lawful, and in Charlie's best interests, for artificial ventilation to be withdrawn; that it is lawful, and in Charlie's best interests, for his treating clinicians to provide him with palliative care only; and that it is lawful, and in Charlie's best interests, not to undergo nucleoside therapy provided always that the measures and treatments adopted are the most compatible with maintaining Charlie's dignity" (Bailii, 2017).
The court while supported GOSH's position, the case when further moved to the Volume 2 Issue 1, December 2017 European Court of Human Rights (ECHR), ECHR refused to intervene.After several months of tension between court and Charlie's parents, in July 2017, GOSH applied to the High Court for a new hearing after receiving a letter signed by several international experts defending the potential of the treatment and providing new evidence (GOSH, 2017).
It is during this time, Dr. Hirano could make time to visit Charlie at GOSH and after examining scans of Charlie's muscles, Dr. Hirano declared that it's been too late for the treatment to help Charlie.Dr. Hirano's declaration obliged Charlie's parents to abide by the court order and to agree to the withdrawal of life support.The second court hearing, which had been arranged to hear and examine the new evidence then became concerned with the arrangements for the withdrawal of life support.On 27 July, by court order and parent's consent, Charlie was transferred to a hospice; mechanical ventilation was withdrawn, and he breathed his last on the very next day at the age of 11 months and 24 days.
Charlie's mother, made an emotional farewell statement with reference to the time.She rightly pointed out about the timely access to the medical care, the time taken for the decision, for the observation.She clarified "Had Charlie been given the treatment sooner he would have had the potential to be a normal, healthy little boy" (The Telegraph, 2017).She also mentioned her son "had a greater impact on and touched more people in this world in his 11 months than many people do in a lifetime."(The Telegraph, 2017).She was true in her view.At the tender age of few months, Charlie, with the help of the media, attracted widespread attention; became a major concern in Britain and around the world.President Donald Trump and Pope Francis expressed their concerns and assistance to baby Char-lie.The case even attracted international media for at the time of Charlie's death, The Washington Post reminding the difference between American and English healthcare system, wrote the case "became the embodiment of a passionate debate over his right to live or die, his parents' right to choose for their child, and whether his doctors had an obligation to intervene in his care" (Gaffney, 2017).
Involving several agencies, conflicts of rights and interests, the case gave rise to several ethical issues and opened the scope for the bioethicists to refocus on some of the bioethical concerns.This commentary highlights some of them.
The Ethical Issues
Access to medical care: When GOSH medical team decided to put Charlie out of mechanical ventilation, Charlie's parents decided to take Charlie to the United States to try for the experimental treatment.And GOSH took refuge to the court for the possible treatments in this case was beyond the scope of long-term medical and social obligations.
However, it took time for the parents, in this case, to accept the fact that nothing can be further done to improve the longterm health and well-being of the baby, for its been late.In short, GOSH's decision, perhaps, was considered as the denial of access to the high-quality treatment by Charlie's parents.Charlie's timely access to high quality NHS treatment, possibly, could have avoided debates and court.The timely focus on the just and fair explanation of health and well-being, rather than consistent focus on suffering and dying with dignity could have shaped the right decisions at the right time.
Volume 2, Issue 1, December 2017 Balancing rights, harm, benefit, and safety: The case has given rise to the serious debate over the physicians and the court overruling the parents' decisions on behalf of their child.The reaction in the society turned out to be violent later with the hospital staffs getting threats from the civilians for their paternalistic behavior.Without delving into the depth of the debates, this commentator would like to state that a just medical decision (considering the facts of "medical necessity" and "medical futility" (Ruger, 2010) of the case), balancing the rights of the patients and doctors, could only be undertaken when there is a shared commitment of thoughts and actions-it can commence through the shared responsibility of the parents (if patient is incapable to decide), the hospital staffs, the ethics consultants (not just clinical ethicists working in the hospital setting but ethicists/bioethicists potential enough to work as consultants), medical scientists, social and other medias, and the society collectively.This could also balance the medical harm and benefit with proper consideration of "clinical and economic solutions" (Ruger, 2010); minimize the consequent threats and harms on the physicians and nurses.A joint participation in the decision-making process could also improve the trust and expectation of the people on the healthcare system.
Intervention of Media:
The case at hand had witnessed overwhelming coverage of media which captured the attention of the whole world including President Trump and Pope Francis.However, the onus also remains on the media to consider the issue that the coverage should not compel the parents (or the patient), involved in the case, to be stigmatised; that the case is not sensationalised to the extreme for the public to take the law at hand to abuse the physicians and other medical personnels involved in the case.
Conclusion
In the context of Charlie Grad's case while the debate was about the overruled patient's rights, balancing harm, and benefit, about the strong involvement of the media, however, the case has been an instance for the discussion of varied bioethical issues in the England.The case, perhaps, has also provoked the discussion of the extent of the involvement of the ethicists-do the cases need to be only within the medical and clinical ethics domain to analyse the moral implications?; or, does it need the involvement of the ethicists, beyond the boundary of the hospital, to discuss the case in bigger context ?; do medical cases always necessarily need to be referred to the court in the England or do they also need an ethical decision from bioethicists before being referred to the court?.While some of these questions are prompted by the case of Charlie Gard, it remains to be seen whether these questions are dealt with great responsibility and obligation in the context of similar such cases in the future.
Conflict of Interest
The author declared no conflicts of interest with respect to the research, authorship and/or publication of this article. | 2,560.6 | 2017-12-31T00:00:00.000 | [
"Business",
"Philosophy"
] |
Self-Polarized P(VDF-TrFE)/Carbon Black Composite Piezoelectric Thin Film
Self-polarized energy harvesting materials have seen increasing research interest in recent years owing to their simple fabrication method and versatile application potential. In this study, we systematically investigated self-polarized P(VDF-TrFE)/carbon black (CB) composite thin films synthesized on flexible substrates, with the CB content varying from 0 to 0.6 wt.% in P(VDF-TrFE). The presence of –OH functional groups on carbon black significantly enhances its crystallinity, dipolar orientation, and piezoelectric performance. Multiple characterization techniques were used to investigate the crystalline quality, chemical structure, and morphology of the composite P(VDF-TrFE)/CB films, which indicated no significant changes in these parameters. However, some increase in surface roughness was observed when the CB content increased. With the application of an external force, the piezoelectrically generated voltage was found to systematically increase with higher CB content, reaching a maximum value at 0.6 wt.%, after which the sample exhibited low resistance. The piezoelectric voltage produced by the unpoled 0.6 wt.% CB composite film significantly exceeded the unpoled pure P(VDF-TrFE) film when subjected to the same applied strain. Furthermore, it exhibited exceptional stability in the piezoelectric voltage over time, exceeding the output voltage of the poled pure P(VDF-TrFE) film. Notably, P(VDF_TrFE)/CB composite-based devices can be used in energy harvesting and piezoelectric strain sensing to monitor human motions, which has the potential to positively impact the field of smart wearable devices.
Introduction
Recent advancements in flexible piezoelectric materials have paved the way for the potential realization of self-powered flexible devices in wearable electronics and other fields [1][2][3].These materials have the ability to efficiently convert various forms of mechanical force into electrical power, eliminating the need for external power sources.Among the materials explored for this purpose, polyvinylidene fluoride (PVDF) and its copolymer P(VDF-TrFE) have stood out for their outstanding properties, including high piezoelectric coefficients, improved crystallinity, enhanced remnant polarization, and superior temperature stability [4][5][6][7].P(VDF-TrFE) is classified as a ferroelectric polymer with an inherent β phase structure, which is achieved by changing the TrFE molar ratio with respect to PVDF [8,9].However, P(VDF-TrFE) has a relatively low piezoelectric coefficient [9][10][11].To enhance the piezoelectric coefficient and optimize energy conversion efficiency, aligning the dipoles within P(VDF-TrFE) films in a specific orientation is crucial.Traditional methods, such as polarization under a high electric field [3,12], electrospinning [13,14], corona poling [15,16], or thermal poling [17], have been employed to achieve this self-alignment.However, these methods often involve complex processing steps, are time-consuming, and may lead to dielectric breakdown within the film when a high electric field is applied, leading to reduced yield and constraints on practical implementation.P(VDF-TrFE) (55:45 molar ratio) powder was purchased from Piezotech (Arkema Group, Wetherby, UK).The CB powder, with a particle size of 30 nm and a specific surface area of 254 m 2 /g, was obtained from the Cabot Corporation (Boston, MA, USA).In our experiments, six different weight percentages (ranging from 0 to 1 wt.%) of CB powder and P(VDF-TrFE) were dissolved in N, N-dimethylformamide (DMF) for 12 h at 40 • C to obtain a homogeneous solution.
Figure 1a depicts a schematic of the fabrication process for P(VDF-TrFE)/CB composite films.We used ITO-coated PET substrates in which the ITO layer served as the bottom electrode.Before spin coating, the PET substrate was cut into 2 × 2 cm pieces and cleaned with acetone and IPA.Then, the solution was spin-coated onto the ITO-coated PET substrate at 3000 RPM for 30 s to achieve a ~5 µm thickness film.Subsequently, the film was placed on a hotplate and baked at 60 • C for 1 h to remove the solvent.Following this, the film was annealed at 140 • C for 2 h at room temperature to enhance its crystallinity, as previous studies have reported that crystallization occurring at 140 • C yields the most stable form of the β-phase with a high dielectric constant [1,5,7].
After the sample was cooled to room temperature, an adhesive copper tape was placed on the composite film to establish the top electrode.As seen in Figure 1b, the films gradually became darker with an increasing weight percentage of CB in the polymer matrix.The thickness of the prepared films was measured via a profilometer (Tencor AS-200) and found to be 5, 5.1, 5.18, 5.3, 5.4, and 5.5 µm of 0, 0.2, 0.4, 0.6, 0.8, and 1wt.% of CB, respectively.For poling the samples, a 100 V/µm electric field was used for an hour using a high-power DC supply (Hewlett Packard 6515A, USA).The poling voltage was increased in steps of 100 V/µm every 10 min to avoid electrical breakdown due to sudden and nonuniform charge accumulation [7].
Material Characterization
Following synthesis, the surface morphology of the resulting P(VDF-TrFE)/CB composite films was examined.Optical microscope images were captured using Olympus BX41M-LED at 50× magnification.In addition, atomic force microscopy (AFM, Veeco Dimension 3100) operated in tapping mode was employed to provide higher-resolution images of the composite films, and the AFM images were subsequently processed using the After the sample was cooled to room temperature, an adhesive copper tape was placed on the composite film to establish the top electrode.As seen in Figure 1b, the films gradually became darker with an increasing weight percentage of CB in the polymer matrix.The thickness of the prepared films was measured via a profilometer (Tencor AS-200) and found to be 5, 5.1, 5.18, 5.3, 5.4, and 5.5 µm of 0, 0.2, 0.4, 0.6, 0.8, and 1wt.% of CB, respectively.For poling the samples, a 100 V/µm electric field was used for an hour using a high-power DC supply (Hewlett Packard 6515A, USA).The poling voltage was increased in steps of 100 V/µm every 10 min to avoid electrical breakdown due to sudden and non-uniform charge accumulation [7].
Material Characterization
Following synthesis, the surface morphology of the resulting P(VDF-TrFE)/CB composite films was examined.Optical microscope images were captured using Olympus BX41M-LED at 50× magnification.In addition, atomic force microscopy (AFM, Veeco Dimension 3100) operated in tapping mode was employed to provide higher-resolution images of the composite films, and the AFM images were subsequently processed using the dedicated AFM software.To determine the effect of blending CB to the P(VDF-TrFE) polymer matrix and the crystallinity of the P(VDF-TrFE)/CB composite films, X-ray diffraction (XRD) measurements (Rigaku Smart Lab system) were made on the composite films (with CB varying from 0 to 1 wt.%) using Cu Kα radiation (wavelength 15.406 nm) in the 2θ range from 5 • to 90 • with a step size of 0.5 • .
Furthermore, FTIR spectra were measured (model no: Thermo Scientific Nicolet380) in the range of 4000-400 cm −1 with 64 scans at a 4 cm −1 resolution.The percolation threshold (transition point from insulator to conductor) and conductivity measurements were conducted using a Source Measure Unit (SMU, B2902A, Keysight, Santa Rosa, CA, USA).To measure the piezoelectric voltage output of the composites, they were excited by an external shaker (LDS V201, Brüel & Kjaer, London, UK), and the voltage waveforms were recorded using a digital storage oscilloscope (DSO 5102P, Hantek, Qingdao, China).
Figure 2a shows the XRD spectrum of raw carbon black and P(VDF-TrFE) powder with a molar ratio of 55:45.Raw P(VDF-TrFE) powder exhibits a prominent β-phase peak (110/200) at 2θ = 19.1 • , which experimentally confirms the presence of the TrFE unit in more than 20%, directly crystallized into the β-phase within the polymer [33,34].Additionally, a broader peak at 40.8 • corresponds to the diffraction plane (111/201), further validating the presence of the β-phase in the polymer matrix.Notably, no significant peak was observed at 2θ = 18.27 • , corresponding to the (100) crystal planes of the α-phase of the P(VDF-TrFE) polymer [35].In the XRD results for raw CB powder, the (002) diffraction peak appears at 24.5 • , along with a broader and weaker (001) peak at 43 • , consistent with previous reports [36,37].In particular, we did not observe any significant peak for CB due to its amorphous Figure 2b shows the XRD diffraction peaks of the 55/45 copolymer films crystallized at different temperatures (T cr ) to determine the optimum crystallization temperature for these films.Typically, crystallization begins when the film is subjected to a temperature above the Curie temperature (T c = 60 • C for 55:45 mol ratio).We found that at a crystallization temperature (T cr ) of 60 , which is close to 20.12 • , corresponding to the Bragg diffraction of (110)/(200) of the β-phase.However, the diffraction peak intensity of the composites annealed at 60 • C is relatively small compared to peak intensities at other crystallization temperatures and existed within the amorphous region.As the crystallization temperature (T cr ) increased, the amorphous region gradually disappeared, and the peak intensities became narrower and sharper.Meanwhile, the diffraction angle (2θ) shifted to a lower value, changing from 20.12 • to 19.3 • (with an increase in d-spacing from 4.46 to 4.59 Å) as displayed in Figure 2b.This shift was due to the ferro-to-paraelectric transition occurring during the crystallization phase, which changed the trans-planar conformation (TT) to the trans-gauge conformation (TG).Consequently, it shifted the prominent β-phase peak from 2θ = 20.12• to lower values and increased peak intensities as the crystallization temperature (T cr ) increased [38].Moreover, the full width at half-maximum (FWHM) value, which is directly related to the degree of crystallinity, gradually improved as the annealing temperature increased from 60 to 140 • C.This observation clearly indicates an enhancement in the electroactive polar β-phase content in the composite films.
We investigated the pure P(VDF-TrFE) film under various annealing temperatures (e.g., 60 • C, 80 • C, and 100 • C) and found a similar trend (see Supplementary Figure S1).From the XRD results, we can conclude that annealing the composite at 140 • C results in optimal crystalline quality, corresponding to the most stable β-phase in the film.Table 1 summarizes the diffraction peak angles (2θ), interplanar spacing (D), FWHM values for the prominent β-phase peak, and corresponding peak intensities of the 0.6 wt.% CB film annealed at various crystallization temperatures.Figure 2c displays the XRD pattern of P(VDF-TrFE)/CB composite films, ranging from 0 to 1 wt.%, within the scan range of 10 • to 90 • .An analysis of the XRD pattern reveals that a well-defined diffraction peak appears at an angle of 19.3 • , corresponding to the (110)/(200) planes of the β-phase, which comprises all-trans TT conformation [39].In particular, we did not observe any significant peak for CB due to its amorphous nature and the low percentage of CB present in the polymer matrix.This clearly indicates that the addition of CB does not significantly alter the crystalline structure of P(VDF-TrFE).Figure 2d shows the magnified view of XDR spectra of different composite films in the scan range of 17 • -22 • , varying from 0 to 1 wt.%.With an increase in CB content from 0 to 0.2, 0.4, 0.6, 0.8 wt.%, and 1 wt.% in the composite, XRD peak intensity varied from 5805 to 6589, 7903, 9266, 7892, and finally to 4986, respectively.Above 0.6 wt.%, a reduction in the diffraction peak intensity and an increase in FWHM were observed, as seen in the inset image of Figure 2d, indicating that the best crystalline properties were achieved for the 0.6 wt.% composition.However, when the amount of CB percentage exceeds the optimum amount of 0.6 wt.%, the aggregation created by CB reduces the formation of the β-phase in the polymer.The homogeneous dispersion of carbon black particles within the polymer matrix is a major factor in the increased intensity.Similarly, Yaseen et al. [40] observed the same trend with P(VDF-TrFE)/reduced graphene oxide (rGO) composite films.The observed intensities for all composite films, along with interplanar spacing (D) and FWHM, are tabulated in Table 2. FTIR characterization of the films was also conducted to confirm the XRD results and study the interaction between the nanoparticle's surface and P(VDF-TrFE).The formation of the beta phase in P(VDF-TrFE) was identified by examining three important absorbance peaks (850 cm −1 , 1288 cm −1 , and 1400 cm −1 ) in the FTIR spectra.The 1400 cm −1 band corresponds to the -CH 2 wagging vibration, while the 1288 cm −1 and 850 cm −1 bands are attributed to the -CF 2 symmetric stretching, with dipoles parallel to the b-axis [41].Figure 3a illustrates the FTIR spectra of P(VDF-TrFE)/CB thin films ranging from 0 to 1 wt.%, and the prominent peaks for the β-phase are consistent for all CB compositions within the IR detection limit (1400 cm −1 to 400 cm −1 ).This indicates that the crystalline quality remains unaffected by the incorporation of CB nanoparticles. in the P(VDF-TrFE) molecular chains (see Supplementary Figure S2).This explains the possible electrostatic interaction between positively charged hydrogen atoms drawn from the hydrophilic tail group (-OH) of carbon black and negatively charged fluorine atoms from P(VDF-TrFE), as seen in Figure 4.The P(VDF-TrFE) film and other CB composite films show increasing intensity in all observed peaks (1400 cm −1 , 1290 cm −1, and 850 cm −1 ) as the CB composition is increased up to 0.6 wt.% beyond which it remains constant or even decreases somewhat.This increase is attributed to the specific interaction between hydroxyl (-OH) groups found on the surface of carbon nanofillers and CF 2 segments of P(VDF-TrFE).This interaction becomes more pronounced with an increase in CB content, reaching a maximum of 0.6 wt.%. Figure 3b provides a magnified view of the peaks in the scan range of 750 cm −1 to 900 cm −1 , allowing for the calculation of the percentage of β-phase crystallization F(β) by measuring the absorbance intensity of the β-phase and α-phase using the following formula: [42] F Polymers 2023, 15, 4131 7 of 20 where X α and X β are the crystalline mass fractions of the α and β-phases, and A α and A β correspond to absorbance at 764 cm −1 and 850 cm −1 , respectively [40,43].The values of the absorption coefficients result in K β /K α = 1.26.FTIR measurements were carried out to calculate F(β) for various CB composites, and the results are plotted in the inset of Figure 3b and listed in Table 2.As shown in Figure 3b inset, F(β) is approximately 76% for the pure P(VDF-TrFE) film prepared and crystallized at 140 • C. It increases monotonically until it reaches a maximum of ~97% for the 0.6 wt.% CB composition.However, at higher CB contents, the incorporation of carbon particles has a negative impact on the β-phase formation, leading to a reduction in the percentage of beta crystallinity to 75% [44].These results are in good agreement with the XRD results discussed earlier, indicating that the best film quality is obtained for 0.6 wt.% CB.Moreover, the broadened absorbance peak occurring between 3600 and 3400 cm −1 implies the formation of intermolecular hydrogen bonding between -CF2-dipoles and the hydrophilic groups from CB, as well as the remaining oxygen-containing groups from CB [40,44].The OH stretching is much stronger for the 0.6 wt.% concentration than at the lower concentration (0 wt.%), clearly indicating that more -OH groups of CB form bonds with the most negatively charged fluorine atoms in the P(VDF-TrFE) molecular chains (see Supplementary Figure S2).This explains the possible electrostatic interaction between positively charged hydrogen atoms drawn from the hydrophilic tail group (-OH) of carbon black and negatively charged fluorine atoms from P(VDF-TrFE), as seen in Figure 4.
Polymers 2023, 15, x FOR PEER REVIEW 7 of 21 in the P(VDF-TrFE) molecular chains (see Supplementary Figure S2).This explains the possible electrostatic interaction between positively charged hydrogen atoms drawn from the hydrophilic tail group (-OH) of carbon black and negatively charged fluorine atoms from P(VDF-TrFE), as seen in Figure 4.Such bonding is favored due to the large electronegativity differences between the atoms involved.
The hydrophilic nature of the -OH groups causes the seed layer to align perpendicularly to the substrate.As shown in the enlarged view in Figure 4, other induced dipoles resulting from hydrogen intermolecular bonding can interact with each other within subsequent polymer matrices.This interaction occurs between carbon black and -CH2 dipoles, leading to local alignment during crystallization [24,25,28,45].The interaction between -CF2-CH2dipoles and carbon black can be confirmed by investigating the -CH2 Such bonding is favored due to the large electronegativity differences between the atoms involved.
The hydrophilic nature of the -OH groups causes the seed layer to align perpendicularly to the substrate.As shown in the enlarged view in Figure 4, other induced dipoles resulting from hydrogen intermolecular bonding can interact with each other within subsequent polymer matrices.This interaction occurs between carbon black and -CH 2 dipoles, leading to local alignment during crystallization [24,25,28,45].The interaction between -CF 2 -CH 2 -dipoles and carbon black can be confirmed by investigating the -CH 2 symmetric and asymmetric stretching vibrational bands at 3012 cm −1 and 2978 cm −1 in the FTIR spectra, which are not associated with any other vibrational bands.These vibrational bands shifted to lower frequencies as the CB loading increased; meanwhile, the absorbance peak intensity increased with respect to carbon weight percentage [20,40] (see details in Supplementary Figure S2).
Figure 5 shows optical images of different CB composite films at 50× magnification with a 500 µm scale bar, ranging from 0 to 1 wt.%.In Figure 5a, the smooth surface of the pure P(VDF-TrFE) film is illustrated, while Figure 5b-d show the distribution of CB particles within the polymer matrix.These CB particles are clearly noticeable in optical images, consistent with an earlier report [46].As shown in Figure 5b, CB particles diffuse randomly and form tiny agglomerates at lower CB wt.%.As the CB fraction increases, these agglomerates become larger and larger, ultimately creating a conductive path between them.However, at very high CB content (~1%), structured agglomerates are no longer formed.Instead, the polymer matrix becomes saturated, resulting in a continuum of particles, indicated by a uniform dark color, as seen in the inset of Figure 5d.We also studied the surface morphologies of the composite films using AFM to analyze nanoscale variations in surface roughness caused by CB incorporation.
Polymers 2023, 15, x FOR PEER REVIEW 8 of 21 symmetric and asymmetric stretching vibrational bands at 3012 cm −1 and 2978 cm −1 in the FTIR spectra, which are not associated with any other vibrational bands.These vibrational bands shifted to lower frequencies as the CB loading increased; meanwhile, the absorbance peak intensity increased with respect to carbon weight percentage [20,40] (see details in Supplementary Figure S2).
Figure 5 shows optical images of different CB composite films at 50× magnification with a 500 µm scale bar, ranging from 0 to 1 wt.%.In Figure 5a, the smooth surface of the pure P(VDF-TrFE) film is illustrated, while Figure 5b-d show the distribution of CB particles within the polymer matrix.These CB particles are clearly noticeable in optical images, consistent with an earlier report [46].As shown in Figure 5b, CB particles diffuse randomly and form tiny agglomerates at lower CB wt.%.As the CB fraction increases, these agglomerates become larger and larger, ultimately creating a conductive path between them.However, at very high CB content (~1%), structured agglomerates are no longer formed.Instead, the polymer matrix becomes saturated, resulting in a continuum of particles, indicated by a uniform dark color, as seen in the inset of Figure 5d.We also studied the surface morphologies of the composite films using AFM to analyze nanoscale variations in surface roughness caused by CB incorporation. Figure 6 displays AFM images (5 × 2.5 µm) of different films with CB concentrations ranging from 0 to 0.6 wt.%.These images generally reveal uniformly distributed "rice grain"-like crystallites with dimensions in the tens of nanometers.Previous studies have also reported similar rice grain domains for pure P(VDF-TrFE) films annealed at 140 °C [47].In contrast, when the films were subjected to temperatures near their melting point (Tm = 153 °C), we observed more interconnected nanofiber-like crystallites, characterized by a higher roughness of approximately 36.8 nm for the 0 wt.%CB sample (see Supplementary Figure S3).In general, nanofillers tend to increase the surface roughness [48], as observed in these P(VDF-TrFE)/CB composites annealed at 140 °C.The lowest roughness, approximately 5 nm, was observed for the 0 wt.%CB film.This roughness increased Figure 6 displays AFM images (5 × 2.5 µm) of different films with CB concentrations ranging from 0 to 0.6 wt.%.These images generally reveal uniformly distributed "rice grain"-like crystallites with dimensions in the tens of nanometers.Previous studies have also reported similar rice grain domains for pure P(VDF-TrFE) films annealed at 140 • C [47].In contrast, when the films were subjected to temperatures near their melting point (T m = 153 • C), we observed more interconnected nanofiber-like crystallites, characterized by a higher roughness of approximately 36.8 nm for the 0 wt.%CB sample (see Supplementary Figure S3).In general, nanofillers tend to increase the surface roughness [48], as observed in these P(VDF-TrFE)/CB composites annealed at 140 • C. The lowest roughness, approximately 5 nm, was observed for the 0 wt.%CB film.This roughness increased progressively with increasing CB content: 5.2 nm, 8 nm, 21 nm, and finally 37 nm for the CB compositions of 0.2 wt.%, 0.4 wt.%, 0.5 wt.%, and 0.6 wt.%, respectively.A Polymers 2023, 15, 4131 9 of 20 600 nm line profile across an elevated carbon aggregate "island" region on the 0.5 wt.% CB film is shown in Figure 6e, which indicates a height and span of ~400 nm for the island.progressively with increasing CB content: 5.2 nm, 8 nm, 21 nm, and finally 37 nm for the CB compositions of 0.2 wt.%, 0.4 wt.%, 0.5 wt.%, and 0.6 wt.%, respectively.A 600 nm line profile across an elevated carbon aggregate "island" region on the 0.5 wt.% CB film is shown in Figure 6e, which indicates a height and span of ~400 nm for the island.
Resistivity Measurement
Carbon black is conductive in nature, and its introduction in P(VDF-TrFE)/CB composites can help tune the resistivity of the insulating polymer (apart from boosting its energy harvesting performance), which has been gaining more attention in recent years.To find the optimal amount of CB for the composites (which provides maximum output voltage without making the film too conducting), the electrical characteristics of these films, with varying CB content, were systematically characterized.As shown in Figure 7a, four contacts of 0.5 mm 6 mm were established with varying gaps of (0.5 mm, 1 mm, 1.5 mm, and 2 mm) to perform transmission line-type measurements.The resistances for various CB % for the four gaps are shown in Figure 7b, with the inset showing a close-up of the measurement setup with the sample.The contact resistance (Rc) and sheet resistance (Rs) of the composites were estimated from the least square fits using MATLAB programming (details provided in Supplementary Information, Figure S4).
We found that composite films with CB ranging from 0 to 0.6 wt.% are insulating, which indicates that the CB agglomerates are spatially well separated within the polymer matrix, and a percolation path does not exist [30].Beyond 0.6 wt.% of CB, the P(VDF-
Electrical Characterization 4.1. Resistivity Measurement
Carbon black is conductive in nature, and its introduction in P(VDF-TrFE)/CB composites can help tune the resistivity of the insulating polymer (apart from boosting its energy harvesting performance), which has been gaining more attention in recent years.To find the optimal amount of CB for the composites (which provides maximum output voltage without making the film too conducting), the electrical characteristics of these films, with varying CB content, were systematically characterized.As shown in Figure 7a, four contacts of 0.5 mm × 6 mm were established with varying gaps of (0.5 mm, 1 mm, 1.5 mm, and 2 mm) to perform transmission line-type measurements.The resistances for various CB % for the four gaps are shown in Figure 7b, with the inset showing a close-up of the measurement setup with the sample.The contact resistance (R c ) and sheet resistance (R s ) of the composites were estimated from the least square fits using MATLAB programming (details provided in Supplementary Information, Figure S4).
We found that composite films with CB ranging from 0 to 0.6 wt.% are insulating, which indicates that the CB agglomerates are spatially well separated within the polymer matrix, and a percolation path does not exist [30].Beyond 0.6 wt.% of CB, the P(VDF-TrFE)/CB composites became slightly conductive because of the barrier tunneling effect between the polymer chains and CB agglomerates, and a finite resistance was measured.
The sheet resistance (R s ) was determined to be 46 kΩ/ for 0.8 wt.% CB content, which was reduced to 12 kΩ/ for 1 wt.%CB.Further, R s decreases sharply with CB % until 1.5 wt.%, beyond which it reaches a saturation value of ~3.3 kΩ/ .Due to significant film conductivity, the piezoelectrically generated voltage could only be measured for CB content up to 0.6 wt.%, which is discussed below.
Polymers 2023, 15, x FOR PEER REVIEW 10 of 21 TrFE)/CB composites became slightly conductive because of the barrier tunneling effect between the polymer chains and CB agglomerates, and a finite resistance was measured.The sheet resistance (Rs) was determined to be 46 kΩ/ for 0.8 wt.% CB content, which was reduced to 12 kΩ/ for 1 wt.%CB.Further, Rs decreases sharply with CB % until 1.5 wt.%, beyond which it reaches a saturation value of ~3.3 kΩ/ .Due to significant film conductivity, the piezoelectrically generated voltage could only be measured for CB content up to 0.6 wt.%, which is discussed below.
Experimental Setup
The experimental setup in Figure 8 was utilized to measure the piezoelectrically generated output voltage from the fabricated P(VDF-TrFE)/CB composite films for various CB content.In these experiments, an adjustable extended fixed arm attached to an XYZ positioner was used to mount the device at the bottom surface, which was pressed periodically using a cylinder attached to a shaker, as shown in Figure 8, and its insets show the image of fabricated PENG and Force sensing resistor (FSR) attachment to the shaker.The output voltage transients were measured and recorded using a digital storage oscilloscope as the fabricated composite devices were subjected to stress generated by the mechanical shaker (LDS, V201).A force-sensing resistor (FSR) was carefully calibrated using a reference chart provided by the manufacturer (details provided in Supplementary Information Figure S5) and placed on top of the cylinder to measure the applied periodic force on the film.
Experimental Setup
The experimental setup in Figure 8 was utilized to measure the piezoelectrically generated output voltage from the fabricated P(VDF-TrFE)/CB composite films for various CB content.In these experiments, an adjustable extended fixed arm attached to an XYZ positioner was used to mount the device at the bottom surface, which was pressed periodically using a cylinder attached to a shaker, as shown in Figure 8, and its insets show the image of fabricated PENG and Force sensing resistor (FSR) attachment to the shaker.The output voltage transients were measured and recorded using a digital storage oscilloscope as the fabricated composite devices were subjected to stress generated by the mechanical shaker (LDS, V201).A force-sensing resistor (FSR) was carefully calibrated using a reference chart provided by the manufacturer (details provided in Supplementary Information Figure S5) and placed on top of the cylinder to measure the applied periodic force on the film.
Piezoelectric Measurement
The generated output voltage response of (PVDF-TrFE)/CB films, varying from 0 to 0.6 wt.%, are shown in Figure 9b-e under periodic force provided by the shaker at 1 Hz frequency, using the setup shown in Figure 8.The force applied by the shaker to the film was determined using an FSR, which utilized a simple voltage divider circuit and was compared with a calibration chart provided by the manufacturer, as shown in Supplementary Figures S5a-c.The maximum output voltages obtained for 0 wt.%, 0.2 wt.%, 0.4 wt.%, and 0.6 wt.% under a 6 N applied force (determined from the FSR response shown in Figure 9a) were found to be 0.5 V, 1 V, 1.9 V, and 3 V, respectively (Figure 9b-e).The enlarged view from the 0.6 wt.% CB composite demonstrates a single cycle of pressing and releasing, accompanied by damping.This is clear evidence of oscillatory behavior in response to the external force applied by the shaker.When subjected to gentle finger tapping, the unpoled 0.6 wt.% composite generates a peak-to-peak output voltage of 3 V (see Supplementary Figure S6).This suggests that this self-poled PENG is suitable for detecting human motions, including touching and walking.We also observed that the poled composites, subjected to 100 V/µm for an hour, exhibited significantly higher output voltages: 3.8 V compared to 0.5 V for the unpoled 0 wt.%CB sample, and 8 V compared to 3 V for the unpoled 0.6 wt.% CB sample.This increase in output voltage is attributed to the highly aligned dipoles resulting from the poling process.Table 3 presents the generated output voltages of the fabricated PENGs with different weight percentages under both poled and unpoled conditions.
Piezoelectric Measurement
The generated output voltage response of (PVDF-TrFE)/CB films, varying from 0 to 0.6 wt.%, are shown in Figure 9b-e under periodic force provided by the shaker at 1 Hz frequency, using the setup shown in Figure 8.The force applied by the shaker to the film was determined using an FSR, which utilized a simple voltage divider circuit and was compared with a calibration chart provided by the manufacturer, as shown in Supplementary Figures S5a-c.The maximum output voltages obtained for 0 wt.%, 0.2 wt.%, 0.4 wt.%, and 0.6 wt.% under a 6 N applied force (determined from the FSR response shown in Figure 9a) were found to be 0.5 V, 1 V, 1.9 V, and 3 V, respectively (Figure 9b-e).The enlarged view from the 0.6 wt.% CB composite demonstrates a single cycle of pressing and releasing, accompanied by damping.This is clear evidence of oscillatory behavior in response to the external force applied by the shaker.When subjected to gentle finger tapping, the unpoled 0.6 wt.% composite generates a peak-to-peak output voltage of 3 V (see Supplementary Figure S6).This suggests that this self-poled PENG is suitable for detecting human motions, including touching and walking.We also observed that the poled composites, subjected to 100 V/µm for an hour, exhibited significantly higher output voltages: 3.8 V compared to 0.5 V for the unpoled 0 wt.%CB sample, and 8 V compared to 3 V for the unpoled 0.6 wt.% CB sample.This increase in output voltage is attributed to the highly aligned dipoles resulting from the poling process.Table 3 presents the generated output voltages of the fabricated PENGs with different weight percentages under both poled and unpoled conditions.We found that the unpoled 0.6 wt.% P(VDF-TrFE)/CB composite film produced a maximum peak-to-peak output voltage of 3 V, which is quite comparable to previously reported conductive nanofiller-based PENGs despite our film thickness being much smaller.This resulted in much higher energy densities compared to earlier reports for a similar magnitude of applied force, as shown in Table 4.We utilized unpoled 0.6 wt.% CB film to determine the output power performance with a 1 MΩ load resistance.The piezoelectric power generated by the film can be calculated as P = V 2 /R L , where V is the voltage applied to the load resistor R L .The unpoled 0.6 wt.% CB composite generated an output voltage and current of 1.5 V and 1.5 µA, respectively, resulting in an output power of µW.A detailed of the various performance metrics of the as-fabricated self-poled P(VDF-TrFE)/CB composite film with previously reported results based on other nanocomposite PENGs is included in Table 4 [49][50][51][52][53][54].We observe that our composite films, with a very low thickness of 5 µm and realized through a facile fabrication process, exhibit the best output voltage per unit thickness and power density, achieving 0.3 V/µm and 1.1 mW/cm 3 for unpoled films and 1 V/µm and 12 mW/cm 3 for poled 0.6 wt.% CB composite films, respectively.These figures are several times higher than the best results reported in the literature.The output voltage of poled P(VDF-TrFE)/CB films was measured under the same applied force of 6 N, and the results are shown in Figure 10a-c.As expected, the peak-to-peak output voltage increases for the composite films after poling, reaching 3.8 V and 8 V for 0 and 0.6 wt.% CB films, respectively, as opposed to 0.5 V and 3 V for their unpoled counterparts.However, it is worth noting that the alignment of the dipoles diminishes significantly over time, as our study further indicated.To demonstrate the possible practical application of this self-poled P(VDF-TrFE)/CBbased PENG, a simple full-wave rectifier bridge circuit was designed with an output capacitor (2.2 µF), four diode rectifiers (IN 4007), a switch, and a light-emitting diode (LED, 515-520 nm, and 0.6 µW) as shown in Figure 11a.We also investigated the charging of a 2.2 µF capacitor (C) under the same loading condition, where the output voltage was found to reach a steady state of 2.6 V after 35 s, with 6 N applied force, and the energy stored in the capacitor reached 7.4 µJ (E = 1 2 CV 2 ).This stored energy successfully lit up a green LED for a few seconds, as shown in the inset Figure 11b.A video link for this has been added in the Supplementary Section in Figure S7 with an image of glowing RGB color LEDs.
To evaluate the loss in piezoelectric performance of the poled composite films over time, we conducted tests for a duration of 7 days.We determined the change in their polarization by measuring the peak-to-peak output voltages as a function of time.Table 5 summarizes the output voltages for the poled and unpoled 0 wt.% and 0.4 wt.% CB samples, as well as the poled 0.6 wt.% CB sample over a one-week period.Figure 12a illustrates the reduction in percentage output voltage for these films to facilitate better comparison.We observed a significant reduction in output voltage (and therefore polarization) for poled composite films over time, resulting in a loss of approximately 27% to 55% of their polarization within 7 days (see Figure 12a).The significant decrease in polarization observed in the poled films aligns with an earlier report [55].As expected, over the 7-day period, the unpoled film showed no loss in polarization.Figure 12b provides a direct comparison between the 0 and 0.6 wt.% CB composite films under poling and unpoling conditions in terms of the retention of their piezoelectric properties over time.
We observed that the piezoelectric properties of the unpoled 0.6 wt.% CB film remained essentially unchanged even after a week, consistently producing an output voltage of ~3 V.In contrast, the poled 0 wt.%CB film lost 36.8% of its original polarization during the same timeframe, resulting in a output voltage of 2.4 V compared to the initial 3.8 V immediately after poling.Indeed, as shown in Figure 12b, the output voltage of an unpoled 0.6 wt.% CB film (3 V) remained 0.6 V higher than the unpoled 0 wt.%CB film, which generated 2.4 V after 7 days when the output voltages stabilized.Moreover, poled 0.8 wt.% CB film lost its polarization over time gradually, resulting in a voltage of only 5.2 V.These results clearly indicate that self-aligned dipoles created by the chemical incorporation of additives are much more stable than dipole alignment achieved during poling by applying an electric field.To demonstrate the possible practical application of this self-poled P(VDF-TrFE)/CBbased PENG, a simple full-wave rectifier bridge circuit was designed with an output capacitor (2.2 µF), four diode rectifiers (IN 4007), a switch, and a light-emitting diode (LED, 515-520 nm, and 0.6 µW) as shown in Figure 11a.We also investigated the charging of a 2.2 µF capacitor (C) under the same loading condition, where the output voltage was found to reach a steady state of 2.6 V after 35 s, with 6 N applied force, and the energy stored in the capacitor reached 7.4 µJ (E = ½CV 2 ).This stored energy successfully lit up a green LED for a few seconds, as shown in the inset Figure 11b.A video link for this has been added in the Supplementary Section in Figure S7 with an image of glowing RGB color LEDs.To evaluate the loss in piezoelectric performance of the poled composite films over time, we conducted tests for a duration of 7 days.We determined the change in their polarization by measuring the peak-to-peak output voltages as a function of time.Table 5 summarizes the output voltages for the poled and unpoled 0 wt.% and 0.4 wt.% CB samples, as well as the poled 0.6 wt.% CB sample over a one-week period.Figure 12a illustrates the reduction in percentage output voltage for these films to facilitate better comparison.We observed a significant reduction in output voltage (and therefore polarization) for poled composite films over time, resulting in a loss of approximately 27% to 55% of their polarization within 7 days (see Figure 12a).The significant decrease in polarization observed in the poled films aligns with an earlier report [55].As expected, over the 7-day period, the unpoled film showed no loss in polarization.Figure 12b provides a direct comparison between the 0 and 0.6 wt.% CB composite films under poling and unpoling conditions in terms of the retention of their piezoelectric properties over time.
We observed that the piezoelectric properties of the unpoled 0.6 wt.% CB film remained essentially unchanged even after a week, consistently producing an output voltage of ~3 V.In contrast, the poled 0 wt.%CB film lost 36.8% of its original polarization during the same timeframe, resulting in a reduced output voltage of only 2.4 V compared to the initial 3.8 V immediately after poling.Indeed, as shown in Figure 12b, the output voltage of an unpoled 0.6 wt.% CB film (3 V) remained 0.6 V higher than the unpoled 0 wt.%CB film, which generated 2.4 V after 7 days when the output voltages stabilized.Moreover, poled 0.8 wt.% CB film lost its polarization over time gradually, resulting in a voltage of only 5.2 V.These results clearly indicate that self-aligned dipoles created by the chemical incorporation of additives are much more stable than dipole alignment achieved during poling by applying an electric field.The d33 coefficient is an important indicator of the piezoelectric performance of films and is particularly useful for comparing films of different sizes and thicknesses.It is influenced by various factors, including the degree of poling and the type and content of nanomaterials in composites [16].In our experimental setup, we measured the applied force to the film using an FSR, as depicted in Figure 8.However, since the exact area of the force The d 33 coefficient an important indicator of the piezoelectric performance of films and is useful for comparing films of different sizes and thicknesses.It is influenced by various factors, including the degree of poling and the type and content of nanomaterials in composites [16].In our experimental setup, we measured the applied force to the film using an FSR, as depicted in Figure 8.However, since the exact area of the force application is uncertain, we estimated the variation of the d 33 coefficient, assuming the average d 33 values of 0 wt.%CB content film (pure P(VDF-TrFE) film) reported in the literature, and then determining the relative change in d 33 with CB composition.Hu et al. [44] reported the d 33 value for annealed P(VDF-TrFE) film without any nanofiller as (3 pC/N), which agrees well with the d 33 value for the 140 • C annealed film reported by Chen et al. [56] of 2.0 ± 0.8 pC/N.Thus, we assumed a d 33 value for our 0 wt.%CB film as 2.8 pC/N based on the above reports.The output voltage generated by a piezoelectric film of thickness (l), under a force (F), applied over an effective area A eff is given by the equation where d 33 , k, ε are the piezoelectric strain coefficient, dielectric constant of the P(VDF-TrFE), and permittivity, respectively.The effective area (A eff ) was found to be 1.4 mm 2 , a small fraction of the actual sample area of 4 cm 2 .Most of the parameters on the right-hand side of Equation ( 2) remain the same for the films, except d 33 and thickness (which increased slightly with increasing CB content).We can calculate the d 33 values for composites with various CB percentages.The calculated d 33 values, both with and without annealing, are plotted in Figure 12c and listed in Table 5.We particularly observed a significant improvement in the d 33 value, which increased from 2 pC/N to 10.5 pC/N when 0.6 wt.% CB was added to P(VDF-TrFE) under the same fabrication conditions.This structural enhancement is reflected in the much higher intensity of the maximum β-phase peak in the XRD spectra, as depicted in Figure 2d.Microscopically, such an enhancement is expected because an increased CB percentage leads to a higher fraction of β-crystallite formation through specific interactions between the hydroxyl groups found in CB and the CF 2 segments of P(VDF-TrFE).The d 33 value for P(VDF-TrFE) composite films has been reported by Hu et al. [44] to be 6 pC/N for unpoled P(VDF-TrFE)/GO composites.Similarly, Gwang Ho Kim et al. [57] fabricated PVDF/MWCNT nanocomposites and reported a d 33 value of 7.5 pC/N.To date, the highest reported d 33 value has been achieved by Badatya et al. [58] for self-poled PVDF/CNT composite foam, reaching a value of 9 pC/N.However, these d 33 values are still lower than the d 33 coefficient of 10.5 pC/N estimated for self-poled 0.6 wt.% CB composite films in this work.As expected, the d 33 value further increased with poling.For the 0 wt.%CB film, the d 33 increased sharply from 2 pC/N to 20 pC/N immediately after poling, slightly higher than the d 33 values reported for poled pure P(VDF-TrFE) in earlier studies, which were 16 and 18 pC/N [16,59].Similarly, for the 0.6 wt.% CB film, the change is also significant, with d 33 rising more than three times from 10.5 pC/N to 35 pC/N.Once again, the d 33 value of our poled 0.6 wt.% CB composite film, measured immediately after poling, surpasses the best-reported d 33 values of carbonbased nanocomposites to date [42,44,60].In fact, the d 33 value is also higher than that of recent inorganic piezoelectric nanoparticle-based P(VDF-TrFE) composites, including Ag, ZnO, and BaTiO3 [61][62][63].However, the value of d 33 for both poled 0 and 0.6 wt.% CB films significantly decreased after 7 days, stabilizing at values of 10 pC/N and 18.9 pC/N, respectively, the poled 0.6 wt.% CB film still exhibits a higher d 33 value compared to the best-reported d 33 values for poled composite films containing graphene oxide (GO) and carbon nanotubes (CNT) of 10.5, 12.25, and 16 pC/N, respectively [64,65].Our experimental findings highlight the advantages of piezoelectric composite films with CB, whether poled or not, for practical applications.These advantages include an easy fabrication process, exceptional material properties, thin film design, and high piezo coefficients.This device shows promise for sequentially charging multiple capacitors over time, enabling the storage of substantial energy for applications such as wearable/implantable bio-electronic devices and smart systems [66][67][68].They also open up applications in sensing force, and pressure, offering credible competition to existing inorganic piezo-based material sensors, including those based on PZT [69], LiNbO3 [70], and III-Nitrides [71][72][73].
Conclusions
The composite films were investigated using multiple characterization techniques, demonstrating their high material quality across all CB percentages.The piezoelectric voltage generated via the composite films, under similar applied force, increased monotonically with higher CB concentration for both poled and non-poled films, reaching a peak in piezoelectric voltage generation at 0.6 wt.%, beyond which the films exhibited low resistance due to conducting bridges formed by the CB.At a 0.6 wt.% CB composition, we measured the highest peak-to-peak output voltage of 3 V, which is six times higher than that of the unpoled 0 wt.%CB film.The piezoelectric properties of the unpoled composite films also exhibited excellent stability with time, in contrast to the rapid reduction observed for poled films, leading to superior piezoelectric performance for the unpoled 0.6 wt.% CB film compared to the poled 0 wt.%CB film after a week.The superior piezoelectric performance of the unpoled 0.6 wt.% composite films was further enhanced with poling, resulting in high d 33 values of 10.5 and 35 pC/N, respectively, which are among the best reported so far for all carbon-based composite P(VDF-TrFE) films.
Figure 1 .
Figure 1.(a) Schematic representation for the fabrication process of the flexible P(VDF-TrFE)/CB composite films.(b) Photo images of the fabricated P(VDF-TrFE)/CB composite films on glass substrates with CB content varying from 0 wt.% to 1 wt.%.
Figure 1 .
Figure 1.(a) Schematic representation for the fabrication process of the flexible P(VDF-TrFE)/CB composite films.(b) Photo images of the fabricated P(VDF-TrFE)/CB composite films on glass substrates with CB content varying from 0 wt.% to 1 wt.%.
Figure 2 .
Figure 2. XRD spectra for (a) raw carbon black and P(VDF-TrFE) powder.(b) Temperature vs. 2 variation for 0.6 wt.% CB composite film, varying from 60 to 140 °C.(c) P(VDF-TrFE)/CB composite films, varying from 0 to 1 wt.%, over the scan range of 10° to 90° to study the diffraction peaks from (110/200) planes of the P(VDF-TrFE) β-phase formation at 19.3°.(d) A magnified view of the XRD spectra in the range of 17-22° for demonstrating the effect of adding CB.The inset shows FWHM for different CB composite films, varying from 0 to 1 wt.%.
Figure 2 .
Figure 2. XRD spectra for (a) raw carbon black and P(VDF-TrFE) powder.(b) Temperature vs. 2θ variation for 0.6 wt.% CB composite film, varying from 60 to 140 • C. (c) P(VDF-TrFE)/CB composite films, varying from 0 to 1 wt.%, over the scan range of 10 • to 90 • to study the diffraction peaks from (110/200) planes of the P(VDF-TrFE) β-phase formation at 19.3 • .(d) A magnified view of the XRD spectra in the range of 17-22 • for demonstrating the effect of adding CB.The inset shows FWHM for different CB composite films, varying from 0 to 1 wt.%.
Figure 3 .
Figure 3. FTIR spectra of (a) P(VDF−TrFE)/CB composite films varying from 0 to 1 wt.%.The dashed lines indicate β-phase characteristic peaks at the wavenumber 850 cm −1 , 1290 cm −1 , and 1400 cm −1 .(b) A magnified view of the FTIR spectra between 700 and 900 cm -1 representing the intensity change in absorbance peaks of the α and β phase upon the addition of CB into P(VDF−TrFE).The inset shows the percentage of β-phase crystallinity vs. different CB wt.%.
Figure 3 .
Figure 3. FTIR spectra of (a) P(VDF−TrFE)/CB composite films varying from 0 to 1 wt.%.The dashed lines indicate β-phase characteristic peaks at the wavenumber 850 cm −1 , 1290 cm −1 , and 1400 cm −1 .(b) A magnified view of the FTIR spectra between 700 and 900 cm -1 representing the intensity change in absorbance peaks of the α and β phase upon the addition of CB into P(VDF−TrFE).The inset shows the percentage of β-phase crystallinity vs. different CB wt.%.
Figure 3 .
Figure 3. FTIR spectra of (a) P(VDF−TrFE)/CB composite films varying from 0 to 1 wt.%.The dashed lines indicate β-phase characteristic peaks at the wavenumber 850 cm −1 , 1290 cm −1 , and 1400 cm −1 .(b) A magnified view of the FTIR spectra between 700 and 900 cm -1 representing the intensity change in absorbance peaks of the α and β phase upon the addition of CB into P(VDF−TrFE).The inset shows the percentage of β-phase crystallinity vs. different CB wt.%.
Figure 4 .
Figure 4. Schematic representation of electrostatic interaction between PVDF−TrFE chains and CB indicating the formation of self-aligned dipoles.The enlarged view shows possible intermolecular hydrogen bonding between positively charged hydrogen atoms from the hydrophilic group(−OH) of carbon atoms and negatively charged fluorine atoms.
Figure 4 .
Figure 4. Schematic representation of electrostatic interaction between PVDF−TrFE chains and CB indicating the formation of self-aligned dipoles.The enlarged view shows possible intermolecular hydrogen bonding between positively charged hydrogen atoms from the hydrophilic group(-OH) of carbon atoms and negatively charged fluorine atoms.
Figure 7 .
Figure 7. (a) Schematic diagram showing parallel metal contacts with varying gaps for TLM measurements to determine the sheet resistance of the films with higher CB content.(b) Measured resistance vs. gap for different composite films with CB content varying from 0.8 to 2 wt.%.
Figure 7 .
Figure 7. (a) Schematic diagram showing parallel metal contacts with varying gaps for TLM measurements to determine the sheet resistance of the films with higher CB content.(b) Measured resistance vs. gap for different composite films with CB content varying from 0.8 to 2 wt.%.
Polymers 2023 , 21 Figure 8 .
Figure 8. Schematic representation of the experimental setup for piezoelectric output voltage measurement using periodic mechanical force generated by a shaker.The top-left inset shows a magnified view of the sample and force-sensing resistor, while the top−right inset shows the optical image of a fabricated energy harvester device with electrical contacts to the top and bottom surfaces of the sample.
Figure 8 .
Figure 8. Schematic representation of the experimental setup for piezoelectric output voltage measurement using periodic mechanical force generated by a shaker.The top-left inset shows a magnified view of the sample and force-sensing resistor, while the top−right inset shows the optical image of a fabricated energy harvester device with electrical contacts to the top and bottom surfaces of the sample.
Figure 9 .
Figure 9. Frequency−dependent calibrated output voltage of different unpoled P(VDF−TrFE)/CB composite films under 6 N applied force with 1 Hz frequency.The output voltages from (a) FSR, (b) 0 wt.% unpoled, (c) 0.2 wt.% unpoled, (d) 0.4 wt.% unpoled, (e) 0.6 wt.% unpoled films, and magnified plot from a single cycle of press and release (by the shaker) of unpoled 0.6 wt.% CB film shown by the dotted rectangle in (e).Clear evidence of damping can be observed from the oscillatory behavior with reducing amplitude.
Figure 9 .
Figure 9. Frequency−dependent calibrated output voltage of different unpoled P(VDF−TrFE)/CB composite films under 6 N applied force with 1 Hz frequency.The output voltages from (a) FSR, (b) 0 wt.% unpoled, (c) 0.2 wt.% unpoled, (d) 0.4 wt.% unpoled, (e) 0.6 wt.% unpoled films, and magnified plot from a single cycle of press and release (by the shaker) of unpoled 0.6 wt.% CB film shown by the dotted rectangle in (e).Clear evidence of damping can be observed from the oscillatory behavior with reducing amplitude.
Figure 11 .
Figure 11.(a) Full-wave bridge circuit for charging the capacitor.(b) Charging transient for the 2.2 µF capacitor using an unpoled P(VDF-TrFE)/CB composite film with 0.6 wt.% of CB under applied force (6 N) and 1 Hz frequency.The inset shows a picture of a glowing LED using the harvested energy.
Figure 11 . 21 Table 5 .
Figure 11.(a) Full-wave bridge rectifier circuit for charging the capacitor.(b) Charging transient for the 2.2 µF capacitor using an unpoled P(VDF-TrFE)/CB composite film with 0.6 wt.% of CB under applied force (6 N) and 1 Hz frequency.The inset shows a picture of a glowing LED using the harvested energy.
Figure 12 .
Figure 12.(a) Piezoelectrically generated output voltage of poled and unpoled P(VDF-TrFE)/CB composite films measured over a duration of 7 days.(b) Comparison of the peak-to-peak output voltage for poled and unpoled CB films over 7 days.(c) Bar charts comparing the calculated d33 coefficients for 0 and 0.6 wt.% P(VDF-TrFE)/CB composites with and without poling.
Figure 12 .
Figure 12.(a) Piezoelectrically generated output voltage of poled and unpoled P(VDF-TrFE)/CB composite films measured over a duration of 7 days.(b) Comparison of the peak-to-peak output voltage for poled and unpoled CB films over 7 days.(c) Bar charts comparing the calculated d 33 coefficients for 0 and 0.6 wt.% P(VDF-TrFE)/CB composites with and without poling.
Table 1 .
Summary of XRD spectra of synthesized 0.6 wt.% CB composite film under different crystallization temperatures (Tcr).
Table 1 .
Summary of XRD spectra of synthesized 0.6 wt.% CB composite film under different crystallization temperatures (T cr ).
Table 2 .
Summary of XRD spectra, FTIR measurements, and AFM-measured surface roughness of different CB wt.% varied from 0 to 1 and annealed at 140 • C.
Table 3 .
Generated output voltage and d 33 coefficient value for different poled and unpoled CB wt.% composite films under 1 Hz excitation and 6 N force.
Table 3 .
Generated output voltage and d33 coefficient value for different poled and unpoled CB wt.% composite films under 1 Hz excitation and 6 N force.
Table
Comparison of piezoelectric of the PVDF and its copolymer-based composites, including the P(VDF-TrFE)/CB composite film from this work (shown in bold). | 12,125.4 | 2023-10-01T00:00:00.000 | [
"Engineering",
"Materials Science",
"Physics"
] |
On the Equivalence of Causal Propagators of the Dirac Equation in Vacuum-Destabilising External Fields
In QED, an external electromagnetic field can be accounted for non-perturbatively by replacing the causal propagators used in Feynman diagram calculations with Green’s functions for the Dirac equation under the external field. If the external field destabilises the vacuum, then it is a difficult problem to determine which Green’s function is appropriate, and multiple approaches have been developed in the literature whose equivalence, in many cases, is not clear. In this paper, we demonstrate for a broad class of external fields that includes all that act for a finite time, that four Green’s functions used in the literature are equivalent: Schwinger’s “proper-time” propagator; the “causal propagator” used in the “Bogoliubov transformation” method based on the canonical quantization of the field operator; and two defined using analytic continuation from complexified parameters. To do so, we formulate Schwinger’s “proper-time quantum mechanics" as a Schrödinger wave mechanics, and use this to re-derive Schwinger’s expression for the propagator as a statement relating solutions of the inhomogeneous Dirac equation to those of the inhomogeneous “proper-time Dirac equation”. This is done by constructing direct integral spectral decompositions of the Hamiltonians of both equations, and deriving a form for solutions of the inhomogeneous Dirac equation in terms of these decompositions. We then show that all four propagators return solutions of the inhomogeneous Dirac equation that satisfy the same boundary condition, which under a physically reasonable assumption is sufficient to specify the solution uniquely.
Introduction
The approach of Furry and Feynman [1,2] to account for an external electromagnetic field in quantum electrodynamics non-perturbatively is to replace causal propagators of the free particle Dirac equation in Feynman diagram calculations with "causal propagators" for the Dirac equation under an external field. This method, though, is only unambiguous if the field is such that, over the course of the scattering event, positive energy states stay as positive energy and negative stay as negative energy. Physically, this is the case if the vacuum is stable under the external field. When we generalise to the case of a vacuum-destabilising external field, such as a constant electric field, two related problems arise: it is not clear what propagator is appropriate, and the interpretation of the "vacuum" becomes problematic. We address the former problem in this paper.
Multiple approaches have been developed to the problem of QED in a vacuumdestabilising external field [3]. We are largely interested in two of the most widely used. First, Schwinger developed a "proper-time" technique for calculating a propagator and the effective action [4]. This was generalised by DeWitt to account for curved spacetimes [5], and by later authors for the general gauge theory [6], as is reviewed [7]. The effective action approach to QED in a vacuum-destabilising field has continued to make heavy use of the proper-time method [8]. Further, the "stringinspired worldline formalism" [9] approach to effective actions has had success in application to nonperturbative particle production in QED [10,11]. The worldline formalism bears a striking resembles to Schwinger's proper-time method, though is carried out with both Euclidean coordinate-time and Euclidean proper-time.
Second, the "Bogoliubov transform" method based on the canonical quantization of the bispinor field operator [12][13][14][15] represents an especially systematic account of QED in a vacuum-destabilising field. It is summarised in [16], and we shall refer to the method from here on as being that of "FGS" after this work's authors. FGS introduce many propagators, associated with electrons and positrons defined with respect to different vacua. It is demonstrated by explicit calculation in Chap. 6 of [16] that their "causal propagator" is equivalent to Schwinger's proper-time representation of the propagator in the case of a constant field superimposed with a plane wave. There is a "strong belief" [17] that the two propagators are equivalent in the general case, but no proof. In this paper we demonstrate equivalence for a broad class of external fields which includes all that act for a finite time.
We do so by considering the Green's function as an operator, Ĝ , on source profiles, J(x), that returns solutions to the inhomogeneous Dirac equation, We shall from here on refer to Eq. 2 as the "inhomogeneous spacetime Dirac equation", to distinguish it from the proper-time equation defined in Sect. 2.1. We restrict attention to the case that J(x) is supported only on a finite time, between t in < 0 and t out > 0. (The assumption that such an operator defines the Green's function well is discussed in Sect. 5.3.1.) We then impose the condition that before the time t in < 0 (2) (i ( + ieA )) − m 0 ) (x) = −J(x). and after time t out > 0 there is no electric field, and that the gauge field is constant in time. This implies that it can be written with the following restricted dependencies, For our purposes, Schwinger's principle result is the operator relation where The bulk of this paper, Sect. 2, is devoted to a re-derivation of Eq. 4 as a statement relating solutions of partial differential equations, followed by the result that Ĝ J necessarily obeys the "Feynman boundary condition", defined in Sect. 2.2.3. Demonstrating equivalence with Schwinger's propagator (4) is then trivial, as shown in Sect. 4.1. In Sect. 3 we demonstrate that solutions derived using FGS's causal propagator also obey the Feynman boundary condition, and in Sect. 4.2 we demonstrate the same for solutions derived using two different varieties of analytic continuation from complexified parameters. Under an additional assumption discussed in Sect. 2.2.3, which we share with FGS, this boundary condition is sufficient to determine the solution of the inhomogeneous equation, and hence the propagator. We therefore demonstrate the equivalence of four different causal propagators, with caveats discussed in Sect. 5.
This acts as an "interpretation" of Schwinger's proper-time formalism, which could be of independent interest to work involved in interpreting the proper-time quantum mechanics as "physically significant", as is reviewed in [18]. In doing this we have also modernised the formalism in which Schwinger's proper-time quantum mechanics is expressed. Schwinger formulated his proper-time quantum mechanics using Dirac's bra-ket notation, which does not account for the difficulties involved with unbounded operators and their continuous eigenbases [19]. FGS similarly circumvent such issues by assuming a discrete eigenbasis for the Dirac Hamiltonian. This work applies formalisms to Schwinger's proper-time quantum mechanics, such as von Neumann's direct integral [20], which have been applied in rigorous formulations of non-relativistic quantum mechanics to account for unbounded operators [21]. Our argument, though, is not a full rigorous proof, as through Sect. 2 we make a number of mathematical assumptions. As discussed in Sect. 5.3, these assumptions are the sort that uses of the bra-ket formalism frequently make implicitly. Using this formalism has the advantage that it makes mathematical assumptions explicit that the more conventional physics formalism leaves implicit. It therefore acts as an initial step towards formulating Schwinger's proper-time quantum mechanics in the rigorous terms that have been developed for regular quantum mechanics since he wrote.
Basic Definitions
Define M and S as the manifolds formed by attaching a bispinor to every point in spacetime and space, respectively. We are interested in the Hilbert spaces defined by their representation as square-integrable functions on M and S, where "P.T." stands for "proper-time" and "S.T." stands for "Spacetime". Denote the inner products on these spaces ( , ) P.T. and ( , ) S.T. . There are three basic operators that we consider: Ĥ on H P.T. (5) and two operators on H S.T. , The operator (8) is the "Dirac Hamiltonian" for times t ≤ t in or t ≥ t out , since at these times the homogeneous spacetime Dirac equation with mass m can be written on elements of C 1 (ℝ;H S.T. ) as In Sects. 2.2 and 2.3 we construct representations of, respectively, H S.T. and H P.T.
in which Ĥ in∕out m and Ĥ are represented by multiplication operators. To do this, we use the "direct integral" version of the spectral theorem, as presented in e.g. [21]. If  is a self-adjoint operator, then we denote its spectrum by (Â), its corresponding representation of the Hilbert space by HÂ, and the unitary transformation from the abstract space to H by Û . The spectral theorem tells us that that there exists a measure,  , on (Â), such that Elements ∈ H are sections on the spectrum with values in the generalised subspaces, ( ∈ (Â)) ∈ HÂ. We write the product on these subspaces as (a, b) , and the Hilbert space product is represented bŷ in∕out and Ĥ 2 are symmetric. We assume that they are also self-adjoint, which means we assume that their domain equals the domain of their adjoint. This allows us to use the spectral theorem on them directly, and we then use their spectral representations to construct those of Ĥ in∕out m and Ĥ . The relationship between these representations is examined in Sects. 2.4 and 2.5. In Sect. 2.6 these results are used to analyse the relationship between the solutions of the inhomogeneous spacetime Dirac equation (2) and the inhomogeneous proper-time Dirac equation, defined on elements of C 1 (ℝ;H P.T. ), We use the convention that the same symbol is used to represent the same vector as it appears in different representations of the same Hilbert space, with the representation being distinguished by the argument of the vector, i.e. if a vector in the abstract space is written as ∈ H then [Û ]( ) = ( ). We will also write vectors in Hilbert spaces defined as direct sums, H A ⊕ H B , as column vectors. The convention we use is that the top row of the column contains the vector in the space on the left side of the sum, i.e.
Construction of the Representation
As discussed in Sect. 2.1, we can define a direct integral representation of H S.T. on which ̂i n∕out is represented by a multiplication operator, Because 0 is a bounded operator that anticommutes with ̂i n∕out , it can be represented as a transformation between the generalised subspaces, written in the form Since this is an invertible unitary transformation, we know from its existence that is in the point spectrum iff − is, that is in the continuous spectrum iff − is, and that dim(H in∕out ) = dim(H − in∕out ) . We can therefore choose the measure to be such that we can define a new representation H in∕out,|̂| , We write Û in∕out |̂| for the unitary transformation from H P.T. to H in∕out,|̂| , and (a, b) ⊕− for the product on the generalised subspaces. We write sections in this representation as in∕out ( ) , with the superscript included to distinguish the representation since in this case the usual practice of distinguishing by the argument would be ambiguous. Now consider the operators on and on H 0 in∕out , We neglect the ≠ 0 , m = ±i case, where the operator Ĥ in∕out m is not diagonalizable. We argue in Sect. 5.3.2 that the assumption that this will not affect our overall argument amounts to a minimal assumption on the spectrum of Ĥ and ̂i n∕out . These operators obey (P ± in/out, ,m ) 2 =P ± in/out, ,m and 1 = ± a m ∶=P ± in, ,m a, ± a m ∶=P ± out, ,m a
The Bipartition of H S.T. and Feynman Boundary Conditions
Define P ± in/out,m as the operator on H S.T. induced by the P ± in/out, ,m operators on the generalised subspaces, P ± in/out,m ∶ ( ) ↦P ± in/out, ,m ( ) . We can then define the target spaces of P ± in,m as ± H m S.T.
, and the target spaces of P ± out,m as ± H m S.T. , such that Note that this bipartition is orthogonal if m is real, and The name is chosen as the boundary condition is a natural generalisation of that discussed by Feynman for the free particle causal propagator [2]. It is a straightforward consequence of the linearity of the boundary condition that it uniquely determines a solution of the inhomogeneous spacetime Dirac equation if and only if there exists no nontrivial solution of the homogeneous spacetime Dirac equation that satisfies the boundary condition. A closely related condition is discussed by FGS [16,Chap. 2.4]. They demand that the determinant of the transformation matrix between the basis of negative energy in-states and negative energy out-states is non-zero. This would be the case if and only if there are no vectors in the space of negative energy in-states which transform to vectors with no components in the negative energy out-space -i.e. there are no nontrivial solutions to the homogeneous spacetime Dirac equation which satisfy the Feynman boundary condition. FGS introduce this as a condition for the Fock spaces formed by the action of the creation operators on the in and out vacua to coincide. The physical implications of this condition being violated are unclear, but probably significant: it seems to correspond to a situation where the vacuum states at the in and out times are too radically different to be described in terms of particle perturbations of each other, and hence the whole approach to externalfield QED that thinks in terms of perturbative particle processes expanded about the transition from vacuum to vacuum breaks down. Therefore, in physical situations where any of the approaches to external-field QED being considered in this paper are appropriate, this condition ought to be satisfied.
A Representation of H P.T. in Which Ĥ is Diagonal
As discussed in Sect. 2.1, we can define a direct integral representation of H P.T. on which Ĥ 2 is represented by a multiplication operator, Consider the representation of Ĥ on this space. Since it commutes with Ĥ 2 , it must be able to be represented by an operator Ĥ ( 2 ) on every H 2 H 2 space, and since (Ĥ( 2 )) 2 = 2 , we know that if ≠ 0 then Ĥ ( 2 )∕ is defined everywhere on this space [22]. We can therefore define the operators, for 2 ≠ 0, These obey P 2 =P and 1 =P +P − . They are therefore a complete set of projection operators, and we can define their target spaces as HĤ such that This bipartition is orthogonal if is real. Define also P 0 ∶= 1. We can then define HĤ and ÛĤ ∶ H P.T. → HĤ by where Ĥ is the push-forward of Ĥ2 by = sign( ) (Considering 2 as an independent variable.) Note that since ( (Ĥ)) 2 = (Ĥ 2 ), (Ĥ) is confined to the real and imaginary axes of the complex plane. It directly follows from Eqs. 24 and 26 that Ĥ is represented in HĤ as a multiplication operator, Ĥ ∶ ( ) ↦ ( ). To derive the representation of the Hilbert-space product in HĤ, first define This gives where (a, b) is the inner product of HĤ . In the last equality we have moved the sum over ± outside the integral, which we must assume to be possible.
Generalised Eigenvectors of Ĥ
Consider a vector in one of the generalised subspaces that makes up the direct integral HĤ , a ∈ H 0 H . If 0 is in the point spectrum, then a is a true eigenvector of Ĥ . If 0 is in the continuous spectrum, though, then this "generalised eigenvector" is not a vector in the Hilbert space proper. Whether 0 is in the continuous or point spectrum, it can be seen as a representation-independent object by its action as a linear functional, This functional action is well-defined on any ∈ HĤ for which ̄ is of finite magnitude at = 0 . This includes the whole Hilbert space iff 0 is in the point spectrum. These generalised eigenvectors are functional solutions of the homogeneous spacetime Dirac equation with mass m = − 0 . We assume that they are able to be chosen to have some desirable properties. First, we assume that they are classical solutions at t ≤ t in and t ≥ t out . Specifically, for every a ∈ HĤ , there exists t is a sequence of ℂ-valued functions that act as a nascent delta function centred on t as n → ∞ . This means that we can define a mapping from every HĤ to H S.T. for every time t ≤ t in or t ≥ t out , a ↦ a(t) , and that for times t, t ′ ≤ t in or t, t ′ ≥ t out these are related by a(t) =T − (t, t � )a(t � ) as defined in Eqs. 20a and 20b.
We need two other results. First, it follows straightforwardly from Eqs. 20a and 20b and (a, a) P.
, and E out ± ( , ) must have negative imaginary component for every non-zero ± a − ( ;t out ) . A true eigenstate of Ĥ cannot have a component of real energy. We want a similar though less strict restriction on the generalised eigenstates, which we assume rather than demonstrate. We assume that the generalised eigenvectors a ∈ HĤ do not grow exponentially. This would necessarily be true if the external field is smooth with all derivatives polynomially bounded, as then Ĥ leaves the Schwartz class invariant, and hence we could use the nuclear spectral theorem to determine that our eigenstates are tempered distributions [23].
Projecting a Vector in H P.T. onto a Vector in H S.T.
Since H P.T. ≅ L 2 (ℝ;H S.T. ) , for any ∈ H P.T. we can assign, for every t ∈ ℝ , (t) ∈ H S.T. . This means of projecting a Hilbert-space state onto a time must be consistent with the projection of the generalised eigenvectors just discussed. Therefore, Working in the H in∕out,|̂| this becomes Assuming that we can change the order the integrals and the implicit sum over the basis sections of H in∕out,|̂| , this gives The primary aim of this subsection is to convert the RHS of this equation into an inverse Fourier transform for times t ≤ t in and t ≥ t out . Call I ± in∕out the open vertical half-line in the upper (+ case) or lower (− case) complex half-plane that has eA in∕out 0 as its finite limit point. Call I in∕out the verticle line in the complex plane that intersects the real axis at eA in∕out 0 . Call iℝ the imaginary axis, and iℝ ± the open positive/ negative imaginary half-axes. Extend the measure Ĥ to the whole imaginary and real axes by stipulating Ĥ ( ) = 0 if ∩ (Ĥ) is empty. Then we can use Eqs. 20a and 20b to write Eq. 33 as where we assume it is possible to bring the sum over ± outside of the integral. Define and such that (32) Then, splitting the integrals in Eq. 34 in half, we use Eq. 37 to write them in a form amenable to a change of variables, where we have used our assumption, discussed at the end of Sect. 2.4, that generalised eigenvectors cannot exponentially grow to eliminate half the integral over the vertical line. Define where the "u" and "l" superscript refer to the fact that u∕l can be taken as an analytic function of E on the whole upper/lower half complex plane. Define also such that We proceed, in the rest of this subsection, to convert the integral over imaginary energies to one over real energies, possible by virtue of the assumption that exponential increase is forbidden. This completes the conversion of the RHS of Eq. 33 into an inverse Fourier transform. We need quite a general result, for which we assume that we can express ± ( ;E) and ± ( ;E) in the form where g u∕l (E) is a complex-valued meromorphic function on the upper/lower halfplanes which is bounded on I in∕out ∪ ℝ and as |E| → ∞ . Note that g u∕l (E) could depend on ± and , but since this possible dependence does not affect the following manipulations, we neglect it here. Define where the sum runs over poles of g(E) in the upper/lower half plane. Then, by the residue theorem and Jordan's lemma, by closing the E integral in the upper plane for the "in" case and the lower plane for the "out" case. Assuming that we can exchange the order of the integrals along the vertical lines, i.e.
(42) ± ( ;E) = g u (E) ± ( ;E), ± ( ;E) = g l (E) ± ( ;E), and This allows us to write where, and for real E, where in∕out ( ;E) ∈ [0, ∞) . This expression for the measure is possible since we know that true eigenvectors of Ĥ cannot have components with real energy, hence in∕out E, for real E must be absolutely continuous with respect to the Lebesgue measure.
The Relationship Between Solutions of the Inhomogeneous Spacetime and Proper-Time Dirac Equations
The inhomogeneous proper-time Dirac Eq. (11) can be written in HĤ as (45b) The term "retarded solution" of course implies that this is the unique solution that satisfies this condition, which seems likely but which we do not have a proof for, due to the awkward properties of Ĥ , and hence how little knowledge we have of its spectrum. This does not strictly affect our argument, though, since we do not use this condition as our definition. We want to consider the response to a plane wave driving source. The solution, though, is not a well-defined section at = −m 0 , and it cannot be directly defined as being zero before the source acts, since a plane-wave source acts forever. We therefore have to define it as a functional solution of the Dirac equation, reached as a limit of a sequence of H P.T. solutions. Specifically, we say Definition (retarded response to a plane wave) Say J( ) = Je im 0 . The retarded response to this source is given by the functional limit of the sequence of solutions given by Eq. 49a, 49b and 49c to the inhomogeneous proper-time Dirac equation with source profile (47) (i − ) ( ; ) = −J( ; ). where it is possible to bring the limit into the integral, once the limit has been brought outside. (Strictly, "continuous" should be interpreted as "Hölder-continuous" for the principal value to be well defined [24].) Therefore, the retarded response to a plane wave source J( ) ∈ HĤ , of frequency −m 0 , which is continuous at = −m 0 , is a functional, ( ) , with a defined action on all ∈ HĤ for which ̄ is also continuous at = −m 0 . This solution can also be seen as the limit of the H P.T. states as → 0 + . Using this, Therefore ( ) , the retarded response to a plane wave of proper-time frequency −m 0 , is a functional solution of the inhomogeneous spacetime Dirac equation (2) with mass m 0 and source profile J. This is the fundamental result that reflects Schwinger's operator relation (4).
The Retarded Response to a Plane Wave Obeys the Feynman Boundary Condition
The functional solution of the inhomogeneous proper-time Dirac equation projects onto a functional on some subset of H S.T. at a particular time. By Eq. 33 this can be written, with t ≤ t in or t ≥ t out . Use Eqs. 41c and 41d to write Define which is a meromorphic function in the upper/lower plane and uniformly bounded as |E| → ∞ . We can therefore use Eqs. 46c and 46d with g u∕l (E) = 1 to write and with g u∕l (E) as defined in Eq. 57, We know that J in ( , t) is supported only on t > t in and J out ( , t) is supported only on t < t out . In Appendix 3 we argue that we can treat both ± components in the sum on the RHS of Eqs. 58a and 58b as also independently satisfying this condition. Therefore, we can use Eq. 98 to carry out the integrals, where the sum runs over poles in the upper and lower half plane in Eqs. 60a and 60b, respectively. This gives Note that the integral over p in Eq. 59 has cancelled with that in the definition of J in Eqs. 46c and 46d. g u∕l ,± (E, ) has poles at with residues ±m 0 ∕ √ m 2 0 + 2 + O( ) . Therefore in the "in" case we capture the negative energy pole, and in the "out" case we capture the positive energy pole. Tak- where we have used Eqs. 41a, 41b, 41c and 41d to write the RHS. It is clear that this is in H S.T. as a direct consequence of our assumption that the generalised eigenvectors projected onto times t ≤ t in and t ≥ t out take values in H S.T. (30). It is also clear from Eq. 22 that it obeys the Feynman boundary condition.
The "Causal Propagator" of Fradkin, Gitman & Shvartsman
FGS [16] require that their external field's instantaneous energy spectrum at t in and t out has a gap that covers E = 0 . They also assume that the Hamiltonian at t in and t out , Ĥ in∕out The term in round brackets is Schwinger's expression for his Green's function (4), with an infinitesimal negative imaginary inserted. Schwinger inserted the infinitesimal negative imaginary during calculations that would otherwise explicitly return a divergence. Later authors [5] formalised this procedure, and say that the expression is defined for negative imaginary mass, with the prescription that solutions for the real mass are to be derived by then taking the limit of the imaginary component to zero, perhaps after appropriate integrations. In this work this procedure is understood as returning a functional solution of the Dirac equation with a domain smaller than H P.T. , with action ⟨ , ⟩ = lim →0 + ( , ) P.T. .
The m 2 − i Prescription and Continuation from Euclidean Time
Consider a solution of the inhomogeneous spacetime Dirac equation with mass m 0 that takes values in H S.T. for t ≤ t in and t ≥ t out , before and after the source acts. At these times they are just solutions to the homogeneous spacetime Dirac equation, so we can write, in the H in∕out,|̂| representations according to Eqs. 20a and 20b, Now consider that we demand that these solutions are each analytic functions of m 0 in some open region, confined to the lower half complex plane, which has m 0 as a limit point. Further, we demand that in this region, no component grows exponentially. The m 0 dependence in the ± m 0 ( ;t � ) and ± m 0 ( ;t � ) terms are here insignificant, so we can focus on the mass-dependence in the exponential, which is in fact a dependence on m 2 0 . Specifically, we can enforce this demand by asking that there exists an > 0 such that for all masses m 2 ( ) ∶= m 2 0 − i , for all ∈ (0, ] , the expression (75) does not grow exponentially as t → ±∞ . This is true if and only if + m 0 ( ;t ≤ t in ) = − m 0 ( ;t ≥ t out ) = 0 , which is the Feynman boundary condition. Next, consider making the same demand, that the solution does not grow exponentially, if we enact the replacement So long as |eA in∕out 0 | < m 0 , this enforces exactly the same requirement. This is a version of the idea that the causal solutions are to be derived by analytic continuation of solutions for "Euclidean time" [25]. Both these requirements are therefore equivalent to imposing the Feynman boundary condition. Note that this demand for a lack of exponential growth is often enforced in the literature implicitly. One way of doing so is to demand that the solution has a Fourier transform. This is the most common way in less mathematically rigorous works that use the " m 2 − i prescription". Another way of doing so is to demand that the solutions are tempered distributions. This is the procedure used in axiomatic treatments of Euclidean green's functions [25].
There is cause for caution here. To get the same boundary condition, we have needed to demand that the actual solutions for imaginary mass or imaginary time obey certain constraints on growth at infinity, not the terms of a perturbative series. If we were to demand that each of the solutions that form the asymptotic series approximation to the correct solution do not exponentially grow at infinity, then this would be neither necessary nor sufficient for their sum to not exponentially grow at infinity. This explains Gitman's observation [12] that FGS's causal propagator does not equal that derived by applying the m 2 − i prescription to the perturbative series expression of the propagator. In Feynman-diagrammatic terms, the important thing for the m 2 − i or Euclidean-time prescriptions to give the Feynman boundary condition is that the "leg" connecting the input and output particles to infinity is treated as propagation under the external field, not as a free propagator.
The Result
The principal result of this paper is the demonstration that, for a broad class of external fields (those satisfying the form (3)) and under reasonable mathematical assumptions, Schwinger's proper-time propagator, FGS's causal propagator, and propagators derived by analytic continuation of the complexified mass or time all obey what we call the "Feynman boundary condition". This can loosely be stated as the requirement that they propagate positive-energy solutions into the future and negative-energy solutions into the past. Under a further assumption discussed in Sect. 2.2.3, that there exists no solution to the homogeneous equation which is wholly negative-energy at the initial time and wholly positive-energy at the final time, this is a demonstration of the equivalence of all these propagators. To derive this result, we have interpreted Schwinger's operator relationship (4) as a statement relating the solutions of two partial differential equations: the retarded solution of the inhomogeneous proper-time Dirac equation (11) for a plane-wave driving source of proper-time frequency −m 0 is a solution of the inhomogeneous spacetime Dirac equation (2) with mass m 0 . When applied to fields of form (3), this also gives a novel expression for this solution before the in-time and after the out-time in terms of the decomposition of the source profile in the generalised eigenbasis of Ĥ (63). This result might be of independent interest. We now discuss the two caveats just mentioned, the class of external field and the mathematical assumptions made, in turn.
Conditions on the External Field
While Schwinger's propagator and the proper-time method described in Sect. 2 have been demonstrated to be wholly equivalent for any external field, the other three propagators considered have only been demonstrated as equivalent by their obedience of the Feynman boundary condition. Their obedience of the Feynman boundary condition is contingent on the field satisfying the conditions (3), so equivalence has only been demonstrated for fields satisfying these conditions. There are also some subtle distinctions in the conditions applied to some of the propagators, which we now discuss. First, the continuation from Euclidean time and FGS's causal propagator require |eA in∕out 0 | < m 0 , such that the "negative energy" states genuinely all have negative energy and the "positive energy" states all have positive energy. The proper-time method and the m 2 − i prescription do not. This is a technicality entangled with issues to do with the normalisation with respect to the vacuum, and besides can be fixed by a partial gauge constraint.
More substantially, FGS's causal propagator is only defined for times t out ≥ t ≥ t in . Say the field used for FGS's causal propagator is A (x) , and define A ′ satisfies the conditions (3) if and only if A (x) has no spatial variation at t in or t out . Therefore, the solution derived using the proper-time method, the m 2 − i prescription and continuation from Euclidean time matches on this temporal region if we use the field A � (x;t in , t out ) and A (x) has no spatial variation at t in or t out . We can therefore, using Eq. 77, derive a solution using any of the former three methods that matches that derived using FGS's causal propagator on the region t out ≥ t ≥ t in with a field constrained only by a partial gauge condition.
FGS derive a solution for all time by taking the limits t in → −∞ , t out → ∞ . We therefore have (78) lim for sufficiently large-magnitude t in and t out , and hence we get equality of all four methods on all time, We have therefore demonstrated the equality of all four propagators for all fields that obey the constraints (3) for all time. In this sense, equality has been proven for all "physical" situations, in which we can confine the action of the external field to some finite time. The limitation is important to state, though, since fields that do not obey condition (3) include such important theoretical cases as the everywhere uniform electric field considered by Schwinger [4]. FGS prove equivalence in this specific case by direct calculation [16], though, so there is some reason to suspect that the proper time and FGS propagators are equivalent in all cases. This paper's result could be extended to cover this general case if we knew that the mapping from external field profiles to inhomogeneous spacetime Dirac equation solutions, with fixed source profile, was continuous, and hence
The Green's Function is Well-Defined as a Mapping from Compactly Supported Source Profiles
We assume that the ascription of a (functional) solution of the inhomogeneous equation for every source profile that is compactly supported in time defines the Green's function well. There is no single mathematical result that justifies this, since we are demonstrating the equivalence of Green's functions as used in literature which does not share a strict definition of what mathematical object the Green's function is. Schwinger's definition of Ĝ as an operator on the Hilbert space is insufficient, as even when looking at our restricted class of source profiles, the solutions returned are not necessarily in the Hilbert space. To give the idea plausibility, consider that in axiomatic treatments of QFT [25] the Green's functions are often treated as tempered distributions on ℝ 3⊕1 ⊗ ℝ 3⊕1 . In this case, we can use the Schwartz kernel theorem to prove an isomorphism between this class and continuous linear mappings from source profiles in the Schwartz class to tempered-distributional solutions of the inhomogeneous equation [26]. The continuity of this mapping ensures that defining it on the compactly supported functions defines it well on the Schwartz class, since the compactly supported functions are dense in the Schwartz class. All uses we make of our H S.T. representations in which Ĥ in∕out m for imaginary m is diagonal proceeds from Eq. 33. Suppose in this equation, we set in∕out ( ; ;t) = 0 for = ±i . This would only alter the LHS of the equation if i or −i were in the point spectrum of Ĥ . Assuming this to be the case, for this alteration of the LHS to affect the Hilbert space state that in∕out ( ;t) represents, we require in∕out ( ;t) to be altered on a region of finite in∕out -measure. Since the point spectrum of Ĥ covers a region of Lebesgue-measure 0, the only way for this to be the case would be if were in the point spectrum of ̂i n∕out . Therefore, the neglect of the case where m = ±i can only matter if there exists a real number which is in the point spectrum of ̂i n∕out , and ±i is in the point spectrum of Ĥ . We therefore must assume this not to be the case.
Other Assumptions
There are three further classes of substantial mathematical assumptions made in this paper. The first class is that two operators which are known to by symmetric, ̂ and Ĥ 2 , are self-adjoint, as mentioned in Sect. 2.1. Proving that Hamiltonians with various potentials are self-adjoint is a known, difficult problem in the case of non-relativistic quantum mechanics [27]. The extension of this work to the proper-time case would be substantial. The second class is that the relevant solutions to the homogeneous and inhomogeneous spacetime Dirac equation are equal to H S.T. states at times t ≤ t in and t ≥ t out (30), and that they do not grow exponentially in the future or past. The third class is that we can exchange the order of various infinite sums and integrals, as done to derive Eqs. 28, 33, 34 and 46c,d. These are all the sorts of assumptions that are frequently made implicitly in calculations performed in the bra-ket formalism, where, respectively, unbounded operators are treated as operating on the whole Hilbert space, their eigenvectors are treated as if in the Hilbert space, and integrals and infinite summations over ket-vector bases are manipulated symbolically as finite summations. A significant reason it has been necessary to make them is that we have used very little knowledge of Ĥ : in particular its spectrum and the properties of its generalised eigenstates are largely unknown. A substantial work of functional analysis of Ĥ as an operator on H P.T. would be needed to validate our assumptions, which would probably necessitate some regularity constraints on the external field A (x) . This would act as an extension of some of the results derived from functional analysis for putting regular quantum mechanics on a mathematically rigorous footing [21,28] to Schwinger's proper-time quantum mechanics. This paper has not supplied the proofs needed for this extension. We believe it is clear, though, that the assumptions made are no more egregious than are commonplace in physics literature that uses the bra-ket formalism, and in making its assumptions explicit acts as a derivation of some plausible sufficient conditions for the validity of the proper-time method. The validation of these assumptions, or the derivation of fewer or less restrictive assumptions, is a substantial area for future work.
where in the first line we have used the Plancherel theorem, in the second we have used Eq. 86 and in the third we have used the known support of F u∕l (t) to extract a maximum value of e −2ty and used Eq. 83. Now write Next, write the interval I u y = [y, 0] , with y < 0 assumed, and I l y = [0, y] , with y > 0 assumed. Then define the positive integral Now consider where Fubini's theorem allows us to change the order of the integral. We can now use Eq. 88 to get Therefore for every fixed y, Λ u∕l ( , y) is an integrable function of on the real line. This means that there exists a sequence, { j ∈ ℝ} j , such that as j → ∞ [30], Define Γ u , as the anticlockwise rectangular contour with corners at (± , 0) , (± , ) , , ∈ ℝ + , which does not include the real line. Define, similarly, Γ l , as the clockwise contour with corners at (± , 0) , (± , − ) which does not include the real line. Also suppose the function h u∕l (z) has bounded absolute value |h u∕l (z)| as |z| → ∞ on the upper/lower complex plane, and is meromorphic on the upper/lower complex plane. Then we can write If we take j → ∞ , then the second two terms in the brackets vanishes by Eq. 93. If we then take → ∞ then the first term vanishes by Eq. 88, so long as t < B in the "u" case and t > A in the "l" case.. Sup Γ u∕l j , |h u∕l (z)| 2 stays finite by assumption, and hence Therefore, there exists a way of taking Γ u∕l to be an infinite rectangular contour in the upper/lower half plane excluding the real line, such that and hence, by the residue theorem, if t < B in the "u" case and if t > A in the case "l" case. ± = +∕− in the "u/l" case, and the z 0 sum runs over poles in the upper/lower half plane. and use known results from semigroup operator methods for solving evolution equations, specifically as presented in [31,. The classical initial-value problem gives a unique classical solution if Ĉ ∶= +B is an infinitesimal generator for a strongly continuous semigroup, T m (t) . We write of such an operator, Any operator that is skew-adjoint is in G(1, 0) . This is true of  always, and  +B iff m is real. If m is not real, we can use the result that if  ∈ G(1, ) and B is bounded, with ||B|| = |m| , then  +B ∈ G(1, + |m|) , or in this case,  +B ∈ G(1, |m|).
Appendix C: The ± Components of the Source can be Treated as Supported on Finite Time Individually
Consider Eq. 58a. Define We know that J in ( ;t) is supported on t > t in . Now define and call its Fourier transform ±J in 2 ( ;E) . Clearly, and hence, by the linearity of the Fourier transform, Consider then the integral we want to evaluate, the first half of the RHS of Eq. 59a, Therefore we can treat both the ± components of the source as being supported on t ≤ t in , given only the knowledge that their sum is. The argument for the t ≥ t out case proceeds analogously. | 9,926 | 2022-02-01T00:00:00.000 | [
"Physics"
] |
Speeding genomic island discovery through systematic design of reference database composition
Background Genomic islands (GIs) are mobile genetic elements that integrate site-specifically into bacterial chromosomes, bearing genes that affect phenotypes such as pathogenicity and metabolism. GIs typically occur sporadically among related bacterial strains, enabling comparative genomic approaches to GI identification. For a candidate GI in a query genome, the number of reference genomes with a precise deletion of the GI serves as a support value for the GI. Our comparative software for GI identification was slowed by our original use of large reference genome databases (DBs). Here we explore smaller species-focused DBs. Results With increasing DB size, recovery of our reliable prophage GI calls reached a plateau, while recovery of less reliable GI calls (FPs) increased rapidly as DB sizes exceeded ~500 genomes; i.e., overlarge DBs can increase FP rates. Paradoxically, relative to prophages, FPs were both more frequently supported only by genomes outside the species and more frequently supported only by genomes inside the species; this may be due to their generally lower support values. Setting a DB size limit for our SMAll Ranked Tailored (SMART) DB design speeded runtime ~65-fold. Strictly intra-species DBs would tend to lower yields of prophages for small species (with few genomes available); simulations with large species showed that this could be partially overcome by reaching outside the species to closely related taxa, without an FP burden. Employing such taxonomic outreach in DB design generated redundancy in the DB set; as few as 2984 DBs were needed to cover all 47894 prokaryotic species. Conclusions Runtime decreased dramatically with SMART DB design, with only minor losses of prophages. We also describe potential utility in other comparative genomics projects.
Introduction
The comparative approach is one of the oldest and most powerful methods in biology, expressed thus by Aristotle: "first we must grasp the differences, then try to discover the causes" (History of Animals I.6).For any given trait under study, there is an appropriate degree of relatedness among the compared organisms, that will reveal the similarities and differences required to best define the trait.Comparative genomics, being typically computational, is often formulated as a comparison of a query genome to one or more reference genomes, i.e., a reference genome database (DB).We have used comparative genomics [1,2] for mapping genomic islands (GIs); these are mobile genetic elements that play critical roles in evolution, integrating at specific sites in bacterial and archaeal chromosomes and bearing genes affecting traits such as pathogenicity and metabolism.We find that the taxonomic level of species is often appropriate for comparative GI mapping; for any GI in a query genome, another genome from the species can often be found that lacks the GI, providing the Aristotelian difference required to identify and precisely map the GI.However, some species have few genomes available, and in these cases reaching to higher taxa may be required to apply comparative genomics.The systematically reconstituted bacterial and archaeal taxonomic system of the Genome Taxonomy DataBase (GTDB) project [3] aids such work.
Our comparative genomic software, TIGER [1], identifies and precisely maps GIs through a ping-pong application of BLASTN [4]: segments of the query genome likely to contain one end of a candidate GI are used to search a reference genomic DB, and hits are used to collect reference sequences that are then searched back to the query genome to find the other end of the GI.Reference genomes that map a GI call presumably have an intact (uninterrupted by any GI) integration site for the GI; the number of such reference genomes serves as a support metric for the GI.This approach misses ancient GIs that may have lost key features (their integrase gene or their flanking attachment sites), but the numerous GIs that it does find are more likely to be actively mobile.Despite the success of TIGER in precise mapping of numerous GIs in bacterial and archaeal genomes, false positives can also arise, perhaps from other chromosomal rearrangement events that occurred in a small number of reference genomes.Execution of TIGER was often slow and we suspected this was due to our original choice to use a small number of very large reference DBs (Methods).Here we explore alternatives involving small species-focused DBs, and the consequences for GI yields.
Different DB design problems arise for large (many genomes available) and small species.For large species, should we draw DB genomes only from within the species and is there an optimal number of genomes?For small species, should we draw additional genomes from outside the species, and if so, to what phylogenetic/taxonomic extent?An algorithm was developed for constructing a DB set that covers all species of any GTDB release.Because it allows spread to higher taxa for smaller species, it produces redundancy in the DB set; as few as 2984 DBs were needed to cover all 47894 species of GTDB release 202.These new species-tailored DBs are far smaller than those we used previously, allowing our comparative software to run much faster.Aside from mobile element detection, these DBs can serve other comparative genomic goals, such as within-species survey of any genomic region of interest.We present software for revision of the DB set upon GTDB update.
Smaller DBs for large species
With our original large reference DBs (Table 1), TIGER performance in identifying GIs was slow, motivating an exploration of alternative DB composition.For the 195,890 properly treated genomes (Methods), we estimate based on the benchmarking studies presented below that a total of 18.0 CPU years was spent on the BLASTN and subsequent TIGER steps.On the other hand the large DBs provided much information on how often distantly related genomes support a GI.Because different GI types may respond differently to DB composition, we sorted each GI call based on gene content into various types, such as Phage, Integrative Conjugative Element (ICE), or Non-Phage/Non-ICE (NonPI) [1].The ICE type was further split into ICE1 (more ICE-like) and ICE2 (less ICE-like).Similarly, the Phage type was split into Phage1 and Phage2, as well a third category PhageFil (filamentous).Here we introduce a new type "Reject" for any GI call with size or other characteristics (specified in Methods) that our spot checks have never found to produce convincing GIs; we consider these to be nearly all false positives.Although Reject calls could easily be immediately discarded, study of their properties may help uncover additional false positives.They also serve as negative controls for understanding some of the results presented below.In contrast, we consider the Phage1 GIs (prophages) to be nearly all true positives based on previous benchmarking against gold standards [1] and experimental results on inducibility [5].Support values (number of genomes found with precise deletion of the GI) are substantially different for these two types, averaging 5212 for the prophages, but only 700 for the Rejects.The largest category of GIs, NonPI, has an intermediate average support value of 1999.
We began by examining a species with numerous genomes available, Escherichia flexneri (herein we employ species names from GTDB release 202; this is the species containing the classical E. coli K-12 strains).We collected 9089 genome assemblies explicitly included in E. flexneri by GTDB and 843 additional genomes placed in the species by our assignment software (Methods).TIGER was applied to all these query genomes using our original large DB containing 27868 genomes from the Enterobacteriaceae family (Table 1).TIGER output provides for each GI call a list of all the reference genomes that supported the GI.For each GI we could use its list of supporting genomes to measure the power of various smaller (subset) DBs to recover the GI.To test effects of reference DB size, an ordered list of the GTDB genomes Table 1.Original large DBs.DBs were assembled based on taxonomy as assigned at NCBI, aiming for roughly even distribution of all genomes collected.After assignment to GTDB r202 species, small numbers of genomes were found to be improperly treated by placement in a different large DB than the bulk of the species' genomes; these improperly placed genomes were excluded from further analysis and are not counted in the Species or Genomes columns.The two DBs limited to genus (Salmonella and Campylobacter) were not treated further because taxonomic outreach could not be studied, leaving 11 DBs studied herein, with totals at bottom.For these 11 DBs, the genomes treated and species composition are reported in S1 and S2 Files in S1 Data, respectively.was prepared either by random shuffling or by a ranking algorithm partly involving genome assembly quality and mainly based on genome diversity (Methods).Then nested sets of various sizes from the top of the list were collected and evaluated for GI recovery.Fig 1 explores the use of subsets from the 9089 GTDB E. flexneri genomes to recover each GI, reporting the average GI count per query genome for each GI type, as database size is varied.Recovery of prophages (a large group of particularly reliable calls, marked Phage1) plateaus, with few added as DB size rises above 200.In contrast the Reject category of unreliable calls rises continuously, especially with DB size above 200.The similar behavior of random and ranked composition methods shows that rises at high DB size are not due to the concentration of lower quality genomes in the largest ranked DB.
Large
Like the Rejects, the NonPI category shows a rise in recovery above DB size 200, suggesting that this category contains some false positives.However, NonPIs are intermediate between Phage1s and Rejects by multiple metrics, suggesting that they also include legitimate GIs.To examine these hypotheses, we manually inspected 70 large NonPI families (based on integration site usage) from seven diverse large species.Inspection suggested that most were valid, with predicted genes for metabolism cassettes, restriction enzymes, and toxin/anti-toxin addiction cassettes, among others.However, 10 of the GI families examined (14.3%) were apparent false positives, distinguished by such gene content features as numerous transposase genes, numerous housekeeping genes, or only a portion of a single gene (the integrase gene itself).
To examine these trends in other large species, we identified all 29 species with sufficient yields of the key GI types: prophage, Reject and NonPI (Methods and S1 .Similar trends to those for E. flexneri were observed for the other large species, although for species with fewer than 500 genomes, the large-DB rise in Reject and NonPI GIs is muted.Same-genus species pairs sometimes differ in absolute yields and curve shapes of the key GI types, especially for the NonPI category (e.g., E. coli vs. E. flexneri), perhaps due to high strain specificity and species penetration of individual GIs.
For the large species combined, limiting DB composition to genomes within the species had a small cost, resulting in the loss of 1.4% (1384 total) of all their prophages (S2 Table in S1 Data, line 30).However these lost prophage GIs generally had low support values, usually of 5 or less.It would thus be difficult to use simple principles to design small DBs that could support these lost prophages.Moreover, limiting composition to within-species had a positive effect, eliminating a far higher fraction (20%) of the Reject GIs.NonPI GI loss is intermediate; thus losses from within-species DB composition may simply correlate with average support values.This shows that limiting DB composition to members of the same species is valuable, at least when genome numbers are sufficiently high.
Expanding DBs to higher taxa for small species
Most species have insufficient genomes to fill DBs of size 200.Indeed, GTDB lists only a single genome for 30777 of 47894 species.An option for small species is to fill their DBs by reaching beyond the species to higher taxa.This raises questions of whether such outreach would be effective, whether there is a reasonable taxonomic limit for such reach, and whether false positive rates might become unacceptable.The above result, that the Rejects had a much larger fraction than did the prophages of GIs with support only from outside the species, might indicate that false positives would be favored by reaching to higher taxa.To investigate these questions, we used the data-rich large species to simulate small species, by omitting all support from genomes within the same species.Surprisingly this showed that Reject GIs more frequently had support only from inside the species (S2 Table in S1 Data, line 30), over two-fold more often than for prophages.The seemingly opposing results, that Rejects were more frequently supported only from outside the species and were more frequently supported only from inside the species, may both be due to the low average support values of Reject GIs.These trends generally (but not always) hold for individual large species.
For each large species, GI yields were substantial after excluding support from the same species itself and, as noted for all large species combined, losses for the desirable Phage1 GIs were low while losses for the undesirable Reject GIs were high.These trends showed promise for use of out-species reference genomes for small species.We tested further taxonomic reach by omitting support from higher taxa: omitting all support from within the genus, or from within the family, or from within the order.Fig 3 shows the combined result for the entire GI set.Yields drop to 2-3% for family and order omissions, but Phage1 fractional yields are higher than for Rejects at each omission step.
Fig 3 was based on taxonomic ranks, but we were also able to examine GI support decay with the finer criterion of phylogenetic distance, using the bacterial and archaeal species trees provided by GTDB; these trees are robust, based on ~100 proteins for each species For each GI in the full set, the list of supporting genomes from the large DB was filtered by removing all genomes from the same species, or from the same genus, family or order.This simulates small species that may have no other genomes available from the same species, or the same genus, etc.For the three large DBs that are limited to a single family, all GIs are lost when omitting same-family genomes, so the GIs from these DBs were excluded from the denominator for the family-omission and order-omission treatments.GIs from the single-order DB EnterobacteralesOther were similarly excluded from the denominator of the order-omission treatment. https://doi.org/10.1371/journal.pone.0298641.g003 representative.Fig 4 shows actual/possible support values plotted against phylogenetic distance (panel C), comparing with the shared taxonomic rank and Mash distance.Mash distance (panel A) is a useful metric within a species or its close relatives, whereas the phylogenetic species distance (panel B) is zero and therefore uninformative for same-species genomes but becomes a useful metric when comparing genomes from different species or higher taxa.In panel C, the y-axis (species distance) value of zero corresponds to using only references genomes from the same species as the query genome, allowing us to assess the effect of a For each GI (separately treating the three main types: Phage1, NonPI and Reject), there was list of possible supporting genomes, i.e. all the genomes in the large DB used to evaluate it.The tree distance (substitutions per site) was taken from the GI's source genome to all possible supporting genomes based on the multi-protein species trees of GTDB release 202; intra-species genome pairs always receive a distance score of zero.The possible support distance counts were placed into 50 bins from 0 to 3.7.TIGER also reports a list of actual supporting genomes for each GI, whose distances to the GI source genome were likewise taken.To aggregate data for all islands, the actual and possible support counts were summed (by type) in each bin.Finally actual support totals were divided by possible support totals for each bin.Note the logarithmic y-axis.Panel B: For each genome pair in every large DB, the shared taxonomic rank was taken, and species distances tallied (middle panel, with counts for each rank's trace normalized to the maximum count in the trace).Panel A: For each genome pair, Mash distances at or below the reliability threshold (0.2) were taken and binned by species distance; by tree distance 0.2, Mash distance has plateaued at its maximum, after which percentages of measurable genome pairs decrease until cutting off reporting after tree distance 0.5.https://doi.org/10.1371/journal.pone.0298641.g004possible DB-building rule where only same-species genomes are allowed.Thus mimicking same-species-only DBs, we observe that actual/possible support is lowest for the Reject type and highest for Phage1.There is a large drop in actual/possible support as we move from using same-species genomes to using genomes from other species in the same genus.At approximately the genus level of distance (phylogenetic distance ~0.4), the Reject/Phage1 trend reverses and Reject GIs receive more actual/possible support than Phage1.This result differs from the Fig 3 result on fractional yields, and reveals a cost to using more distant reference genomes, although this may be acceptable when very few closely related genomes are available.
SMART DB software
Based on the above considerations we settled on the following design scheme for SMAll Ranked Tailored (SMART) DBs: 1) DB size is capped at a maximum number of genomes; here we tested maxima of 200, 300 and 500, based on the performance in this range observed in Fig 1 and S1. 2) This cap is reached phylogenetically, meaning that after exhausting the same-species ranked genome list, genomes from additional species are brought in according to species distance taken from the GTDB tree.3) Phylogenetic filling is limited to the taxonomic rank of order, which corresponds to what remains after omitting same-family genomes (the category "Family" in Fig 3).We have developed the SMARTDB software pipeline (Fig 5) that automates design and preparation of DBs for all species, or as many species as desired, including the step of collecting any needed genome assemblies.Benchmarking studies for three genomes from each large species (S2 Fig in S1 Data) showed useful speedup from capping DB size; the within-species DBs capped at 200 genomes had an average speedup of 2.4-fold relative to those capped at 500 genomes, and 65-fold relative to the original large DBs.
Our original set of GTDB-assigned genomes covered only 28500 of the 47894 species.We ran our software to collect additional genomes, increasing our collection to 348,547 that included all genomes known for GTDB release 202 species with fewer than 500 genomes, and at least 500 genomes each for the larger species.Designing the SMART DB set for all GTDB species, we observed redundancy; the design feature of phylogenetic reach produced many mixed-species DBs, and moreover many cases where the same mixed-species DB serves multiple species.As few as 2984 unique DBs were needed to cover all 47894 prokaryotic species (Table 2, line 3).Because of the cap on DB size, only 55.7% of available genomes were needed to build all DBs.
The GTDB project is ongoing and produces occasional updates that tend to change taxonomic assignments and increase species numbers.After the work herein was initiated, GTDB updated to releases 207 and 214, increasing the species count.The SMART DB pipeline operates in an update mode, and we used this to design SMART DB sets for the new releases (Table 2), with similar conclusions as for the earlier release.In addition to the de novo and update Design modes, our pipeline operates in a Quick Update mode, where the user can begin with our precalculated DB design file to avoid GTDB file download and the design calculation phase.
Discussion
The problem of identifying GIs through the comparative approach is important in its own right, but also stands in for similar problems about other classes of mobile genetic elements and, more broadly, about the "accessory" (non-core) fraction of the pan-genome for a prokaryotic species.In principle, a single genome per species could suffice for GI finding; the GTDB system already designates a single representative genome for each species.At another extreme, a large reference DB containing all available genomes for a species, and perhaps beyond the species, could be used.Here, to our knowledge for the first time, we systematically evaluate these simple DB design strategies and intermediate alternatives in terms of recovery, false discovery rate, and efficiency.We show that use of a single reference genome generally suffers from low recovery, while overlarge DBs can yield excess false positives and slow runtimes.When numerous genomes are available for a species, DB sizes of ~200 diverse genomes provide an excellent balance between recovery of true positives, avoidance of false positives, and fast runtimes.An algorithm, supported by software, is presented for preparing a high-performance reference genome DB for any prokaryotic species.
Our category "Reject", nearly all false positives, is readily defined and can quickly be filtered out.However, retaining them was useful for this study, revealing characteristics that should help identify and remove additional false positives among other groups, especially the NonPIs.We observed that Reject GIs were more frequently supported only by genomes outside the species (20.5%) than were the reliable Phage1 GIs (1.4%).Paradoxically, Reject PIs were also more frequently supported only by genomes inside the species (49.0%) than were Phage1 GIs (20.5%).Rearrangement of a reference genome chromosome by mechanisms other than integrase action can lead to false positive GI calls, and such rare rearrangements may occur either within the species or in reasonably close relatives outside the species.This rare false positive explanation is borne out by statistics; average support values of Rejects are simply much lower (7.45-fold)than those of the prophages.
In some ways the work herein is particular to GIs and to our software for their detection.For example, TIGER demands BLASTN hits of > = 500 bp at both flanks of each GI; more taxonomically distant reference genomes tend to fall below BLASTN detection limits.Nonetheless, with the simple design principles of the SMART DB sets, we envision additional uses in other comparative genomics applications.Our TIGER software is also capable of mapping the set of transposable elements (TEs) within a genome [1].Faster performance now enables survey of TEs among prokaryotes.There are 2.4-fold more transposases than integrases among our genomes; applying the formulae of S2 Fig in S1 Data to each of the properly treated genomes, we estimate that transposable element search completion would take 26.5 CPU years with the old large DBs, but only 0.78 CPU years with the 200-genome SMART DB set.Further speedup may be possible using alternatives to BLASTN or improved hardware architecture [6].The DBs may also help survey such highly variable gene sets as the capsule and lipopolysaccharide clusters of Proteobacteria [7].Precise mapping of the boundaries of such gene clusters may help reveal mechanisms of their variability, even when recombination enzymes such as integrases do not appear to explain their evolution.More broadly the DBs should serve the endeavor to define the two main genomic fractions of a species pan-genome [8,9], the conserved core and the sporadically-occurring accessory genome that includes GIs.The SMART DBs can be said to well define the core genome of the species.We found that ~200 genomes from a species are generally sufficient to provide the integration site of each GI in its uninterrupted form.Certainly there are species-defining genomic islands that might be missed by our species-limited DBs, such as the SPI1 and SPI2 of Salmonella enterica, but these are not found by TIGER anyway; they are so ancient that they have lost their mobility function, including the integration module, and moreover have lost the sharp borders sought by TIGER [10].
Conclusion
We show that species-focused reference DBs capped at 200 genomes are sufficient to recover most high quality GIs while precluding some low quality GIs.They greatly speed GI search software.For species with fewer genomes available, effective DBs can be built by reaching outside the species.Software for building and updating DB sets are described.Other comparative genomic uses for these DBs will be surveys of transposable elements and pan-genome analysis.
Genome assemblies for GI detection
We began with a collection of 288,451 genome assemblies downloaded from GenBank [11] in July 2019.These were placed into 13 large DBs based on NCBI taxonomy (Table 1), and the GI-mapping program TIGER v. 1.0 [1] was applied to each genome using the DB that contained it; a full report on the results will be forthcoming.We subsequently reassigned taxonomy using the system of the GTDB release 202, using the explicit GTDB species assignment when available, otherwise applying our script Speciate [2]; species assignment failed for 1831 genomes.These GTDB assignments occasionally disagreed with NCBI assignments, and showed that the large DB set had split some species, leaving 338 total genomes placed in the wrong large DB.Furthermore, 501 entire species were placed in the wrong DB.Because we were interested in the taxonomic reach of TIGER, we also excluded the genomes from the Salmonella and Campylobacter DBs, which included no reference genomes outside the genus.The above-described genomes that were unassigned, misplaced or in single-genus DBs were excluded from further analysis, leaving 195,890 properly treated genomes from 27999 of the 47895 GTDB r202 species.
GI set
For each genome, the orthogonal GI-mapping program Islander [12] was also run, and results from TIGER and Islander were unified using the TIGER package script "Resolve".Islander is not comparative, finding GIs that are in tRNA genes by a within-genome BLASTN-based approach.Islander may refine genome coordinates of raw TIGER calls.However, use of Islander here was effectively irrelevant for our study, because we only included GIs with TIGER support and were not evaluating genome coordinates.The properly treated genomes yielded 666,602 GI calls with any TIGER support.Because support values can be depressed for a GI in a tandem, i.e., abutting another GI at the same integration site, these were excluded from further analysis, leaving 610525 non-tandem GIs in our final GI set.The list of genomes supporting each GI (i.e., the genomes for which an uninterrupted GI integration site could be found) was collected from the TIGER output uninterrupted.txtfiles.Typing was performed as before [5], assigning GIs a type as either a Phage or Integrative Conjugative Element (ICE) variety or as NonPI (non-Phage, non-ICE).A new type "Reject" was introduced, applied to GI calls either with size < 5 kbp, without any serine or tyrosine integrase candidates, or with identity blocks between left and right integration sites of length > 300 bp; such calls were never found convincing in numerous spot checks and as a class can be considered putative false positives.The three most abundant types were NonPI, Phage1 and Reject (263704, 126828 and 128975 GI calls, respectively).GI data are reported in S3 File in S1 Data.
Large island-rich species were selected as having more than 300 genomes, with more than 100 each of three main island types (Phage1, NonPI, and Reject), and more than 1000 total for those three types, yielding 29 species (S1
SMART DB software pipeline
The pipeline automates genome collection, DB design, and updates paralleling those of GTDB.Two modes are available: Design (blue steps in Fig 5), which designs and prepares a DB set covering all species in a GTDB release, or Quick Setup (green steps in Fig 5), where the user chooses a subset of DBs (or all) to prepare from a precalculated (downloaded) DB design file.The Design mode requires certain data from a GTDB release, and has five main conceptual steps: collecting genome assemblies, calculating pairwise distances (both between genomes within a species and between the species), ranking genomes within each species, designing and preparing each DB.The software negotiates collection of needed genome assemblies from the NCBI FTP server; since some downloads may fail in any session, collection attempts repeat until either all needed genomes are downloaded, or the number of missing genomes stops decreasing.The latter may occur when small numbers of genomes are suppressed or missing on the FTP server.Because these missed genomes may yet be available through the NCBI web site, the user is allowed to halt pipeline progress, for manual download of any desired missing genomes; however these missing genomes are not required as the software will adapt to calculate databases without them.All pairwise distances between genomes within a species are taken using Mash [13] with default settings.Pairwise distances between archaeal or bacterial species are taken from the GTDB species representative tree.The genomes of each species are ranked as follows: 1) The species representative is removed from the list, to be returned later.
2) The genome is doubly sorted for quality; first by the entry for "mimag _quality" in the GTDB metadata table (in the order high, medium, low), and then by contig count from low to high values.3) The 10% with the lowest quality remain in place at the bottom of the list.4) The top 90% are reordered according to diversity: the species representative is placed first in the list; the second genome is the one most distant (by Mash distance) to the first; the third genome is the one with the highest summed distance to the first and second; and so on.The SMART DB for each species, with a given cap on DB size, is designed as follows.1) The DB is filled using the ranked list for the species.2) If the cap is not reached, filling continues with the closest species (by tree distance), and so on with other species according to distance from the species.3) No genomes from outside the taxonomic order are allowed, which means that some DBs do not reach the cap.After DB design is completed for each species, we observe that many species share the same DB composition as another, such that far fewer DBs need to be created than the number of species.Numerous DBs were extremely small (containing less than 5 genomes), reflecting the small genome count for certain taxonomic orders.There were 633 for the GTDB 202 release (Table 2), representing a total of 1096 species.Although these very small DBs are created without issue, they may be significantly less apt to find GIs.The program therefore warns the user that such DBs were created, and specifies them.BLASTN databases are created for each unique DB design (although this step can be omitted if only the design information is desired).This Design mode can be run de novo on the first GTDB release analyzed, or when updating to a new GTDB mode.
The Quick Setup mode of the pipeline does not require download of GTDB data, instead using a precalculated DB design file available at our GitHub repository (below).This mode additionally allows the user to prepare only a subset of the SMART DBs, for example when only a limited group of bacteria are under study.This abbreviated pipeline collects needed genomes and builds the DBs, skipping distance measurements and DB design, the slowest steps of the pipeline.
To assist in deciding which DB to apply to a new query genome, we recommend our utility script Speciate, which quickly determines the GTDB species of the genome.It should be noted that very small (< 200 kbp) genomes, such as Carsonella, are not treated by GTDB, nor by our system.Both pipeline modes prepare a Mash sketch database (for all the species whose representative genome has been collected), in support of Speciate.Software dependencies are Mash v2.3 [13] and BLAST v2.6.0 [4], with higher versions likely to be compatible; Speciate additionally requires fastANI [14] (no version assigned).The SMART DB pipeline and auxiliary scripts and data are available at github.com/sandialabs/SmartDBs.
Benchmarking
Three genomes were selected from each large species (the top three from each ranked list) for TIGER runtime measurements for a total of 87 genomes tested.The genome annotation steps of a de novo TIGER run were skipped, supplying previously determined annotation files; only the BLASTN and GI merging steps were performed.For each genome, four intra-species SMART DBs were tested, capping at 200, 300, or 500 genomes, or not capping (using all genomes available for the species).A fifth DB was also tested, the original large DB.This set totaled 435 tests.From the LINUX tool "time", the "user" and "sys" times were summed, and the cache was routinely cleared after each run to prevent cache-based artifacts.
Fig 1 .
Fig 1. E. flexneri GI calls recovered with various DB sizes.The GI identification program TIGER was run on 9932 E. flexneri query genomes using the large reference DB Enterobacteriaceae that contained a set ("All") of 9089 reference E. flexneri genomes.GI calls were typed, and those calls that either had no support from All or were in tandem arrays were discarded.DBs of various sizes that were subsets of All, were designed using the random or ranked protocols (Methods).Average count of GIs recovered per query genome (supported by at least one genome in the test DB) were taken for each GI type.Here, the PhageFil lines are obscured by the ICE1 lines.https://doi.org/10.1371/journal.pone.0298641.g001
Fig 3 .
Fig 3. Utility of higher taxa for GI detection.For each GI in the full set, the list of supporting genomes from the large DB was filtered by removing all genomes from the same species, or from the same genus, family or order.This simulates small species that may have no other genomes available from the same species, or the same genus, etc.For the three large DBs that are limited to a single family, all GIs are lost when omitting same-family genomes, so the GIs from these DBs were excluded from the denominator for the family-omission and order-omission treatments.GIs from the single-order DB EnterobacteralesOther were similarly excluded from the denominator of the order-omission treatment.
Fig 4 .
Fig 4. Actual/possible support.Main panel C: For each GI (separately treating the three main types: Phage1, NonPI and Reject), there was list of possible supporting genomes, i.e. all the genomes in the large DB used to evaluate it.The tree distance (substitutions per site) was taken from the GI's source genome to all possible supporting genomes based on the multi-protein species trees of GTDB release 202; intra-species genome pairs always receive a distance score of zero.The possible support distance counts were placed into 50 bins from 0 to 3.7.TIGER also reports a list of actual supporting genomes for each GI, whose distances to the GI source genome were likewise taken.To aggregate data for all islands, the actual and possible support counts were summed (by type) in each bin.Finally actual support totals were divided by possible support totals for each bin.Note the logarithmic y-axis.Panel B: For each genome pair in every large DB, the shared taxonomic rank was taken, and species distances tallied (middle panel, with counts for each rank's trace normalized to the maximum count in the trace).Panel A: For each genome pair, Mash distances at or below the reliability threshold (0.2) were taken and binned by species distance; by tree distance 0.2, Mash distance has plateaued at its maximum, after which percentages of measurable genome pairs decrease until cutting off reporting after tree distance 0.5.
Fig 5 .
Fig 5. SMART DB software pipeline.As described in Methods, the Design mode (blue) operates on an initial GTDB release or update, collects needed genomes, and designs and builds the DB set.The Quick Update mode starts with a precalculated DB design file (and an optional list of desired species) and builds DBs.Scripts employed at each step (and a potential manual genome collection phase) are in parentheses.https://doi.org/10.1371/journal.pone.0298641.g005
Table 2 . SMART DB sets for two GTDB releases.
Submaximal DBs were those containing fewer genomes than the maximum.Taxonomic filling was stopped at the rank of order. https://doi.org/10.1371/journal.pone.0298641.t002 Table in S1 Data). | 8,076.6 | 2024-03-13T00:00:00.000 | [
"Computer Science",
"Biology"
] |
Fission barriers of odd-mass nuclei within the HF-BCS and HTDA approaches
Within two mean-field plus correlation descriptions (Hartree-Fock plus BCS or plus Highly Truncated Diagonalization Approaches) we study here some static properties of two odd-neutron nuclei (235U, 239Pu) from the ground-state deformation to the fission isomeric well, using three different Skyrme force parametrizations. A specific study of the polarization effects due to the account of relevant time-odd density functions is performed.
Introduction
Microscopic calculations of stationary points (stable or unstable) along the average fission paths of heavy nuclei have been calculated, over the years, through mean field approaches supplemented by some more or less crude treatments of nuclear correlations (see e.g.[1]).The latter include pairing correlations as well as those related to the restoration of some broken symmetries.Most of the efforts have been concentrated so far on the description of even-even fission barriers.
In the case of odd-mass, not to mention odd-odd nuclei, a proper evaluation of these potential energy curves is contingent upon a realistic description of polarisation effects brought in by the addition of one, or two different, nucleons as compared to the even-even case.In such unpaired systems, most of the exact time-even part of the one-body density could be treated appropriately by averaging over the contributions of both partners of the Kramers pair associated with the extra nucleonic state (as obtained in an even-even core description).This approximation is embodied within an Hartree-Fock-Bogoliubov or (-BCS) approach as the so-called Equal Filling Approximation (EFA).Calculations of the fission barriers of two odd-nuclei within this EFA framework have been already published in Refs.[2] and [3].
EPJ Web of Conferences
A full microscopic treatment should a priori include the effects of the time reversal symmetry breaking inherent to the description of a fermionic system involving an odd-number of identical particles.Whereas specific polarization effects impacting the magnetic properties of nuclei are expected and found in such approaches (see e.g.[4]), we are mostly concerned here about their consequence on the total energy, in general, and as a function of the quantum numbers of the extra nucleon state, in particular.As functions of these quantum numbers, we are interested in the variation of the so-called specialization energies (introduced by Newton and Wheeler in 1955, to emphasize the variation of spontaneous fission half-lives occurring between even and odd heavy nuclei, see e.g.[5]).As an example, we may quote the search for the variation between the fission barrier heights and hence the fission half-lives of the ground (7/2 − ) and isomeric (1/2 + ) states in the 235 U nucleus.
Throughout this paper, we assume the validity of the axial symmetry, the intrinsic parity symmetry as well as of the Bohr-Mottelson ansatz to generate out of our intrinsic solution a nuclear state by coupling with an axial rotor further (not allowing for Coriolis coupling).This yields I = K (with usual notation) in our configurations.The first assumption is clearly a crude approximation for most of the considered isotopes in the vicinity of the first barrier, while the second would be totally inappropriate in the second barrier region.
In odd-nuclei, one expects that pairing correlations are quenched with respect to what they would be in neighbouring even isotopes due to the blocking of orbitals (close to the Fermi level for ground or weakly excited nuclear states).This situation places the BCS approximation at the limit of its validity when the single particle level density around the Fermi level is weak.This is why we performed beyond the usual BCS blocking treatment, a more elaborate approach preserving the particle number named the Highly Truncated Diagonalization Approach (HTDA) [6].
Theoretical considerations
The effective Hamiltonian in use here, includes a usual Skyrme-type interaction.The added Coulomb interaction is treated exactly for what concerns its direct contribution and through the Slater approximation for its exchange part.The center of mass correction has been approximated considering only the one-body part of its kinetic energy by a renormalization of the total kinetic energy operator through a factor (1 − 1 A ).The Skyrme Hamiltonian density which, as shown in e.g.Refs.[7] and [8], is a function of time-even local density functions (density , kinetic energy density , spin current tensor J) and time-odd density functions (spin density s, current density j, spin kinetic density T).
The Hartree-Fock equations are obtained by varying the total energy with respect to the single particle states.The expression for the Hartree-Fock Hamiltonian can be found e.g. in [9] where the fields entering the Hamiltonian are functions of the local densities defined e.g. in [8].In selecting the type of Skyrme parametrization, one can opt from either an interaction or functional point of view.From interaction point of view, one should take into account all the terms appearing in Skyrme Hamiltonian density.Otherwise, if one adopts the functional point of view one has the option of neglecting some terms in the energy functional (yet preserving some conservation laws).The Skyrme parameters have normally been fitted to even-even nuclei, such that the time-odd local densities vanishes in this case.Then, when performing calculation for odd-mass nuclei (where time-odd densities are not vanishing) one can choose between incorporating all the time-odd densities related terms or to maintain a minimal time-odd densities terms (in combination with time-even densities) to respect some symmetries.In the latter case, terms proportional to (s • s) and possibly also the (J 2 − s • T) terms (depending on the conditions of the fit) are neglected.We shall refer to this as minimal time-odd densities while the inclusion of all the terms will be referred to as full time-odd densities.
We have considered three types of Skyrme parametrizations for the current study.This includes the SLyIII.xxforces [10] (xx being the value of the nuclear matter effective mass chosen to be 0.8 for the one considered here) where the spin current (tensor) density was included in the fitting process.It is Fission 2013 worth noting that this force does not lead to spin (ferromagnetic) instability in contrast with some other newly fitted Skyrme forces such as TIJ [11] and SLy5 [12] parameter sets.The other two forces that we used are the SkM * parametrization which yields good surface properties and has been fitted to the liquid drop fission barrier of 240 Pu [13] and the SIII parametrization [14] which provides reasonably good spectroscopic properties (see [15] and [16]).
In order to account for the pairing correlations, we have used two different approaches: the usual Bardeen-Cooper-Schrieffer (BCS) method with a seniority force and the HTDA method.In both cases, we have restricted ourselves to the |T z | = 1 (neutron-neutron and proton-proton) channels.
In the BCS case, the strength of the pairing interaction is given by the antisymmetrized matrix element between pairs of time-reversed conjugate states written as ii|v| j j (q) = − G 0 11+N q with G 0 (n) = 14.5 MeV and G 0 (p) = 14.66 MeV while N q is the nucleon number of the q-charge state.Single particle states participating in the BCS approach were defined with a single particle energy cut-off of 6 MeV above the Fermi level for both charge states (with a diffuse Fermi type boundary defined by a usual diffusivity parameter equal to 0.2 MeV).
Main features of the HTDA method can be found e.g. in Section II of Ref. [17].The strengths of the zero range pairing interaction in the T = 1 channel only, V (T =1) 0 , have been fitted with respect to the oddeven binding energy differences of actinide nuclei.The retained values of V (T =1) 0 for the calculations with the SIII, SkM * and SLyIII.0.8 interactions are 440, 420 and 400 (MeVfm 3 ) respectively.The manybody basis is made of single-pair, double-pair and triple-pair excitations above the quasi-vacuum state with unperturbed excitation energies, lower than or equal to three times the empirical inter-shell energy h = 41A −1/3 (MeV).
Results and discussions
Calculations have been made in two approaches with respect to the time-odd terms entering the expression of the energy density: including first only minimal time-odd densities, and secondly, incorporating the full time-odd terms.To respect the conditions of the fit, however, the results for the SIII and SkM * parametrizations reported here, are obtained with a minimal inclusion of time-odd terms in the energy density functional.The results for SLyIII.0.8 are obtained with full time-odd densities since the spin current tensor was taken into account in fitting process.The effect of including all time-odd terms for SIII is discussed in the last subsection.
The single particle eigenstates resulting from the solution of the Hartree-Fock equations have been projected onto axially symmetrical harmonic oscillator basis states with a deformation-dependent cutoff corresponding to 13 spherical major shells (see [18]).
Ground state spectra
Calculations of the energy spectra of the 239 Pu and 235 U nuclei with 3 different Skyrme forces has been performed (spectra not shown here).In 239 Pu, we reproduce the experimental ground state quantum numbers 1 2 + in all three calculations.The energy levels calculated with SLyIII.0.8 and SkM * appears to be slightly compressed as compared to the experimental levels.On the other hand, the calculated energy spectra in 235 U appears to be spread over a too large energy range as compared to the experiment.There are some reordering of the energy levels going from one force to another.The SkM * and SLyIII.0.8 interactions yield a 1/2 + ground state while the first excited state (7/2 − ) is found at 34 keV for the former and 42 keV for the latter.This is at variance with the experimental situation where both states are almost degenerate (the 1/2 + state having a 76.5 eV excitation energy).Yet, we remain clearly within the expected range of accuracy of the whole approach.
Fission barrier heights and specialization energies
For some relevant K values, we have performed calculations in the ground state and near the top of the first barrier.The obtained ground state fission barrier heights in 235 U and 239 Pu are shown in Table 1.
The differences of specialization energies defined with respect to the ground state values are listed in Table 2. Clearly, as compared to experimental values, these barrier heights are much too high.Yet, they are overestimated in that the deformation dependence of zero-point rotational energy corrections and the effect of the triaxial instability have not been taken care of.To these sources of overestimation, one should add another slight contribution due to the relatively small basis size in use for the description of single particle states (see the discussion of [19]).On the other hand, our barrier heights are slightly underestimated due to the use of the Slater approximation for Coulomb exchange terms [20].
Isomeric well
We present our calculated nuclear spectra in the isomeric well in Table 3, together with the results of Ref. [2] and experimental data when available.The different Skyrme forces gives results which are reasonably consistent within themselves and when compared with available energies from the calculation of Ref. [2] and experimental data for 239 Pu.Notably, all three forces reproduce the ordering of the energy levels in 239 Pu (the 5/2 + state being the lowest, followed by a 9/2 − state).The 04004-p.4 Fission 2013 energy difference between these two levels varies slightly depending on the choice of the Skyrme parametrization.The results obtained with SLyIII.0.8 seems to agree best with experimental data, especially if one were to take into account the effect of Coriolis coupling which is about 100 keV, as indicated in the earlier work of Ref. [16].Our calculated 11/2 + state is much too high, at about 500 keV above the 5/2 + state as compared to a 11 keV energy difference obtained in Ref. [2].The consistency of the results obtained for 235 U is less manifest.The SIII and SLyIII.0.8 interactions predict 3/2 + as the lowest energy state, while a 3/2 − ground state is obtained with SkM * .Neither of these agree with the results of Ref. [3] which predicts a 5/2 + state.
The lowest fission isomeric energies E I I are reported in Table 4 for the two nuclei for all three interactions and compared with experimental data [21] when available.
In both nuclei, the SkM * force produced a significantly lower isomeric energy compared to the results obtained with the other two forces.It should be noted however that although the value obtained for SkM * appears to be in good agreement with experimental data, corrections for other effects e.g.due to the rotational motion should lower the isomeric energy to unrealistic values.
Effect of the pairing treatment with HTDA
In order to illustrate the effect of treating the pairing part using a particle number conserving approach, we show the first barrier height obtained from HF + BCS and HTDA calculation in Table 5.In general, with the parametrization of the residual interaction in use, the effect of proper treatment of pairing results in an increase of the fission barrier height.The amount of correction depends on the choice of the Skyrme force being considered.Calculations performed with SkM * shows a large difference between the barrier heights calculated from the two pairing approaches.For example, the barrier height of 5/2 + in 239 Pu with SkM * calculated with HF + BCS can be lowered as much as 1.5 MeV compared to the HTDA solution.In fact, large differences between the barrier heights are reported for SkM * which exceeds 1 MeV.On the other hand, the difference in the barrier height is small (less than 0.2 MeV) for SIII calculations with three of the four states.The same effect on the difference in barrier height between HF + BCS and HTDA solution is also visible for 235 U. Calculation with SkM * gives the largest difference of about 1.2 MeV, while the difference for SIII is about 0.3 MeV.Calculations with SLyIII.0.8 in both nuclei gives a difference between 0.6 to 1.2 MeV.
Effect of the neglected terms in the energy functional
We present in this section the effect of neglected time-odd terms in the energy density functional which was not taken into account in the fitting process of the SIII and SkM * force.The results are presented for the SIII force in 239 Pu.As can be seen from the ground state spectra of 239 Pu in Figure 1, the inclusion of all the time-odd terms causes the compression of the energy spectra.We have checked that the term corresponding to (s • s) has a negligible effect on the energy spectra, whereas the terms involving the spin-current tensor with the combination (J 2 − s • T) have a dominant effect.
We have also calculated the first fission barrier height with and without the full time-odd terms using the SIII force for 239 Pu.In going from a minimal to a full time-odd scheme, we found a systematic lowering of the first fission barrier height of 0.95, 0.72, 0.54 and 1.04 MeV for 1/2 + , 7/2 − , 7/2 + and 5/2 + respectively.At the same time, we found a lowering of E A by 1.0 MeV upon using the full functional for a 240 Pu core, which is consistent with the above.This study shows that the absence of spin current tensor density in the original fit of the Skyrme force can be quite significant as the effect of this term on some observables-such as relative energies-cannot be absorbed in the fitted parameters.
Conclusion
We have presented here some static nuclear properties along the fission path of the 235 U and 239 Pu nuclei with three different Skyrme forces.The first fission barrier heights are overestimated in the present work.Relevant corrections will be taken into account in future work.
We have in particular shown the energy spectra at the ground state and isomeric wells.The SIII force appears to give a better agreement with the experimental data in terms of energy level spacing in the ground state.Nevertheless, the results obtained with the SkM * and SLyIII.0.8 interactions are quite reasonable.
In order to study the effect of pairing correlation from a particle number conserving approach, we have compared the fission barrier heights obtained from HF + BCS and HTDA calculations with the SIII and SkM * interactions.Finally, we have discussed the effect of including a spin current tensor density in the energy density functional in 239 Pu with the SIII force.At ground state deformation, the addition of this density caused a strong compression of the energy spectra.The first fission barrier heights were
Figure 1 .
Figure 1.Ground state spectra of 239 Pu calculated with the SIII force with minimal and full time-odd terms as compared to experimental data.
Table 1 .
Heights of the first fission barrier of the 235 U and 239 Pu nuclei (in MeV) corresponding to the ground state quantum numbers calculated with three Skyrme forces.
Table 2 .
Differences of specialization energies (in MeV) of the the first barrier height in 235 U and 239 Pu.
Table 3 .
[21]]ar spectra in the isomeric well for the 235 U and 239 Pu nuclei.The Gogny D1S results are taken from[2,3]and experimental data from[21].Energies are given in keV.
Table 5 .
Heights of the first fission barrier (in MeV) obtained from HF + BCS and HTDA calculations. | 3,985.8 | 2013-12-01T00:00:00.000 | [
"Physics"
] |
Numerical Modelling of the Mechanical Behaviour of Carbon and Non-Carbon Nanotubes and Their Complex Structures
Systematic research efforts have been focused on the development of low-dimensional structures, such as nanotubes (NTs), because of the potential of their use in nanodevices and in applications in nanoelectronics and biomedicine [...].
Systematic research efforts have been focused on the development of low-dimensional structures, such as nanotubes (NTs), because of the potential of their use in nanodevices and in applications in nanoelectronics and biomedicine. After intense investigation on carbon nanotubes (CNTs), nanotubes made up of elements other than carbon, called non-carbon nanotubes (N-CNTs), have also attracted research attention, as they can be more suitable for electronic and optical engineering applications than their carbon counterparts. Success in assembling CNTs and N-CNTs together has opened the perspective of integrating these innovative complex structures into advanced NT-based systems. As experimental studies on the mechanical behaviour of CNTs and N-CNTs are limited by experimental difficulties in characterizing nanomaterials at the atomic scale, theoretical, analytical and numerical studies to predict the mechanical properties of NTs are of great importance.
This Special Issue, comprised of a total of five research articles, is dedicated to recent developments in the modelling and numerical simulation of the mechanical properties of graphene sheets [1]; CNTs and their complex structures [2,3], such as heterojunctions [4]; and, to conclude, boron nitride nanotubes (BNNTs) [5], on which, among other N-CNTs, strong research efforts have been produced so far. The first study by Wang et al. [1] deals with the molecular dynamic (MD) simulation of the Atomic Force Microscopy (AFM) nanoindentation test performed on a single-layer wrinkled graphene sheet to extract its mechanical properties. The deflection of the graphene sheet (GS) under AFM nanoindentation was used to study the effect of wrinkles on the GS's elastic properties, specifically its Young's modulus. It was found that surface wrinkling leads to a decrease in the GS's Young s modulus. Their results contributed to a better understanding of how to take into account the GSs' surface morphology to achieve an accurate characterization of the elastic properties of graphene. This is a useful development to study the mechanical response of CNTs, as it can be seen as a rolled-up graphene sheet.
The next two research articles [2,3] of the Special Issue are devoted to multi-walled carbon nanotubes (MWCNTs), which are CNT structures composed of 3 to 50 concentric, single-walled carbon nanotubes (SWCNTs). Sakharova et al. [2] investigated the elastic properties of non-chiral (armchair and zigzag) MWCNTs with up to 20 constituent SWCNTs under tensile, bending, and torsional loading conditions using a simplified finite element (FE) model and without taking into account the van der Waals interactions between layers. The tensile, bending, and torsional rigidities were evaluated. The relationships established between each of the three rigidities and the outer NT diameter constituted the robust methods for assessing the Young s and shear moduli of the non-chiral MWCNTs. This can be particularly valuable when modelling the mechanical behaviour of MWCNT-reinforced composites and MWCNT-based complex structures is required. In this context, the main goal of the work by Carneiro and Simões [3], who studied the influence of the MWCNTs on the mechanical properties of metal matrix nanocomposites, was to correlate the results, assessed by numerical simulation, with those obtained experimentally and to validate the available methodologies for predicting the strengthening of CNT-reinforced composites. For this purpose, a detailed characterization of the MWCNTs was performed in order to evaluate the inner and outer NTs' diameters, lengths, number of layers, constituents of MWCNTs, and interlayer distances. Considerable improvement in the mechanical properties, i.e., increases in the hardness values of CNT-based metal nanocomposites, was achieved when straight MWCNTs with large outer diameters were used for reinforcement. From the results, it was possible to validate the existing methodologies, which used MD simulations, developed to predict the mechanical properties of MWCNT-reinforced composites. Moreover, the extensive experimental characterization of the structure and morphology of multi-walled CNTs is mainly useful to feed numerical models of MWCNTs, as described in the work of Sakharova et al. [2].
The research article of Pereira et al. [4] is dedicated to correctly describing the deformation behaviour of SWCNT heterojunctions (HJs), whose structure can be understood as that of two SWCNTs connected by an intermediate region. Therefore, a systematic characterisation of the mechanical properties of armchair-armchair and zigzag-zigzag SWCNT HJs was performed. Three-dimensional (3D) FE simulation was used to carry out a parametric study on the tensile, bending, and torsional rigidities of SWCNT HJs. As a result, analytical methods were formulated for easy assessment of the elastic properties of HJs, in a wide range of their geometrical parameters. As the strength and productivity of the nanodevices and nanosystems strongly depend on the mechanical properties of their components, and CNT HJs are potential candidates for such applications, the work by Pereira et al. [4] represents a substantial contribution to the knowledge on the elastic behaviour of CNTs-based structures.
The last article by Sakharova et al. [5] provides a benchmark with regard to the determination of the elastic properties of single-walled boron nitride nanotubes (SWBNNTs) by numerical and analytical methods. In this study, a systematic characterization of the mechanical behaviour of SWBNNTs was performed for a wide range of chiral indices, diameters, and lengths using the 3D FE simulation method. A comprehensive study of the influence of input parameters on FE modelling of computed elastic properties, such as the tensile, bending, and torsional rigidities, and, subsequently, the shear and Young's moduli and the Poisson s ratio of SWBNNTs was also performed. As BNNTs have a great potential to replace CNTs in practical applications and taking into account the perspective of hybrid NT-based structures, consisting of BNNTs and CNTs, the results of this article serve as a guide for the correct design of such novel nanostructures.
The works of this Special Issue promote research for the evaluation of the mechanical properties of carbon and non-carbon nanotubes and CNT-based structures by mostly numerical approaches. As a Guest Editor, I believe that the overall quality of the methodologies and achievements presented in this Special Issue contributes to the progression in our understanding of the mechanical behaviour of carbon and non-carbon nanotubes, aiding the future design and optimization of advanced nanotube-based structures. Acknowledgments: The guest editor would like to thank the authors, the reviewers, and the editorial team of Materials for their prized contribution to this Special Issue.
Conflicts of Interest:
The author declares no conflict of interest. | 1,505 | 2022-10-26T00:00:00.000 | [
"Chemistry"
] |
Optimization of a Confined Jet Geometry to Improve Film Cooling Performance Using Response Surface Methodology (RSM)
: This study investigates the interrelated parameters a ff ecting heat transfer from a hot gas flowing on a flat plate while cool air is injected adjacent to the flat plate. The cool air forms an air blanket that shield the flat plate from the hot gas flow. The cool air is blown from a confined jet and is simulated using a two-dimensional numerical model under three variable parameters; namely, blowing ratio, jet angle and density ratio. The interrelations between these parameters are evaluated to properly understand their e ff ects on heat transfer. The analyses are conducted using ANSYS-Fluent, and the performance of the air blanket is reported using local and average adiabatic film cooling e ff ectiveness (AFCE). The interrelation between these parameters and the AFCE is established through a statistical method known as response surface methodology (RSM). The RSM model shows that the AFCE has a second order relation with the blowing ratio and a first order relation with both jet angle and density ratio. Also, it is found that the highest average AFCE is reached at an injection angle of 30 degree, a density ratio of 1.2 and a blowing ratio of 1.8.
Introduction
The use of a cool air blanket to shield a solid surface from high temperature gases is considered an effective way to protect the solid surface from a harsh environment. Such a technique is considered a very common and an effective thermal management technique that is used in gas turbine engines to guard the high pressure turbine blades from the hot combusted gases. Current gas turbine engines operate at elevated temperatures that exceed 1200 • C [1,2]. These high temperatures cause hot spot formation and increased wall thermal stresses on turbine's blade, which reduce the turbine blade life. To assure realistic turbine blade life, the variation on the blade wall temperature must be limited [3]. Remarkable work has been done in the field of material science and cooling techniques to increase the turbine maximum allowed inlet gas temperature while achieving realistic durability goals. Since the introduction of aircraft gas turbine in 1941, the average rate of increasing the maximum allowable inlet temperature using cooling techniques is around 20 degree per year which is more than double the rate achieved by material scientist [4]. Most of today's advanced gas turbines utilize cooling techniques in their gas turbine blades. Cooling techniques are classified into internal cooling methods such as internal jet impingement [5][6][7][8][9], and external methods such as transpiration cooling [10,11] and film cooling [12][13][14]. Film cooling protects the blade by forming air blankets, which reduces the heat transfer between the hot mainstream gas and the turbine blade wall. This allows a higher mainstream gas temperature to enter the turbine without negatively affecting the turbine durability [13].
The cool air blanket is mainly used to cut convective heat transfer to the blade surface. The effectiveness of the air blanket mainly depends on three main parameters, which are flow blowing ratio, jet angle and density ratio. These parameters are interrelated and they affect the film cooling in divergent ways. Different studies have investigated the effect of these parameters on film cooling, but limited studies are available on how these parameters are interrelated. Radial basis function neural network and genetic algorithms has been implemented to optimize a fan-shaped hole to improve film cooling performance [15]. The current study is implementing the RSM to optimize a confined jet flow that forms a cool air blanket film over a flat plate.
Blowing ratio represents the ratio of velocity and density of coolant flow to mainstream flow. A numerical study by Nijo et al. [16], showed that as the blowing ratio increases to 1.5, the adiabatic film cooling effectiveness (AFCE) improves. However, operating at blowing ratios above 2 reduces the AFCE directly after the hole and later increases the AFCE at a distance greater than x/D = 8. This effect is due to the detachment of coolant film from the wall that causes wakes and vortices formation within the film cooling boundary layer [17]. Plesniak and Cusano [18] presented a flow regime map to describe the relation between the blowing ratio, injection angle and the development length of the film cooling. They showed that for any injection angle, increasing the blowing ratio will always increase the jet penetration to the mainstream flow. This changes the behavior of the coolant jet from a wall attached jet to a free jet, which reduces AFCE significantly [17]. The same conclusion has been found in the experimental work of Yuen and Martinez-Botas [19], where they have studied a wide range of both injection angles and blowing ratios at a low turbulence intensity (1.7%). They reported that for every injection angle there is a specific blowing ratio at which separation of coolant jet occurs. Mayhew et al. [20] have explored the effect of turbulence intensity on previous studies and found that low turbulence intensity experiments agreed with the previous results. However, at the same blowing ratio, high turbulence intensities (more than 10%) required a higher injection angle to cause detachment of the coolant fluid [19]. This result has been confirmed independently by the experimental work of Mouzon et al. [21]. It has been reported that inclined jet (hole) angle influences the effectiveness of cooling uniformity [22]. The effect of different hole shape has been explored in literature [23] and it is reported that fan-shaped hole shows improved film cooling effectiveness when compared to a cylindrical hole. To sum up, the main outcome from the previous studies [15][16][17][18][19][20][21][22] is that for a specific turbulent intensity value at a specific angle, increasing the blowing ratio increases the film cooling effectiveness (FCE) up to a critical blowing ratio. When this critical value is reached, the coolant jet fails to stay attached to the wall and it will penetrate to the mainstream causing the FCE to fall drastically. On the other hand, increasing the turbulent intensity increases the tendency of the coolant jet to stay attached to the plate wall, which allows the use of a higher blowing ratio. This leads to better shielding of the blade from the hot mainstream which means a higher value of film cooling effectiveness.
Density ratio (DR) represents the ratio of density of coolant flow to mainstream flow. The density ratio of the hot gas to the cool gas is a significant parameter that affects the effectiveness of film cooling which has been investigated by different research groups [24][25][26][27][28][29][30]. The experimental work of Johnson et al. [29] has shown that at a fixed blowing ratio, increasing the density ratio increases the wall area averaged AFCE in the range of DR between 0.97 and 1.53. This is mainly due to the decrease of velocity ratio, which gives the jet relatively lower momentum to escape wall boundary layer. Singh et al. [30] has numerically studied the effect of DR by varying DR values from 1 to 12. For the investigated range, a critical density ratio has been found. Singh et al. [30] has reported that increasing the DR beyond this critical density ratio value reduces the span-wise area-averaged AFCE. The study [30] has reported that as the injection angle increases, for a fixed blowing ratio, the critical density ratio decreases. However, as the blowing ratio increases, for a specific injection angle, the critical density ratio increases. In general, gas turbines operational regions are at DR values between 1 and 3, blowing ratios less than 3, and an injection angle lower than 45 • [19,31,32]. In this specified region, the overall trend is that as the DR increases the averaged AFCE decreases.
The injection angle represents the angle between the cool air inlet velocity vector and the surface tangent vector (the mainstream velocity vector). Multiple geometrical parameters affect the AFCE; namely film injection angle (α), hole shape, number of holes, jet delivery channel length and hole to hole spacing. In this study, to narrow these geometric parameters and to properly investigate the effect of other parameters, a two-dimensional single jet has been selected.
Jia et al. [33] carried out a very extensive experimental and numerical work for angles ranging between 16 and 90 degree, and a wide range of blowing ratio ranging between 0.5 and 9. They concluded that at different values of blowing ratios, an injection angle of 30 degree achieves the highest FCE. The same conclusion has also been found at low blowing ratios and at different ratio of transverse pitch to injection angle [23]. Numerical studies on film cooling technique are mostly focused on selecting the best turbulence model to effectively estimate film-cooling performance. Most of the published work employs Reynolds-Averaged Navier-Stokes equations in predicting FCE. Flat-plate configuration is a very efficient approximation to investigate the effect of different flow and geometrical parameters on film cooling performance. A very challenging task is to model film cooling boundary layer which is needed to predict the film cooling efficiency. Ferguson et al. [34] investigated the standard k − ε and Reynold stress models with standard wall formulation, the non-equilibrium wall modelling with two-layer wall treatment, and the RNG k − with standard wall function. They reported that the standard k − ε with the two-layer wall treatment has shown the most accurate approximation of film cooling performance in comparison to the other combinations. Later work by York and Leylek [35] showed that RNG k − ε with two layers wall treatment has successfully predicated the production of turbulent kinetic energy which leads to a good agreement between experimental and numerical film cooling effectiveness. The RNG k − ε with the two-layer wall treatment has been proven to show a good agreement with experimental data under different conditions and geometries by many researchers [30,31,36].
Finally, at fixed velocity ratio (VR) and increasing the mainstream and cool air velocities to achieve higher values of Reynolds number are studied experimentally [37][38][39] and numerically [30]. It has been found that for all the blowing ratios at different flow configurations, as the Reynolds number increases, the film cooling effectiveness increases. This trend between Reynolds number and FCE is expected since as Reynolds number increases, the film cooling layer will have higher momentum which keep the coolant air attached to the wall.
In this study, a numerical ANSYS-fluent simulation is used to study a confined slot jet configuration using a 2D model. There are four main advantages of using slot shaped jet in analyzing film-cooling effect. First, it reduces number of geometrical parameters and magnifies the impact of the jet angle. Second, it reduces the problem size since 2D mesh requires less computation power. Third, it allows reducing the impact of geometrical parameters on other important parameters such as blowing ratio, density ratio, etc. Finally, it is much easier to experimentally validate such geometry, which explains the availability of such published experimental work. The need for more studies on film cooling rise from the interrelated parameters that affect film cooling [40,41]. In this regard, the main objective of this study is to utilize the statistical method to analyze the relation between AFCE and the interrelated parameter (mainly blowing ratio (M), injection angle (α) and density ratio (DR)). The statistical method used in this study is known as response surface methodology (RSM) [42][43][44]. A parametric study is also carried out to assess the significance of these parameters. The RSM is implemented on a group of CFD runs to attain an optimal AFCE response.
Problem Formulation
A schematic diagram of the system is shown in Figure 1. The dimensions are chosen based on O'Malley experimental work [37]. As shown in the figure, the cool jet enters with an angle of 90 degree from the bottom side plate through a slot with a width of D = 40 mm and hot mainstream enters from left-side with channel height of 6D. Then, the mixed flow leaves at the right side of the channel. The size of the computational domain is 12D × 57D. All the walls are assigned to no-slip and adiabatic conditions. In this study, the −ε, k − ω and SST turbulence models are examined to evaluate the appropriateness of these turbulence models for the 2D flat confined jet configuration. Enhanced wall function (EWF) treatment is used with k − ε turbulence models for near-wall modelling which is not required with k − ω and SST models. Furthermore, a zero-gage pressure is used at the outlet.
Resolving the near-wall regions of a turbulent boundary layer is critical for the solution to produce the correct flow behavior [45]. Two approaches can be employed to treat the flow near the wall which are (1) logarithmic-based wall functions or (2) resolving the viscous sublayer flow. Selecting one of these approaches dictated the size of the first grid cell near the wall, which depends on the value of the non-dimensional wall distance value (y + ). In logarithmic-based wall functions approach, the first cell y + has been selected between 30 and 300 while for the viscous sublayer approach, the first cell has been selected 1 or less. Enhanced wall function (EWF) treatment is used with − turbulence models for near-wall modelling which is not required with − and SST models. Furthermore, a zero-gage pressure is used at the outlet.
Resolving the near-wall regions of a turbulent boundary layer is critical for the solution to produce the correct flow behavior [45]. Two approaches can be employed to treat the flow near the wall which are (1) logarithmic-based wall functions or (2) resolving the viscous sublayer flow. Selecting one of these approaches dictated the size of the first grid cell near the wall, which depends on the value of the non-dimensional wall distance value ( ). In logarithmic-based wall functions approach, the first cell has been selected between 30 and 300 while for the viscous sublayer approach, the first cell has been selected 1 or less.
Simulation and Analysis
The performance of film cooling is assessed using film cooling effectiveness (FCE), adiabatic film cooling effectiveness (AFCE) and averaged film cooling effectiveness (AFCE) which are defined as follow, The parameters affecting FCE can be classified into two main groups; (1) flow parameters and (2) geometrical parameters. The flow parameters are generally reported in terms of blowing ratio ( ), density ratio ( ) and turbulence intensity ( ), while geometrical parameters are reported in terms of injection angle ( ), hole shape, number of holes, jet delivery channel length and hole to hole spacing. All these parameters are interrelated which requires a careful analysis to understand their effects on film cooling which usually reported using the FCE.
Blowing ratio represents the ratio of velocity and density of coolant flow to mainstream flow ( = /( )). The relatively cool air that is used to form a protective blanket around the flat plate is called the coolant flow while the hot gas running over the flat plate is known as the mainstream flow. The blowing ratio can also be expressed as = * . The term is known as density ratio and the term is known as velocity ratio. The represents the density ratio between the coolant jet and the mainstream gas, which allows us to study the effect of jet coolant on the mainstream fluid temperatures by means of fixing the blowing ratio and varying the velocity ratio.
In this study, air is assumed as the working fluid for the mainstream and the coolant jet. Air is treated as an incompressible ideal gas; hence density is calculated using the ideal gas equation of state. On the other hand, the specific heat capacity, the thermal conductivity and the dynamic viscosity of the air are considered as function of temperature as reported by Turns [46].
Simulation and Analysis
The performance of film cooling is assessed using film cooling effectiveness (FCE), adiabatic film cooling effectiveness (AFCE) and averaged film cooling effectiveness (AFCE) which are defined as follow, The parameters affecting FCE can be classified into two main groups; (1) flow parameters and (2) geometrical parameters. The flow parameters are generally reported in terms of blowing ratio (M), density ratio (DR) and turbulence intensity (I), while geometrical parameters are reported in terms of injection angle (α), hole shape, number of holes, jet delivery channel length and hole to hole spacing. All these parameters are interrelated which requires a careful analysis to understand their effects on film cooling which usually reported using the FCE.
Blowing ratio represents the ratio of velocity and density of coolant flow to mainstream flow (M = ρ c V c /(ρ h V h )). The relatively cool air that is used to form a protective blanket around the flat plate is called the coolant flow while the hot gas running over the flat plate is known as the mainstream flow. The blowing ratio can also be expressed as M = DR * VR. The term DR is known as density ratio and the term VR is known as velocity ratio. The DR represents the density ratio between the coolant jet and the mainstream gas, which allows us to study the effect of jet coolant on the mainstream fluid temperatures by means of fixing the blowing ratio and varying the velocity ratio.
In this study, air is assumed as the working fluid for the mainstream and the coolant jet. Air is treated as an incompressible ideal gas; hence density is calculated using the ideal gas equation of state.
On the other hand, the specific heat capacity, the thermal conductivity and the dynamic viscosity of the air are considered as function of temperature as reported by Turns [46]. Figure 2 shows a structured non-uniform mesh with a jet angle of 90 degree that has been used in this investigation. To assure y + = 1 near the wall, a fine gradual boundary layer mesh near the wall with starting cell size of 0.00017 of jet inlet width has been constructed. Using index notation, the governed equations of the steady state flow are shown below, where, u i , T and P are the mean velocity, temperature and pressure, respectively. Theú i andT represent the fluctuations in the velocity and temperature. The closure relationships of the turbulent Reynolds stressesú iú j is assumed from the chosen turbulence model. Figure 2 shows a structured non-uniform mesh with a jet angle of 90 degree that has been used in this investigation. To assure = 1 near the wall, a fine gradual boundary layer mesh near the wall with starting cell size of 0.00017 of jet inlet width has been constructed. Using index notation, the governed equations of the steady state flow are shown below, where, , and are the mean velocity, temperature and pressure, respectively. The ́ and represent the fluctuations in the velocity and temperature. The closure relationships of the turbulent Reynolds stresses ́ ́ is assumed from the chosen turbulence model. In this study, the governing equations are discretized using second-order upwind scheme and solved iteratively using the semi-implicit method for pressure linked equations corrected (SIMPLEC). The coupled nonlinear governing equations are solved iteratively, and convergence is realized by setting temperature and velocity residuals to 10 and 10 , respectively.
A mesh refinement has been performed via numerical experimentations to assure the grid independence. As shown in Figure 3, a mesh independence study is carried out by testing three different mesh sizes and monitoring the AFCE value. The mesh independence study has been carried out using RNG − turbulence model with enhanced wall function (EWF) and it redeemed that a mesh with 280,000 nodes is appropriate for this problem. In this study, the governing equations are discretized using second-order upwind scheme and solved iteratively using the semi-implicit method for pressure linked equations corrected (SIMPLEC). The coupled nonlinear governing equations are solved iteratively, and convergence is realized by setting temperature and velocity residuals to 10 −9 and 10 −6 , respectively.
A mesh refinement has been performed via numerical experimentations to assure the grid independence. As shown in Figure 3, a mesh independence study is carried out by testing three different mesh sizes and monitoring the AFCE value. The mesh independence study has been carried out using RNG k − ε turbulence model with enhanced wall function (EWF) and it redeemed that a mesh with 280,000 nodes is appropriate for this problem. Using the parameters shown in Table 1 for the validation case, five different turbulence models have been assessed as shown in Figure 4. Out of the five models, the RNG − model with EWF has shown the best match compared to the published work in [31] with an overall deviation of 1.7% in calculating the AFCE. Under the same conditions, velocity profile is validated with O'Malley [37] and Bayraktar and Yilmaz [31] as shown in Figure 5.
The suitability of the RNG − model with EWF to current problem, mainly when compared to other four models comes from the way turbulence model is resolved using these models. The − model is more suitable when studying free-shear layers and wake region while the standard − model is more suitable in the near wall boundary regions. Since current problem is mainly dominated by the free shear layer, the − model showed best match with the published work. The RNG − model combines a statistical technique called renormalization group (RNG) theory with the − turbulence model. Applying the RNG to the − model produces a modified −equation which improves the prediction of different scales of flow motion. The EWF blends the linear (laminar) and logarithmic (turbulent) laws-of-the-wall using a function suggested by Kader [47]. Table 1 versus against numerical study of Bayraktar and Yilmaz [31]. Using the parameters shown in Table 1 for the validation case, five different turbulence models have been assessed as shown in Figure 4. Out of the five models, the RNG k − ε model with EWF has shown the best match compared to the published work in [31] with an overall deviation of 1.7% in calculating the AFCE. Under the same conditions, velocity profile is validated with O'Malley [37] and Bayraktar and Yilmaz [31] as shown in Figure 5.
The suitability of the RNG k − ε model with EWF to current problem, mainly when compared to other four models comes from the way turbulence model is resolved using these models. The k − ε model is more suitable when studying free-shear layers and wake region while the standard k − ω model is more suitable in the near wall boundary regions. Since current problem is mainly dominated by the free shear layer, the k − ε model showed best match with the published work. The RNG k − ε model combines a statistical technique called renormalization group (RNG) theory with the k − ε turbulence model. Applying the RNG to the k − ε model produces a modified ε−equation which improves the prediction of different scales of flow motion. The EWF blends the linear (laminar) and logarithmic (turbulent) laws-of-the-wall using a function suggested by Kader [47]. Using the parameters shown in Table 1 for the validation case, five different turbulence models have been assessed as shown in Figure 4. Out of the five models, the RNG − model with EWF has shown the best match compared to the published work in [31] with an overall deviation of 1.7% in calculating the AFCE. Under the same conditions, velocity profile is validated with O'Malley [37] and Bayraktar and Yilmaz [31] as shown in Figure 5.
The suitability of the RNG − model with EWF to current problem, mainly when compared to other four models comes from the way turbulence model is resolved using these models. The − model is more suitable when studying free-shear layers and wake region while the standard − model is more suitable in the near wall boundary regions. Since current problem is mainly dominated by the free shear layer, the − model showed best match with the published work. The RNG − model combines a statistical technique called renormalization group (RNG) theory with the − turbulence model. Applying the RNG to the − model produces a modified −equation which improves the prediction of different scales of flow motion. The EWF blends the linear (laminar) and logarithmic (turbulent) laws-of-the-wall using a function suggested by Kader [47]. Table 1 versus against numerical study of Bayraktar and Yilmaz [31]. Table 1 versus against numerical study of Bayraktar and Yilmaz [31].
Results and Discussion
The effect of different interrelated parameters on AFCE is presented in this section. The main three interrelated parameters tested in this study are flow blowing ratio ( ), fluid density ratio ( ) and film injection angle (α). Combinations of these interrelated parameters have been formed into 54 runs as listed in Table 2. A wide range of blowing ratio value has been explored ranging from 0.1 to 2. Also, the density ratio has been explored for three different values of 1.2, 2, and 3. Furthermore, the film injection angle ( ) is tested for three angles of 30, 60, and 90 degree.
At steady state condition, as hot mainstream moves over a flat plate, the flat wall temperature will approach the mainstream high temperature which is not desired. Hence, cool air is injected from a confined 2D slot to form a cooling film that shields the flat wall from the hot mainstream. However, as fluid marches in the -direction, cold and hot streams mix together causing the wall temperature to rise which eventually will approach asymptotic value equal to the hot mainstream temperature. Temperature of the cooler film increases due to the heat transfer and mixing of the hot mainstream flow and cool film flow. As wall temperature approaches the mainstream temperature, the adiabatic film cooling effectiveness deteriorates as shown in Figure 6. The rate of deterioration in AFCE along the -direction is high at the beginning which starts to decrease as the flow moves in the -direction. The main reason for such high rate of deterioration in AFCE near the slot is the thin boundary layer formed by the cool fluid, which starts to grow as flow moves in -direction. Even then, the AFCE still keeps dropping since the heat transfer between the mainstream and flat wall is more pronounced compared to the boundary layer shielding effect. For film cooling with an injection angle of 30 degree, Figure 6a shows that the adiabatic film cooling effectiveness has non-monotonic relation with the blowing ratio ( ), while a monotonic relation is found with 60 and 90 degree injection angles (as shown in Figure 6b,c, respectively). An increase in the AFCE with higher blowing ratio is expected since more fluid discharges from the film hole and thus, a bigger blanket of cool air is formed between the hot mainstream flow and the flat wall, which provides an enhanced wall shield. However, this trend is not indefinite since as film discharge increases beyond = 1.0 (for a blowing angel of 30 degree), the chance of film detachment from the walls increases causing less shielding on the flat wall. The blowing ratio at which the AFCE starts to fall afterwards is identified, in this study, as the critical blowing ratio. For = 1.2 and = 30 degree, the critical blowing ratio is around = 1.0 as shown in Figure 6. From the figure, there is no critical blowing ratio observed for angles 60 and 90 degree with = 1.2. The effect of film cooling detachment can clearly be seen in Figure 6c (with a film injection angle of 90 degree). As shown in the figure, directly after the hole, the local AFCE is lower at the 90 degree angle in comparison to the 30 degree case. More details of the injection angle effect are discussed below. Bayraktar and Yilmaz [31] current CFD model
Results and Discussion
The effect of different interrelated parameters on AFCE is presented in this section. The main three interrelated parameters tested in this study are flow blowing ratio (M), fluid density ratio (DR) and film injection angle (α). Combinations of these interrelated parameters have been formed into 54 runs as listed in Table 2. A wide range of blowing ratio value has been explored ranging from 0.1 to 2. Also, the density ratio has been explored for three different values of 1.2, 2, and 3. Furthermore, the film injection angle (α) is tested for three angles of 30, 60, and 90 degree. At steady state condition, as hot mainstream moves over a flat plate, the flat wall temperature will approach the mainstream high temperature which is not desired. Hence, cool air is injected from a confined 2D slot to form a cooling film that shields the flat wall from the hot mainstream. However, as fluid marches in the x-direction, cold and hot streams mix together causing the wall temperature to rise which eventually will approach asymptotic value equal to the hot mainstream temperature. Temperature of the cooler film increases due to the heat transfer and mixing of the hot mainstream flow and cool film flow. As wall temperature approaches the mainstream temperature, the adiabatic film cooling effectiveness deteriorates as shown in Figure 6. The rate of deterioration in AFCE along the x-direction is high at the beginning which starts to decrease as the flow moves in the x-direction. The main reason for such high rate of deterioration in AFCE near the slot is the thin boundary layer formed by the cool fluid, which starts to grow as flow moves in x-direction. Even then, the AFCE still keeps dropping since the heat transfer between the mainstream and flat wall is more pronounced compared to the boundary layer shielding effect. For film cooling with an injection angle of 30 degree, Figure 6a shows that the adiabatic film cooling effectiveness has non-monotonic relation with the blowing ratio (M), while a monotonic relation is found with 60 and 90 degree injection angles (as shown in Figure 6b,c, respectively). An increase in the AFCE with higher blowing ratio is expected since more fluid discharges from the film hole and thus, a bigger blanket of cool air is formed between the hot mainstream flow and the flat wall, which provides an enhanced wall shield. However, this trend is not indefinite since as film discharge increases beyond M = 1.0 (for a blowing angel of 30 degree), the chance of film detachment from the walls increases causing less shielding on the flat wall. The blowing ratio at which the AFCE starts to fall afterwards is identified, in this study, as the critical blowing ratio. For DR = 1.2 and α = 30 degree, the critical blowing ratio is around M = 1.0 as shown in Figure 6. From the figure, there is no critical blowing ratio observed for angles 60 and 90 degree with DR = 1.2. The effect of film cooling detachment can clearly be seen in Figure 6c (with a film injection angle of 90 degree). As shown in the figure, directly after the hole, the local AFCE is lower at the 90 degree angle in comparison to the 30 degree case. More details of the injection angle effect are discussed below. Figure 7a shows that the effect of injection angle is small at a low blowing ratio of M = 0.1 with very similar AFCE trends for all angles. The averaged AFCE is also relatively lower at low blowing ratios, which can be seen in Figure 7a compared to Figure 7b-d. A low blowing ratio means less cooling fluid is being injected to the mainstream, which explains the lower wall protection and hence a lower averaged AFCE. At low blowing ratios, the injection angle has a weak effect on the AFCE. A low blowing ratio means the flow has low momentum to affect the mainstream flow field, which reduces the effect of injection angle. However once blowing ratio increases beyond M = 0.1, the injection angle becomes an important factor that can alter the flow field. The effect of blowing ratio is intricate since it relates quantitatively the effect of flow linear momentum of two streams without counting the effect of direction of these quantities. Linear momentum is a vector parameter and its impact on the flow field is determined by the quantitative value and the flow vector direction. For blowing ratios equal to 0.5 or higher, as shown in Figure 7b-d, the AFCE increases as the blowing angel decreases. Smaller angles indicate a higher chance of the flow remaining in contact with the flat wall to form a cool blanket and properly shielding the wall from the hot mainstream. However, at low blowing ratio of M = 0.1, as shown in Figure 7a, the angle effect becomes less important and in the contrary to the previous relation, as angle decreases the AFCE decreases. Figure 7a shows that the AFCE is the highest for a blowing angel of 90 degree. At low blowing ratio, injecting air at 90 degree allows thicker protection film which provides better shielding and a higher AFCE. In general, for a wide blowing ratio range of M = 0.5 − 2.0, decreasing the injection angle causes an increase in the AFCE which means film attachment is dominating the wall shielding. On the other hand, at a low blowing ratio of M = 0.1, higher angles form a thicker cooling film and dictates the heat transfer rate. In conclusion, the injection angle has two conflicting effects on the AFCE. A small injection angle provides a low chance of fluid detachment but a thin blanket of cool fluid. Also, a high blowing angle results in a high chance of detachment but a thicker blanket of cool fluid. Note that, these contradicting effects interrelates to blowing ratio as well. cooling fluid is being injected to the mainstream, which explains the lower wall protection and hence a lower averaged AFCE. At low blowing ratios, the injection angle has a weak effect on the AFCE. A low blowing ratio means the flow has low momentum to affect the mainstream flow field, which reduces the effect of injection angle. However once blowing ratio increases beyond = 0.1, the injection angle becomes an important factor that can alter the flow field. The effect of blowing ratio is intricate since it relates quantitatively the effect of flow linear momentum of two streams without counting the effect of direction of these quantities. Linear momentum is a vector parameter and its impact on the flow field is determined by the quantitative value and the flow vector direction. For blowing ratios equal to 0.5 or higher, as shown in Figure 7b-d, the AFCE increases as the blowing angel decreases. Smaller angles indicate a higher chance of the flow remaining in contact with the flat wall to form a cool blanket and properly shielding the wall from the hot mainstream. However, at low blowing ratio of = 0.1, as shown in Figure 7a, the angle effect becomes less important and in the contrary to the previous relation, as angle decreases the AFCE decreases. Figure 7a shows that the AFCE is the highest for a blowing angel of 90 degree. At low blowing ratio, injecting air at 90 degree allows thicker protection film which provides better shielding and a higher AFCE. In general, for a wide blowing ratio range of = 0.5 − 2.0, decreasing the injection angle causes an increase in the AFCE which means film attachment is dominating the wall shielding. On the other hand, at a low blowing ratio of = 0.1, higher angles form a thicker cooling film and dictates the heat transfer rate.
In conclusion, the injection angle has two conflicting effects on the AFCE. A small injection angle provides a low chance of fluid detachment but a thin blanket of cool fluid. Also, a high blowing angle results in a high chance of detachment but a thicker blanket of cool fluid. Note that, these contradicting effects interrelates to blowing ratio as well. Using = * , the effect of density ratio ( ) is studied while keeping the injection angle at a constant value of 30 degree for two blowing ratios as shown in Figure 8. The density ratio ( ) represents the density ratio between the relatively cool fluid and the hot mainstream fluid. At low Using M = DR * VR, the effect of density ratio (DR) is studied while keeping the injection angle at a constant value of 30 degree for two blowing ratios as shown in Figure 8. The density ratio (DR) represents the density ratio between the relatively cool fluid and the hot mainstream fluid. At low blowing ratios, M = 0.1 as shown in Figure 8a, DR has minimum effect on the AFCE since the flow is mainly dominated by the hot mainstream and cool film has little momentum to shield the flat wall. At DR of 0.5 and higher, the effect of DR on the AFCE is more pronounced as shown in Figure 8b-d. The DR has two conflicting effects on heat transfer between hot mainstream fluid and cool film fluid. The first effect, while using fixed value of M, as DR increases the velocity ratio (VR) decreases causing a lower momentum of the injected cooling fluid, which decreases the size of the film cooling blanket covering the flat wall. Hence, increasing DR means less protection on the flat wall. The second effect is that as DR increases the thermal capacity of the cooling fluid increases, which allows it to carry more thermal energy and prevents such energy transfer to the flat wall. The increase in the thermal capacity of the cooling fluid shields the wall from additional heat transfer and boosts the AFCE. blowing ratios, = 0.1 as shown in Figure 8a, has minimum effect on the AFCE since the flow is mainly dominated by the hot mainstream and cool film has little momentum to shield the flat wall. At of 0.5 and higher, the effect of on the AFCE is more pronounced as shown in Figure 8bd. The has two conflicting effects on heat transfer between hot mainstream fluid and cool film fluid. The first effect, while using fixed value of , as increases the velocity ratio ( ) decreases causing a lower momentum of the injected cooling fluid, which decreases the size of the film cooling blanket covering the flat wall. Hence, increasing means less protection on the flat wall. The second effect is that as increases the thermal capacity of the cooling fluid increases, which allows it to carry more thermal energy and prevents such energy transfer to the flat wall. The increase in the thermal capacity of the cooling fluid shields the wall from additional heat transfer and boosts the AFCE. Figure 9 shows that as increases the AFCE decreases for values less than 1, due to the formation of thick film of coolant fluid. However, at high value of = 2, as increases, the effect of thermal capacity of cooling fluid increases, which causes a better shielding against the heat transfer from the hot mainstream fluid and improves the AFCE. As show in Figure 9, at injection angle of 30 degree and = 1.2 the critical is around 1, while no critical is observed at = 2 and = 3. Figure 9 shows that as DR increases the AFCE decreases for M values less than 1, due to the formation of thick film of coolant fluid. However, at high value of M = 2, as DR increases, the effect of thermal capacity of cooling fluid increases, which causes a better shielding against the heat transfer from the hot mainstream fluid and improves the AFCE. As show in Figure 9, at injection angle of 30 degree and DR = 1.2 the critical M is around 1, while no critical M is observed at DR = 2 and DR = 3. The coolant jet velocity streamlines at various film cooling configurations are shown in Figure 10. The coolant jet streamlines starting from jet entrance are used to describe the effect of the interrelated parameters on the AFCE. Figure 10 shows the effect of coolant injection angle and blowing ratio on the coolant jet velocity streamlines. Blowing ratios effect on the film cooling blanket are shown in Figure 10a,c. Higher blowing ratios often cause a higher thickness of the film cooling blanket, which affects the AFCE positively or negatively as discussed earlier. The effect of coolant injection angle on the film cooling thickness is shown in Figure 10b,d. A higher coolant injection angle shows a bigger film cooling thickness. However, a higher coolant injection angle promotes injecting the coolant away from the flat wall, which reduces the wall protection and reduces the averaged AFCE. To explore a relationship between several interrelated parameters affecting the AFCE, response surface methodology (RSM) is used. RSM is a group of statistical and mathematical models that are The coolant jet velocity streamlines at various film cooling configurations are shown in Figure 10. The coolant jet streamlines starting from jet entrance are used to describe the effect of the interrelated parameters on the AFCE. Figure 10 shows the effect of coolant injection angle and blowing ratio on the coolant jet velocity streamlines. Blowing ratios effect on the film cooling blanket are shown in Figure 10a,c. Higher blowing ratios often cause a higher thickness of the film cooling blanket, which affects the AFCE positively or negatively as discussed earlier. The effect of coolant injection angle on the film cooling thickness is shown in Figure 10b,d. A higher coolant injection angle shows a bigger film cooling thickness. However, a higher coolant injection angle promotes injecting the coolant away from the flat wall, which reduces the wall protection and reduces the averaged AFCE. The coolant jet velocity streamlines at various film cooling configurations are shown in Figure 10. The coolant jet streamlines starting from jet entrance are used to describe the effect of the interrelated parameters on the AFCE. Figure 10 shows the effect of coolant injection angle and blowing ratio on the coolant jet velocity streamlines. Blowing ratios effect on the film cooling blanket are shown in Figure 10a,c. Higher blowing ratios often cause a higher thickness of the film cooling blanket, which affects the AFCE positively or negatively as discussed earlier. The effect of coolant injection angle on the film cooling thickness is shown in Figure 10b,d. A higher coolant injection angle shows a bigger film cooling thickness. However, a higher coolant injection angle promotes injecting the coolant away from the flat wall, which reduces the wall protection and reduces the averaged AFCE. To explore a relationship between several interrelated parameters affecting the AFCE, response surface methodology (RSM) is used. RSM is a group of statistical and mathematical models that are To explore a relationship between several interrelated parameters affecting the AFCE, response surface methodology (RSM) is used. RSM is a group of statistical and mathematical models that are used to explore the relationship between numerous independent variables and response variables [44]. The averaged AFCE is define as in Equation (3), which represents the area weighted average of the AFCE. In RSM analysis, all factors must be reported for at least three different levels. In this work, four levels of the blowing ratio, three levels of the injection angles and three levels of the density ratio are considered in the RSM analysis as shown in Table 3. This combination of parameters results in 36 reported averaged AFCE. More levels are taken for the blowing ratio to increase the resolution of the RSM model in capturing the blowing ratio effect. RSM statistically measures the contribution of all the variables on the area weighted average AFCE. It reports the solely effect of a parameter, known as the main parameter effect, and how the different parameters are interacting with each other. These models are generally performed using a statistical software. In this study, a commercial software named MINITAB is used to develop the RSM model and to determine the effect of the variables in Table 3 on the averaged AFCE. The significance of a term is identified by its corresponding p-value and T-value. T-value is the calculated difference represented in units of standard error. Lower p-value and greater T-value is a characteristic of a significant term that has a big influence on the reported response value. Table 4 shows the summary of the RSM model generated by MINITAB. The table shows that the terms M, M 2 , α, DR and M * DR have the highest effect on the averaged AFCE.
The RSM generated regression model used to describe the averaged AFCE is shown in Equations (7) and (8). Equation (7) correlates the effect of all the terms on the averaged AFCE. While Equation (8) is generated using the terms in Table 4 that have a p-value of 0.1 and below. The relative error in estimating the AFCE is 7.90% and 7.97% for Equations (7) and (8), respectively. Therefore, Equation (8) can be used to accurately estimate the average AFCE within the minimum and maximum levels of the three different parameters in Table 4.
The blowing ratio has two terms (M, M 2 ) in the generated regression model, which have conflicting effect on the overall averaged AFCE. Increasing the blowing ratio (M) will increase the AFCE until the squared term (M 2 ) starts to affect the AFCE negatively. The model also shows that increasing the injection angle will decrease the AFCE. The density ratio can contribute positively to the AFCE at higher values of the blowing ratio. These results agree with the results discussed previously. Figure 11 shows the interaction of three different variables. Figure 11a,b suggest that the highest value of AFCE is achievable by working at lower values of injection angles and density ratios. Figure 11c shows that working at high values of blowing ratio achieve high AFCE regardless of the DR value. The quadratic effect of the blowing ratio given by Equation (8) can be seen in Figure 11a, where a negative effect on the AFCE is observed. Figure 11 shows the interaction of three different variables. Figure 11a,b suggest that the highest value of AFCE is achievable by working at lower values of injection angles and density ratios. Figure 11c shows that working at high values of blowing ratio achieve high AFCE regardless of the value. The quadratic effect of the blowing ratio given by Equation (8) can be seen in Figure 11a, where a negative effect on the AFCE is observed.
Equation (8) is optimized using generalized reduced gradient (GRG) nonlinear solver using MS Excel solver. This solver method uses the gradient of the objective function (AFCE) and keep changing input values ( , and ) until reaching an optimum solution when the partial derivatives equal zero. Using the GRD solver on selected range, the optimum point will be for at injection angle of 30°, = 1.2 and = 1.8. Blowing ratio for different density ratios at = 30.
Conclusions
In this study, the effect of three main interrelated parameters on film cooling performance has been explored using a statistical approach. These interrelated parameters are the jet blowing ratio, the cooling fluid density ratio, and the jet injection angle. The RNG − model with EWF has deemed appropriate to model slot film cooling as it captures the low-Reynolds number effects close to the wall. This turbulence model shows the best accuracy in reporting the AFCE compared to the other turbulence models. Sensitivity analysis has shown that blowing ratio has the major effect on the AFCE. However, the most optimum parameter configuration is a combination of all affecting Equation (8) is optimized using generalized reduced gradient (GRG) nonlinear solver using MS Excel solver. This solver method uses the gradient of the objective function (AFCE) and keep changing input values (α, DR and M) until reaching an optimum solution when the partial derivatives equal zero. Using the GRD solver on selected range, the optimum point will be for at injection angle of 30 • , DR = 1.2 and M = 1.8.
Conclusions
In this study, the effect of three main interrelated parameters on film cooling performance has been explored using a statistical approach. These interrelated parameters are the jet blowing ratio, the cooling fluid density ratio, and the jet injection angle. The RNG k − ε model with EWF has deemed appropriate to model slot film cooling as it captures the low-Reynolds number effects close to the wall. This turbulence model shows the best accuracy in reporting the AFCE compared to the other turbulence models. Sensitivity analysis has shown that blowing ratio has the major effect on the AFCE. However, the most optimum parameter configuration is a combination of all affecting parameters. For the considered parameters configuration in the practical range for film cooling, the combination of injection angle of 30 • , DR = 1.2 and M = 1.8 offer the highest average AFCE. | 11,422.6 | 2020-02-18T00:00:00.000 | [
"Physics",
"Engineering"
] |
Quantum dissipation in a scalar field theory with gapped momentum states
Understanding quantum dissipation is important from both theoretical perspective and applications. Here, we show how to describe dissipation in a scalar field theory. We treat dissipation non-perturbatively, represent it by a bilinear term in the Lagrangian and quantize the theory. We find that dissipation promotes a gap in momentum space and reduces the particle energy. As a result, particle mass becomes dressed by dissipation due to self-interaction. The underlying mechanism is similar to that governing the propagation of transverse collective modes in liquids. We discuss the interplay between the dissipative and mass terms, the associated different regimes of field dynamics and the emergence of ultraviolet and infrared cutoffs due to dissipation.
Theoretical description of dissipation in quantum systems is an interesting and challenging problem of fundamental importance related to the foundations of quantum theory itself (see, e.g. 1,2 ). Quantum dissipation has seen renewed recent interest in areas related to non-equilibrium and irreversible physics, decoherence effects and complex systems. Starting from early work (see, e.g. 3,4 ), a common approach to treat dissipation is to introduce a central dissipative system of interest, its environment modelled as, for example, a bath of harmonic oscillators and an interaction between the system and its environment enabling energy exchange (see, e.g. 5,6 for review). In this picture, dissipative effects can be discussed by solving models using approximations such as linearity of the system and its couplings.
Here, we propose a conceptually different description of dissipation based on recent insights of wave propagation in liquids and supercritical fluids [7][8][9] . No dissipation takes place when a plane wave propagates in a crystal where the wave is an eigenstate. However, a plane wave dissipates in systems with structural and dynamical disorder such as liquids. An important result is the emergence of the gap in k-or momentum space in the transverse wave spectrum, with the accompanying decrease of the wave energy due to dissipation. We propose that this is a physically relevant mechanism to introduce and discuss dissipation in quantum field theory in a general way because canonical quantization of fields involves expanding field operators in terms of plane waves.
In this paper, we show how dissipation can be introduced in a scalar field theory. Representing dissipation due to field self-interaction by a bilinear term as in liquids, we perform canonical quantization of scalar fields. We find that particle energy is reduced by dissipation which promotes the gapped momentum state (GMS). Particle mass becomes dressed by dissipation as a result. The underlying mechanism is similar to that governing transverse modes in liquids. We discuss the interplay between the dissipative and mass terms, the associated different regimes of field dynamics as well as ultraviolet and infrared cutoffs due to dissipation.
We start with recalling how liquid transverse modes develop a GMS and how this effect can be represented by a Lagrangian. We note first-principles description of liquids is exponentially complex and is not tractable because it involves a large number of coupled non-linear oscillators 7 . At the same time, liquids have no simplifying small parameters as in gases and solids 10 . However, progress in understanding liquid modes can be made by using non-perturbative approach to liquids pioneered by Maxwell and developed later by Frenkel. This programme involves Maxwell interpolation: where s is shear strain, η is viscosity, G is shear modulus and P is shear stress.
(1) Reflects Maxwell's proposal 11 that shear response in a liquid is the sum of viscous and elastic responses given by the first and second right-hand side terms. Notably, the dissipative term containing viscosity is not introduced as a small perturbation: both elastic and viscous deformations are treated in (1) and use this η in the Navier-Stokes We have carried this idea forward 7 and, considering small v, wrote: where v is the velocity component perpendicular to x, η τ ρ τ = = G c 2 and c is the shear wave velocity. Equation (2) can also be obtained by starting with the solid-like equation for the non-decaying wave and, using Maxwell interpolation (1), generalizing the shear modulus to include the viscous response 9 .
In contrast to the Navier-Stokes equation, (2) contains the second time derivative and hence gives propagating waves. We solved Eq. (2) in ref. 7 : seeking the solution as τ → ∞ in (3) and the absence of dissipation in (2) correspond to an infinite range of propagation of the plane shear wave as in the crystal. A finite τ implies dissipation of the wave in a sense that it acquires a finite propagation range. Indeed, the dissipation takes place over time approximately equal to τ according to (3). This corresponds to the propagation range of the shear wave being finite and equal to cτ (this can be inferred directly from the Frenkel's discussion: if τ is the time during which shear stress can exist in a liquid, cτ is the distance over which a shear wave propagates). τ sets the physical time scale during which we consider the dissipation process: if an observation of an injected shear wave starts at = t 0, time τ ≈ t is the end of the process because over this time the wave amplitude and energy appreciably reduce.
An important property is the emergence of the gap in k-space or GMS: in order for ω in (3) to be real, k k g > should hold, where k g c 1 2 = τ increases with temperature because τ decreases. Recently 8 , detailed evidence for GMS was presented on the basis of molecular dynamics simulations. Figure 1 illustrates these findings.
The GMS is interesting. Indeed, the two commonly discussed types of dispersion relations are either gapless as for photons and phonons, E p = ( = c 1), or have the energy gap for massive particles, E p m 2 2 = + , where the gap is along the Y-axis. On the other hand, (3) implies that the gap is in momentum space and along the X-axis, similar to the hypothesized tachyon particles with imaginary mass 14 . It has been realized that in addition to liquids, GMS emerge in a surprising variety of areas, including strongly-coupled plasma, electromagnetic waves, non-linear Sine-Gordon model, relativistic hydrodynamics and holographic models 15 . www.nature.com/scientificreports www.nature.com/scientificreports/ An important question from field-theoretical perspective is what Lagrangian gives Eq. (2) and the associated GMS? The challenge is to represent the viscous term ∝ τ 1 in (2) . This can be represented by a scalar field φ (we note that different dissipation effects of scalar fields and their interplay 16 are considered in cosmological applications, although GMS are not discussed), giving the term L . Another way to see this is note that the viscous term d dt d dt To circumvent this problem, we proposed to operate in terms of two fields φ 1 and 2 φ 9 and constructed the dissipative term as a combination of φ φ d dt , namely as ( ) . We note that a two-coordinate description of a localised damped harmonic oscillator was discussed earlier 17,18 . Increasing the number of degrees of freedom was also involved in describing dissipation with gapless dispersion relations and in the hydrodynamic regime only 19 .
The Lagrangian becomes: where we added the mass term, assumed = c 1 and, for simplicity, considered one-dimensional case. We note that (4) without the mass term follows from the two-field Lagrangian using the transformation employed in the complex field theory: The advantage of using (4) in terms of 1 φ and 2 φ is that the equations of motion for φ 1 and 2 φ decouple as we see below. This is not an issue, however: one can use (5) to obtain the system of coupled equations for ψ 1 and 2 ψ and decouple them using the same transformation between φ and ψ, resulting in the same equations for φ as those following from (4). Note that the imaginary term in (5) may be related to dissipation 1,20-22 , however the Hamiltonian corresponding to (5) does not explicitly contain an imaginary term: = where terms with τ cancel out and where the real parts of ψ 1 and 2 ψ are implied. τ → ∞ corresponds to no particle jumps and L d = 0,in which case L in (4) takes the form of the complex scalar field theory (this corresponds to the short-time regime τ t in the solution of (4) as shown below). The dissipative term ∝ 1 τ in (4) and (5) can be viewed as a coupling term between two sectors describing φ 1 and 2 φ (ψ 1 and 2 ψ ). As discussed below, this coupling results in the flow of energy from one field to another. The coupling breaks time reversal symmetry of Lagrangian t t → − , however the Lagrangian is invariant under the combination of time reversal symmetry and internal symmetry 1 . Combinations of spacetime and internal symmetries in condensed matter systems are discussed more generally, e.g., in ref. 23 .
We now consider the Hamiltonian of the dissipative system and its quantization. Applying the Euler-Lagrange equation to (4) gives two decoupled equations where the equation for 1 φ is the same as (2) when = m 0. A solution for φ 1 and φ 2 can be written as: where, for simplicity, we absorbed the factor of 2 in τ. E p in (7) is the same as in (3) (6)). φ 1 and 2 φ in (6) can be viewed as energy exchange between waves 1 φ and 2 φ : φ 1 and φ 2 appreciably decrease and grow over time τ, respectively. This process is not dissimilar from phonon scattering in crystals due to defects or anhar-www.nature.com/scientificreports www.nature.com/scientificreports/ monicity where a plane-wave phonon ( 1 φ ) decays into other phonons (represented by φ 2 ) and acquires a finite lifetime τ as a result.
The momenta from (4) are (recalling that τ τ → 2 ): and the Hamiltonian density is where terms ∝ 1 τ cancel out. We now proceed to quantization. (6) are solutions of the dissipative Lagrangian (4). Setting τ → ∞ in (4) and considering the short-time regime τ t in (6) corresponds to the absence of dissipation and to the complex scalar field theory, which is quantized using operators acting on particles and antiparticles 22 . Therefore, it is convenient to quantize the full Hamiltonian (7). In the short-time regime t τ where dissipation can be neglected, (11) is the mode expansion used to quantize the complex scalar field theory 22 .
As in (3), the time scale over which we consider and describe the dissipation process in both (6) and (11) is τ because the phonon with the k-gap (3) dissipates after time comparable to τ.
A persisting open problem in using quantum mechanics to describe dissipation involved two dual Bateman oscillators where commutation relations did not hold 18 . On the other hand, the quantization based on the mode expansion proposed here satisfies the required commutation relations for the field operators. The commutators [ φ φ = for the same reason as in the standard complex field theory. The commutator φ π x y [ ( ), ( )] 1 1 because φ 1 and 2 φ commute. Considering equal times and using (11) . Swapping the sign of p in the first term and integrating gives − as required because the terms with τ 1 cancel. The same cancellation mechanism gives 1 2 , using the earlier results for Using (11) in (10) www.nature.com/scientificreports www.nature.com/scientificreports/ Using (7), (12) simplifies, after normal ordering, to with the energy spectrum (7) where F 1 ω = τ is the Frenkel hopping frequency. Equations (13) and (14) represent a canonically quantized theory with dissipation. The first term in (13) describes the excitations of particles and antiparticles as in the complex scalar field theory, albeit with energies reduced by the dissipation according to (14) due to the presence of the field hopping process with frequency ω F (see below for a more detailed discussion). If the number of particles † ∫ = N dpa a p pp 3 and the number of antipar- are equal, the second term in (13) is zero. In this case, (13) is real, corresponding to the stationary state of the system. N N a p ≠ in (13) corresponds to non-zero imaginary term, which is related to particle decay and dissipation [20][21][22] . We will discuss the relationship between the dissipation and the anharmonic interaction potential below.
We note that similarly to (6), there is a choice of assigning factors e t − τ and e t τ to φ 1 and 2 φ in (11). If e t 1 φ ∝ τ and e 2 t φ ∝ − τ , the imaginary term in (13) changes sign. Time-dependent properties of this model will be discussed elsewhere. Here, we note that the dissipation is not related to a change of the total energy of the system (a conserved property); rather, it is related to the dissipation of harmonic excitations in the strongly-anharmonic potential as is the case of dissipation of plane waves in structurally and dynamically disordered liquids where a plane wave acquires a finite lifetime and propagation range as discussed earlier.
We pause for the moment and comment on the canonical quantization performed in (11) and (14). Canonical quantization is believed to be possible only for Lagrangians quadratic in fields and its derivatives, with the result that the system is the sum of non-interacting single particles in momentum states. In contrast, interacting theories involving higher powers of fields can not be diagonalized, and for this reason their canonical quantization is believed to be impossible 22 . Our proposed procedure (11) and (14) diagonalizes the Hamiltonian of the strongly interacting field but, notably, this interaction is represented by the bilinear form in (4) rather by the higher-order terms. The idea behind introducing parameter τ in L d is the same as in liquids.
Although not derived from first-principles, the introduction of τ in liquid theory achieves two important results: (a) it simplifies an exponentially complex problem of coupled non-linear oscillators describing the motion of liquid particles in the anharmonic multi-well potential and thus provides a way to treat strongly-anharmonic interactions non-perturbatively 7 ; and (b) it quantifies an important and independently measurable liquid property (liquid relaxation time) directly linked to viscosity. This, in turn, enables developing a theory of liquid thermodynamics and provide relationships between different liquid properties 7 . Similarly, introducing the dissipative term L d in (4) represents a way to treat strongly anharmonic self-interaction of the field non-perturbatively. Indeed, if the field self-interaction has a multi-well form in Fig. 2, the field, in addition to oscillating in a single well, can move from one minimum to another (by either thermal activation or tunneling as discussed in, e.g., ref. 24 ). This motion is completely analogous to diffusive particle jumps in the liquid responsible for the viscous term ∝ 1 τ in (2) and the dissipative term ∝ 1 τ in (4). Therefore, L d describes the hopping motion of the field between different wells with frequency 1 τ . Note that this effect implies strong self-interaction of the field and can not be treated by usual perturbation methods in quantum field theory.
The important point from the above discussion is that the GMS and τ are related to the multi-well potential in Fig. 2. We note that Fig. 2 is a general construction giving rise to three regimes of particle dynamics and three states of matter: solids, liquids and gases. Particles oscillate in a single minimum in solids, oscillate and diffusively move between different minima in liquids and ballistically move above the potential barrier in gases. We propose that similar regimes of field dynamics may exist in quantum field theory. In condensed matter physics, the potential barrier U is set by the interatomic potential 12 . For self-interacting fields, we similarly assume that field self-interaction gives the landscape characterized by a single U.
We now return to our main results (13) and (14) and other properties of our model. (14) can be viewed as the appearance of a dressed mass m d due to field self-interaction: where the difference between m d and m can be large, as expected from our non-perturbative approach. This interpretation holds as long as m F ω < . When ω = m F , the dissipation term annihilates the mass in the dispersion relation (14) which becomes photon-like and gapless. When m F ω > , the gap in momentum space opens up, as in (3) (see Fig. 1), and increases with ω F : We now discuss an interplay between real and imaginary terms in (13). These correspond to the energy and decay (half-width) of particles 20,21 . The important effect concerns the crossover between propagating and non-propagating modes (PNM). The PNM crossover can be approximately defined as the equality between the www.nature.com/scientificreports www.nature.com/scientificreports/ mode period and decay time. In terms of energy, this corresponds to equality of E p and ω F in (13) (for simplicity, we assume that the energy of anti-particles is small compared to that of particles). Three regimes of the dissipative field dynamics follow.
In the first regime, all modes in (11) remain propagating despite dissipation. Indeed, the energy gap in (14), . Under this condition, ω > E p F for any p, as illustrated in Fig. 1.
In the second regime, F ω increases so that m F 2 ω > but remains small enough so that ω < m F and the energy gap still exists as discussed above, i.e. ω ω < < m 2 F F . In this case, the energy gap is smaller than ω F : E g F ω < , and the PNM crossover takes place for all modes with E p F ω < (see Fig. 1). Accordingly, all modes with momenta with p m 0 2 F 2 2 ω < < − become non-propagating and do not contribute to the system energy. In the third regime ω > m F , the gap in momentum space opens up, and propagating modes start with p p g > (see (16)). In this case, the PNM crossover implies that all modes with momenta in the range ω < < − p p m 2 g F 2 2 become non-propagating (see Fig. 1). Together with the > p p g , this implies that the range of non-propagating modes is ω < < − p m 0 2 F 2 2 as in the second regime. In the second and third regimes, the infra-red divergences are removed from evaluating integrals over p because an integration starts from a finite value. Importantly, our model has an ultraviolet cutoff. In addition to E p and ω F , there is a third energy scale in our model: the height of the potential energy barrier U in Fig. 2. The formalism of creation and annihilation operators assumes the quadratic form of the potential which provides the restoring force for the oscillator. For the potential in Fig. 2, this applies as long as the energy is smaller than U. For the energy above U, the potential provides no restoring force, and the formalism no longer applies. Therefore, the upper integration limit in all quantities of interest is approximately U, removing ultraviolet divergences in calculations. This results from the form of the potential in Fig. 2 only (and not from other ingredients of the theory such as, e.g., quantization). Notably, the GMS and the ultraviolet cutoff are related: the gap in momentum space emerges due to a finite τ (ω F ) in (7), (14) or (16) which, in turn, arises from the potential in Fig. 2 with a finite U.
In summary, we represented dissipation due to field self-interaction by a bilinear term as in liquids and derived a quantized theory with dissipation. We found that particle energies are reduced by the dissipation which promotes the gap in momentum space and that particle mass becomes dressed by dissipation. We discussed the interplay between the dissipative and mass terms, different regimes of field dynamics as well as ultraviolet and infrared cutoffs emerging. | 4,779.6 | 2019-05-01T00:00:00.000 | [
"Physics"
] |
Entropy, Uncertainty, and the Depth of Implicit Knowledge on Musical Creativity: Computational Study of Improvisation in Melody and Rhythm
Recent neurophysiological and computational studies have proposed the hypothesis that our brain automatically codes the nth-order transitional probabilities (TPs) embedded in sequential phenomena such as music and language (i.e., local statistics in nth-order level), grasps the entropy of the TP distribution (i.e., global statistics), and predicts the future state based on the internalized nth-order statistical model. This mechanism is called statistical learning (SL). SL is also believed to contribute to the creativity involved in musical improvisation. The present study examines the interactions among local statistics, global statistics, and different levels of orders (mutual information) in musical improvisation interact. Interactions among local statistics, global statistics, and hierarchy were detected in higher-order SL models of pitches, but not lower-order SL models of pitches or SL models of rhythms. These results suggest that the information-theoretical phenomena of local and global statistics in each order may be reflected in improvisational music. The present study proposes novel methodology to evaluate musical creativity associated with SL based on information theory.
INTRODUCTION Statistical Learning in the Brain: Local and Global Statistics
The notion of statistical learning (SL) (Saffran et al., 1996), which includes both informatics and neurophysiology (Harrison et al., 2006;Pearce and Wiggins, 2012), involves the hypothesis that our brain automatically codes the nth-order transitional probabilities (TPs) embedded in sequential phenomena such as music and language (i.e., local statistics in nth-order levels) (Daikoku et al., , 2017bDaikoku and Yumoto, 2017), grasps the entropy/uncertainty of the TP distribution (i.e., global statistics) (Hasson, 2017), predicts the future state based on the internalized nth-order statistical model (Daikoku et al., 2014;Yumoto and Daikoku, 2016), and continually updates the model to adapt to the variable external environment (Daikoku et al., 2012(Daikoku et al., , 2017d. The concept of brain nth-order SL is underpinned by information theory (Shannon, 1951) involving n-gram or Markov models. TP (local statistics) and entropy (global statistics) are used to estimate the statistical structure of environmental information. The nth-order Markov model is a mathematical system based on the conditional probability of sequence in which the probability of the forthcoming state is statistically defined by the most recent n state (i.e., nth-order TP). A recent neurophysiological study suggested that sequences with higher entropy are learned based on higher-order TP whereas those with lower entropy are learned based on lower-order TP (Daikoku et al., 2017a). Another study suggested that certain regions or networks perform specific computations of global statistics (i.e., entropy) that are independent of local statistics (i.e., TP) (Hasson, 2017). Few studies, however, have investigated how perceptive systems of local and global statistics interact. It is important to examine the entire process of brain SL in both computational and neurophysiological areas (Daikoku, 2018b).
Statistical Learning and Information Theory
Local Statistics: Nth-Order Transitional Probability Research suggests that there are two types of coding systems involved in brain SL (see Figure 1): nth-order TPs (local statistics at various order levels) (Daikoku et al., 2017a;Daikoku, 2018a) and uncertainty/entropy (global statistics) (Hasson, 2017). The TP is the conditional probability of an event B, given that the most recent event A has occurred-this is written as P(B|A). The nth-order TP distributions sampled from sequential information such as music and language can be expressed by nth-order Markov models (Markov, 1971). The nth-order Markov model is based on the conditional probability of an event e n+1 , given the preceding n events based on Bayes' theorem [P(e n+1 |e n )]. From a psychological viewpoint, the formula can be interpreted as positing that the brain predicts a subsequent event e n+1 based on the preceding events e n in a sequence. In other words, learners expect the event with the highest TP based on the latest n states, and are likely to be surprised by an event with lower TP. Furthermore, TPs are often translated as information contents [ICs, -log 2 1/P(e n+1 |e n )], which can be regarded as degrees of surprising and predictable (Pearce and Wiggins, 2006). A lower IC (i.e., higher TPs) means higher predictability and smaller surprise whereas a higher IC (i.e., lower TPs) means lower predictability and larger surprise. In the end, a tone with lower IC may be one that a composer is more likely to predict and choose as the next tone compared to tones with higher IC. IC can be used in computational studies of music to discuss the psychological phenomena involved in prediction and SL.
Global Statistics: Entropy and Uncertainty
Entropy (i.e., global statistics, Figure 1) is also used to understand the general predictability of a sequence (Manzara et al., 1992;Reis, 1999;Cox, 2010). It is calculated from probability distribution, interpreted as uncertainty (Friston, 2010), and used to evaluate the neurophysiological effects of global SL (Harrison et al., 2006) as well as decision making (Summerfield and de Lange, 2014), anxiety (Hirsh et al., 2012), and curiosity (Loewenstein, 1994). A previous study reported that the neural systems of global SL were partially independent of those of local SL (Hasson, 2017). Furthermore, reorganization of learned local statistics requires more time than the acquisition of new local statistics, even if the new and previously acquired information sets have equivalent entropy levels (Daikoku et al., 2017d). Some articles, however, suggest that the global statistics of sequence modulate local SL (Daikoku et al., 2017a). Furthermore, uncertainty of auditory and visual statistics is coded by modalitygeneral, as well as modality-specific, neural systems (Strange FIGURE 1 | Relationship between order of transitional probabilities, entropy, conditional entropy, and MI illustrated using a Venn diagram. The degree of dependence on X i for X i+1 is measured by MI (MI (I(X;Y)) = entropy (H(X i+1 )]conditional entropy [H(X i+1 |X i ))). The MI of sequences in this figure is more than 0. Thus, each event X i+1 in the sequence is dependent on a preceding event X i . Nastase et al., 2014). This suggests that the neural basis that codes global statistics, as well as local statistics, is a domain-general system. Although domain-general and domainspecific learning system in the brain are under debate (Hauser et al., 2002;Jackendoff and Lerdahl, 2006), there seems to be neural and psychological interactions in perceptions between local and global statistics.
Depth: Mutual Information
Mutual information (MI) and pointwise MI (PMI) are measures of the mutual dependence between two variables. PMI refers to each event in sequence (local dependence), and MI refers to the average of all events in the sequence (global dependence). In the framework of SL based on TPs [P(e n+1 |e n )], MI explains how an event e n+1 is dependent on the preceding event e n . Thus, MI is key to understanding the order of SL. For example, a typical oddball sequence consisting of a frequent stimulus with high probability of appearance and a deviant stimulus with low probability of appearance has weak dependence between two adjacent events (e n , e n+1 ) and shows low MI, because event e n+1 appears independently of the preceding events e n . In contrast, an SL sequence based on TPs, but not probabilities of appearance, has strong dependence on the two adjacent events and shows larger MI. For example, a typical SL paradigm that consists of the concatenation of pseudo-words with three stimuli has large MI until second-order Markov or tri-gram models [i.e., P(C|AB)] whereas it has low MI from third-order Markov or four-gram models [i.e., P(D|ABC)]. Thus, MI is sometimes used to evaluate levels of SL in both neurophysiological (Harrison et al., 2006) and computational studies (Pearce et al., 2010). In sum, the three types of information-theoretical evaluations of SL models (i.e., IC, entropy, and MI) can be explained in terms of psychological aspects. (1) IC reflects local statistics. A tone with lower IC (i.e., higher TPs) may be one that a composer is more likely to predict and choose as the next tone compared to tones with higher IC. (2) Entropy reflects global statistics and is interpreted as the uncertainty of whole sequences. (3) MI reflects the levels of orders in statistics and is interpreted as the dependence of preceding sequential events in SL. Using them, the present study investigated how local statistics, global statistics, and the levels of the orders in musical improvisation interact.
Musical Improvisation
Implicit statistical knowledge is considered to contribute to the creativity involved in musical composition and musical improvisation (Pearce and Wiggins, 2012;Norgaard, 2014;Wiggins, 2018). Additionally, it is widely accepted that implicit knowledge causes a sense of intuition, spontaneous behavior, skill acquisition based on procedural learning, and creativity, and is also closely tied to musical expression, such as composition, playing, and intuitive creativity. Particularly, in musical improvisation, musicians are forced to express intuitive creativity and immediately play their own music based on long-term training associated with procedural and implicit learning (Clark and Squire, 1998;Ullman, 2001;Paradis, 2004;De Jong, 2005;Ellis, 2009;Müller et al., 2016). Thus, compared to other types of musical composition in which a composer deliberates and refines a composition scheme for a long time based on musical theory, the performance of musical improvisation is intimately bound to implicit knowledge because of the necessity of intuitive decision making (Berry and Dienes, 1993;Reber, 1993;Perkovic and Orquin, 2017) and auditory-motor planning based on procedural knowledge (Pearce et al., 2010;Norgaard, 2014). This suggests that the stochastic distribution calculated from musical improvisation may represent the musicians' implicit knowledge and creativity in music that has been developed via implicit learning. Few studies have investigated the relationship between musical improvisation and implicit statistical knowledge. The present study, using realworld improvisational music, first proposed a computational model of musical creativity in improvisation based on TP distribution, and examined how local statistics, global statistics, and hierarchy in music interact. Dimensions, 1984) were used in the present study. The highest pitches with length were extracted based on the following definitions: the highest pitches that can be played at a given point in time, pitches with slurs that can be counted as one, and grace notes were excluded. In addition, the rests that were related to highestpitch sequences were also extracted. This spectral and temporal information were divided into four types of sequences: [1] a pitch sequence without length and rest information (i.e., pitch sequence without temporal information); [2] a temporal sequence without pitch information (i.e., temporal sequence without pitches); [3] a pitch sequence with length and rest information (i.e., pitch sequence with temporal information); and [4] a temporal sequence with pitch information (i.e., temporal sequence with pitches).
Pitch Sequence Without Temporal Information
For each type of pitch sequence, all of the intervals were numbered so that an increase or decrease in a semitone was 1 and −1 based on the first pitch, respectively. Representative examples were shown in Figure 2. This revealed the relative pitch-interval patterns but not the absolute pitch patterns. This procedure was used to eliminate the effects of the change in key on transitional patterns. Interpretation of the key change depends on the musician, and it is difficult to define in an objective manner. Thus, the results in the present study may represent a variation in the statistics associated with relative pitch rather than absolute pitch.
Temporal Sequence Without Pitches
The onset times of each note were used for analyses. Although, note onsets ignore the length of notes and rests, this methodology can capture the most essential rhythmic features of the music (Povel, 1984;Norgaard, 2014). To extract a temporal interval between adjacent notes, all onset times were subtracted from the onset of the preceding note. Then, for each type of temporal sequence, the second to last temporal interval was divided by the first temporal interval. Representative examples are shown in Figure 2. This revealed relative rhythm patterns but not absolute rhythm patterns; it is independent of the tempo of each piece of music.
Pitch Sequence With Temporal Information
The two methodologies of pitch and temporal sequences were combined. For each type of sequence, all of the intervals were numbered so that an increase or decrease in a semitone was 1 and −1 based on the first pitch, respectively. Additionally, for each type of pitch sequence, all onset times were subtracted from the onset of the preceding note, and the second to last temporal intervals were divided by the first temporal interval. The representative examples were shown in Figure 2. On the other hand, a temporal interval of first-order model was calculated as a ratio to the crotchet (i.e., quarter note), because only a temporal interval is included for each sequence and the note length cannot be calculated as a relative temporal interval. Thus, the patterns of pitch sequence (p) with temporal information (t) were represented as [p] with [t].
Temporal Sequence With Pitches
The methodologies of sequence extraction were the same as those of the pitch sequence with rhythm (see Figure 2), whereas the TPs of the rhythm, but not pitch, sequences were calculated as a statistic based on multi-order Markov chains. The probability of a forthcoming temporal interval with pitch was statistically defined by the last temporal interval with pitch to six successive temporal interval with pitch (i.e., first-to six-order Markov chains). Thus, the relative pattern of temporal sequence (r) with pitches (p) were represented as [t] with [p].
Modeling and Analysis
The TPs of the sequential patterns were calculated based on 0th−5th-order Markov chains. The nth-order Markov chain is the conditional probability of an event e n+1 , given the preceding n events based on Bayes' theorem: P (e n+1 |e n ) = P(e n+1 ∩ e n ) P(e n ) The ICs (I[e n+1 |e n ]) and conditional entropy [H(B|A)] in the nth-order TP distribution (hereafter, Markov entropy) were calculated using TPs in the framework of information theory.
I (e n+1 |e n ) = log 2 1 P (e n+1 |e n ) (bit) H (B|A) = − i j P(ai)P bj ai log 2 P bj ai (bit) (3) where P(bj|ai) is a conditional probability of sequence "ai bj." Then, MI [I(X;Y)] were calculated in 1st-, 2nd-, and 3rdorder Markov models. MI is an information theoretic measure of dependency between two variables (Cover and Thomas, 1991). The MI of two discrete variables X and Y can be defined as where p(x,y) is the joint probability function of X and Y, and p(x) and p(y) are the marginal probability distribution functions of X and Y, respectively. From entropy values, the MI can also be expressed as where H(X) and H(Y) are the marginal entropies, H(X|Y) and H(Y|X) are the conditional entropies, and H(X,Y) is the joint entropy of X and Y (Figure 1). Based on psychological and information-theoretical concepts, the Equation (5) can be regarded that the amount of entropy (uncertainty) remaining about Y after X is known. That is, the MI is corresponding to reduction in entropy (uncertainty). Then, the transitional patterns with 1st−20th highest TPs in all musicians, which show higher predictabilities in each musician, were used as local statistics of familiar phrases. The applied familiar phrases and the TPs were shown in Supplementary material. The TPs of familiar phrases were averaged. Repeated-measure analysis of variances (ANOVAs) with factors of order and type of sequence were conducted in each IC, entropy, and MI. Furthermore, the global statistics and MI in each order were compared with local statistics of familiar phrases by Pearson's correlation analysis. Statistical significance levels were set at p = 0.05 for all analyses.
Local vs. Global Statistics
The means of IC, conditional entropy, and mutual information were shown in Figure 3. The means of IC, conditional entropy, and mutual information were shown in Figure 3.
Local vs. Global Statistics
All of the results in correlation analysis are shown in Figure 4.
Psychological Notions of Information Theory
The present study investigated how local statistics (TP and IC), global statistics (conditional entropy), and levels of orders (MI) in musical improvisation interact. The TP, IC, conditional entropy, and MI can be calculated based on Markov models, which are also applied to psychological and neurophysiological studies on SL (Harrison et al., 2006;Furl et al., 2011;Daikoku, 2018b). Based on psychological and neurophysiological studies on SL (Harrison et al., 2006;Pearce et al., 2010;de Zubicaray et al., 2013;Daikoku et al., 2015;Monroy et al., 2017), these three pieces of information can be translated to psychological indices: a tone with lower IC (i.e., higher TPs) may be one that a composer is more likely to predict and choose as the next tone compared to tones with higher IC whereas entropy and MI are interpreted as the global predictability of the sequences and the levels of order for the prediction, respectively. Previous studies also suggest that musical creativity in part depends on SL (Pearce, 2005;Pearce et al., 2010;Omigie et al., 2012Omigie et al., , 2013Pearce and Wiggins, 2012;Hansen and Pearce, 2014;Norgaard, 2014), and that musical training and experience is associated with the cognitive model of probabilistic structure in the music involved in SL (Pearce, 2005;Pearce andWiggins, 2006, 2012;Pearce et al., 2010;Omigie et al., 2012Omigie et al., , 2013Hansen and Pearce, 2014;Norgaard, 2014). The present study, using improvisational music by three musicians, FIGURE 3 | The means of information content (IC), Conditional entropy, and mutual information (MI). Error bars represent standard errors of the means. P, pitch sequence; R, rhythm sequence; PwR, pitch sequence with rhythms; RwP, rhythm sequence with pitches.
examined how local and global statistics embedded in music interact, and discussed them from the interdisciplinary viewpoint of SL.
Local vs. Global Statistics
In pitch sequence with and without temporal information, higher-order (1st−5th order) models detected positive correlations between global (conditional entropy) and local statistics (IC) in musical improvisation whereas no significance was detected in a lower-order (0th order) model. To understand the local statistics of familiar phrases, the present study used only the transitional patterns that showed the 1st−20th highest TPs for all musicians, which can be interpreted as higher predictabilities for each musician. Thus, the results suggest that, when the TPs of familiar phrases are decreased, the conditional entropy (uncertainty) of the entire TP distribution is increased. This finding is mathematically and psychologically reasonable. When improvisers are attempting to use various types of phrases, the variability of sequential patterns is increasing. In the end, the ICs (degree of surprise) of familiar phrases are positively correlated with the conditional entropy (uncertainty) of the entire sequential distribution. It is of note that this correlation could not be detected in a lower-order (0th order) model, and that no correlation was detected in a temporal sequence without pitches. This suggests that the interaction between local and global statistics may be stronger in the SL of spectral sequence compared to that of temporal sequence. Furthermore, these correlations may be detectable in higher-order models. This may suggest that higher-order SL can connect with grasping entropy. In sum, skills of musical improvisation and intuition may strongly depend on SL of pitch compared with that of rhythm. In addition, this phenomenon on intuition may occur in higher-, but not lower-order levels in SL. The higher-order SL model of pitches may be important FIGURE 4 | The correlation analysis between conditional entropy (global statistics) and ICs of familiar phrases (local statistics) based on zeroth-to fifth-order Markov models of pitch and temporal (rhythm) sequences.
FIGURE 5 | The correlation analysis between MI and ICs of familiar phrases (local statistics) based on zeroth-to fifth-order Markov models of pitch and temporal (rhythm) sequences.
to grasp the entire process of hierarchical SL in musical improvisation.
Local Statistics vs. Hierarchy
In pitch sequences without temporal information, higher-order (3rd−5th order) models showed negative correlations between dependence of previous events (MI) and local statistics (IC), and no significance was detected in lower-order (0th−2nd order) models. This finding is also mathematically and psychologically reasonable. When players strongly depend on previous sequential information to improvise music, they tend to use familiar phrases because familiar phrases with higher TPs P(X i+1 |X i ) tend to have strong dependence on previous sequential information (X i ).
In the end, the ICs (degree of surprise) of familiar phrases are decreased when improvisers depend on previous sequential information that can be detected as larger MIs. Interestingly, this correlation could not be detected in a lower-order model (0th order), and no correlation was detected in the temporal sequence without pitches. As shown in the correlation between local and global statistics, the interaction between local statistics and levels of orders may be stronger in the SL of spectral sequence compared to that of temporal sequence. Furthermore, these correlations may be detectable in higher-order models.
In contrast, fourth-and fifth-order models of pitch sequence with temporal information did not show correlations. Thus, rhythms may modulate the levels of orders in the SL of pitches in improvisational music (Daikoku, 2018c). This hypothesis may be supported in the models of temporal sequence with pitches.
No correlation was detected in temporal sequence (Daikoku et al., 2018) with pitches. Future study is needed to investigate how rhythms affect improvisational music, and how the SL of rhythms interact with those of pitches. It is of note that the present study did not directly investigate the improviser's statistical knowledge of music, as only the statistics of music were analyzed. However, the transition probabilities shape only a small part of their respective styles. Future study should investigate the SL of music from many improvisers using interdisciplinary approaches of neurophysiology and informatics in parallel. The methodologies in this study are missing important information that constructs music such as beat, stresses, and ornamental note, which inspire the rhythm and intonation. Furthermore, the present study only analyzed three improvisers. To discuss universal phenomena in SL associated with improvisation, future study will be needed to examine a body of pieces of music.
CONCLUSION
The present study investigated how local statistics (TP and IC), global statistics (entropy), and levels of orders (MI) in musical improvisation interact. Generally, the interactions among local statistics and global statistics were detected in higher-order SL models of pitches, but not lower-order SL models of spectral sequence or SL models of temporal sequence. The results of the present study suggested that information-theoretical phenomena of local and global statistics in each hierarchy can be reflected in improvisational music. These results support a novel methodology to evaluate musical creativity associated with SL based on information theory.
AUTHOR CONTRIBUTIONS
The author confirms being the sole contributor of this work and has approved it for publication. | 5,216.4 | 2018-12-19T00:00:00.000 | [
"Computer Science"
] |
Changes in Mechanical Properties of Fabrics Made of Standard and Recycled Polyester Yarns Due to Aging
Over the years, the demands on the durability and quality of polyester fabrics used for sportswear have increased, as these fabrics contribute to athletes’ performance. At the same time, the use of recycled polyester material is increasingly being promoted for environmental reasons. This study focused on investigating the properties of standard and recycled polyester fabrics before and after aging according to the developed aging protocol. The surface morphology, thickness, elongation at break, force at break, bursting force, mass loss due to abrasion and moisture management of the fabrics were tested. The results showed that the aging process had no influence on the surface changes in the fabrics. More specifically, there were neither surface cracks on the fibre surface nor chemical changes. The highest decrease in force at break for standard polyester fabrics with elastane was up to 26%, and up to 15% for fabrics made of recycled polyester. The loss of mass due to abrasion was greater for recycled polyester than for standard polyester fabrics. The average ability of the fabrics to absorb moisture decreased by up to 23% after aging, while the wetting time increased by up to 30%, with the highest increase observed in recycled fabrics.
Introduction
Playing football is possible both as a leisure activity and actively.In active football, there are beginners, cadets, juniors, seniors and veterans.The typical football activities depend on the level of football practice, as well as the position in which the player plays (striker, midfielder, defender and goalkeeper).Fitness training, tactics and recovery training are common.The fabrics for football sportswear are usually made of polyester and elastane and, more recently, recycled polyester fabrics [1,2].They are exposed to wear and tear, the effects of perspiration, aging through care and maintenance and atmospheric conditions.Changes in the mechanical properties of polyester materials, including sportswear fabrics, can be caused by temperature, sunlight (UV), humidity, rain and wind and pollutants [3,4].Wind with various particles can have an abrasive effect on the surfaces of the materials.Fluctuations in temperature and humidity lead to uneven stress and surface cracking in polyester.In addition, UV light has a chemical effect on polyester through photodegradation.The amount of UV light depends on latitude, season and cloud cover.All these factors, together with various pollutants, make the aging process of football sportswear complex [3,4].
Outdoor weathering, i.e., exposure to the natural environment, is still the standard for material aging, although test methods and instruments have been developed to accelerate aging [5].Accelerated aging uses enhanced conditions such as heat, humidity and sunlight in environmental chambers to accelerate the normal aging processes, or accelerated mechanical testing [5].Natural or accelerated weathering of polyesters leads to scission, i.e., breaks and splits in the polymer chains centred on the ester linkages.Polyesters and many other polymers hydrolyse in the presence of water [3,6].The hydrolysis of polyesters is usually carried out with the addition of a base to accelerate the reaction.The process has advantages and disadvantages: biodegradability, but also the deterioration of mechanical properties.
Several studies on the change in the mechanical properties of polyester during aging relate to technical textiles.In one study [7], high-strength polyester yarns with different linear densities for the reinforcement of conveyor belts were aged at temperatures of 140, 160, 200 and 220 • C for a duration of 6, 12 and 35 min.It was confirmed that the aging parameters significantly affect the mechanical and surface structural properties when the exposure temperature is 220 • C. The results of the mechanical properties and aging behaviour tests of palm/polyester composite for automotive industry showed that this composite has excellent tensile strength and abrasion resistance, and the FTIR and SEM data after the climate aging test confirmed the durability [8].In another study [9], polyester composites intended for sewer rehabilitation were subjected to artificial aging with heat and water.The samples aged in water were stored in ventilated ovens at 40 • C, 60 • C and 80 • C or kept at room temperature (20-22 • C).Half of the samples were aged in air only.It was found that aging in water at high temperatures resulted in greater effects on the material than aging under dry conditions [9].Accelerated aging of polyester multifilament yarns containing nanoparticles or microparticles was carried out in a climatic chamber at 50 • C, 50% Rh and UVA irradiation of 1.4 W/m 2 between 21 and 170 days [10].The results showed that there was a deterioration in the thermal and mechanical properties of all yarns, possibly due to the scission of the polymer chains that make up the polymer matrix [10].
Several studies have been carried out on polyester textile fabrics intended for the clothing industry.After three months of natural outdoor aging, the water vapour resistance of polyester textiles coated with polyurethane decreased, which correlates with the reduced thickness of the textile.The average reduction in water vapour resistance after aging was 11.4% in summer and 16.7% after the winter season [11].There was a partial degradation of the polyurethane layer, which was not related to the deterioration of the polyester fabric substrate [11].As for outdoor aging compared to pool aging up to 21, 42 and 63 h, the deterioration of the surface is more pronounced after outdoor aging, confirming the effect of UV radiation on the fibrillation of polyester and polyamide [12].All measured properties, tensile strength, drying and fluid transfer, with the exception of elongation during indoor aging, confirm the influence of water and chlorine and especially solar radiation on the degradation of polyester [12].
The behaviour of recycled polyester is less studied, although there are more and more commercially available products made from recycled polyester, including sportswear.One study shows that the final properties of the recycled polymers differ from the properties of the samples before reprocessing [13].During their lifetime, polymers are exposed to various environmental stresses that can greatly alter their chemical and molecular structure and morphology, as well as further recycling [13].In another study, the recyclability of the four plastics most commonly found in the sea (nylon, PE, PET and PP) was investigated.They were exposed to UV radiation in seawater for 6.5 months.The properties of all materials were affected, resulting in inadequate quality of the recycled material compared to virgin material [14].
A fibre that is often added to polyester to improve the elastic properties of sportswear is elastane.The presence of elastane has a significant influence on the material properties before and after aging.Elastane includes polyetherurethane or polyterurethane polymers.It is known that polyester urethanes are at risk of hydrolysis with aging [15], which affects mechanical properties.The shortcomings of elastane also lie in its chemical resistance and temperature stability, which can lead to fibre degradation and loss of elasticity [16].Further research into the aging of sportswear fabrics with elastane is a necessity for product quality.
Despite the increased interest in the development of highly functional polyester fabrics for the production of sportswear, to our knowledge scientists have not yet studied the aging of polyester fabrics for sportswear in depth.In particular, this concerns the development and testing of different protocols defined considering a specific group of fabrics for a single use.Knowing the behaviour of the material and its properties due to aging is important because it can affect comfort during sports competitions, reduce durability during maintenance and increase the possibility of the material tearing in direct contact between two football players.
In the previously published study [17], steps were taken to develop a specific procedure for the aging of polyester sportswear fabrics.The aging process was correlated with 12 training sessions (1 month) and 24 training sessions (2 months) of football training.It was emphasized that future studies should focus on a longer aging period.In this study, a new aging protocol is established with a longer exposure period corresponding to 1 month to 3 months of training.After aging, a series of tests were performed on the fabrics to determine the mechanical and comfort properties of the fabrics, such as elasticity and moisture management, which are very important for the well-being of the athlete [18,19].The focus is on comparing the behaviour of standard polyester and recycled polyester to determine the extent to which recycled polyester can be an adequate substitute for standard polyester when exposed to severe aging.
Material
For this study, a number of representative materials were selected that are predominantly used in the manufacture of football sportswear.These were knitted fabrics made of standard polyester with elastane added and fabrics made of recycled polyester without elastane.The aim was to investigate the changes in the properties of the two material groups as a result of aging.All fabrics are made of polyester filament yarns (more precisely from polyethylene terephthalate), which are twisted in the Z-direction and have an average thickness of 1.1 mm.During production, the elastane yarn is plated into every second course of stitches.The fabrics were not dyed.The fabric ID and the description can be found in Table 1.
Aging Protocol
When defining the aging protocol, it was important to include a wide range of influencing parameters that affect aging in order to simulate as accurately as possible the environment and influences under which the material is expected to perform.In this study, the protocol for the aging of fabrics used for football sportswear is defined following a survey of professional athletes, additional interviews and information from the literature reviewed.The survey was conducted using an online questionnaire approved by the Ethics Committee of the University of Zagreb Faculty of Textile Technology.A total of 86 Croatian football players were included in the survey.The survey was created and processed using SurveyTool v8.4 (3S, Stockholm, Sweden).
The protocol comprised a series of steps, i.The aging was carried out according to the aging protocol (details shown in Table 2).The target groups were football players in the junior and senior categories.Juniors and seniors train three times a week.The duration of each training session averages 2 h, resulting in a total of 24 h of training per month.Converted into minutes, this results in a total time of 1440 min per month.The cycle with exposure of fabrics, corresponding to one month of training, is labelled A1, while the cycle corresponding to three months of training is labelled A2.The unexposed cycle is referred to as A0.During the 120-min individual training session, the fabric for athlete's clothing was exposed to sweat for approximately 105 min, i.e., 1260 min during the entire training month.As the training took place outdoors, the fabrics were also exposed to other external factors such as the sun.Usually, the sports jersey must be washed after every single training session.The required number of washes for each specified aging cycle and the average washing time are indicated in Table 2.
The fabrics were exposed to weathering, simulating typical use by football players.This involved static outdoor weathering to which artificial sweat was added.The weathering was conducted during the summer season (July-August) at the coordinates 45 • 48 055.4364N, and 15 • 57 059.6448E. The average air temperature was 31 • C (with a range of 28 • C to 35 • C and a coefficient of variation of 7.36%).The average UV index was 8 (with a range of 6 to 9 and a coefficient of variation of 14.49%).The average humidity was 58% (between 48% and 64%, with a coefficient of variation of 17.27%).The average wind speed was 7.5 km/h (6 km/h to 9 km/h; coefficient of variation 18.37%) and the air pressure was 1015 mbar (varied from 1008 mbar to 1029 mbar; coefficient of variation 0.66%).The overall air quality was 81 AQI (65 AQI to 90 AQI; coefficient of variation 11.69%).All data were monitored by the European Meteorological Center ECMWF using model weather forecasts HRES [20].The duration of exposure of the fabric to sun and sweat is given in Table 2.A dilution of acid sweat powder (AS) with a pH of 5.5, prepared in accordance with BS EN ISO 105-E04 [21], was added to the samples 15 min after the start of the exposure to the sun.After each 2-h simulated training session, the fabric was washed at 30 • C using the ECE detergent (without phosphate and optical brighteners).Washing was carried out in accordance with the EN ISO 6330: 2012 standard [22].After each wash cycle the fabrics were air-dried in the shade (i.e., they were not exposed to the sun during air-drying).
Characterization Methods
This study focused on the following aspects: surface morphology characterization, thickness, elongation at break, force at break, bursting force, moisture management and mass loss due to abrasion.
Surface Morphology Characterization
A Dino-Lite Edge AM7915MZT digital microscope (Dino-Lite, Almere, The Netherlands) was used to assess the topography of the selected fabrics.The samples, both non-aged (A0) and aged (A1, A2), were conditioned in a standard atmosphere (i.e., at an air temperature of 20 ± 2 • C, and a relative humidity of 65 ± 5% [23]).The images of the samples were taken at 150× magnification.DinoCapture 2.0 software was used to observe the appearance of the surface of the fabrics, and the shape of the stitches forming the structure of the knitted fabric.It was also used to measure the length of the horizontal inner space of the stitches (L in-avg ).The microscope FE-SEM (Tescan, Brno, Czech Republic) was also used to observe the surface of the fabric.The samples were coated with chromium, and the acceleration voltage during the measurements was 5 kV.
Thickness
The thickness was measured according to the principles described in [24] using a DM-2000 thickness meter (Wolf Messtechnik GmbH, Freiberg, Germany).The pressure of the device was set to 1 kPa, and 10 measurements were taken.The thickness of the fabric was given as the average of the measurements.
Elongation at Break and Force at Break
The elongation at break and force at break were measured with the Statimat M tensile tester (Textechno, Mönchengladbach, Germany) at a constant elongation rate, according to ISO standard [25].The test speed was set to 100 mm•min −1 , and the load cell was 1000 N. The gauge length was set to 100 mm, with an error of ±1 mm.For testing are prepared rectangular specimens in dimensions 5 × 20 cm.The tests were carried out in wales and courses direction.The average result was expressed as the mean value of 5 measurements.
Bursting Force
A burst tester (Apparecchi Branca, Milano, Italy) was used to measure the bursting force.The device is equipped with a steel ball with a 25.40 ± 0.005 mm diameter.The tests were carried out in accordance with the ASTM D3787 standard [26].According to the method used, a force was applied to the sample, which caused the sample to burst.The probe was circular, with a diameter of 50 ± 1 mm.The number of samples for each fabric was 5.The force was recorded at the moment of break.
Moisture Management
The parameters describing the fabric moisture management were tested using the Moisture management tester, model M290 (SDL Atlas, Rock Hill, SC, USA).The measurements were performed according to the AATCC TM 195-2021 standard [27].The wetting time, absorption rate and spreading speed were measured.The wetting time (WT) was measured on the top surface of the fabric (WTT), and on its bottom surface (WTB).WT is defined as the time required to wet the top and bottom of the fabric, measured from the start of wetting.The absorption rate (AR) is the average moisture absorption capacity of the surface (top side-TAR, and bottom side-BAR).It is represented as the slope of a curve between the point at which the sample begins to wet and the maximum point on the water content vs. time graph.The spreading speed (SS) is the cumulative spreading velocity.The device measures the top spreading speed (TSS), and the bottom spreading speed (BSS).
The overall moisture management capability (OMMC) is an index calculated from the values of the measured parameters, i.e., where the OMMC is overall moisture management capability; the AR B is absorption rate; the R is one-way transport capability; the SS B is spreading speed, and C 1 , C 2 and C 3 are the weighting values for the listed properties.
Abrasion
The AquAbrasion Tester (James Heal, Halifax, UK) was used to measure the abrasion of materials.This is a special device based on the Martindale principle, developed for testing materials exposed to different weather conditions.The tester is compatible with the international standard [28].According to the standard, the samples were cut to a diameter of 38 ± 5 mm.The standard wool fabric (with the properties defined in the mentioned standard) was used for abrasion.The sample was clamped in the sample holder of the tester and subjected to a load of 9 kPa.It was rubbed against the abrasive medium in a motion following the Lissajous curve.The mass loss method was used to estimate the abrasion resistance of the tested fabrics.Accordingly, each sample was weighed before the test and after a certain number of test cycles (500, 1000, 2500 and 7500).A KERN ALJ-220 analytical balance (Kern & Sohn GmbH, Balingen, Germany) with an accuracy of +/− 0.001 g was used for weighing.
Fourier Transform Infrared Analysis
Fourier Transform Infrared Analysis was performed using the Perkin Elmer spectrometer (Perkin Elmer Inc., Waltham, MA, USA).Ten scans with a resolution of 4 cm −1 in a range from 4000 to 450 cm −1 were performed for each sample.
Results of the Surface Morphology Characterization
Regarding the surface morphology of investigated fabrics, the differences between the fabrics made of standard and those made of recycled polyester are observed.To explain the differences, images of one standard polyester fabric (PE92-197) and one recycled polyester fabric (P100-185) are shown in Figure 1.Before aging, the differences between fabrics made of standard polyester and recycled polyester yarn are clearly visible.The structure of the stitches (i.e., the basic units that form the knitted fabric) of standard polyester fabrics is strictly vertically aligned, and the units are clearly visible.In contrast, the structure of recycled polyester fabric does not follow a clear vertical orientation, and the stitches are not uniformly shaped.In addition, the number of protruding fibres increased, which affected the increase in the average diameter of the yarn.The size of the internal cavity within the stitches is difficult to distinguish.In both standard and recycled fabrics, the aging process caused the increase in foreign particles that have become entangled in the fabric structure.Moreover, there was the increase in protruding fibres in higher length classes from the structure of the fabrics.The structure of the recycled fabric and the shape of the stitches are even less recognizable.As can be seen from Figure 1, the average values of the measured length of the horizontal inner space of the stitches (i.e., L in-avg ) decrease after the fabrics are exposed to the sun.More specifically, L in-avg is 0.028 mm for the non-aged fabrics PE92-197 and P100-185.The values decrease to 0.021 mm and 0.015 mm after aging A2.Considering the length of exposure, it can be concluded that longer exposure causes a further decrease in the length of the inner space of the stitches.The reason for this can be found in the shrinkage of all fabrics.The decrease in the length of the inner space of the stitches and fabric shrinkage is again more pronounced in recycled fabric.This observation is consistent with the conclusions of the study on the effect of heat treatment on the physical properties of nonwovens [29].This study confirmed that the shrinkage of the recycled polyester nonwovens was higher than that of standard polyester, regardless of the heat temperature, and exposure duration.
Figure 2 shows a representative SEM image of the aged standard polyester fabric at a magnification of 3.00 kx.The results of the SEM analysis showed no age-related surface cracks on the fibre surface.However, the image of the aged fabric (Figure 2) shows an accumulation of particles on the fibre surface (marked in red) that were not present prior to material aging.The water with an average hardness of 15 • dH was used to wash the fabric in this experiment.Therefore, it is very likely that these particles are limescale or detergent residues that were not completely removed during the washing process.The SEM images (of both standard and recycled polyester) showed no noticeable differences after aging.Figure 2 shows a representative SEM image of the aged standard polyester fabric at a magnification of 3.00 kx.The results of the SEM analysis showed no age-related surface cracks on the fibre surface.However, the image of the aged fabric (Figure 2) shows an accumulation of particles on the fibre surface (marked in red) that were not present prior to material aging.The water with an average hardness of 15° dH was used to wash the fabric in this experiment.Therefore, it is very likely that these particles are limescale or detergent residues that were not completely removed during the washing process.The SEM images (of both standard and recycled polyester) showed no noticeable differences after aging.
Results of Thickness Testing
The results of the thickness test of non-aged fabrics are shown in Figure 3a.The change in thickness of fabrics due to aging is shown in Figure 3b.The results show that aging of all tested fabrics in both aging protocols caused an increase in thickness com-
Results of Thickness Testing
The results of the thickness test of non-aged fabrics are shown in Figure 3a.The change in thickness of fabrics due to aging is shown in Figure 3b.The results show that aging of all tested fabrics in both aging protocols caused an increase in thickness compared to the thickness of the unexposed fabric (the p-values are higher than 0.05, which means that there is no statistically significant difference).These results complement the behaviour of the materials observed in the previous section, and confirm that aging affects the shrinkage of the materials.This increase in thickness can also be explained by the increase in the number of protruding fibres.It can be seen that aging A2 caused an additional increase in the thickness of the fabrics made of standard polyester compared to the increase after A1.In contrast, the increase in thickness of the fabrics made of recycled polyester is the same after A1 and A2 (i.e., in both cases the increase is 0.015 mm).
Results of Thickness Testing
The results of the thickness test of non-aged fabrics are shown in Figure 3a.The change in thickness of fabrics due to aging is shown in Figure 3b.The results show that aging of all tested fabrics in both aging protocols caused an increase in thickness compared to the thickness of the unexposed fabric (the p-values are higher than 0.05, which means that there is no statistically significant difference).These results complement the behaviour of the materials observed in the previous section, and confirm that aging affects the shrinkage of the materials.This increase in thickness can also be explained by the increase in the number of protruding fibres.It can be seen that aging A2 caused an additional increase in the thickness of the fabrics made of standard polyester compared to the increase after A1.In contrast, the increase in thickness of the fabrics made of recycled polyester is the same after A1 and A2 (i.e., in both cases the increase is 0.015 mm).
Results of Elongation and Force at Break Testing
As the knitted structure can elongate, it can better adapt to the human body and respond appropriately to the stretching that occurs during sporting events.Therefore, it is desirable to know what happens to the elongation of the fabric subjected to aging.Figure 4 shows the elongation at break for non-aged and A2-aged fabrics (three months of training).The tests were carried out both in the direction of wales and courses.It is apparent that recycled polyester fabrics have a much lower elongation at break than standard polyester fabrics with elastane.The results showed that the elongation at break of standard polyester fabrics with elastane is lower after aging, and this is statistically significant for the direction of wales only (p-value is 0.04).For recycled fabrics, the situation is reversed.The observed parameter on average increases, except for the sample P110-185.There are no statistically significant differences between the elongations at break of the recycled fabrics (p-value is greater than 0.05).The results obtained show that standard polyester fabrics with elastane still perform better in terms of elongation at break, despite the fact that their elongation at break decreases after three months of aging.
The results of the measured force at break are shown in Figure 5. On average, the force at break of fabrics decreases with aging.The highest decrease for standard polyester fabrics with elastane is up to 26%, while it is up to 15% for fabrics made of recycled polyester.There are statistically significant differences between forces at break for the direction of courses (p-value between A0 and A1 samples is 0.04; p-value between A0 and A2 samples is 0.03).There are no significant differences for the direction of the wales (i.e., p-value ≥ 0.05).Figure 6 shows a plot of the specific force-elongation curves (i.e., F/E curves) for samples PE92-197 and P100-130 under conditions A0 and A2.As can be observed, standard polyester material with elastane has a much higher elongation at break than recycled polyester material.It is most probably because of the presence of elastane.In addition, the force at the maximum point of elasticity (F E ) is higher for standard polyester fabric with elastane than for recycled polyester fabric.The force at break for both fabrics is similar, but at this force, the standard fabric with elastane stretches almost twice as much as the recycled fabric, which does not contain elastane in its structure.4 shows the elongation at break for non-aged and A2-aged fabrics (three months of training).The tests were carried out both in the direction of wales and courses.It is apparent that recycled polyester fabrics have a much lower elongation at break than standard polyester fabrics with elastane.The results showed that the elongation at break of standard polyester fabrics with elastane is lower after aging, and this is statistically significant for the direction of wales only (p-value is 0.04).For recycled fabrics, the situation is reversed.The observed parameter on average increases, except for the sample P110-185.There are no statistically significant differences between the elongations at break of the recycled fabrics (p-value is greater than 0.05).The results obtained show that standard polyester fabrics with elastane still perform better in terms of elongation at break, despite the fact that their elongation at break decreases after three months of aging.The results of the measured force at break are shown in Figure 5. On average, the force at break of fabrics decreases with aging.The highest decrease for standard polyester fabrics with elastane is up to 26%, while it is up to 15% for fabrics made of recycled polyester.There are statistically significant differences between forces at break for the direction of courses (p-value between A0 and A1 samples is 0.04; p-value between A0 and A2 samples is 0.03).There are no significant differences for the direction of the wales (i.e., p-value ≥ 0.05).Figure 6 shows a plot of the specific force-elongation curves (i.e., F/E curves) for samples PE92-197 and P100-130 under conditions A0 and A2.As can be observed, standard polyester material with elastane has a much higher elongation at break than recycled polyester material.It is most probably because of the presence of elastane.In addition, the force at the maximum point of elasticity (FE) is higher for standard polyester fabric with elastane than for recycled polyester fabric.The force at break for both fabrics is similar, but at this force, the standard fabric with elastane stretches almost twice as much as the recycled fabric, which does not contain elastane in its structure.
Results of Bursting Force Testing
The results of bursting force testing can be found in Figure 7.It can be seen that the bursting force of all tested samples increased after aging A1.This observation is consistent with the conclusions on the retention of excellent strength of polyester composites re-
Results of Bursting Force Testing
The results of bursting force testing can be found in Figure 7.It can be seen that the bursting force of all tested samples increased after aging A1.This observation is consistent with the conclusions on the retention of excellent strength of polyester composites re-
Results of Bursting Force Testing
The results of bursting force testing can be found in Figure 7.It can be seen that the bursting force of all tested samples increased after aging A1.This observation is consistent with the conclusions on the retention of excellent strength of polyester composites reported in the previous study [8].The increase in bursting force could be related to the increase in thickness observed in all exposed samples.Indeed, the thicker material could provide a higher resistance to bursting with a steel ball, which is reflected in the higher values of bursting force.After the aging A2, the bursting force decreases for all samples compared to the results of the aging A1.Nevertheless, samples PE92-197 and P100-130 retain higher values compared to the non-exposed samples.The results show that, despite the aging process, samples PE92-197 and P100-130 respond better to the bursting force to which the fabrics are frequently exposed in contact sports such as football.In contrast to the study [14], in which the properties of recycled fabrics exposed to UV radiation and seawater were strongly negatively affected, the results do not show the insufficient quality of the observed properties of recycled fabrics in terms of bursting force.
Moisture Management Test Results
The moisture management test results, including WT, AR and SS, are shown in Figure 8.The results show that the wetting time (WT) increased on both surfaces (bottom-WTB and top-WTT) for all samples after A2 aging, except for sample PE87-141.A significant increase in wetting time (30% on average) can be observed for the samples made of recycled polyester.The increase in wetting time can be linked to the increase in fabric thickness caused by the aging.The average ability to absorb moisture (AR) on the surface of the fabric on both sides (top-TAR and bottom-BAR) decreased by an average of 23% for all tested samples after exposure to aging A1 and by an average of 20% after exposure to aging A2.This can be related to the shrinkage of the fabric, and the decrease in the length of the inner space of basic units (observed in Section 3.1).The spreading speed rate decreased for all samples, except for PE87-141.The results confirm the strong negative correlation between the values of WT (both WTT and WTB) and SS (both TSS and BSS) with correlation coefficients −0.86727, −0.85289, −0.88493 and −0.87779 (Table 3).After the aging A2, the bursting force decreases for all samples compared to the results of the aging A1.Nevertheless, samples PE92-197 and P100-130 retain higher values compared to the non-exposed samples.The results obtained show that, despite the aging process, samples PE92-197 and P100-130 respond better to the bursting force to which the fabrics are frequently exposed in contact sports such as football.In contrast to the study [14], in which the properties of recycled fabrics exposed to UV radiation and seawater were strongly negatively affected, the results do not show the insufficient quality of the observed properties of recycled fabrics in terms of bursting force.
Moisture Management Test Results
The moisture management test results, including WT, AR and SS, are shown in Figure 8.The results show that the wetting time (WT) increased on both surfaces (bottom-WTB and top-WTT) for all samples after A2 aging, except for sample PE87-141.A significant increase in wetting time (30% on average) can be observed for the samples made of recycled polyester.The increase in wetting time can be linked to the increase in fabric thickness caused by the aging.The average ability to absorb moisture (AR) on the surface of the fabric on both sides (top-TAR and bottom-BAR) decreased by an average of 23% for all tested samples after exposure to aging A1 and by an average of 20% after exposure to aging A2.This can be related to the shrinkage of the fabric, and the decrease in the length of the inner space of basic units (observed in Section 3.1).The spreading speed rate decreased for all samples, except for PE87-141.The results confirm the strong negative correlation between the values of WT (both WTT and WTB) and SS (both TSS and BSS) with correlation coefficients −0.86727, −0.85289, −0.88493 and −0.87779 (Table 3).The results of the changes in the OMMC index after exposure to aging are shown in Figure 9.The illustration of the fingerprint of the polyester fabric PE92-197 before aging is shown in Figure 10.The strongest increase in the index, after the A1 aging process, was observed for the recycled polyester fabrics.For the standard polyester fabrics, it was lower than before the aging.Comparing the results of the index before aging, and after aging A2, a decrease was observed in all samples.The exception is a sample P100-130 with a slight increase in OMMC index.The results of the changes in the OMMC index after exposure to aging are shown in Figure 9.The illustration of the fingerprint of the polyester fabric PE92-197 before aging is shown in Figure 10.The strongest increase in the index, after the A1 aging process, was observed for the recycled polyester fabrics.For the standard polyester fabrics, it was lower than before the aging.Comparing the results of the index before aging, and after aging A2, a decrease was observed in all samples.The exception is a sample P100-130 with a slight increase in OMMC index.All samples, both before and after aging, were characterized as fast-absorbing and quick-drying.However, the changes in the OMMC value after aging were not statistically significant for all fabrics tested (p-value was 0.755).For the OMMC values, which were recorded on a scale of 1 to 5, changes were visible before and after the aging process.Namely, for the samples made of standard polyester (PE92-197 and PE 87-141), grade 3 was assigned before aging.After the A-1 aging it was downgraded to 2. The grade did not change after either aging process.for two samples made of recycled polyester.All samples, both before and after aging, were characterized as fast-absorbing and quick-drying.However, the changes in the OMMC value after aging were not statistically significant for all fabrics tested (p-value was 0.755).For the OMMC values, which were recorded on a scale of 1 to 5, changes were visible before and after the aging process.Namely, for the samples made of standard polyester (PE92-197 and PE 87-141), grade 3 was assigned before aging.After the A-1 aging it was downgraded to 2. The grade did not change after either aging process.for two samples made of recycled polyester.All samples, both before and after aging, were characterized as fast-absorbing and quick-drying.However, the changes in the OMMC value after aging were not statistically significant for all fabrics tested (p-value was 0.755).For the OMMC values, which were recorded on a scale of 1 to 5, changes were visible before and after the aging process.Namely, for the samples made of standard polyester (PE92-197 and PE 87-141), grade 3 was assigned before aging.After the A-1 aging it was downgraded to 2. The grade did not change after either aging process.for two samples made of recycled polyester.
Results of Abrasion Testing
The abrasion test was carried out on fabrics after aging A2 only.The results are shown in Figure 11.The changes in mass per unit area due to abrasion are compared to the mass per unit area of the non-abraded fabrics.The comparison was made after 500, 1000, 2500 and 7500 cycles.After 7500 abrasion cycles, the samples were additionally exposed to airflow to remove residual fibre particles that had been abraded from the structure of the fabric.The mass per unit area of some samples showed a slight increase after 500-2500 abrasion cycles, which is due to the increase in foreign particles/fibres that have penetrated the fabric structure.After 7500 abrasion cycles, a significant loss of mass can be observed, especially in aerated samples.For aerated samples, the foreign particles are removed with compressed air.The test results for the PE87-141 sample show a particularly low mass per unit area loss, and a correspondingly high resistance to the abrasion process.The loss of the mass per unit area is particularly pronounced for the fabrics made of recycled polyester (P100-130 and P100-185).These results indicate a significantly lower quality of these two fabrics when they are exposed to abrasion.The latter is likely to affect the visual perception of the fabric as well as the touch properties.This may result in a negative impact on the perception of comfort.The results are in accordance with the results of the study conducted by Yaping et al. [30].The researchers used the AquaAbrasion tester to investigate the influence of abrasion of synthetic textiles on the formation of microplastic fibres and fibrils.Yaping et al. showed that abrasion of material can release ten times more microplastic fibres (MPF) into the environment than a single washing process.
Results of Abrasion Testing
The abrasion test was carried out on fabrics after aging A2 only.The results are shown in Figure 11.The changes in mass per unit area due to abrasion are compared to the mass per unit area of the non-abraded fabrics.The comparison was made after 500, 1000, 2500 and 7500 cycles.After 7500 abrasion cycles, the samples were additionally exposed to airflow to remove residual fibre particles that had been abraded from the structure of the fabric.The mass per unit area of some samples showed a slight increase after 500-2500 abrasion cycles, which is due to the increase in foreign particles/fibres that have penetrated the fabric structure.After 7500 abrasion cycles, a significant loss of mass can be observed, especially in aerated samples.For aerated samples, the foreign particles are removed with compressed air.The test results for the PE87-141 sample show a particularly low mass per unit area loss, and a correspondingly high resistance to the abrasion process.The loss of the mass per unit area is particularly pronounced for the fabrics made of recycled polyester (P100-130 and P100-185).These results indicate a significantly lower quality of these two fabrics when they are exposed to abrasion.The latter is likely to affect the visual perception of the fabric as well as the touch properties.This may result in a negative impact on the perception of comfort.The results are in accordance with the results of the study conducted by Yaping et al. [30].The researchers used the AquaAbrasion tester to investigate the influence of abrasion of synthetic textiles on the formation of microplastic fibres and fibrils.Yaping et al. showed that abrasion of material can release ten times more microplastic fibres (MPF) into the environment than a single washing process.
Results of Fourier Transform Infrared Analysis
In order to investigate possible chemical changes in the observed fabrics, an FTIR analysis is carried out.Figure 12 shows a typical plot for the fabrics studied, in which the spectral data of the non-aged and aged fabrics are superimposed.
Results of Fourier Transform Infrared Analysis
In order to investigate possible chemical changes in the observed fabrics, an FTIR analysis is carried out.Figure 12 shows a typical plot for the fabrics studied, in which the spectral data of the non-aged and aged fabrics are superimposed.
The results indicate that no chemical changes have taken place during the aging of both the standard and the recycled polyester, as the spectra of the initial fabric (i.e., the non-aged fabric) cannot be distinguished from the spectra of the aged fabrics.
Figure 1 .
Figure 1.Microscopic images of standard and recycled polyester fabric in stages A0, A1 and A2.
Figure 2 .
Figure 2. SEM image of aged standard polyester fabric.
Figure 2 .
Figure 2. SEM image of aged standard polyester fabric.
Figure 3 .
Figure 3.The thickness of fabrics (a) thickness of non-aged fabrics, (b) change in thickness (Δt) due to aging (A1 and A2) in comparison to thickness of non-aged fabrics.Figure 3. The thickness of fabrics (a) thickness of non-aged fabrics, (b) change in thickness (∆t) due to aging (A1 and A2) in comparison to thickness of non-aged fabrics.
Figure 3 .
Figure 3.The thickness of fabrics (a) thickness of non-aged fabrics, (b) change in thickness (Δt) due to aging (A1 and A2) in comparison to thickness of non-aged fabrics.Figure 3. The thickness of fabrics (a) thickness of non-aged fabrics, (b) change in thickness (∆t) due to aging (A1 and A2) in comparison to thickness of non-aged fabrics.
Figure 4 .
Figure 4. Elongation at break of non-aged (A0) and A2 aged fabrics in the direction of (a) wales, (b) courses.
Figure 5 .Figure 5 .Figure 6 .
Figure 5. Force at break of non-aged and aged fabrics in the direction of (a) wales, (b) courses.
Figure 11 .
Figure 11.Changes in mass per unit area of A2 aged fabrics due to abrasion in comparison to the mass of non-abraded aged fabrics.
Figure 11 .
Figure 11.Changes in mass per unit area of A2 aged fabrics due to abrasion in comparison to the mass of non-abraded aged fabrics.
Table 1 .
Fabric ID and description.
Table 2 .
Details of aging procedure.
Table 3 .
Correlation coefficients for moisture management indices.
Marked correlations are significant at p < 0.5000.Legend WTT-wetting time top, WTB-wetting time bottom, TAR-absorption rate top, BAR-absorption rate bottom, TSS-spreading speed top, BSS-spreading speed bottom.
Table 3 .
Correlation coefficients for moisture management indices. | 9,521.4 | 2023-11-23T00:00:00.000 | [
"Materials Science"
] |
Exact Solution for PTT Fluid on a Vertical Moving Belt for Lift with Slip Condition
Objectives: This attempt is made to investigate the problem of a study of thin film flow for lift while considering a steady, incompressible, non-isothermal, Phan-Thien Tanner fluid on a vertical belt with slip condition. Method/Comparative analysis: The nonlinear differential equation has been derived from the continuity and momentum equations. Exact solution has been obtained, which gives us velocity-profile of fluid, flow rate, temperature, average velocity of fluid and net upward flow. The special cases such as the linear PTT (LPTT), quadratic PTT (QPTT), cubic PTT (CPTT), exponential PTT (EPTT) and upper convected Maxwell (UCM) models are considered, from the same model of PTT fluid. The behavior the velocity and depth is discussed, in effect of various parameters. The velocity and temperature are compared for those special cases. Findings: The analogy of the EPTT, CPTT, QPTT, LPTT and UCM fluid models for the velocity profile and temperature distribution reveals that the velocity profile of the UCM fluid model increases quickly as compared to the velocity of the EPTT fluid. The temperature distribution for EPTT fluid is higher than the temperature for its special case: UCM fluid model. The velocity of PTT fluid is observed to be increased with incorporation of slip condition on vertical belt. Improvements: None of the previous work has been done using no-slip boundary conditions, however slip conditions are used in piece of work. Also, a thorough discussion on cases is novelty in this work.
Introduction
The non-Newtonian fluids have applications in many areas including biology, chemical engineering, polymer industry. Thus it has attracted overwhelmingly attention from researchers recently. Because of its vast applicability, the non-Newtonian fluid problems are hard to be modeled using a single model (1). Thus many equations have been proposed over the time to model problems involving non-Newtonian fluids (2)(3)(4)(5). Such models include Phan-Thien-Tanner fluid model, Sisco fluid model, second and third order fluid model, and Power law fluid model. Out of these, the Phan-Thein Tanner fluid model is extensively researched, because of its clarity, simplicity and various applications in many areas of engineering and industry (6)(7)(8).
For these models, the techniques to obtain exact solution are rarely discussed for the equation of motion specially for non-Newtonian fluids, because of the nonlinear nature of these equations (9,10). The accuracy of numerical techniques is compromised in general and such techniques are of less use especially for fluid problem, as parameter tuning become more difficult. The exact solution techniques are more preferred (5,(11)(12)(13)(14), for reasons, including above, that those methods give simple dynamics of fluids, also help for validation. Also the accuracy is not compromised, leading to fair comparison with results obtained from simulations and experiments.
Here our principal concentration is investigation of thin layer flow concerning a PTT fluid with slip condition (8,15). The fluid is partly bounded at side, whereas another liquid is considered at next boundary. The study of thin layer flow is significant concerning chemical processing. The flow of a films in the human eye membrane, paint on the wall and rainwater falling down the window (6,7,16,17) are some real life examples.
In this manuscript, we studied thin-film flow on belt moving upwards, lifting thin layers, considering PTT fluid along with slip condition on boundary of solid wall. The exact solution of the consequential differential equation has been chalked out, while considering boundary conditions. For the slip parameter, we obtain velocity in case of linearly viscous fluid (6). Four estates are examined, namely CPTT, QPTT, LPTT and UCM. As the best of our insight the results by using perturbation method is not accounted anywhere.
This paper is structured as follows: Section 2 provides basic equation's for the PTT fluid. The formulation of the problem and solution is chalked out in Section 3. Section 4 is dedicated to Results and discussion and conclusions are drawn in Section 5.
Basic Equations
The governing equations for incompressible PTT fluid including thermal effects are (5) The symbol V represent velocity vector, ρ constant density, p dynamic pressure, b body force, S extra stress tensor, η is the constant viscosity, θ is the temperature, Cp is specific heat constant, k is thermal conductivity. The operator D Dt denotes the material derivative and A 1 be the 1 st Rivlin Ericksen tensor, which is The equation of an incompressible PTT fluid model (6,8) can be read as Here λ is the relaxation time and S ∇ be the upper convected derivative which is Five PTT models, frequently used are Where ε is elongational behavior and δ 1 δ 2 are parameters for QPTT and CPTT. Higher the value of parameter ε , the thinner the fluid is. In other words, the value of ε defines the shear thinning effect. In such case, flow problem is modeled using Phan-Thien Tanner flow model. Further the exponential PTT is specified for thinner fluid, than in case of linear PTT. Also the ε is inversely proportional to elongational viscosity 6 -8 .
Formulation of the Problem and Solution
Consider a belt, of substantial width, is moving vertically in a container filled in PTT fluid, against gravitational force in the container with constant velocity U, as illustrated in Figure 1. While moving, a film of fluid is moving alongwith belt. The δ is thickness of the film, which uniform. Further assumptions are; the flow is steady, laminar and parallel under atmospheric pressure p. Accordingly we assume that The corresponding free space and slip boundary conditions are: S xy = 0 and = 0 at x = δ Free space condition (13) v =U -βS xy | x=0 and θ = θ 0 at x = 0 Slip boundary condition (14) It is permanent to note that the equation (12) satisfies continuity equation (1). Further, incorporation of equation (12) into equation (2) gives the non-zero momentum at atmospheric pressure and equation (3) leads to energy equation, with incorporation of equation (12), Also the value of first Rivlin Ericksen tensor is used in equation (16).
Integrating equation (15) with respect x and incorporating boundary conditions from equation (13), it leads to equation Inserting equation (12) into the equations (4)-(6), after considerable calculations once we obtain: Since f(trS) has one of the values given in equation (7) -(11), therefore. f(trS) ≠ 0 Which implies that By applying these values from equation (22) into the equations (19)-(21) we get Joining equations (24) and (25), we get The shear and normal stresses are related in Eq. 26.
After applying equations (22) and (26), the trace of extra stress tensor is given as The normal stress is obtained from equation (26), while using sheer stress from equation (17), which is given as equation (24) can be rewritten as (13)-(14) are obtained for five cases (7)-(11) in the following sections:
Solutions of UCM Model Velocity Profile
Using UCM model, which is given in (7), in equation (29) and then applying equation (14), we get
Flow Rate
The Q denotes the flow rate between 0 to δ, which is Using equation (30), we get
Average Velocity
The equation (33) is average velocity;
Net upward flow
The net upward flow of the fluid described as
Solutions for Linear PTT (LPTT) Model
In the same way as in Section 3.1, the solutions for velocity profile, average velocity, net upward flow and energy equation for LPTT model (8), as follows:
Solutions for Quadratic PTT (QPTT) Model
Now by substituting the value of QPTT model (9), all the required solutions are: 28
Solutions for Cubic PTT (CPTT)
In the same manner substituting the value of CPTT model (10), hence the required solutions are:
Solutions for Exponential PTT Model (EPTT Model)
Finally replacing the value of QPTT model (11), all the required solutions are given
Results and Discussion
We have extensively discussed steady thin film flow problem for lift, which is modeled by a Phan-Thein Tanner fluid for uniform thickness. The fluid is characterized as isothermal, steady incompressible. This leads to nonlinear differential equation. The exact solution, which gives velocity profile of fluid and temperature distribution, is obtained. The various parameters influence the behavior of velocity vx and temperature distribution θ(x) of fluid. The relation of various parameters to velocity and temperature is investigated. The effects of the Slip parameter β, uniform thickness δ, constant viscosity η, elongational behavior ε, relaxation time λ, constant density ρ on velocity of fluid are presented in Figs. 2-7 respectively. The effect of the uniform thickness δ, elongational behavior ε, constant density ρ, thermal conductivity k, relaxation time λ , constant viscosity η on temperature distribution are shown in the Figs. 8-13. In the Fig. 2-7, one can observe that the parameters β and η are directly proportional with the magnitude of velocity; i.e. increase in these parameters causes increase in velocity. Further, the parameters δ ε λ and ρ are inversely proportional to the magnitude of velocity; i.e decrease in these parameters leads to the increase in velocity. In the Fig. 8-13, it can easily be perceived that the temperature profile decreases when the increase in parameter k and λ . Also one can observe that an increase in parameters δ ε η and ρ causes increase in temperature. The velocity profile of PTT fluid with velocity of fluid with the velocity of fluid for its special cases is thoroughly compared in Table 1, when certain parameters are fixed. Such mention can be comprehended from caption of Table. The numerically computed velocity at normal axis to the belt is presented in Table 1.The lower velocity of EPTT fluid, as compared to the velocity of its special cases is evident in Table 1. In the same pattern, Table 2 presents comparison of temperature distribution of PTT fluid with temperature distribution of its special cases. The caption of table indicates the parameters, which are kept fixed. Table also indicates that the temperature of EPTT fluid at various normal axis to the belt is higher than the temperature of fluid of its special cases.
Conclusions
We have obtained the exact solutions of the thin film flow using Phan-Thein Tanner fluid model, characterized as incompressible and isothermal thermal for uniform thickness on a vertical belt. We have also obtained solutions of the special cases such as UCM, LPTT, QPTT, CPTT and as well as EPTT.
Here we have noted that if we increase the slip effect on a vertical belt then PTT fluid model will uplift quickly as compare to no slip, EPTT fluid model will flow against the direction of gravitation slowly as compare to CPTT, QPTT and UCM fluid model and for temperature distribution UCM fluid model has les temperature as compare to LPTT, QPTT, CPTT and EPTT. | 2,494.8 | 2019-08-01T00:00:00.000 | [
"Engineering",
"Physics"
] |
Tailoring the Structural and Optical Properties of Germanium Telluride Phase-Change Materials by Indium Incorporation
Chalcogenide phase-change materials (PCMs) based random access memory (PCRAM) enter the global memory market as storage-class memory (SCM), holding great promise for future neuro-inspired computing and non-volatile photonic applications. The thermal stability of the amorphous phase of PCMs is a demanding property requiring further improvement. In this work, we focus on indium, an alloying ingredient extensively exploited in PCMs. Starting from the prototype GeTe alloy, we incorporated indium to form three typical compositions along the InTe-GeTe tie line: InGe3Te4, InGeTe2 and In3GeTe4. The evolution of structural details, and the optical properties of the three In-Ge-Te alloys in amorphous and crystalline form, was thoroughly analyzed via ab initio calculations. This study proposes a chemical composition possessing both improved thermal stability and sizable optical contrast for PCM-based non-volatile photonic applications.
PCMs can be switched rapidly and reversibly between their amorphous and crystalline phases via Joule heating induced by electrical or optical pulses [1,35]. The notable contrast in either electrical resistivity or optical reflectivity between each phase is utilized to encode digital information [1]. Several demanding requirements, such as high programming speed, good thermal stability, low power consumption, stable property contrast window and long cycling endurance, have to be well satisfied for high-performance PCRAM. Germanium chalcogenides, in particular, GeTe and GeTe-Sb 2 Te 3 pseudo-binary compounds (GST), especially Ge 2 Sb 2 Te 5 [36], are one of the most successful material families that could meet these challenging requirements simultaneously. Doping and alloying are frequently used to tailor the material properties for faster speed and/or better retention temperature, targeting different application scenarios [37][38][39][40][41][42][43][44].
For decades, indium has been an important alloying element used in rewritable optical data storage products [45]. The flagship PCM is AgInSbTe [45][46][47][48]. Recently, indium-alloyed GeTe [49][50][51][52] and GST [53,54] were reported, and their enhanced amorphous stability makes them suitable candidates for high-temperature PCRAM applications. In addition, indium forms a unique PCM In 3 SbTe 2 [55][56][57][58][59] that exhibits metallic behavior in its crystalline phase, but semiconducting behaviors in its amorphous phase, in contrast to conventional PCMs, which remain semiconducting during memory programming. It has been suggested that even InTe could also be a potential PCM for non-volatile electronics [53,60]. In this work, we focus on the InTe-GeTe (IGT) tie line, in particular, the three stoichiometric compositions, namely InGe 3 Te 4 , InGeTe 2 and In 3 GeTe 4 . By performing thorough ab initio calculations and chemical bonding analyses, we elucidate the role of indium in altering the structural and optical properties of GeTe.
Computational Details
We performed ab initio molecular dynamics (AIMD) simulations based on density functional theory (DFT) to generate melt-quenched amorphous structures [61]. The secondgeneration Car-Parrinello method [62] as implemented in CP2K package [63] was employed along with Perdew-Burke-Ernzerhof (PBE) functional [64] and the Goedecker pseudopotentials [65]. The canonical NVT ensemble was used and the time step was set at 2 fs. Vienna Ab-initio Simulation Package (VASP) [66] was employed to relax the amorphous structures and crystalline counterparts, prior to the calculations of electronic structure and optical response. For VASP calculations, we applied the PBE functional and projector augmented-wave (PAW) pseudopotentials [67]. The energy cutoff for plane waves was set at 500 eV. Chemical bonding analyses were conducted with the LOBSTER code [68][69][70]. Crystal orbital Hamilton populations (COHP) were applied to separate the covalent interactions into bonding (positive −COHP) and antibonding (negative −COHP) contributions. Bader charges were calculated to evaluate the atomic charge transfer in the structures [71]. Frequency-dependent dielectric matrix was calculated within the independent-particle approximation without considering local field effects and many body effects, which proved to be adequate to account for the optical contrast between crystalline and amorphous PCMs [72][73][74]. The absorption α(ω) and reflectivity R(ω) can be calculated from the dielectric functions [75]: where ε 1 and ε 2 are the real and imaginary parts of the dielectric function. n and k are the refractive index and extinction coefficient, which can be calculated from the dielectric functions: Van der Waals correction based on the Grimme's D3 method was considered in all AIMD and DFT calculations [76,77]. All the electronic structures, chemical bonding and optical properties were calculated using relaxed structures at zero K with VASP. For standard calculations, only gamma point was used to sample the Brillouin zone of the supercell models, while a 3 × 3 × 3 k-point mesh was used to converge the optical response calculations. For statistics, we built three crystalline and three amorphous models for each composition.
Results and Discussion
As reported in Ref. [78], a single-phase rock-salt structure was obtained over a wide compositional range of 8-75 mole% InTe in IGT at ambient conditions, in which Te atoms occupied one sublattice, while Ge and In atoms shared the other one. The three IGT compositions considered in this work, namely InGe 3 Te 4 , InGeTe 2 and In 3 GeTe 4 , fall in this compositional range, and were expected to take the rock-salt structure. To account for the compositional disorder of Ge and In atoms on the cation-like sublattice, we built 3 × 3 × 3 supercells (216 atoms in total) and distributed Ge and In atoms using a quasirandom number generator. Three independent models were considered for each composition. Each supercell model was fully relaxed with respect to both atomic coordinates and cell volume by DFT calculations. The relaxed cell-edge of crystalline (c-) InGe 3 Te 4 , InGeTe 2 and In 3 GeTe 4 is 18.21, 18.28 and 18.55 Å, respectively. The corresponding unit cell lattice parameters, 6.07, 6.09 and 6.18 Å, are in good agreement with experimental values (5.97, 6.00 and 6.06 Å) [78]. The relaxed structure of c-InGeTe 2 is shown in Figure 1a and the structures of the other two compositions are shown in Figure S1. Nanomaterials 2021, 11, x FOR PEER REVIEW 3 of optical properties were calculated using relaxed structures at zero K with VASP. F standard calculations, only gamma point was used to sample the Brillouin zone of t supercell models, while a 3 × 3 × 3 k-point mesh was used to converge the optical respon calculations. For statistics, we built three crystalline and three amorphous models for ea composition.
Results and Discussion
As reported in Ref. [78], a single-phase rock-salt structure was obtained over a wi compositional range of 8-75 mole% InTe in IGT at ambient conditions, in which Te atom occupied one sublattice, while Ge and In atoms shared the other one. The three IGT com positions considered in this work, namely InGe3Te4, InGeTe2 and In3GeTe4, fall in this com positional range, and were expected to take the rock-salt structure. To account for t compositional disorder of Ge and In atoms on the cation-like sublattice, we built 3 × 3 × supercells (216 atoms in total) and distributed Ge and In atoms using a quasi-rando number generator. Three independent models were considered for each compositio Each supercell model was fully relaxed with respect to both atomic coordinates and c volume by DFT calculations. The relaxed cell-edge of crystalline (c-) InGe3Te4, InGeT and In3GeTe4 is 18.21, 18.28 and 18.55 Å, respectively. The corresponding unit cell latti parameters, 6.07, 6.09 and 6.18 Å, are in good agreement with experimental values (5.9 6.00 and 6.06 Å) [78]. The relaxed structure of c-InGeTe2 is shown in Figure 1a and t structures of the other two compositions are shown in Figure S1. The relaxed crystalline supercells were then used to generate amorphous (a-) mode following a melt-quench protocol [61]. The supercell models were quickly heated to very high temperature to remove the crystalline order. After randomization at 3000 K f 15 ps, the models were quenched down to and equilibrated at 1200 K, above the meltin point of IGT alloys (∼550-750 °C) [49] for 30 ps. Amorphous models were then generat by quenching the liquids down to 300 K with a cooling rate of 12.5 K/ps. During th quenching process, we stopped the simulation after every 100 K, and the simulation b size was increased to reduce the internal stress. Within each temperature window, o NVT calculation was performed using a fixed box size. The model was equilibrated at 3 K for 30 ps. This density value was then used to generate two additional melt-quench amorphous models for each composition. All three amorphous models show The relaxed crystalline supercells were then used to generate amorphous (a-) models following a melt-quench protocol [61]. The supercell models were quickly heated to a very high temperature to remove the crystalline order. After randomization at 3000 K for 15 ps, the models were quenched down to and equilibrated at 1200 K, above the melting point of IGT alloys (∼550-750 • C) [49] for 30 ps. Amorphous models were then generated by quenching the liquids down to 300 K with a cooling rate of 12.5 K/ps. During this quenching process, we stopped the simulation after every 100 K, and the simulation box size was increased to reduce the internal stress. Within each temperature window, one NVT calculation was performed using a fixed box size. The model was equilibrated at 300 K for 30 ps. This density value was then used to generate two additional melt-quenched amorphous models for each composition. All three amorphous models showed consistently low pressure values below 3 kbar. The obtained cell edges of amorphous InGe 3 Te 4 , InGeTe 2 and In 3 GeTe 4 are 18.90, 19.08 and 19.32 Å, respectively. This increase in the cell edge of the amorphous phase is consistent with the trend observed in their crystalline counterparts.
Further optimization of the internal stress or the use of the NPT ensemble for melt-quench simulations could potentially lead to some numerical differences in the mass density, but is not expected to alter the amorphous structures much.
The amorphous structure of InGeTe 2 is shown in Figure 1a and the snapshots of the other two compositions are in Figure S1. The partial radial distribution functions (RDFs) of each atomic pair in the three amorphous compounds are shown in Figure 1b. The peak positions of the heteropolar bonds In-Te (2.87 Å) and Ge-Te (2.78 Å) are not varied with composition, whereas the homopolar or "wrong" bonds show small shifts. As developed in our previous work [79], the "bond-weighted distribution function (BWDF)" provides direct information on the length of chemical bonds in amorphous IGT alloys ( Figure S2). Despite the change in chemical composition, the bond length shows very similar values in amorphous IGT alloys, i.e., Ge-Te 3.20 Å, In-Te 3.40 Å, Ge-Ge 3.20 Å, In-In 3.25 Å and Ge-In 3.40 Å. In all three amorphous IGT alloys, Te-Te shows mostly antibonding interactions. These bond length values are used as cutoffs for the interatomic distance for the following structural analysis.
The angle distribution function (ADF) of the three amorphous structures (Figure 2a) shows that In and Ge atoms mainly form local motifs with the central bond angles ranging from 90 • to 109.5 • , which corresponds to the bond angles in octahedral and tetrahedral motifs, respectively. As the concentration of indium increases, the ADF peak for indium atoms clearly shifts toward 109.5 • , implying an increase in indium-centered tetrahedral motifs. We used bond order parameter q [80] to quantify the fraction of tetrahedral motifs in amorphous IGT alloys. Such parameters are frequently used for the structural analysis of amorphous PCMs [81][82][83]. As shown in Figure 2b, as indium concentration increases, the total fraction of In-and Ge-centered tetrahedral motifs (short as tetra-In and tetra-Ge) increases from 31.6% (a-InGe 3 Te 4 ), 33.5% (a-InGeTe 2 ) to 42.4% (a-In 3 GeTe 4 ) in relation to the total number of In and Ge atoms. Specifically, the fraction of tetra-In increases from 10.1%, 18.6% to 34.6%, while the fraction of tetra-Ge decreases from 21.5%, 14.9% to 7.8%. The fraction of tetrahedrons for a-InGeTe 2 is smaller than that reported in previous work (38 % in total, with 31.5% for tetra-In and 6.5% for tetra-Ge) [50], due to the different choice of cutoff values for the interatomic distance and the deviation in calculated density values (vdW interactions were included in the current work). The ratios of tetrahedral motifs in amorphous IGT alloys are all higher than that of their parent phase-GeTe, where 25-30% tetrahedral atoms are typically found in the rapidly quenched amorphous phase [84][85][86].
In addition to the increase in the total number of tetrahedral motifs from a-InGe 3 Te 4 to a-In 3 GeTe 4 , the local bonding configuration also shows a major difference. Despite the change in chemical compositions, nearly all the tetra-Ge atoms are bonded with at least one Ge or In atom, while the majority of tetra-In atoms are heteropolar-bonded in the three amorphous IGT alloys. To quantify the role of "wrong" bonds, we carried out a projected COHP (pCOHP) analysis. As shown in Figures 3 and S3, the pCOHP of heteropolar-bonded tetra-Ge atoms demonstrates sizable antibonding interactions right below Fermi energy (E F ), and the presence of wrong bonds (including Ge-Ge and Ge-In) largely reduces such antibonding contributions, stabilizing the tetrahedral motifs locally. In contrast, the pCOHP of tetra-In atoms with and without wrong bonds mostly shows bonding interactions below E F . These results are consistent with the bonding configuration in the two parent phases, a-GeTe [79] and a-InTe [83], though In-Ge bonds are present in all three amorphous IGT alloys. Since indium atoms do not require homopolar bonds to stabilize tetrahedral motifs, the ratio of tetrahedral units is increased with the indium concentration. As compared to their crystalline counterparts, where all In and Ge atoms are octahedrally bonded, the enlarged structural deviation will enhance the thermal stability of amorphous IGT alloys. This observation is consistent with experimental findings, as the crystallization temperature T x of doped InGeTe 2 [49] and undoped InTe thin films [60] is increased to ∼276 and ∼300 • C, respectively, as compared to that of GeTe T x ∼190 • C [87].
is increased to ∼276 and ∼300 °C, respectively, as compared to that of GeTe Tx ∼190 [87]. The calculated density of states (DOS) of the three IGT alloys in both crystalline a amorphous forms are shown in Figure 4a,b. Regarding the crystalline models, the over DOS profiles are quite similar, and all three alloys exhibit metallic features. By contra all three amorphous models are narrow-gap semiconductors. Statistical sampling yie consistent results ( Figure S4). The large difference in DOS between the crystalline a amorphous IGT results in a wide resistance contrast window for PCRAM applicatio The calculated density of states (DOS) of the three IGT alloys in both crystalline an amorphous forms are shown in Figure 4a,b. Regarding the crystalline models, the over DOS profiles are quite similar, and all three alloys exhibit metallic features. By contra all three amorphous models are narrow-gap semiconductors. Statistical sampling yiel consistent results ( Figure S4). The large difference in DOS between the crystalline an amorphous IGT results in a wide resistance contrast window for PCRAM applicatio The calculated density of states (DOS) of the three IGT alloys in both crystalline and amorphous forms are shown in Figure 4a,b. Regarding the crystalline models, the overall DOS profiles are quite similar, and all three alloys exhibit metallic features. By contrast, all three amorphous models are narrow-gap semiconductors. Statistical sampling yields consistent results ( Figure S4). The large difference in DOS between the crystalline and amorphous IGT results in a wide resistance contrast window for PCRAM applications [49]. The Bader charge analysis (Figure 4c) details larger net charges for In atoms than for Ge atoms due to the difference in electronegativity. The bimodal feature of the charges of indium atoms is consistent with previous work [50], stemming from different local environments of indium atoms. The enlarged charge transfer in amorphous structures increases the probability of long-distance electromigration under the transient electrical field induced by programming pulses [88], which is detrimental to the cycling endurance of devices [89,90]. For RESET operations, the higher the melting temperature T m , the greater the power consumption. The melting temperature for IGT alloys has a "W" shape profile, according to the InTe-GeTe phase diagram, which shows that InGeTe 2 has a higher melting temperature T m (740 • C) than GeTe and InTe whose T m are 715 and 688 • C, respectively [49]. Interestingly, the two other compositions, InGe 3 Te 4 and In 3 GeTe 4 , demonstrated reduced T m (645 and 565 • C). Taking into account all these factors for practical applications, we would suggest keeping the IGT composition within the range of InGeTe 2 to In 3 GeTe 4 for balanced device performance. [49]. The Bader charge analysis (Figure 4c) details larger net charges for In atoms than Ge atoms due to the difference in electronegativity. The bimodal feature of the charges indium atoms is consistent with previous work [50], stemming from different local en ronments of indium atoms. The enlarged charge transfer in amorphous structures creases the probability of long-distance electromigration under the transient electri field induced by programming pulses [88], which is detrimental to the cycling enduran of devices [89,90]. For RESET operations, the higher the melting temperature Tm, greater the power consumption. The melting temperature for IGT alloys has a "W" sha profile, according to the InTe-GeTe phase diagram, which shows that InGeTe2 has a high melting temperature Tm (740 °C) than GeTe and InTe whose Tm are 715 and 688 °C, resp tively [49]. Interestingly, the two other compositions, InGe3Te4 and In3GeTe4, demo strated reduced Tm (645 and 565 °C). Taking into account all these factors for practi applications, we would suggest keeping the IGT composition within the range of InGe to In3GeTe4 for balanced device performance. The enhanced amorphous stability is also useful for non-volatile photonic appli tions [91], yet the incorporation of indium makes IGT alloys metallic, which could aff the optical contrast between the amorphous and crystalline phase. The significant contr of ∼30% in the optical reflectivity of PCMs stems from a fundamental change in bondi nature from covalent to metavalent bonding (MVB) upon crystallization [92][93][94][95][96][97][98][99]. Ho ever, in comparison with GeTe and GST, which have three p electrons per site (a key f ture of MVB), InTe has a deficient number of p electrons, turning the rock-salt phase fro semiconducting to metallic. As a result, MVB in IGT alloys is expected to be weakened For verification, we carried out optical response calculations using the relaxed cr talline and amorphous IGT structures. We focused on the spectrum range from 400 to 16 nm, covering both the visible light region (∼400 nm to 800 nm) for optical displays [1 The enhanced amorphous stability is also useful for non-volatile photonic applications [91], yet the incorporation of indium makes IGT alloys metallic, which could affect the optical contrast between the amorphous and crystalline phase. The significant contrast of ∼30% in the optical reflectivity of PCMs stems from a fundamental change in bonding nature from covalent to metavalent bonding (MVB) upon crystallization [92][93][94][95][96][97][98][99]. However, in comparison with GeTe and GST, which have three p electrons per site (a key feature of MVB), InTe has a deficient number of p electrons, turning the rock-salt phase from semiconducting to metallic. As a result, MVB in IGT alloys is expected to be weakened.
For verification, we carried out optical response calculations using the relaxed crystalline and amorphous IGT structures. We focused on the spectrum range from 400 to 1600 nm, covering both the visible light region (∼400 nm to 800 nm) for optical displays [19][20][21] and the telecom wavelength bands (∼1500 to 1600 nm) for silicon-waveguideintegrated photonic applications [23][24][25][26]. As shown in Figure 5a, the optical absorption and reflectivity profiles vary slightly with the chemical compositions in the amorphous phase, while strong changes are found in the crystalline phase. For InGe 3 Te 4 and InGeTe 2 , sizable contrast in reflectivity between the crystalline and amorphous phases is observed over the whole spectrum, with an average value ∼20%. However, for In 3 GeTe 4 , the contrast in reflectivity nearly vanishes at around ∼900 nm, and it becomes greater below 700 nm, or above 1000 nm. 21] and the telecom wavelength bands (∼1500 to 1600 nm) for silicon-waveguide-integrated photonic applications [23][24][25][26]. As shown in Figure 5a, the optical absorption and reflectivity profiles vary slightly with the chemical compositions in the amorphous phase, while strong changes are found in the crystalline phase. For InGe3Te4 and InGeTe2, sizable contrast in reflectivity between the crystalline and amorphous phases is observed over the whole spectrum, with an average value ∼20%. However, for In3GeTe4, the contrast in reflectivity nearly vanishes at around ∼900 nm, and it becomes greater below 700 nm, or above 1000 nm. The three IGT crystals have a crossover at ∼1100 nm. For long wavelength or small photon energy (below ∼1 eV) regions, the optical excitation is mainly determined by states near EF. With increased DOS near EF by heavier indium alloying (Figure 4a), the absorption in the long wavelength region is enhanced. However, for the short wavelength or large photon energy (above ∼2 eV) region, the electronic states of a wider energy range would participate in the optical excitation. According to the projected DOS (Figure 5b), the valence states below EF are mainly contributed by Te atoms for all three crystals. However, indium alloying shifts the DOS peak in the conduction band to a higher energy range. Since fewer excited states of low energy could contribute to short wavelength excitation, c-In3GeTe4 shows the smallest absorption and reflectivity in the short wavelength region (Figure 5a).
We note that our optical calculations were performed using DFT-PBE functional with an independent-particle approximation, excluding local field effects and many body The three IGT crystals have a crossover at ∼1100 nm. For long wavelength or small photon energy (below ∼1 eV) regions, the optical excitation is mainly determined by states near E F . With increased DOS near E F by heavier indium alloying (Figure 4a), the absorption in the long wavelength region is enhanced. However, for the short wavelength or large photon energy (above ∼2 eV) region, the electronic states of a wider energy range would participate in the optical excitation. According to the projected DOS (Figure 5b), the valence states below E F are mainly contributed by Te atoms for all three crystals. However, indium alloying shifts the DOS peak in the conduction band to a higher energy range. Since fewer excited states of low energy could contribute to short wavelength excitation, c-In 3 GeTe 4 shows the smallest absorption and reflectivity in the short wavelength region (Figure 5a).
We note that our optical calculations were performed using DFT-PBE functional with an independent-particle approximation, excluding local field effects and many body effects. Therefore, the absolute values of optical profiles could vary if more advanced methods are employed. Nevertheless, the observation of weakened optical contrast due to heavier indium alloying should remain valid. Taking into account the enhanced crystallization temperature and the reduced melting temperature, we predict an optimal IGT composition within the ranges of InGeTe 2 and In 3 GeTe 4 for high-performance non-volatile photonics. To the best of our knowledge, thorough optical measurements of IGT alloys are still lacking. Therefore, we anticipate future experiments exploring the suitability of IGT alloys for optical and photonic PCM applications.
Conclusions
In summary, we have carried out systematic ab initio calculations for three typical compositions of indium incorporated GeTe compounds, InGe 3 Te 4 , InGeTe 2 and In 3 GeTe 4 , to elucidate the evolution of structural and optical properties along the InTe-GeTe tie line. Upon indium alloying, the crystalline phase of all the three alloys turns metallic, while their amorphous counterparts all show semiconducting features with narrow band gaps. This stark contrast in the electronic structure guarantees a large resistance window between amorphous and crystalline In-Ge-Te alloys for electrical PCRAM. Yet, too much indium should be avoided, because the stronger charge transfer could be harmful to cycling endurance due to electromigration. Regarding optical properties, both InGe 3 Te 4 and InGeTe 2 show sizable optical contrast between the crystalline and amorphous phases in the spectrum range from 400 nm to 1600 nm, covering both visible-light and telecom bands. Meanwhile, In 3 GeTe 4 shows a less robust contrast window, due to weakened MVB. Moreover, the increased indium concentration enlarges the ratio of tetrahedral motifs in the amorphous phase and consequently increases the structural barrier for crystallization. The InTe-GeTe phase diagram establishes that the melting temperature reaches minimum around In 3 GeTe 4 , indicating lowest power consumption for melt-quench amorphization. Taking all these factors into account, we suggest that the optimal chemical composition for In-Ge-Te alloys should be located in the range between InGeTe 2 and In 3 GeTe 4 , which could result in the most balanced device performance for PCM-based non-volatile electronic and photonic applications. Our work should serve as a stimulus for further investigations into indium-incorporated PCMs.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/ 10.3390/nano11113029/s1. Figure S1: Atomic structures of crystalline and amorphous InGe 3 Te 4 and In 3 GeTe 4 (denoted as c/a-134 and 314); Figure S2: Bond population (left panel) and bond weighted distribution functions BWDFs (right panel) for each interatomic pair in the three amorphous compounds. The crossover values from positive to negative in the BWDFs represent cutoff values for bonding interactions, which are used for structural analysis. Further technical details about BWDF can be found in [79] of the main text; Figure S3: Projected COHP (pCOHP) for tetra-In and tetra-Ge motifs in a-InGe 3 Te 4 and a-In 3 GeTe 4 . Tetra-hedral motifs are grouped as the ones with only heteropolar bonds, denoted as In[In 0 Ge 0 Te 4 ] and Ge[Ge 0 In 0 Te 4 ], and the others with at least one wrong bond indicated as In[In x Ge y Te 4−x−y ] and Ge[Ge x In y Te 4−x−y ] (x or y ≥ 1, x + y ≤ 4). In the a-314 structure, Ge[Ge 0 In 0 Te 4 ] motif is absent; Figure S4: Density of states (DOS) for crystalline and amorphous structures of the three IGT compositions. Three models for each composition were built, which show consistent results.
Author Contributions: Investigation, visualization, X.W., X.S. and S.S.; writing-original draft preparation, X.W.; conceptualization, funding acquisition, writing-review and editing, W.Z. All authors have read and agreed to the published version of the manuscript.
Funding: This work was funded by National Natural Science Foundation of China (61774123) and 111 Project 2.0 (BP2018008).
Data Availability Statement:
The data presented in this study are available on request from the corresponding author. | 6,227.2 | 2021-11-01T00:00:00.000 | [
"Materials Science"
] |
Reliable Detection of Myocardial Ischemia Using Machine Learning Based on Temporal-Spatial Characteristics of Electrocardiogram and Vectorcardiogram
Background: Myocardial ischemia is a common early symptom of cardiovascular disease (CVD). Reliable detection of myocardial ischemia using computer-aided analysis of electrocardiograms (ECG) provides an important reference for early diagnosis of CVD. The vectorcardiogram (VCG) could improve the performance of ECG-based myocardial ischemia detection by affording temporal-spatial characteristics related to myocardial ischemia and capturing subtle changes in ST-T segment in continuous cardiac cycles. We aim to investigate if the combination of ECG and VCG could improve the performance of machine learning algorithms in automatic myocardial ischemia detection. Methods: The ST-T segments of 20-second, 12-lead ECGs, and VCGs were extracted from 377 patients with myocardial ischemia and 52 healthy controls. Then, sample entropy (SampEn, of 12 ECG leads and of three VCG leads), spatial heterogeneity index (SHI, of VCG) and temporal heterogeneity index (THI, of VCG) are calculated. Using a grid search, four SampEn and two features are selected as input signal features for ECG-only and VCG-only models based on support vector machine (SVM), respectively. Similarly, three features (S I , THI, and SHI, where S I is the SampEn of lead I) are further selected for the ECG + VCG model. 5-fold cross validation was used to assess the performance of ECG-only, VCG-only, and ECG + VCG models. To fully evaluate the algorithmic generalization ability, the model with the best performance was selected and tested on a third independent dataset of 148 patients with myocardial ischemia and 52 healthy controls. Results: The ECG + VCG model with three features (S I ,THI, and SHI) yields better classifying results than ECG-only and VCG-only models with the average accuracy of 0.903, sensitivity of 0.903, specificity of 0.905, F1 score of 0.942, and AUC of 0.904, which shows better performance with fewer features compared with existing works. On the third independent dataset, the testing showed an AUC of 0.814. Conclusion: The SVM algorithm based on the ECG + VCG model could reliably detect myocardial ischemia, providing a potential tool to assist cardiologists in the early diagnosis of CVD in routine screening during primary care services.
INTRODUCTION
Myocardial ischemia is a condition in which the perfusion of heart muscle is insufficient due to an obstructive plaque, coronary artery spasm, or coronary microvascular dysfunction (Liu H. et al., 2020;Paolo Severino, 2020). Myocardial ischemia can lead to cardiovascular events including acute myocardial infarction death and sudden cardiac death (SCD) (Moran et al., 2014). It accounts for 16% of the world's total deaths and has been listed as a leading cause of mortality by the World Health Organization (WHO), with the prevalence rate per 100,000 population supposed to increase from 1,655 to 1845 by the year 2030 (Khan et al., 2020).
Clinically, the gold standard of myocardial ischemia diagnosis is the invasive measurement of fractional flow reserve (FFR) and index of microcirculatory resistance (IMR) using a coronary guidewire (Kaski et al., 2018;Geng et al., 2022). Clinical imaging techniques have also been applied to myocardial ischemia detection, including invasive coronary angiography, computed tomography (CT) coronary angiography, nuclear myocardial perfusion imaging, and cardiac magnetic resonance (CMR) (Kaski et al., 2018). However, due to their invasiveness, radiation, high cost, and complicated operations that need special training, the guidewire measurements and imaging modalities are usually applied to patients with existing ischemic symptoms. There is an increasing clinical need for a non-invasive, lowcost, and convenient method to achieve early detection of myocardial ischemia.
An electrocardiogram (ECG) is a non-invasive and low-cost method to detect cardiac electrophysiology. Myocardial ischemia can lead to specific changes in the ECG waveform. As shown in Figure 1, the earliest manifestations of myocardial ischemia in the ECG waveform include transient ST-elevation or STdepression and T-wave changes (Thygesen et al., 2012). These typical changes in T wave and ST segment are commonly used as indicators of myocardial ischemia. At present, ECG is the firstline diagnostic tool in the assessment of patients with suspected myocardial ischemia (Fihn et al., 2014). Due to the difficulty of capturing subtle changes in ST-T segments, the sensitivity of manual inspection in diagnosing myocardial ischemia is only about 60% Stefan Weber et al., 2014). Even patients with severe coronary stenosis may have no observable ECG changes (Barstow et al., 2017).
To overcome the limitations of manual inspection, computeraided diagnostic frameworks based on myocardial ischemiarelevant ECG features have been proposed (Alizadehsani et al., 2019).To improve the sensitivity in myocardial ischemia classification, most algorithms used for myocardial ischemia classification and diagnosis focus on the feature extraction from heart rate variability (HRV) (Goldenberg et al., 2019), beat-based techniques (Acharya et al., 2016) or frame-based schemes (a few consecutive beats) (Sharma and Sunkaria, 2017;Braun et al., 2020;Butun et al., 2020).
In particular, vectorcardiogram (VCG) can further empower the ECG-based automatic detection of myocardial ischemia. VCG is a special form of ECG and can be mathematically synthesized from standard 12-lead ECG. The VCG consists of three orthonormal leads (X, Y, and Z), reflecting cardiac electric activity in the frontal, horizontal, and sagittal planes (Grishman et al., 1951). Compared with the standard 12-lead ECG, VCG represents both the magnitude and spatial information of heart activity (Burger et al., 1956). Hence, VCG provides higher sensitivity than ECG in diagnosing myocardial ischemia, e.g., 70% using manual inspection , without sacrificing specificity (Hurd et al., 1981;Sascha et al., 2021). The combination of ECG and VCG could achieve even better performance (Lee et al., 1968;Correa et al., 2016). Authors demonstrated that combination of ECG and ECGreconstructed VCG can achieve comparable performance to the combination of ECG and measured VCG in detecting myocardial ischemia Kors et al., 1992). Therefore, VCG-enhanced automatic early detection of myocardial ischemia has gained increasing popularity (Ansari et al., 2017).
Deep features can be extracted from ECG or VCG in heart beats or frames using various mathematical transforms (Acharya et al., 2016). The number of features is highly diverse in existing studies. 12 nonlinear ECG features (Liu J. et al., 2020), 72 multiscale energy and eigenspace ECG features (Sharma et al., 2015), 288 ECG features in time, frequency, nonlinear, and entropy domains (Liu et al., 2019), 7 (Correa et al., 2013) and 52 features of 3-lead ECG (Chuang et al., 2020), 290 multidimensional parameters of 5-lead VCG (Braun et al., 2020), 22 features of 6-lead VCG , and 322 pseudo-VCG features (Aranda Hernandez et al., 2018). These Frontiers in Physiology | www.frontiersin.org May 2022 | Volume 13 | Article 854191 features are fed into machine learning (ML) models (Aranda Hernandez et al., 2018;Chuang et al., 2020) to develop computeraided diagnostic models of myocardial ischemia, achieving higher efficiency and accuracy than manual inspection. Existing computer-aided approaches for myocardial ischemia detection suffer from some limitations. Firstly, there are few studies on the combination of ECG and VCG in detecting myocardial ischemia. It has been demonstrated that the models with both VCG and ECG features yielded the highest performance, followed by the VCG-only and ECGonly models, while the details of the algorithms were not disclosed Kors et al., 1992). In 2021, Pollard et al. drew a similar conclusion using eight different models based on global electrical heterogeneity extracted from ECGs and VCGs (Pollard et al., 2021). Secondly, the high-dimensional features lead to an oversaturation of small datasets and a high computational burden. Some features are correlated or insignificant for the classification (Pollard et al., 2021). The minimization of the feature set is essential to enhance the recognition capabilities of a model. Thirdly, beat-or frame-based approaches are usually used, which results in the incapacity to detect the subtle ST-T changes in continuous cardiac cycles and oversampling. Oversampling may weaken the model's feasibility and adaptability (Fu et al., 2020). Longer ECG records can avoid the oversample and enhance the total scheme efficiency and overall accuracy for the myocardial ischemia diagnosis algorithm (Li et al., 2021).
To overcome the above-mentioned limitations, we propose a novel algorithm for myocardial ischemia detection based on three selected features extracted from ST-T segments of 20 s, 12-lead ECGs, and derived 3-lead VCGs. Three support vector machine (SVM) models fed with different signal features (ECG-only, VCG-only, and ECG + VCG) are trained and tested. The model with the best performance was selected as a potential approach towards accurate, non-invasive, and low-cost detection of myocardial ischemia. Figure 2, work consists of four parts: data collection, preprocessing, feature calculation, and classification. Firstly, 20-second (20 s), 12-lead ECGs were Frontiers in Physiology | www.frontiersin.org May 2022 | Volume 13 | Article 854191 4 collected and converted into 3-lead VCGs. The onset of ST-wave and offset of T-wave were marked on the ECGs and VCGs. Then, multi-domain characteristics analysis was performed to extract the features, including sample entropy (SampEn) from ECGs' and VCGs' ST-T segments, as well as spatial heterogeneity index (SHI) and temporal heterogeneity index (THI) from VCGs' ST-T segments. Subsequently, the most effective features were selected from the training dataset, combined (i.e., ECG-only, VCG-only, ECG + VCG), and deployed in support vector machine (SVM) models for myocardial ischemia identification. To validate the feature selection results, the classification performance of the selected features was compared with that of principal component analysis (PCA)-derived features. With 5-fold cross validation based on clinical diagnosis, the results of three SVM models (ECG-only, VCG-only, and ECG + VCG) were comprehensively evaluated and compared to investigate if VCG features can improve the accuracy of myocardial ischemia detection. Finally, the final selected model was tested on a third independent dataset.
Data Collection
The 10-second (10 s) ECG is common in clinical practice, whilst longer ECGs can improve the total scheme efficiency and overall accuracy of myocardial ischemia detection algorithms (Li et al., 2021). However, it is difficult for some patients to stay in the supine posture for long period to get high-quality ECGs. Consequently, 20sec segments are adopted in this work.
Datasets for Training and Validation
In this study, clinical data was collected from 429 subjects in two cohorts. The data of 52 healthy controls (age: 43 ± 17 years; 41 males and 11 females) were from the Physikalisch-Technische Bundesanstalt (PTB) diagnostic ECG database (https://www.physionet.org/content/ ptbdb/1.0.0/) (Bousseljot et al., 1995;Goldberger et al., 2000). The ECGs in this collection were obtained using a non-commercial, PTB prototype recorder with 16-bit resolution at a resolution of 0.5 μV/LSB and a sampling frequency of 1,000 Hz.
From November 2014 to November 2015, the data of 377 patients with myocardial ischemia were obtained from FuWai Hospital, Beijing, China, with approval from the local ethics committee for sharing and analyzing retrospective anonymized patient data with informed consent form waived. Inclusion criteria were suspected patients with coronary artery disease (CAD) for coronary angiography with simultaneous ECG records. The exclusion criteria were as follows: 1) The presence of heart diseases such as heart valve disease, congestive heart failure, pulmonary arterial hypertension, or left ventricular hypertrophy; 2) The presence of bundle branch blocks, as well as of non sinus or paced rhythm.
The hospital diagnosis of myocardial ischemia, which was used as the ground truth, was made by professional cardiologists based on comprehensive analysis of clinical data and the following positive indicators: 1) Suggestive clinical history and clinical examination; 2) Presence of coronary stenosis of >50%.
The 20 s, 12-lead resting ECGs were recorded using a commercially available ECG device (Mindray Bene-Heart R12, Shenzhen, China) with 16 bit precision at a resolution of 1 μV/ LSB and a sampling frequency of 1,000 Hz. The characteristics of 377 ischemic patients are presented in Table 1.
Finally, the 20 s, 12-lead ECGs from two groups (377 ischemic patients and 52 healthy controls, as positive and negative samples, respectively) were sampled at 1,000 Hz frequency with 16-bit precision. Figure 1 shows the ECGs of two subjects from the ischemic patient and control groups.
A Third Independent Database for Testing
To fully evaluate algorithmic generalization ability, a third independent dataset was implemented for testing. The data was collected from 200 subjects in two cohorts. Regarding positive samples, 148 20 s ECGs were collected from 148 patients with myocardial infarction (age: 60 ± 11 years, 108 males and 40 females, 67 smokers, systolic blood pressure: 121 ± 19 mmHg, and diastolic blood pressure: 74 ± 13 mmHg) of the PTB diagnostic ECG database with 16 bit precision at a resolution of 0.5 μV/LSB and a sampling frequency of 1,000 Hz (Goldberger et al., 2000).
Data Preprocessing
Firstly, the baseline drift and low-frequency fluctuations (e.g., respiratory movements) were removed using a high-pass Butterworth filter at 0.67 Hz. The cutoff frequency setting in high-pass filtering could significantly influence the morphology of ST segments. The cutoff frequency of 0.67 Hz is recommended for diagnostic purposes since it could remove baseline drifts with Subsequently, high-frequency noises, including power-line interference (50/60 Hz) and electromyogram noise (10-230 Hz) (Yazdani et al., 2017), should be removed since they can affect the localization of ST-segments in ECG waves and affect the detection of myocardial ischemia (Christov et al., 2017). Band-pass filtering is widely used in ECG signal processing for eliminating high-frequency noise and performs well in R-peak detection. Regarding two commonly used cutoff frequencies (i.e., 40 and 150 Hz) in lowpass filtering of ECGs, 40 Hz could effectively eliminate the highfrequency noises but lead to the elevation of J-point, i.e., the junction between QRS termination and ST-segment onset (Nakagawa et al., 2014;Christov et al., 2017), resulting in inaccuracy of the onset of the ST segment, whereas 150 Hz could overcome this problem but cause a high level of residual noise (Ricciardi et al., 2016;Christov et al., 2017). As compared with a band-pass filter, the discrete wavelet transform could perform better in terms of eliminating highfrequency noise and keeping the morphology feature points of the ECG signal (Addison, 2005;Singh and Pradhan, 2018;Chen et al., 2020), as illustrated in Supplementary Figure S1. Therefore, highfrequency noise was removed using discrete wavelet transform and wavelet thresholding (Kumar et al., 2021). Coif4 was utilized as a wavelet basis function to decompose noise-containing ECGs into four layers. The denoized ECGs were reconstructed using the inverse of the discrete wavelet transform followed by the elimination of noise by an adaptive threshold.
Next, 20 s,12-lead ECGs were standardized based on 25 mm/s using a gain setting of 10 mm/mV (Kossmann et al., 1967) and then transformed into VCGs (Jaros et al., 2019): Finally, the ST-T segments of ECGs and of VCGs were detected employing a hybrid approach . The three-dimensional (3D) ST-T segments of VCGs are shown in Figure 3.
Feature Extraction
Feature extraction is the process of revealing hidden ischemiarelated characteristics from ECGs and VCGs, which lays the groundwork for detecting myocardial ischemia. In our proposed scheme, features were extracted from ST-T segments in the entropy domain, frequency domain, and Lyapunov index, separately.
SampEn
For detecting myocardial ischemia, various entropies calculated from HRV (Udhayakumar et al., 2019), ST segments Wei et al., 2012) or filtered 12-lead ECGs (Liu et al., 2019) have been used. To quantitatively evaluate the complexity of physiological time-series and diagnose diseases, Richman and Moorman refined the approximate entropy algorithm and introduced sample entropy (SampEn) by excluding the selfmatching of templates' data length (Richman and Moorman, 2000). SampEn, defined as the negative natural logarithm of a conditional probability, was employed in this study, since it is largely independent of record length and enables more consistent calculation results compared with approximate entropy (Richman and Moorman, 2000). Given that two data sequences are similar for m points, they remain similar at the next point, within a tolerance "r" that represents a fraction of the series standard deviation. SampEn is positively related to the signal complexity of each ECG lead. Overall, the SampEn obtained from the ST segment of healthy controls was less than that of ischemic patients . Therefore, SampEn may be an early indicator of myocardial ischemia.
In our method, SampEn values were calculated from the ST-T segments of ECGs (S i , i I, II, III, AVR, AVL, AVF, V1, V2, V3, V4, V5, V6) and VCGs (S i , i V x , V y , V z ) based on existing methods (Richman and Moorman, 2000;Antonio Molina-Picó et al., 2011;Marwaha and Sunkaria, 2016). The major steps are as follows: Firstly, for each ECG or VCG lead, its time series, i.e., {x(n)} x(1), x(2), /, x(N) was formed by splicing beatto-beat ST-T segments followed by standardization: x x−μ σ . where μ and σ are mean value and the standard deviation of the whole time series. N is the length of the time series.Then, the vectors X m (1), /, X m (N − m + 1) and X m+1 (1), /, X m+1 (N − m) with a dimension of m and m + 1 were formed, respectively. Here Subsequently, the distance between X m (j) and X m (z) was defined as: (2) FIGURE 3 | Three-dimensional VCGs' ST-T segments derived from 20sec, 12-lead ECGs.
Frontiers in Physiology | www.frontiersin.org May 2022 | Volume 13 | Article 854191 A j (m, r) and A j (m + 1, r) were defined as: Here n j (m, r) presents the number of vectors X m (j) within r of vector X m (z): d(X m (j), X m (z)) < r. r is the error tolerance range of similar regions and is recommended between 0.1 and 0.25 times the standard deviation of time series. n j (m + 1, r) presents the number of vectors X m+1 (j) within r of vector Here φ(m, r) and φ(m + 1, r) are the probability that two sequences match at m and m + 1 points, respectively. Finally, SampEn was calculated as follows: where the parameters r and m were set to the best value (Richman and Moorman, 2000;Marwaha and Sunkaria, 2016) of r 0.1, m 2.
SHI and THI
The spatial heterogeneity index (SHI) and temporal heterogeneity index (THI) reflect the spatial and temporal heterogeneity of 3D trajectory, respectively (Deng et al., 2017). SHI (Deng et al., 2017) was calculated based upon the Lyapunov index to describe the spatial characteristics of VCGs' ST-T segments, as described in Eq. 8.
where N presents the length of VCGs' ST-T segments, d n1 is the distance between the n th data point and its nearest data points, and d n2 denotes the distance between the n th data points and its nearest data points after 10 steps. THI (Deng et al., 2017) was calculated to reveal the temporal characteristics of VCGs' ST-T segments: where F is the Fourier transform, and Vs i represents the VCGs' ST-T segments.
Then, the f i (w) was fitted as an exponential function with an exponent λ i .
Finally, THI was calculated as follows: 2.4 Myocardial Ischemia Detection Using SVM
The Proposed Models
The SVM model is one of the most frequently utilized ML models for cardiovascular disease detection (Alizadehsani et al., 2019) and is constructed by projecting input vectors into a higher dimensional space via a kernel function and capturing the decision boundary (formally known as a hyperplane) with the maximum margin between different classes. It has the advantages of reducing empirical errors, preserving the complexity level of the mapping function, and ensuring better performance. Thus, an SVM model with the Gaussian radial basis function (RBF) kernel was employed in this study to distinguish between healthy controls and ischemic patients. The extracted features were combined into vectors and fed into the SVM model to classify the subjects (i.e., healthy control vs. ischemic patients). For the model design, the ECG-only model presented the SVM framework fed with ECGs' SampEn only. Similarly, the VCG-only model employed only the VCGs' features in the SVM framework. Finally, the ECG + VCG model presented the SVM framework utilizing selected ECG and VCG features.
Feature Selection
Feature selection plays a critical role in improving the performance of classification algorithms by identifying relevant features and discarding irrelevant ones. Generally, a subset of available features includes all relevant features, whereas the remaining irrelevant features do not contribute to the classification (Urbanowicz et al., 2018).
To minimize the number of the selected features and reduce the computational burden, a grid search was implemented to select the most influential features on the training dataset for each model, as shown in Figure 4. Firstly, all the features with an average accuracy of over 0.6 on the training dataset were selected for the ECG-only and VCG-only models, separately. Then, all possible permutations of the selected features were separately fed into the corresponding SVM models to pick out the most effective one for each model.
Regarding the ECG + VCG model, the selected ECG and VCG features rather than all of the ECG and VCG features (17 in total: 15 SampEn, SHI, THI) were fed into the SVM model. Subsequently, all possible permutations of the features with an average accuracy of over 0.6 were selected using the grid search to pick out the most useful one.
Finally, to verify that the grid search method can select the most useful features with the fewest features, for each model (i.e., ECGonly, VCG-only, ECG + VCG), the classification results using the features selected by the grid search were compared with those using the eigenvectors developed by the PCA algorithm, which is the Frontiers in Physiology | www.frontiersin.org May 2022 | Volume 13 | Article 854191 commonest method for feature reduction (Alizadehsani et al., 2019). The eigenvector developed using the PCA algorithm for each model was titled as PCA-derived features. In the PCA algorithm, Minka's maximum likelihood estimation was utilized to obtain the dimension of eigenvectors.
Evaluation Criteria
We evaluated the classification performance of the constructed models using the area under the curve (AUC) of the receiver operating characteristic (ROC) curve and calculated the following metrics: accuracy, specificity, sensitivity, and F1 score according to the expressions in Eqs 12-15.
Accuracy TP + TN TP
where TP, TN, FP, and FN represent the true positive, true negative, false positive, and false negative cases, respectively.
Cross-Validation
Considering the limited size of our dataset, to avoid any overfitting caused by out-of-sample validation, we adopted a 5-fold cross-validation approach to evaluate the performance of the proposed models. The data was randomly divided into five groups, of which four groups were used for training and the last group was used as a test dataset for verification. This process was repeated five times, and the corresponding evaluation criteria for each calculation were recorded.
Testing on a Third Independent Dataset
ECG parameters vary with ethnicity, age, gender, and region in different populations (Tan et al., 2016;Ching-Hui Sia, 2019). To further investigate the applicability and generalization ability of our final selected model, i.e., the ECG + VCG model employing (S I , THI, and SHI) for different populations, the testing was performed on a third independent dataset.
Statistical Analysis
The statistical analysis was performed on SPSS (Version 25.0, IBM Corp). Continuous values were presented as mean ± standard deviation (SD) for normally distributed data and median value (lower-upper quartiles) for non-normally distributed data. The categorical data was presented as numbers and percentages. The Kolmogorov-Smirnov test (K-S test) was used to check whether the data was normally distributed. Student's t test (for normal distribution) or Wilcoxon signed rank test (for non-normal distribution) was deployed when appropriate. Statistical significance was defined as p values less than 0.05.
Development Environment
The experimental setup comprised an<EMAIL_ADDRESS>CPU and 32GB of RAM. The data preprocessing and feature extraction were implemented using the (R2014; The MathWorks Inc., Natick, United States). The SVM models were designed and tested in Python 3.7 using Tensorflow 2.0 and the PCA algorithm.
ECG-Only Model for Myocardial Ischemia Classification
The values of SampEn extracted from ECGs' ST-T segments are shown in Figure 5A. The SampEn's mean values of ischemic ECGs are obviously higher than those of healthy ones in most leads except S V2 and S V3 . Figure 5B shows the average training accuracy of the SVM models fed with SampEn of each ECG lead, i.e., S i . It can be observed that S I , S II , S AVR , S AVF , and S V6 are more influential than the remaining features, with an accuracy higher than 0.6. Table 2 lists two feature combinations selected using the grid search on Thus, (S I , S II , S AVF , S V6 ) was selected as the input feature combination for the ECG-only model. For validation, the grid search results were compared with those derived from PCA-derived features, as listed in Table 3. (S I , S II , S AVF , S V6 ) selected using the grid search outperformed PCAderived features in all evaluation criteria. Therefore, (S I , S II , S AVF , S V6 ) was verified as the best candidate for the ECG-only model.
VCG-Only Model for Myocardial Ischemia Detection
The values of SampEn, SHI, and THI extracted from VCGs' ST-T segments are exhibited in Figure 6. Compared with healthy controls, the patients with myocardial ischemia show higher SampEn and THI ( Figures 6A,B, respectively) but lower SHI ( Figure 6C).
In the grid search, (S Vy , THI, SHI) and (THI, SHI) were selected for further comparison with their corresponding performance listed in Table 4, while the remaining feature permutations were excluded. On the training dataset, the SVM model utilizing (THI, SHI) outperformed that using (S Vy ,THI, SHI) in major evaluation criteria except the training sensitivity and AUC. Therefore, (THI,SHI) was chosen as the candidate for the VCG-only model.
In Table 5, the VCG-only model employing (THI, SHI) selected using the grid search outperforms the model with PCA-derived features in most items except specificity and AUC. Therefore, (THI, SHI) was verified as the input feature combination for the VCG-only model.
ECG + VCG Model for Myocardial Ischemia Diagnosis
To determine the best feature combination for the ECG + VCG model, all the selected features (i.e., S I , S II , S AVR , S V6 , SHI, and THI) of the ECG-only and VCG-only models were included and selected using a grid search. In a grid search, (S I , S V6 , THI, SHI) and (S I , THI, SHI) were picked up for further comparison with their corresponding modeling evaluation criteria listed in Table 6, while other permutations were ruled out. Table 6 demonstrates that (S I , THI, SHI) yields better performance than (S I , S V6 , THI, SHI) on the training dataset. Thus, (S I , THI, SHI) were selected as the best candidates for the ECG + VCG model.
In Table 7, the ECG + VCG model employing (S I , THI, SHI) selected by a grid search outperforms that employing PCAderived features in all evaluation criteria. Therefore, (S I , THI, SHI) were validated as the optimal feature combinations for the ECG + VCG model. Figure 7 shows the quantitative comparison of evaluation criteria among ECG-only, VCG-only, and ECG + VCG models. The ECG + VCG model achieves higher median and mean values for the evaluation criteria than any of the remaining models. The Student's t-tests show that the ECG + VCG model is significantly better than the ECG-only model in all evaluation criteria (p < 0.05 for all). Meanwhile, it is significantly superior to the VCG-only model in terms of sensitivity and AUC (p < 0.05 for both). Therefore, the ECG + VCG model employing (S I , THI, SHI) was the optimal one for myocardial ischemia detection.
Testing of the Selected Model on a Third Independent Dataset
On the third independent dataset, the testing results of the selected ECG + VCG model employing (S I , THI, SHI) were 0.790 accuracy, 0.764 sensitivity, 0.865 specificity, 0.843 F1 score, and 0.814 AUC.
Summary of Results: In Comparison With Existing Studies
In this work, we developed a reliable ECG + VCG SVM model for myocardial ischemia detection using the features extracted from VCGs' and ECGs' ST-T segments. The classification effectiveness of three models was comprehensively compared across five evaluation criteria.
The comparison of our model against state-of-the-art myocardial ischemia detection approaches is listed in Table 8. Our model yields better effectiveness by using a much lower number of features but longer ECG and VCG signals. The major reason behind this is that the comprehensive utilization of ECGs' and VCGs' ST-T segments could capture more ischemia-induced temporal and spatial changes. Specifically, ischemia-related beatto-beat changes in ST-T segments were measured by the temporal and spatial features used in this work, while beat-based (Correa et al., 2014;Aranda Hernandez et al., 2018;Braun et al., 2020) ML models only utilized the changes in a single heartbeat. Beat-tobeat changes in the T wave or ST segment result from the increase in ischemia-induced repolarization dispersion between ischemic and healthy regions as well as between different ischemic regions . SHI was extracted to evaluate the beat-to-beat changes of VCGs in 3D space. Besides, ischemia-induced temporal changes can be reflected in the VCG waveform and the time delays among ECG leads (Correa et al., 2014). Therefore, the temporal characteristics of beat-to-beat changes in ST-T segments were assessed by VCGs' THI and ECGs' SampEn simultaneously. Besides, longer signals used in this work could enhance the total scheme efficiency and overall accuracy (Hussein et al., 2021;Li et al., 2021). In some existing studies, patients with myocardial infarction were selected from the STAFF III database as positive samples of ischemia (Correa et al., 2013;Correa et al., 2014;Aranda Hernandez et al., 2018), in which the ischemic changes in ECG waveform are more obvious than asymptomatic patients. In comparison, we included ischemic patients with CAD but not limited to symptomatic ones with myocardial infarction, which provides a better understanding of ischemia instead of focusing on myocardial infarction. Moreover, the VCGs from the same patient with myocardial infarction before and during the percutaneous transluminal coronary angiography (PTCA) procedure were selected from the STAFF III database as the corresponding negative and positive samples (Correa et al., 2014;Aranda Hernandez et al., 2018). In contrast, our patients and controls were recruited separately, where the effect of clinical intervention could be excluded to better reflect the ischemic changes.
Compared with state-of-the-art myocardial ischemia detection approaches, our final selected model was tested on a third independent database rather than a testing dataset separated from the same cohort. ECG parameters depend on physiological factors including ethnicity, sex, age, and body size (Tan et al., 2016;Ching-Hui Sia, 2019). As a result, ECG-based screening of CAD is influenced by a myriad of factors, including demographics, anthropometrics, level of physical fitness, and population-specific reference ranges among distinct population groups (Ching-Hui Sia, 2019). Therefore, testing on a third independent database can comprehensively evaluate the algorithmic applicability and generalization ability for different populations. As far as we know, we tried the testing in different populations for the first time. Despite the inconsistent data distribution and the heterogeneity between cohorts, the major evaluation criteria are above 0.8, except for the sensitivity and accuracy, which demonstrated that our proposed model provides the possibility for applications in different populations.
Importance of VCG in Detecting Myocardial Ischemia
Our ECG + VCG model outperforms the ECG-only and VCGonly ones for myocardial ischemia detection, which is in accordance with existing studies (Lee et al., 1968;Häggmark et al., 2008;Correa et al., 2016). The ECG measurements are based on the lead theory, which assumes that cardiac electrophysiological activities form a heart vector which moves periodically in 3D space in cardiac cycles, forming VCG loops. Ischemia-induced repolarization dispersion can change the temporal and spatial properties of the heart vector. Thus, the ST vector is called the "ischemia vector" due to its sensitivity to myocardial ischemia. VCG could reflect the dynamics of repolarization abnormalities (Hasan and Abbott, 2016). Both ECG and VCG signals have ischemia-related temporal changes, while VCG uniquely shows the spatial changes. VCG is a recurring, near-periodic pattern of cardiac dynamics and represents the trajectory of the tip of heart vectors in 3D space. From VCG which reflects both the magnitude and direction of the heart vector, the dysfunction of the ischemiarelated back region of the heart can be detected. In contrast, ECG is the secondary projection of VCG loops on the lead axis (Okamoto et al., 1982), which only reflects the magnitude but not the orientation of the heart vector (Hasan et al., 2012). A particular ECG lead describes the heart vector from a fixed direction, making it difficult to detect electrical activity in some areas of the heart. For example, 12-lead ECG has limited sensitivity in detecting an acute posterior injury pattern during circumflex coronary artery ischemia (Khaw et al., 1999). Therefore, VCG plays a key role in improving the accuracy in detecting myocardial ischemia.
Relationship Between Features and Myocardial Ischemia
In this study, S I , THI, and SHI were selected as the most crucial features for the ECG + VCG model. These features can reflect the heterogeneous repolarization process resulting from the decrease in conduction velocity and the duration of action potential leads (Janse and Wit, 1989) during myocardial ischemia.
SampEn extracted from ischemic ST-T segments is higher than that from healthy ones in most leads, as shown in Figure 5A; Figure 6A. The heterogeneous repolarization is reflected in the ECG via the changes in ST-segment and T-wave (Correa et al., 2014), such as ST segment elevation or depression and T-wave changes (e.g., inverted T wave, biphasic T wave, or high-tip T wave). Therefore, these ischemia-related changes increase the complexity of beat-tobeat ST-T segments, leading to a higher SampEn. It is demonstrated that ST segments induced by myocardial ischemia have relatively large morphological variability (Wei et al., 2012). The average SampEn obtained from ischemic ST segments of ECGs was found to be higher than that of healthy subjects . SampEn extracted from the filtered ECGs could reflect ischemia-induced myocardial infarction (Liu et al., 2019). Therefore, SampEn is a reliable feature of myocardial ischemia.
The results in Figures 6B,C and Table 5 suggest that SHI and THI calculated from VCGs' ST-T segments reflect the heterogeneity of ventricular repolarization induced by ischemia. Usually, the heterogeneous repolarization is reflected in the VCG by the changes in the QRS loop, T-wave vector, and ST vector (Correa et al., 2014). Spatial TT′ angle and beat-to-beat variability in T-loop roundness represent intrinsic measures of beat-to-beat repolarization ability (Feeny and Tereshchenko, 2016). Compromised hearts have irregular and distorted T-loops, whilst healthy ones have smooth planar loops. Myocardial ischemia changes the T vector angle and T loop morphology. Meanwhile, the spatial orientations and magnitudes of ST vectors were not stable (ter Haar et al., 2013). Therefore, features of VCGs' ST-T segments can be indicators of myocardial ischemia (Correa et al., 2014;Dong et al., 2018). ST-T interval characterizations have significant differences before starting and during the PTCA procedure in patients with acute myocardial ischemia (Correa et al., 2014). We hypothesize that beat-to-beat changes in T vector and ST vector make ischemic trajectories of VCGs' ST-T segments more chaotic with more perturbations compared with healthy ones. SHI and THI can capture the ischemia-related chaotic spatial and temporal characteristics of VCGs and therefore distinguish ischemic and normal subjects (Deng et al., 2017).
Advantages, Limitations, and Future Directions
Our proposed model affords the possibility of noninvasive detection of myocardial ischemia in different populations. It could be implemented in ECG acquisition systems with VCG mathematically synthesized from standard 12-lead ECG. There will be no extra workload for operators, since feature extraction and classification algorithms are automatic. Compared with PCAderived features calculated from all features using a linear transform, our model is based on the minimal number of features selected using a grid search, which is achievable on wearable devices where the computational resources are limited. Therefore, it could become a practical, easy-to-accept, and cost-effective tool for myocardial ischemia detection in various application scenarios, including routine community screening, older people's homes, and daily monitoring using wearable ECG sensors. The results can provide an important reference for clinicians on the early diagnosis of CAD. There are some limitations to this work. First, the number of samples, specifically negative samples, is relatively small. Secondly, the evaluation criteria of our final selected model on a third independent dataset are lower than those of other state-of-the-art algorithms since ECGs from the training and testing datasets were collected from different populations with different acquisition equipment. Thus, the difference in physiological characteristics may affect the results. Thirdly, we focused on the electrophysiological features, while other clinical examination results were not included in our model. In future studies, the feature extraction from 10 s ECGs can be explored to enable daily clinical use. The combination of ECG features and clinicoradiological parameters can be deployed to achieve higher accuracy in ischemia detection. A large-scale mixed database of multicenter datasets in different populations can be built to further verify our conclusions and improve the accuracy among different populations.
CONCLUSION
The ECG + VCG model can outperform the ECG-only and VCGonly models in identifying myocardial ischemia using only three features (S I , THI, and SHI) extracted from VCGs' and ECGs' ST-T segments, providing a potential tool for non-invasive detection of myocardial ischemia.
DATA AVAILABILITY STATEMENT
The raw data supporting the conclusion of this article will be made available by the authors without undue reservation.
AUTHOR CONTRIBUTIONS
XZ and JZ contributed to the algorithm and the statistical analysis. SW, GC, HW, and YW contributed to the clinical data interpretation. YG, JM, and LX contributed to the funding acquisition, conception, and design of the study. XZ, HL, and LX contributed to the algorithmic optimization and the original manuscript. All authors contributed to the writing, critical reading, and approval of the manuscript. | 8,752.8 | 2022-05-30T00:00:00.000 | [
"Medicine",
"Computer Science"
] |
The dynamics of online activities and its Impact on well-being in urban China
Using data from the China Family Panel Studies, this study examines the socioeconomic characteristics of Internet users, as well as the relationships between the dynamics of different forms of online activities and the subjective well-being of urbanites and rural migrants in urban China. The study finds that online behaviour may clearly reflect differences in individuals’ personal traits and socioeconomic positions. Patterns of the association between online activities and subjective well-being tend to differ among rural migrants and urbanites, especially in terms of depression. A difference-in-differences model is employed to estimate the impact of intensified engagement in online activities on depression and life satisfaction from 2010 to 2016. The results show that increased frequency of online entertainment exhibits a comparatively positive effect on depression and life satisfaction. Spending more time on online social networking has a similar impact on rural migrants, but not on urbanites. These findings suggest that the rapid development of urban China’s online community has important implications for residents’ subjective well-being.
Introduction
China's current, unprecedented economic development is being powered by a huge influx of rural migrant workers.In the last few decades, nearly 300 million rural residents in China have left their land to work in cities across the country.Despite rural migrants' remarkable contribution to the Chinese economic miracle, their livelihood and reception in urban China have never been easy.China's unique household registration (i.e.hukou) system has created an inherent rural-urban division in Chinese cities, functioning as 'a barrier between heaven and earth' (Treiman, 2012).Scholars contend that rural migrants and established urbanites tend to live parallel lives mirrored in inequalities and discriminations against rural migrants from a wide range of perspectives (Li, Zhang, and Kong, 2015).Consequently, there is a growing body of literature investigating the impact of China's rapid urbanisation on Chinese people's subjective well-being (Davey and Rato, 2012;Easterlin et al., 2012;Jiang, Lu, and Sato, 2012;Cheng, Wang, and Smyth, 2013;Bian and Xiao, 2014).These studies have focused on a number of socioeconomic and demographic characteristics of subjective wellbeing.Existing findings suggest that rural migrants' urban experiences often appear to have a negative effect on their subjective well-being and mental health, as rural migrants are more likely than other urban residents to experience stress arising from social exclusion and lack of social support (Wong et al., 2008).
Owing to the development of information and communication technology (ICT) in the past decade, Internet users have become another fast-growing population in urban China.By the end of 2015, 50.3% of the Chinese population had become Internet users, as compared to 8.5% in 2005 (World Bank, 2017).Meanwhile, there are clear urban-rural disparities in terms of Internet access, with more than 70.0% of Internet users being urban residents.The ever-vibrant online society allows more research to explore how the Internet shapes personal and social life in urban China.Consequently, an extensive empirical literature has emerged on the association between Internet adoption and subjective well-being (Caplan, 2002;DiMaggio et al., 2004;Oh, Ozkaya, and LaRose, 2014;Lissitsa and Chachashvili-Bolotin, 2016).Notwithstanding mixed findings, the previous literature has pointed explicitly towards the observation that, in both developed and developing societies, Internet usage may have important social and psychological consequences.This gives rise to the question of how different forms of online activities affect individuals' subjective well-being in urban China, which presents a distinctive social structure underpinned by the hukou system.However, while subjective well-being in urban China is an urgent research topic, its relationship with the dynamics of Internet adoption remains underresearched.Against this background, the present study constructs an innovative analytical framework within which to discuss the nature and mechanisms of Internet influence on subjective well-being among urban Chinese residents.It aims to contribute to the existing research in three ways.Using data from the China Family Panel Studies, the study first examines the determinants of three types of online activities, including information acquisition, entertainment, and social networking, in urban China.Secondly, it compares differences between rural migrants and urbanites in Chinese cities in terms of the net effects of their online activities on their subjective well-being.Finally, to address design deficiencies in previous studies that have used cross-sectional data, the difference-in-differences approach is used to estimate how the dynamics of online activities may affect individuals' subjective well-being over time.
This paper is structured as follows.In the next section, we give a brief review of literature on the connection between subjective well-being and Internet penetration, paying particular attention to the context of urban China in the research paradigm.The third section gives an account of the data and methods to be used for the research, followed by the presentation of the analytical results.In its last two sections, the paper offers a discussion of the implications and conclusions, including a reflection on the limitations of the study.
The issue of well-being
Understanding people's perceptions of their own well-being has thus far been a challenge for both academics and policy makers.The assessing of well-being consists of an objective and a subjective dimension (Cummins, 1995).As far as subjective well-being is concerned, scholars have argued that it should be measured to reflect a comprehensive perception of people's lives from various aspects (Stiglitz, Sen, and Fitoussi, 2009).Social scientists and psychologists often use self-assessment tools to measure subjective well-being domains, including cognitive evaluations of one's life, happiness, life satisfaction, positive emotions such as joy and pride, and negative emotions such as pain and worry (Stiglitz, Sen, and Fitoussi, 2009;Blore et al., 2011;Hicks, 2011).Previous studies on China and in other cultural contexts have either used multiple indicators to assess subjective well-being or focused on one particular domain.In this paper, subjective well-being is identified as a multifaceted construct that includes both cognitive and affective evaluations of life.
In regard to the determinants of subjective well-being, scholars appear to agree on several points.First, a number of personal traits appear to have close connections with subjective well-being.Some researchers have reported a U-shaped association between age and subjective well-being: young and older people appear to display higher levels of subjective well-being than middle-aged people (Diener, 2000;Blanchflower and Oswald, 2008).In addition to age, gender and marital status have been shown to have significant effects on subjective well-being (Easterlin, 2003;Bonini, 2008;Lissitsa and Chachashvili-Bolotin, 2016).According to studies on this topic, women and married individuals tend to enjoy higher levels of life satisfaction than men and those who are single or widowed.Secondly, the association between socioeconomic factors and subjective well-being is not self-evident, as evidenced by the ambiguous findings in this terrain.A prominent example is the debate regarding the Easterlin Paradox in happiness economics.The work of Richard Easterlin and later research reveal that income's effect on well-being tends to vary across different contextual backgrounds, as it is a much more positive and potent factor in developing regions than developed regions (Easterlin, 1974;Diener and Diener, 1995).
Similarly, education has been reported as a positive correlate of well-being (Yip et al., 2007;Hicks, 2011), as well as a negative correlate (Rao, Tamta, and Kumari, 2014;Lissitsa and Chachashvili-Bolotin, 2016).Thirdly, many studies have linked social capital to a variety of outcomes of measures of well-being.The previous literature links most of the key ingredients of social capital, including trust, social participation, social support, and neighbourhood attachment, with higher levels of well-being at both individual and community levels (Helliwell, 2006;Lim and Putnam, 2010;Greenberg et al., 2016).The last factor to note is health, which is one of, if not the, single most consistent correlate of subjective well-being.Better health is shown to be associated with greater subjective well-being (Dolan, Peasgood, and White, 2008).By contrast, people experiencing illnesses or other health issues are significantly more likely to feel unhappy than are their healthy counterparts (Anderson, 2014).
The social implications of Internet adoption
It is almost a cliché that the Internet plays an increasingly significant role in human society.While a vibrant and globalised market of online shopping and social media has emerged, the growing computing and mobile phone industry has also allowed users easier and more frequent access to various online activities.Researchers have therefore devoted more efforts to exploring the social outcomes prompted by the explosive development of the Internet and ICTs, such as well-being and integration (McKenna and Bargh, 2000;Lissitsa and Chachashvili-Bolotin, 2016).
Nevertheless, patterns of the relationship between online activities and subjective well-being appear to be ambiguous as an empirical matter.On the one hand, some findings indicate that Internet adoption is associated with increased subjective well-being (McKenna and Bargh, 2000;DiMaggio et al., 2004;Elgar et al., 2011).A number of studies have revealed a positive association between online activities and perceived quality of life in Asian countries (Lee et al., 2008;Oh, Ozkaya, and LaRose, 2014;Lissitsa and Chachashvili-Bolotin, 2016).Moreover, scholars have attempted to explain the mechanisms through which Internet use may improve subjective well-being.One observation echoed among existing studies is that the Internet can meet various forms of users' human needs by promoting psychological empowerment, belongingness, learning experiences, and the like (Fowler, Gentry, and Reisenwitz, 2015).Similarly, the emergence of online communities has become a sort of social boundary that tends to separate the online 'us' and the offline 'them'.Online communities of both existing acquaintances and strangers tend to cultivate shared values and norms of reciprocal support, which can improve individuals' subjective well-being and are highly exclusive of non-Internet users (McKenna and Bargh, 2000;Stepanikova, Nie, and He, 2015).
On the other hand, there also exists evidence of a negative relationship between Internet adoption and subjective well-being.In particular, researchers have found that Internet use might have a negative impact on social capital and mental health, both of which are considered as pivotal determinants of subjective well-being.In his landmark studies of social capital in America, Robert Putnam (2000Putnam ( , 2015) ) argues that the decline of social connectedness in America results largely from the fact that traditional modes of social involvement have been impeded by the rise of TV, the Internet, and social media.Other researchers have expressed similar concerns, positing that online activities, not least in the form of social networking, tend to work against social connections and social participation in real-life situations and lead to decreased well-being (Valkenburg and Peter, 2007).Furthermore, excessive Internet use and cyber addiction appear to have a detrimental effect on psychological well-being.Many believe that individuals who spend large amounts of time on the Internet display a higher propensity to suffer from mental problems (O' Keeffe and Clark-Pearson, 2011;Cheng and Li, 2014).
The diversity of available online activities also bears a word of explanation.The everwidening range of choices of what one can do on the Internet raises the question of whether different forms of online activities may lead to distinct social and psychological consequences.While more research has been conducted to focus on specific dimensions of digital use, a few studies have assessed the impact of social networking sites on depression (O'Keeffe and Clark-Pearson, 2011).Effects such as enhancement of social competence, strengthening of self-determination, and satisfaction of other psychological needs are cited to explain the ways in which leisure and entertainment activities such as game-playing enhance quality of life (Ryan et al., 2006;Visser, Antheunis, and Schouten, 2013).Therefore, it is necessary to address the diversity issue when measuring Internet adoption, as patterns of the association between Internet adoption and subjective well-being may be distinct across various online activities.
Internet and subjective well-being in the times of Chinese urbanisation
With regard to the determinants of subjective well-being in China, scholars have shown that a number of personal traits and socioeconomic variables, such as age, gender, income, health, social capital, and economic development, are important correlates of cognitive and affective well-being (Easterlin et al., 2012;Bian and Xiao, 2014).The issue of the well-being of rural migrants in China's rapid urbanisation process has gained more attention in the last decade, although findings to date have been somewhat inconclusive (Knight and Gunatilaka, 2010;Nielsen, Paritski, and Smyth, 2010;Nielsen, Smyth, and Zhai, 2010;Jiang, Lu, and Sato, 2011;Cheng, Wang, and Smyth, 2013).As migration experiences are often subject to such problems as unequal policy treatment, long working hours, and public health issues, some argue that rural migrants tend to report lower levels of subjective well-being compared to urban migrants and urban locals (Knight and Gunatilaka, 2010;Easterlin et al., 2012).Hukou-related inequalities and disadvantages in particular tend to erode the happiness of migrants (Jiang, Lu, and Sato, 2011).By contrast, Nielsen and his colleagues' research in Beijing and in the province of Fujian suggests that the circular nature of rural migration, whereby peasant workers who find themselves unable to settle in cities have the option to return home, buffers the pressure and hardships that migrants bear (Nielsen, Paritski, and Smyth, 2010;Nielsen, Smyth, and Zhai, 2010;Davey and Sato, 2012).It is also noteworthy that conditions in the city are often perceived by migrants to be better than in rural areas (Davey and Sato, 2012).Pull factors for migration, such as higher incomes and better job opportunities, may encourage migrants to hold positive attitudes towards their futures in cities.
Despite a burgeoning body of literature on subjective well-being in China, only a very small subset of it has examined the role of Internet.A new study based on the 2010 China Family Panel Survey finds that intensive Internet penetration is negatively associated with happiness and affective well-being and that individuals' subjective perceptions of different forms of online activities have a significant effect on their self-assessments of well-being (Nie, Sousa-Poza, and Nimrod, 2017).Similar observations can be found in clinical researches in China, which have contributed to the previous literature by focusing on the ways in which Internet adoption shapes subjective well-being among adolescents.Accordingly, problematic and addictive Internet use is associated with increased depression and decreased life satisfaction among Chinese adolescents (Lam and Peng, 2010;Wu et al., 2013).Meanwhile, other studies suggest that appropriate Internet use may improve subjective well-being (Wang and Wang, 2011;Lee et al., 2012;Li, Shi, and Dang, 2014).The central argument of these studies is that online communications can satisfy individuals' psychological needs, which consequently increases people's perceived quality of life.Despite these findings, little is known about the ways in which Internet adoption affects the subjective well-being of the millions of rural migrants in urban China.Wei and Gao (2017) have suggested that social media use may contribute to migrants' subjective well-being.Using data collected from online surveys in popular Chinese social media sites, their analysis shows that online activities embedded in social media may help migrants to establish local social networks both on the Internet and in the real world.The information and contacts produced in social media communities on the Internet therefore tend to positively influence migrants' life satisfaction and affective balance (Wei and Gao, 2017).
Research questions
The foregoing discussion suggests that the Internet has an increasingly significant impact on subjective well-being in urban China.This study, therefore, offers a comprehensive analysis of the connections between online activities and subjective wellbeing in urban China.Specifically, it focuses on two important issues that the previous literature has failed to address: first, existing findings have not explained how the interplay of different forms of online activities and hukou status affects subjective well-being in China.They either reflect the effect of a particular type of Internet use (e.g.Wei and Gao, 2017) or neglect the rural-urban divide in urban China (e.g. Lee et al., 2008).Second, and perhaps more importantly, most previous work in this field has been based on cross-sectional data, which does not allow researchers to explore the potential impact of the dynamics of online
Data
The analyses in this paper are based on data from the China Family Panel Survey (CFPS), collected by the Institute of Social Science Survey at Peking University.CFPS currently consists of four waves (2010, 2012, 2014, and 2016).Covering 25 provinces, municipalities, and autonomy regions, it is one of the largest national representative panels in China.The 2010 baseline survey includes 33,600 individual respondents from 14,798 households.Because Internet use questions have only been asked in the 2010 and 2016 waves, the other two waves are not used in the empirical analysis.To distinguish between urban and rural residents, the CFPS follows the China Census Bureau's definition and identifies urban and rural subsamples in the data.The study population in this paper is restricted to the 9,979 adults in the urban subsample whose information on Internet use has been collected.Finally, data collectors of the CFPS provide cross-sectional weights for selection biases, which are used in all analyses reported in this paper.
Independent variables
A number of personal traits and socioeconomic controls are used in the multivariate analysis, including age, gender, marital status, hukou status, education, income, health, and social capital.Respondents' ages are coded into a categorical variable indicative of four age groups ("19 to 30", "31 to 45", "46 to 60", and "61 or above").Marital status includes three categories, namely "married or cohabiting", "divorced or widowed", and "never married".The education variable is measured on a scale of 1 to 5 (1 = "illiterate or semi-literate"; 2 = "elementary"; 3 = "junior high"; 4 = "senior high"; 5 = "college or above").Income is measured by logged annual household income.Respondents are asked to give a selfassessment of their own health conditions on a scale from 1 ("very bad") to 5 ("very good").Social capital is measured by the norm of trust, which is considered as an essential ingredient of social capital (Putnam, 2000).Three trust variables, indicative of trust in parents, neighbours and strangers, respectively, tap into the radius of trust among the respondents.Each of the three variables follows a scale of 0 to 10, with 10 indicating the highest level of trust.
To assess the rural-urban divide in urban China, a binary variable reflecting respondents' hukou status is created.Those urban residents who have rural hukou are classified as rural migrants whereas all other respondents, including urban locals and urbanto-urban migrants, are classified as urbanites.
Online activities
Online activities are classified into three types according to individuals' purposes when accessing the Internet.The first type is called "information acquisition".Individuals who are involved in information acquisition are those who access the Internet for study, work, and business purposes and/or those who look for information on professional websites or search engines.The second type is called "entertainment", which describes the purposes of respondents who access the Internet to, for example, visit gaming websites.Lastly, respondents who are involved in "social networking" access the Internet mainly for the purpose of social interaction, including visiting blogs and social media sites such as the BBS, Renren, Facebook and the like.The frequencies of these online activities are classified using a four-point Likert scale (1 = "never"; 2 = "less than weekly"; 3 = "weekly"; 4 = "daily").
Subjective well-being
Measures for subjective well-being in this study include self-reported levels of depression and life satisfaction, which reflect the affective dimension and the cognitive dimension of well-being, respectively.Depression is measured on a scale of 1 ("never feel depressed") to 5 ("feel depressed almost every day").The CFPS also asks its respondents: "How satisfied are you with your life?" Responses to this question are coded on a five-point scale of 1 ("very unsatisfied") to 5 ("very satisfied").
Table 1 summarizes the mean scores of depression and life satisfaction in 2010 and 2016 organized according to respondents' hukou statuses.Descriptive statistics show that the overall depression level of urban residents in China increased from 2010 to 2016.
Interestingly, this group of respondents became more satisfied with their lives during the same period.As compared to urbanites, rural migrants display a higher propensity to feel depressed whereas they also appear to have a higher level of life satisfaction.
Multivariate analysis
The multivariate analysis in this paper encompasses three parts in order to answer the three research questions.All three analyses were conducted using Stata 14.Because the measures of online activities are ordinal, ordered logistic regression estimations are adopted to examine the determinants of intensity of Internet use.Next, to examine the effects of the three forms of online activities on the two domains of subjective well-being among rural migrants and urbanites, two ordered logistic regression models were fitted with depression and life satisfaction as dependent variables.
Finally, a difference-in-differences (DID) approach is used to predict how the dynamics of different online activities affected individuals' subjective well-being from 2010 to 2016.Evolved from the propensity score matching approach, DID is particularly useful in studying the differential effect of a specific intervention during two or more time periods on a "treatment group" relative to a "control group" which undergoes no intervention (Card and Krueger, 1994).Accordingly, urban residents in the CFPS who reported greater intensity of Internet use in 2016 as compared to 2010 are identified as the treatment group, as they constitute the group of interest on which the effects are being analysed.Others whose frequencies of use either decreased or remained constant during the same time frame are treated as the control group.The design of the analysis can be summarized as follows: At the outset, two continuous variables were calculated as the differences between the 2016 and the 2010 self-reported depression/life satisfaction levels.Then, a regression-based DID model was developed to compare the incremental effects of increased intensity of Internet use on subjective well-being on both the treatment and control groups.The model, which is fitted with kernel matching, consists of three subsets (i.e.information acquisition, entertaining, and social networking), controlling for other confounders, and is applied to rural migrants and urbanites, respectively.The kernel matching method is rigorous in that it matches of each of the observations in the intervened group with all observations in the control group; in addition, the propensity scores of the control group are weighted by their "distance" from a specific propensity score in the treated group.As such, the DID model is arguably an improvement over one-period models in that it allows us to examine how changes in online behaviour affect subjective well-being.
Sociocultural determinants of internet activities
RQ1 asks about the effects of socioeconomic factors, especially hukou, on online activities in China.Table 2 shows ordinal regression coefficients where frequency of engagement in each form of online activity in 2016 is the outcome variable.Apart from hukou, the other control variables are age group, gender, marital status, education, income, health, and three indicators of trust.In all three models, we also control for the prior frequency of online activity (from the 2010 data).
Table 2 shows that, when other variables are controlled, urbanites appear to be significantly more active than rural migrants in all three forms of online activity.This gap is not unexpected given that, as compared to urbanites, rural migrants more often lack the economic resources to purchase computers, mobile phones, or other devices that allow them to access the Internet.
Looking at other factors, we find that age is negatively correlated with frequency of online activity.Single respondents tend to spend more time on the Internet than other people.Education and household income are both associated with more frequent online activity.In terms of effect size, the coefficients of education and income are more significant in the models for information acquisition (Model 1) and social networking (Model 3).While the effects of health are significant across the three models, the three trust indicators exhibit some differing effects.Moreover, trust is in general negatively correlated with frequency of online activities.The effects of trusting in strangers are particularly significant in all three subsets of online activity.These results suggest that individuals who are less trusting are more likely to spend more time on the Internet.
The association between Internet activities and well-being
To compare the association between online activities and subjective well-being among urbanites and rural migrants (RQ2), two ordinal logistic regression models are fitted with self-reported levels of depression and life satisfaction as the dependent variables.As shown in Table 3, each model consists of two subsets, analysing urbanites and rural migrants, respectively.The three forms of online activities as explanatory variables and the variables in Table 2 are simultaneously included as control variables.
First, in the model for depression, we find that frequent online information acquisition is negatively associated with depression for rural migrants, whereas its impact is weak among urbanites.Urbanites who are involved in online entertainment tend to have much lower levels of depression than their counterparts who are inactive online.By contrast, the coefficients for online entertainment show no statistical significance among rural migrants.Rural migrants reporting weekly or daily engagement in online social networking, however, exhibit a considerably lower level of depression than the reference group.Turning to the results for life satisfaction, we find that online entertainment is associated with higher life satisfaction for both urbanites and rural migrants.While online social networking is positively related to life satisfaction level among rural migrants, its impact is relatively weak among urbanites.
Overall, the three forms of online activities have a positive effect on both cognitive and affective well-being in China.However, the key point highlighted in Table 3 is that the patterns of the effects of online activities are largely different between the two sub-groups; this is discernible particularly in the analysis of depression.
Exploring changes in the intensity of online activity
The attention devoted to the dynamics of online activities motivates a closer examination of how changes in online activities may affect individuals' subjective well-being (RQ3).To capture such changes, we compare individuals' frequencies of use of each of the three forms of online activities according to the 2010 and the 2016 CFPS data.Given that the variable uses a four-point Likert scale, the differences between an individual's 2010 and 2016 frequencies are classified using the following strategy: If there is no difference between the individual's 2010 and 2016 frequencies, his/her Internet use is termed 'unchanged'; if there is a difference of one point, he/she is considered to have had 'similar' frequencies of use in 2016 and 2010; if the frequency increased by two or three points in 2016, the individual is classified as showing increased engagement in Internet use; if the frequency decreased by two or three points in 2016, the individual is classified as showing decreased engagement in Internet use.The abovementioned classifications are illustrated in Table 4. Table 5 shows changes in participants' frequencies of online activities between 2010 and 2016.The descriptive results indicate an overall increased frequency of online activities from 2010 to 2016.In all three forms of online activities, observably larger numbers of respondents became more active than less active.The highest rates of increased engagement in online activities can be found in online social networking: 18.3% of urbanites and 15.6% of rural migrants were involved in online social networking more frequently in 2016 than in 2010.Of the three types of online engagement, information acquisition has the lowest rates of increased engagement as well as the highest rates of decreased engagement.Moreover, the rates of increased engagement were higher among urbanites than rural migrants.Overall, however, the results exhibited in Table 5 reveal a more vibrant online society in urban China.The Internet has clearly been playing an increasingly important role in the lives of both urbanites and rural migrants.
How spending more time on the Internet affects subjective well-being
Finally, a difference-in-differences approach was employed to estimate the effect of increased frequency of different forms of online activities on individuals' subjective wellbeing over time.In each subset, Group B consisted of respondents who reported increased engagement in a specific online activity from 2010 to 2016, while Group A included all other respondents (see also results in Table 5).The model assumed the dataset mid-point as the intervention date.Using kernel matching, the regression-based DID model reports how much the differences in subjective well-being between Groups A and B have been shaped by the dynamics of online activities.To address potential sources of bias, we included five covariates in the multivariate analysis, namely age, gender, education, income, and health.The tests of the balancing property of the propensity scores indicate satisfying results in the analyses for both urbanites and rural migrants.The model results are summarized in Tables 6 and 7.Each table first reports the mean scores of depression and life satisfaction of the two groups and then displays the results from the DID model.The study population of the analysis is 5,418.
Looking first at the results for urbanites in Table 6, we find in the descriptive statistics that there is an increase in levels of both depression and life satisfaction in groups A and B. In the subset for online entertainment, the increase in individuals' depression level is much lower in the Group B than in Group A (-0.099, p=.002), while results for life satisfaction (0.091, p=0.011) move in the opposite direction.The remarkable margins in the differences between the two groups in 2010 and 2016 suggest that increased intensity in online entertainment is associated with great subjective well-being in both cognitive and affective terms.It is worth mentioning that increased engagement in online information acquisition tends to have more of a negative impact on depression and life satisfaction among members of Group B, although this impact is not statistically significant.Table 7 shows the results for rural migrants.Similar to the results displayed in Table 6, the mean scores for depression and life satisfaction also slightly increased in the 2016 CFPS data.The first point to note in Table 7 is that increased engagement in online social networking presents significant effects in the analysis: in contrast to Group A, the increase in depression is much lower (-0.086,p=0.008) in Group B, whereas the increase in life satisfaction is discernibly higher in Group B (0.052, p=0.036).This suggests that increased frequency of online social networking has a more positive impact on the subjective wellbeing of rural migrants than it does on urbanites in the Chinese city.Furthermore, intensified online entertainment is found to contribute to an increased gap in subjective well-being between Group A and Group B, although the magnitude of the effect is greater in the case of life satisfaction (0.077, p=0.027) than depression (-0.067, p=0.078).In addition, the increase in depression in Group B appears to exceed that of Group A in the models for information acquisition, suggesting that online information acquisition has a negative impact on subjective well-being over time.
Discussion
This study investigates the socioeconomic characteristics of Internet adoption and the association between different forms of online activities and subjective well-being among urban Chinese dwellers.Specifically, a difference-in-differences model was fitted with data from the Chinese Family Panel Studies to examine how the burgeoning online society in urban China affects depression and life satisfaction among urbanites and rural migrants.As far as we know, this is the first study to use panel data to examine trends in the impact of Internet adoption on both urbanites and rural migrants over time.
Our findings show that the patterns of the online activities considered tend to reflect differences in personal traits and social standing.There is a clear rural-urban distinction in terms of the degree of Internet penetration among urban residents in China, with urban hukou holders shown to be more regularly engaged in online activities than rural hukou holders.
Overall, users of online information acquisition, entertainment, and social networking appear to have similar socioeconomic characteristics.As we expected, younger people and single respondents are more active users of the Internet.Education, income, and health are also positively associated with frequency of online activities.Another salient finding is that trust levels, especially trust in strangers, have negative effects on respondents' online behaviours.This finding coincides with some existing studies that suggest a negative correlation between Internet penetration and real-life relationships (Nie and Erbring, 2000;Putnam, 2000).We thus speculate that distrust and lack of social capital may serve as mechanisms that motivate individuals to spend more time on the Internet; doing so, in turn, further reduces individuals' real-life social networks.
Results in the ordinal logistic regression model based on cross-sectional data reveal an overall positive association between frequency of Internet usage and subjective well-being in urban China, which echoes findings in the previous literature (Wang and Wang, 2011;Lee et al., 2012;Li, Shi, and Dang, 2014).However, the key point is that the patterns of such associations appear to differ between urbanites and rural migrants.For example, while some recent findings suggest that online social networking is positively related to subjective wellbeing among Chinese citizens (Oh, Ozkaya, and LaRose, 2014;Stepanikova, Nie, and He, 2015;Nie, Sousa-Poza, and Nimrod, 2017); our finding indicates that this effect is considerably greater among rural migrants than urbanites.We find similar patterns in our analysis for depression: online entertainment is associated with lower levels of depression among urbanites but displays limited effects among rural migrants; the effects of online information acquisition, however, take the opposite form.These findings, mirroring the imprints of the hukou system, make it feasible to distinguish the divergent effects of Internet adoption in urban China.They suggest that the relationship between online activities and subjective well-being is subject to the unique social structure of urban China, which has segmented residents into two distinctive groups.
The descriptive results in the analysis do reveal that a more vibrant Internet community has emerged in urban China.From 2010 to 2016, both rural migrants and urbanites have become more engaged in all three forms of online activities under consideration, as rates of intensified online activities have clearly exceeded rates of decreased engagement.Consequently, a difference-in-differences regression model was used to assess how the dynamics of online activities affect cognitive and affective well-being in urban China.
The results of the DID model reveal that different forms of online activities have distinct effects on individuals' subjective well-being over time.In contrast to findings derived from cross-sectional data, our results show that increased engagement in online information acquisition appears to have a negative impact on residents' subjective well-being in urban China, although the magnitude of this impact is relatively small.While results from some longitudinal studies in Western societies indicate that seeking information is positively related to well-being (Freese et al., 2006;Lissitsa and Chachashvili-Bolotin, 2016), our study shows a different pattern in the context of urban China.On the contrary, the effects of intensified online engagement in the other two forms of online activities are more positive.Increased use of online entertainment is shown to improve results in the subjective well-being of both urbanites and rural migrants.Previous studies have found that online entertainment may foster positive feelings and satisfy users' psychological needs (Ryan et al., 2006;Li, Shi, and Dang, 2014).It is thus plausible that it plays a similar role in the context of urban China, where people, particularly migrants, often face various sorts of pressure (Wu andTreiman, 2004;Treiman, 2012;Zhang, 2014).Similarly, increased usage of online social networking is found to have a strongly positive impact on rural migrants' subjective well-being, whereas it has only a limited impact on urbanites.
Another important finding concerns identity-related differences in the results for online entertainment and social networking.We find that increased engagement with online entertainment has a more positive impact on depression among urbanites than among rural migrants.A more notable difference can be discerned in the model showing the association between increased usage of online social networking and greater subjective well-being among rural migrants.However, this pattern is not found among urbanites.Many have argued that rural migrants in Chinese cities often lack local social networks and social support (Wu and Treiman, 2004;Wu et al., 2013).In this context, the online community tends to serve as an incubator that fosters and maintains social interactions for rural migrants in their host cities.Moreover, as online social interactions are likely to lower the physical and mental costs of social involvement, they may enhance rural migrants' sense of belonging and satisfy their psychological needs (Mobrand, 2006;Nie, Sousa-Poza, and Nimrod, 2017;Wei and Gao, 2017).The distinction between urbanites and rural migrants provides new findings about the ways in which the imprints of the hukou system shape patterns of online activities and about the impact of those activities on subjective well-being in urban China.
Conclusion
This study yields a number of important findings.In urban China, hukou identity and socioeconomic position appear to be strongly associated with individuals' online behaviour.Although rural migrants are less active Internet uses than urbanites, both groups tended to spend more time online in 2016 than in 2010.Results from our cross-sectional analysis show that the frequencies of online information acquisition, entertainment, and social networking are in general positively associated with cognitive and affective well-being, though the patterns of such associations differ among rural migrants and urbanites.Using a differencein-differences approach, our analysis shows that increased engagement in online entertainment exhibits a significantly positive effect on subjective well-being.Spending more time on online social networking tends to improve rural migrants' subjective well-being, while it displays no significant effect on urbanites.There is a negative and modest association between increased engagement in online information acquisition and subjective well-being in Chinese cities.
The current study has several implications.Methodologically, the difference-indifferences approach aids in the interpretation of previous findings based on cross-sectional data, which are unable to establish any causal relationships among variables.There is currently a paucity of research using panel data in this terrain.Therefore, future studies may advance the understanding of the association between well-being and Internet adoption by taking advantage of the growing body of longitudinal social surveys such as CFPS in China.Empirically, the analyses in this paper demonstrate an observable connection between the dynamics of urban Chinese residents' online activities and those individuals' subjective wellbeing over time.While scholars have been calling for closer examination of determinants of subjective well-being in China (Davey and Rato, 2012;Easterlin et al., 2012;Jiang, Lu and Sato, 2012), we would argue that the Internet is becoming increasingly significant in shaping the subjective well-being of Chinese people.It is thus important for academics and policy makers to understand the long-term effects of urban China's unpreceded digital movement and the varied influences that the outcomes are having on residents' subjective well-being.Meanwhile, our study provides strong evidence for the presence of identity-related disparities in online behaviours and subjective well-being in urban China.For a society with the inherent social segmentation that is embedded in the hukou system, the Internet community may serve as a lubricant for the social integration of rural migrants, who are most sensitive to hukourelated inequalities and segregation.
Limitations
We are aware that the present study has several limitations.First, notwithstanding its implications discussed above, the results of the DID model should be interpreted conservatively.The main limitation concerns the use of self-reported frequency of online activities, as the treatment variable may affect our conclusions.Such frequency might have changed more than once between the two waves, although we have attempted to reduce this possibility by restricting Group B to those who moved more than two points on the relevant Likert scale.Another limitation arises from the fact that our analyses did not account for certain important factors.In particular, the previous literature has pointed to the significant generational and regional differences in well-being among urban Chinese residents (Cheng, Wang, and Smyth, 2013;Bian and Xiao, 2014).However, we were unable to control these variables due to a limited sample size.
Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 25 May 2018 doi:10.20944/preprints201805.0358.v1
Peer-reviewed version available at Soc.Sci.2018, 7, 101; doi:10.3390/socsci7070101activitieson well-being across different time periods.Indeed, the ways in which changes in intensity of Internet use are associated with people's subjective well-being have rarely been explored in the Chinese context.To fill the research gaps mentioned above, this paper aims to answer the following research questions:
Table 1 .
Mean scores of depression and life satisfaction, by sample wave and hukou status
Table 2 .
Ordinal logistic regression coefficients on frequency of Internet activities
Table 3 .
Ordinal logistic regression coefficients on emotional and cognitive well-being
Table 4 .
Changes in frequency of online activities between 2010 and 2016
Table 5 .
Changes in frequency of online activities between 2010 and 2016 Downward Upward Other Downward % Upward %
Table 6 .
Comparison of mean scores of depression and life satisfaction and adjusted difference-in-difference estimates of the impact of online activities on subjective well-being among urbanites, 2010-2016
Table 7 .
Comparison of mean scores of depression and life satisfaction and adjusted difference-in-difference estimates of the impact of online activities on subjective well-being among rural migrants, 2010-2016 | 9,203.6 | 2018-06-25T00:00:00.000 | [
"Economics"
] |
Chloro-Substituted Naphthyridine Derivative and Its Conjugate with Thiazole Orange for Highly Selective Fluorescence Sensing of an Orphan Cytosine in the AP Site-Containing Duplexes
: Fluorescent probes with the binding selectivity to specific structures in DNAs or RNAs have gained much attention as useful tools for the study of nucleic acid functions. Here, chloro-substituted 2-amino-5,7-dimethyl-1,8-naphthyridine (ClNaph) was developed as a strong and highly selective binder for target orphan cytosine opposite an abasic (AP) site in the DNA duplexes. ClNaph was then conjugated with thiazole orange (TO) via an alkyl spacer (ClNaph–TO) to design a light-up probe for the detection of cytosine-related mutations in target DNA. In addition, we found the useful binding and fluorescence signaling of the ClNaph–TO conjugate to target C in AP site-containing DNA / RNA hybrid duplexes with a view toward sequence analysis of microRNAs. ClNaph–TO conjugate (500 nM) in the absence and presence of target AP–DNA duplexes (500 nM) under excitation light with the wavelength of 365 nm, obtained by a digital camera at room temperature. Other solution conditions are the same as those given in Figure Our probe whose sequence is designed so as to be complementary to the target sequence. Figure shows the fluorescence response of the conjugate in combination with the 22-meric AP–DNA probe for let-7i. Selective light-up detection for let-7i was achieved due to the selective binding of the conjugate to target C in the AP–DNA / RNA hybrid formed between the AP–DNA probe and let-7i. These results show the applicability of the ClNaph–TO conjugate for the selective detection of target microRNA sequences based on the hybridization for the construction of the AP–DNA / RNA hybrid as well as the binding-induced light-up response of the conjugate for the orphan C in the resulting hybrid. Our assay can be applied to the analysis of various microRNAs by using the AP site-containing DNA probe whose sequence is designed so as to be complementary to the target sequence. Figure 5B shows the fluorescence response of the conjugate in combination with the 22-meric AP – DNA probe for let-7i. Selective light-up detection for let-7i was achieved due to the selective binding of the conjugate to target C in the AP – DNA/RNA hybrid formed between the AP – DNA probe and let-7i. These results show the applicability of the ClNaph – TO conjugate for the selective detection of target microRNA sequences based on the hybridization for the construction of the AP – DNA/RNA hybrid as well as the binding-induced light-up response of the conjugate for the orphan C in the resulting hybrid.
Introduction
Much attention has been paid to the design of fluorescent probes capable of selective binding to specific structures in DNAs and RNAs [1,2]. This class of fluorescent probes has been designed to bind abasic (apyrimidinic or apurinic; AP) sites [3][4][5][6][7][8], bulges [9,10], mismatched sites [11,12] and overhanging structures [13][14][15], by which the biological functions of these noncanonical base-pairs have been examined. Moreover, these fluorescent probes have great potential to be applied for the analysis of target DNAs and RNAs based on their binding-induced fluorescence signaling. These probes also serve as the affinity-labeling agents in the label-free assays for detecting various analytes [16][17][18].
We developed AP site-binding ligands (APLs) that are conjugated with thiazole orange (TO) for the fluorescence sensing of orphan nucleobases in DNA/DNA duplexes ( Figure 1A) [19,20]. APLs can form the pseudo-base pairing with target orphan nucleobases, which allows the selective binding to the target nucleobase opposite the AP site [3][4][5][6][7]. On the other hand, TO unit connected with the APL unit through an appropriate linker can function as a fluorescent intercalator [21,22]. The TO unit alone shows negligible fluorescence, but its fluorescence is greatly enhanced upon intercalation into the base pairs near the AP site. APL-TO conjugates thus enable the light-up sensing of target orphan nucleobase in the AP site-containing DNA (AP-DNA) duplexes. Such light-up probes are useful for a more sensitive analysis compared to fluorescence quenching probes. We succeeded in the detection of single base mutation in target DNA sequences based on the binding and light-up functions of APL-TO conjugates in combination with an AP-DNA probe (cf. Figure 1A). In addition, these conjugates were applicable to the sequence-selective analysis of microRNAs, a class of small amino-5,6,7-trimethyl-1,8-naphthyridine (ATMND, Figure 1B) was previously used as an APL unit in the conjugate with TO unit for the light-up sensing of target orphan C in the AP-DNA and AP-DNA/RNA hybrid duplexes [19]. The binding selectivity of ATMND toward target C can be rationalized by the complementary base pairing of the N1-protonated form of ATMND with target C through hydrogen bonding ( Figure 1B) [3]. However, ATMND inherently has only moderate selectivity for C over T because of the possible protonation at N8 that allows the recognition of T ( Figure 1B). This should limit the application of the conjugate for the sequence analysis of target DNAs and microRNAs such as the discrimination of C against T or U.
This work describes the enhanced binding selectivity of a 2-amino-1,8-naphthyridine derivative for orphan C by the incorporation of a chloro group. We previously found that the introduction of the electron-withdrawing trifluoromethyl group into 2-amino-7-methyl-1,8-naphthrydine (AMND) led to remarkably enhanced C/T selectivity due to more favorable protonation at N1 compared to N8 [24]. However, the obtained CF3-AMND ( Figure 1B) showed much weaker affinity compared to ATMND. Herein, 2-amino-5,7-dimethyl-1,8-naphthyridine (ADMND), an AMND derivative with an additional methyl group, was explored as the scaffold for the introduction of an electronwithdrawing group considering the fact that ADMND can bind more strongly to target C than AMND [3]. The resulting compound carrying the chloro group at position 6 in the naphthyridine ring (ClNaph) was found to exhibit the strong binding affinity as well as the high selectivity for target C. The use of ClNaph as an APL unit in the conjugate with TO was shown to be useful for the design of a light-up probe toward target C over other nucleobases in the AP-DNA duplexes and AP-DNA/RNA hybrids with a view toward the detection of C-related mutations in DNA and microRNA sequences. in combination with an AP site-containing probe for hybridization; (B) Chemical structures of chlorosubstituted 2-amino-5,7-dimethyl-1,8-naphthyridine (ClNaph) and its related derivatives. Proposed binding of these ligands with cytosine and thymine (two possible patterns) are also shown.
Materials
All of the DNAs and RNAs were purchased from Nihon Gene Research Laboratories, Inc. (Sendai, Japan) and Sigma-Genosys (Hokkaido, Japan), respectively. The other reagents were commercially available and used without further purification. The concentration of DNAs and RNAs were determined from the molar extinction coefficient at 260 nm (ε260) according to the literature [25]. Water was deionized (≥18.0 MΩ cm specific resistance) by an Elix 5 UV water purification system and a Milli-Q synthesis A10 system (Millipore Corp., Bedford, MA, USA). The other reagents were This work describes the enhanced binding selectivity of a 2-amino-1,8-naphthyridine derivative for orphan C by the incorporation of a chloro group. We previously found that the introduction of the electron-withdrawing trifluoromethyl group into 2-amino-7-methyl-1,8-naphthrydine (AMND) led to remarkably enhanced C/T selectivity due to more favorable protonation at N1 compared to N8 [24]. However, the obtained CF 3 -AMND ( Figure 1B) showed much weaker affinity compared to ATMND. Herein, 2-amino-5,7-dimethyl-1,8-naphthyridine (ADMND), an AMND derivative with an additional methyl group, was explored as the scaffold for the introduction of an electron-withdrawing group considering the fact that ADMND can bind more strongly to target C than AMND [3]. The resulting compound carrying the chloro group at position 6 in the naphthyridine ring (ClNaph) was found to exhibit the strong binding affinity as well as the high selectivity for target C. The use of ClNaph as an APL unit in the conjugate with TO was shown to be useful for the design of a light-up probe toward target C over other nucleobases in the AP-DNA duplexes and AP-DNA/RNA hybrids with a view toward the detection of C-related mutations in DNA and microRNA sequences.
Materials
All of the DNAs and RNAs were purchased from Nihon Gene Research Laboratories, Inc. (Sendai, Japan) and Sigma-Genosys (Hokkaido, Japan), respectively. The other reagents were commercially available and used without further purification. The concentration of DNAs and RNAs were determined from the molar extinction coefficient at 260 nm (ε 260 ) according to the literature [25]. Water was deionized (≥18.0 MΩ cm specific resistance) by an Elix 5 UV water purification system and a Milli-Q synthesis A10 system (Millipore Corp., Bedford, MA, USA). The other reagents were purchased from standard suppliers and used without further purification. 1 H NMR spectra were measured with a JEOL ECA-600 spectrometer at 500 MHz. High-resolution ESI-MS spectra were measured with a Bruker APEX III mass spectrometer.
Unless otherwise mentioned, all measurements were performed in 10-mM sodium cacodylate buffer solutions (pH 7.0) containing 100-mM NaCl, 1.0-mM EDTA and ethanol (<2%). Before the measurements, target duplex-containing samples were annealed as follows: heated at 75 • C for 10 min and gradually cooled to 5 • C (3 • C/min), after which the solution temperature was raised again to 20 • C. The probe was then added to the samples.
Fluorescent Measurements
Fluorescence spectra were measured with a JASCO model FP-6500 spectrofluorophotometer equipped with a thermoelectrically temperature-controlled cell holder (Japan Spectroscopic Co., Ltd., Tokyo, Japan) using a 3 × 3 mm quartz cell.
The dissociation constant (K d ) of the probe was determined at 20 • C by fluorescent titration experiments. The changes in fluorescence intensity were analyzed by nonlinear least-squares regression based on a 1:1 binding isotherm [19]. Errors in the K d values are the standard deviations obtained from three independent experiments (N = 3).
Results and Discussion
First, we examined the binding ability of ClNaph (500 nM) to target orphan nucleobases in model 21-meric AP-DNA duplexes (500 nM; 5 -d(GCA GCT CCC AXA GTC TCC TCG)-3 /3 -d(CGT CGA GGG TNT CAG AGG AGC)-5 , X = AP site (Spacer C3, a propyl residue), N = target nucleobase; G, C, A or T) by the fluorescence measurements. As shown in Figure 2, ClNaph showed the emission with the maximum at 393 nm in the absence of DNAs. The addition of AP-DNA duplexes caused a decrease in the fluorescence intensity of ClNaph. The largest fluorescence quenching response was observed for target C, which indicates that ClNaph shows the preferential binding to target C compared to target G, A and T. The binding affinity of ClNaph was assessed by the fluorescence titration experiments (Inset of Figure 2). ClNaph showed the quenching response for target DNA duplexes in a concentration-dependent manner and the resulting titration curves were analyzed by a 1:1 binding model for the determination of the dissociation constants (K d ). The K d value for C was obtained as 70 ± 5.3 nM. Significantly, this affinity is much stronger compared to the parent ADMND and the previously developed CF 3 -AMND and is almost comparable to ATMND (Table 1). In addition, ClNaph showed useful binding selectivity toward target C, in which the K d value for target C was two orders of magnitude smaller than those for other target nucleobases (K d /nM: T, 2020 ± 240, G and A > 5000). The observed selectivity for C over T is much superior to ADMND and ATMND [3] whereas it is slightly moderate in comparison with CF 3 -AMND [24]. We reason that this is due to the more favorable protonation of ClNaph at the N1 position for the complementary base-pairing with orphan C compared to the N8 protonation ( Figure 1B), where the electron-withdrawing effect of the chloro group would be essential as was observed for CF 3 -AMND [24]. We note that the type of the AP site affects the binding of ClNaph. The use of Spacer C3 (propyl residue) allowed the stronger binding to target C compared to the tetrahydrofuranyl residue (dSpacer), presumably due to less steric hindrance ( Figure S3). The observed strong and highly selective binding properties for target C should render ClNaph a useful APL unit in the conjugate with TO unit.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 9 duplexes in a concentration-dependent manner and the resulting titration curves were analyzed by a 1:1 binding model for the determination of the dissociation constants (Kd). The Kd value for C was obtained as 70 ± 5.3 nM. Significantly, this affinity is much stronger compared to the parent ADMND and the previously developed CF3-AMND and is almost comparable to ATMND (Table 1). In addition, ClNaph showed useful binding selectivity toward target C, in which the Kd value for target C was two orders of magnitude smaller than those for other target nucleobases (Kd/nM: T, 2020 ± 240, G and A > 5000). The observed selectivity for C over T is much superior to ADMND and ATMND [3] whereas it is slightly moderate in comparison with CF3-AMND [24]. We reason that this is due to the more favorable protonation of ClNaph at the N1 position for the complementary base-pairing with orphan C compared to the N8 protonation ( Figure 1B), where the electron-withdrawing effect of the chloro group would be essential as was observed for CF3-AMND [24]. We note that the type of the AP site affects the binding of ClNaph. The use of Spacer C3 (propyl residue) allowed the stronger binding to target C compared to the tetrahydrofuranyl residue (dSpacer), presumably due to less steric hindrance ( Figure S3). The observed strong and highly selective binding properties for target C should render ClNaph a useful APL unit in the conjugate with TO unit. [3]. c Value taken from [24].
ClNaph was coupled with the quinolone ring of the TO unit through a long alkyl (C10)-linker according to our previous report [19], which affords the ClNaph-TO conjugate ( Figure 3A). We measured the fluorescence response of the TO unit of the conjugate (500 nM) for the same AP-DNA duplexes (500 nM) as those used for the examination of ClNaph (cf. Figure 2). As shown in Figure 3A, TO unit shows negligible emission in the absence of DNAs due to the free rotation of the benzothiazole and quinolone rings [21]. In contrast, we observed a remarkable light-up response of the TO unit for target C-containing AP-DNA duplex, in which the fluorescence intensity at 526 nm increased by 207-fold. This can be explained by the restriction of the rotation of the TO unit by intercalation into the duplex region (cf. Figure 1A) [19]. In addition, the fluorescence titration [3]. c Value taken from [24].
ClNaph was coupled with the quinolone ring of the TO unit through a long alkyl (C10)-linker according to our previous report [19], which affords the ClNaph-TO conjugate ( Figure 3A). We measured the fluorescence response of the TO unit of the conjugate (500 nM) for the same AP-DNA duplexes (500 nM) as those used for the examination of ClNaph (cf. Figure 2). As shown in Figure 3A, TO unit shows negligible emission in the absence of DNAs due to the free rotation of the benzothiazole and quinolone rings [21]. In contrast, we observed a remarkable light-up response of the TO unit for target C-containing AP-DNA duplex, in which the fluorescence intensity at 526 nm increased by 207-fold. This can be explained by the restriction of the rotation of the TO unit by intercalation into the duplex region (cf. Figure 1A) [19]. In addition, the fluorescence titration experiments revealed that the K d value of ClNaph-TO conjugate for target C reached 6.6 ± 0.3-nM ( Figure S4). This affinity is Appl. Sci. 2020, 10, 4133 5 of 9 one order of magnitude stronger than ClNaph itself (cf. Table 1). Apparently, the conjugation with the TO unit led to the enhanced binding affinity for target C in the AP-DNA duplexes. It should be noted that ClNaph-TO conjugate has high binding selectivity for target C over other three nucleobases ( Figure S4: K d values for T, G and A > 1500 nM). Considering that TO lacks the selectivity for the orphan nucleobases [19], the ClNaph unit is responsible for the observed C-selectivity of the conjugate. This was confirmed by the fluorescence quenching response of the ClNaph unit with high selectivity to target C ( Figure S5). These results showed the useful binding and light-up functions of the ClNaph-TO conjugate for the detection of C-related mutations in target DNA sequences. It is also noteworthy that the strong emission of ClNaph-TO conjugate for target C can be seen even with the naked eyes under UV light irradiation ( Figure 3B). Fluorescence response for target C is clearly distinguishable from those for other target nucleobases, which thus facilitates a simple and rapid analysis of target DNA sequences.
of the ClNaph unit with high selectivity to target C ( Figure S5). These results showed the useful binding and light-up functions of the ClNaph-TO conjugate for the detection of C-related mutations in target DNA sequences. It is also noteworthy that the strong emission of ClNaph-TO conjugate for target C can be seen even with the naked eyes under UV light irradiation ( Figure 3B). Fluorescence response for target C is clearly distinguishable from those for other target nucleobases, which thus facilitates a simple and rapid analysis of target DNA sequences.
We found that the kind of heterocycles of the TO unit, benzothiazole or quinolone rings, that connect to ClNaph unit in the conjugate affected the binding and fluorescence signaling abilities for the binding to AP-DNA duplexes. When the C10-linker was appended to the benzothiazole ring, the resulting conjugate (ClNaph-TO2) showed the selective light-up response for target C in the AP-DNA duplexes ( Figure S6); however, the degree of the response was smaller compared to ClNaph-TO (cf. Figure 3A). This is attributable to the reduced binding affinity of ClNaph-TO2 conjugate to target C (Kd = 71 nM). This indicates that the conjugation of ClNaph unit into the benzothiazole ring hinders the effective intercalation of the TO unit for DNA duplexes as reported in the literature [27]. In addition, we observed moderate selectivity of ClNaph-TO2 conjugate for target C over other three nucleobases in AP-DNA duplexes ( Figure S6) while the reason for this is unclear yet. Hence, the connection of ClNaph unit to the quinolone ring of the TO unit is effective for the strong binding and large light-up response of the conjugate for target C in the AP-DNA duplexes. We found that the kind of heterocycles of the TO unit, benzothiazole or quinolone rings, that connect to ClNaph unit in the conjugate affected the binding and fluorescence signaling abilities for the binding to AP-DNA duplexes. When the C10-linker was appended to the benzothiazole ring, the resulting conjugate (ClNaph-TO2) showed the selective light-up response for target C in the AP-DNA duplexes ( Figure S6); however, the degree of the response was smaller compared to ClNaph-TO (cf. Figure 3A). This is attributable to the reduced binding affinity of ClNaph-TO2 conjugate to target C Appl. Sci. 2020, 10, 4133 6 of 9 (K d = 71 nM). This indicates that the conjugation of ClNaph unit into the benzothiazole ring hinders the effective intercalation of the TO unit for DNA duplexes as reported in the literature [27]. In addition, we observed moderate selectivity of ClNaph-TO2 conjugate for target C over other three nucleobases in AP-DNA duplexes ( Figure S6) while the reason for this is unclear yet. Hence, the connection of ClNaph unit to the quinolone ring of the TO unit is effective for the strong binding and large light-up response of the conjugate for target C in the AP-DNA duplexes.
As described above, the ClNaph-TO conjugate can serve as a useful light-up probe for target C in the AP-DNA duplexes. Meanwhile, we noticed weak binding of the conjugate for AP-RNA duplexes ( Figure 4A and Figure S7). The binding affinity was estimated as > 1300-nM for target C in the AP-RNA duplex (5 -r(GCA GCU CCC AXA GUC UCC UCG)-3 /3 -r(CGU CGA GGG UCU CAG AGG AGC)-5 , X = AP site (Spacer C3), C = target nucleobase), which was three orders of magnitude larger than that for the AP-DNA duplex (cf. Figure S4). We consider that this arises from the preferential binding of the ClNaph-TO conjugate to B-formed AP-DNA duplexes relative to A-formed AP-RNA duplexes [6]. However, when targeting C in single stranded RNA, the use of AP-DNA probe is highly effective. The resulting duplex is the hybrid between RNA and AP-DNA ((5 -d(GCA GCT CCC AXA GTC TCC TCG)-3 /3 -r(CGU CGA GGG UCU CAG AGG AGC)-5 , X = AP site (Spacer C3), C = target nucleobase) that can adopt A-form/B-form intermediate structure [28], under the same measurement conditions used to examine AP-RNA duplexes. As shown in Figure 4B, we observed the significant light-up response of the conjugate for the AP-DNA/RNA hybrid, in which the response was 22-fold larger compared to that for the AP-RNA duplex. The K d for target C in the hybrid was obtained as 22 nM (Figure S7), where the affinity is much superior to that for AP-RNA duplexes. Importantly, the ClNaph-TO conjugate retains its selectivity for target C over U opposite the AP site in the DNA/RNA hybrid, as was observed in AP-DNA duplexes (cf. Figure 3B). These results suggest the potential use of ClNaph-TO conjugate for the detection of microRNAs in combination with AP-DNA hybridization probe (cf. Figure 1A).
Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 9 Other solution conditions are the same as those given in Figure 2.
As described above, the ClNaph-TO conjugate can serve as a useful light-up probe for target C in the AP-DNA duplexes. Meanwhile, we noticed weak binding of the conjugate for AP-RNA duplexes (Figures 4A and S7). The binding affinity was estimated as > 1300-nM for target C in the AP-RNA duplex (5′-r(GCA GCU CCC AXA GUC UCC UCG)-3′/3′-r(CGU CGA GGG UCU CAG AGG AGC)-5′, X = AP site (Spacer C3), C = target nucleobase), which was three orders of magnitude larger than that for the AP-DNA duplex (cf. Figure S4). We consider that this arises from the preferential binding of the ClNaph-TO conjugate to B-formed AP-DNA duplexes relative to Aformed AP-RNA duplexes [6]. However, when targeting C in single stranded RNA, the use of AP-DNA probe is highly effective. The resulting duplex is the hybrid between RNA and AP-DNA ((5′d(GCA GCT CCC AXA GTC TCC TCG)-3′/3′-r(CGU CGA GGG UCU CAG AGG AGC)-5′, X = AP site (Spacer C3), C = target nucleobase) that can adopt A-form/B-form intermediate structure [28], under the same measurement conditions used to examine AP-RNA duplexes. As shown in Figure 4B, we observed the significant light-up response of the conjugate for the AP-DNA/RNA hybrid, in which the response was 22-fold larger compared to that for the AP-RNA duplex. The Kd for target C in the hybrid was obtained as 22 nM (Figure S7), where the affinity is much superior to that for AP-RNA duplexes. Importantly, the ClNaph-TO conjugate retains its selectivity for target C over U opposite the AP site in the DNA/RNA hybrid, as was observed in AP-DNA duplexes (cf. Figure 3B). These results suggest the potential use of ClNaph-TO conjugate for the detection of microRNAs in combination with AP-DNA hybridization probe (cf. Figure 1A). We performed the preliminarily experiments for detection of microRNAs based on the bindinginduced light-up response of ClNaph-TO conjugate for AP-DNA/RNA hybrids. A 21-meric AP-DNA probe was designed for the selective detection of the let-7d sequence among let-7 family [29], as shown in Figure 5A. Hybridization between this probe and let-7d allows the construction of the AP-DNA/RNA hybrid containing an orphan C opposite an AP site. Meanwhile, the hybridization with other let-7 sequences leads to the formation of orphan U-containing hybrids with several mismatch base pairs (Table S1). We observed the significant light-up response of ClNapht-TO for the let-7d-containing hybrid ( Figure 5A). This response is much larger than those for other let-7 sequences, which clearly shows that ClNaph-TO conjugate enables the selective detection probe for let-7d over other let-7 members. The binding affinity of the conjugate for the let-7d-containing hybrid We performed the preliminarily experiments for detection of microRNAs based on the binding-induced light-up response of ClNaph-TO conjugate for AP-DNA/RNA hybrids. A 21-meric AP-DNA probe was designed for the selective detection of the let-7d sequence among let-7 family [29], as shown in Figure 5A. Hybridization between this probe and let-7d allows the construction of the AP-DNA/RNA hybrid containing an orphan C opposite an AP site. Meanwhile, the hybridization with other let-7 sequences leads to the formation of orphan U-containing hybrids with several mismatch base pairs (Table S1). We observed the significant light-up response of ClNapht-TO for the let-7d-containing hybrid ( Figure 5A). This response is much larger than those for other let-7 sequences, which clearly shows that ClNaph-TO conjugate enables the selective detection probe for let-7d over other let-7 members. The binding affinity of the conjugate for the let-7d-containing hybrid (K d = 23 nM) was found to be comparable to that for the model AP-DNA/RNA hybrid (cf. Figure S8). Our assay can be applied to the analysis of various microRNAs by using the AP site-containing DNA probe whose sequence is designed so as to be complementary to the target sequence. Figure 5B shows the fluorescence response of the conjugate in combination with the 22-meric AP-DNA probe for let-7i. Selective light-up detection for let-7i was achieved due to the selective binding of the conjugate to target C in the AP-DNA/RNA hybrid formed between the AP-DNA probe and let-7i. These results show the applicability of the ClNaph-TO conjugate for the selective detection of target microRNA sequences based on the hybridization for the construction of the AP-DNA/RNA hybrid as well as the binding-induced light-up response of the conjugate for the orphan C in the resulting hybrid.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 9 (Kd = 23 nM) was found to be comparable to that for the model AP-DNA/RNA hybrid (cf. Figure S8). Our assay can be applied to the analysis of various microRNAs by using the AP site-containing DNA probe whose sequence is designed so as to be complementary to the target sequence. Figure 5B shows the fluorescence response of the conjugate in combination with the 22-meric AP-DNA probe for let-7i. Selective light-up detection for let-7i was achieved due to the selective binding of the conjugate to target C in the AP-DNA/RNA hybrid formed between the AP-DNA probe and let-7i. These results show the applicability of the ClNaph-TO conjugate for the selective detection of target microRNA sequences based on the hybridization for the construction of the AP-DNA/RNA hybrid as well as the binding-induced light-up response of the conjugate for the orphan C in the resulting hybrid.
Conclusions
In summary, we report that ClNaph served as a strong and highly selective binder for the orphan C opposite an AP site in DNA duplexes. In addition, we demonstrated the usefulness of ClNaph as the APL unit in the conjugate with a TO unit for the design of light-up probes for the detection of Crelated mutations in DNA and microRNA sequences. These results obtained could provide insights needed to design this class of light-up conjugates suitable for the analysis of DNA and microRNA sequences. As shown in our previous works [19,20], the spacer length and structure have a large impact on the binding and fluorescence sensing abilities of APL-TO conjugates. We will examine these concerns for further improvement of the APL-TO conjugates in order to develop the practical assays.
Supplementary Materials: The following are available online at www.mdpi.com/xxx/s1, Figure S1: 1 H NMR spectra of the conjugates; Figure S2: ESI-MS spectra of the conjugates; Figure S3: Fluorescence response of ClNaph to target dSpacer-containing AP-DNA duplexes. Inset: Titration curves for the binding of ClNaph to target nucleobases; Figure S4: Titration curves for the binding of ClNaph-TO conjugate to target nucleobases; Figure S5: Fluorescence response of ClNaph unit in the conjugate to target AP-DNA duplexes. Figure S6: Chemical structure of ClNaph-TO2 conjugate and its fluorescence response to target AP-DNA duplexes; Figure S7: Titration curves of the binding of ClNaph-TO conjugate to target C in the AP-DNA/RNA hybrid and AP-RNA duplex; Table S1: Sequences of let-7 members used in this study. Figure S8. Titration curves for the binding of ClNaph-TO conjugate to the let-7d/DNA probe hybrid.
Conclusions
In summary, we report that ClNaph served as a strong and highly selective binder for the orphan C opposite an AP site in DNA duplexes. In addition, we demonstrated the usefulness of ClNaph as the APL unit in the conjugate with a TO unit for the design of light-up probes for the detection of C-related mutations in DNA and microRNA sequences. These results obtained could provide insights needed to design this class of light-up conjugates suitable for the analysis of DNA and microRNA sequences. As shown in our previous works [19,20], the spacer length and structure have a large impact on the binding and fluorescence sensing abilities of APL-TO conjugates. We will examine these concerns for further improvement of the APL-TO conjugates in order to develop the practical assays.
Supplementary Materials: The following are available online at http://www.mdpi.com/2076-3417/10/12/4133/s1, Figure S1: 1 H NMR spectra of the conjugates; Figure S2: ESI-MS spectra of the conjugates; Figure S3: Fluorescence response of ClNaph to target dSpacer-containing AP-DNA duplexes. Inset: Titration curves for the binding of ClNaph to target nucleobases; Figure S4: Titration curves for the binding of ClNaph-TO conjugate to target nucleobases; Figure S5: Fluorescence response of ClNaph unit in the conjugate to target AP-DNA duplexes. Figure S6: Chemical structure of ClNaph-TO2 conjugate and its fluorescence response to target AP-DNA duplexes; Figure S7: Titration curves of the binding of ClNaph-TO conjugate to target C in the AP-DNA/RNA hybrid and AP-RNA duplex; Table S1: Sequences of let-7 members used in this study. Figure S8. Titration curves for the binding of ClNaph-TO conjugate to the let-7d/DNA probe hybrid. | 6,965 | 2020-06-16T00:00:00.000 | [
"Chemistry",
"Biology"
] |
Observational constraints on the origin of the elements. VIII. Constraining the Barium, Strontium and Yttrium chemical evolution in metal-poor stars
Recently Lian et al. (2023), thanks to Gaia-ESO data, studied the chemical evolution of neutron-capture elements in the regime [Fe/H]>-1. We aim here to complement this study down to [Fe/H]=-3, and focus on Ba, Y, Sr, and abundance ratios of [Ba/Y] and [Sr/Y], which give comprehensive views on s-process nucleosynthesis channels. We measured LTE and NLTE abundances of Ba, Y, and Sr in 323 Galactic metal-poor stars using high-resolution optical spectra with high S/N. We used the spectral fitting code TSFitPy, together with 1D model atmospheres using previously determined LTE and NLTE atmospheric parameters. The NLTE effects are on the order of -0.1 to ~0.2dex depending on the element. T he ratio between heavy and light s-process elements [Ba/Y] varies weakly with [Fe/H] even in the metal-poor regime, consistently with the behavior in the metal-rich regime. The [Ba/Y] scatter at a given metallicity is larger than the abundance measurement uncertainties. Homogeneous chemical evolution models with different yields prescriptions are unable to accurately reproduce the [Ba/Y] scatter at low-[Fe/H]. Adopting the stochastic chemical evolution model by Cescutti&Chaippini (2014) allows to reproduce the observed scatter in the abundance pattern of [Ba/Y] and [Ba/Sr]. With our observations, we rule out the need for an arbitrary scaling of the r-process contribution as previously suggested by the model authors. We have showed how important it is to properly include NLTE effects when measuring chemical abundances, especially in the metal-poor regime. This work shows that the choice of the Galactic chemical evolution model (stochastic vs. 1-zone) is key when comparing models to observations. The upcoming surveys such as 4MOST and WEAVE will deliver high quality spectra of many thousands of metal-poor stars, and this work gives a typical case study of what could be achieved with such surveys.
Introduction
Neutron-capture elements have been extensively studied in the astronomy community for more than three decades, but the chemical evolution of such type of elements in the Milky Way is still a matter of debate (e.g.Sneden et al. 2008;Cowan et al. 2021).Neutron-capture elements are, for instance, essential for Full table of [Ba/Fe], [Sr/Fe], and [Y/Fe] LTE and NLTE abundances, uncertainties, and individual line abundances is available at the CDS via anonymous ftp to cdsarc.cds.unistra.fr(130.79.128.5) or via https://cdsarc.cds.unistra.fr/vizbin/cat/J/A+A/683/A73tracing the accretion history of the Milky Way (e.g.Helmi 2020; Matsuno et al. 2021) and its satellite Galaxies (e.g.Venn et al. 2012).
In particular, the slow-neutron capture (s-process) dominated elements are mainly organised into two peaks (Burbidge et al. 1957).The first peak is located around the neutron magic number 50, and is responsible for the synthesis of the light-s elements Sr, Y, and Zr.The second peak produces Ba, La, Ce, Pr, and Nd around the neutron magic number 82.There is a third peak as well, which produces Pb.It is common to divide the s-process into a "main" process, a "weak" process, and a "strong" process.The main s-process occurs in asymptotic giant branch (AGB) stars (Busso et al. 1999;Bisterzo et al. 2011) while the weak s-process is known to occur in massive stars and it produces nuclei with mass number below 88 (Pignatari et al. 2010).Finally, the strong s-process is responsible for about 50% of solar 208 Pb production by low-metallicity AGB stars (Kaeppeler et al. 1982).
The chemical evolution of neutron-capture elements has been rather well constrained in the Milky Way disc (e.g.Battistini & Bensby 2016;Mishenina et al. 2019).However, not many studies focused on the halo or halo-disc interface.Even with the advent of large-scale spectroscopic surveys (e.g.GALAH; Buder et al. 2019), neutron-capture abundance measurements are available for only a few tens of very metal-poor stars (e.g.Mashonkina et al. 2007;Matsuno et al. 2021), as it requires high-quality and high signal-to-noise spectra in the metal-poor regime ([Fe/H] < −1).Past GCE works have also relied on compilations of abundances from various studies, but these may suffer from systematic biases, owing to the fundamental assumption of local thermodynamical equilibrium (LTE; e.g.Cescutti & Chiappini 2014).High-resolution spectroscopy is indeed a unique technique for determining precise estimates of neutron-capture elemental abundances (e.g.Delgado Mena et al. 2017;Guiglion et al. 2018;Roederer et al. 2022).
Recently Lian et al. (2023) studied the Galactic chemical evolution of Ba and Y using the data from the Gaia-ESO large spectroscopic survey.Most stars in the sample of Lian et al. (2023) cover the metallicity range −1 < [Fe/H] < 0.5 dex, for which Gaia-ESO measured and released high-quality chemical abundances of neutron-capture elements.In this letter, we aim to constrain the chemical evolution of Ba, Y, and Sr in the metal-poor regime (−3 < [Fe/H] < −0.5 dex) in order to further complement the study of Lian et al. (2023).We have also taken one step towards a higher accuracy by computing our abundances in the framework of non-local thermodynamic equilibrium (NLTE).
In Sect.2, we present the spectroscopic data and spectral analysis.In Sect.3, we present LTE and NLTE chemical abundance trends of Sr, Y, and Ba, while we confront Galactic chemical evolution models to our observations in Sect. 4. Finally, we present our conclusions in Sect. 5.
Data and methodology
We have taken advantage of the high-resolution spectra of Galactic disc and halo stars from Ruchti et al. (2011).These targets were originally observed at intermediate resolution by the RAVE survey (Steinmetz et al. 2006;Matijevič et al. 2017).The sample consists of 323 metal-poor stars, covering the ranges 4050 < T eff < 6500 K, 0.5 < log(g) < 4.5, and −2.8 < [Fe/H] < −0.4 (in NLTE; see Fig. 1).The data have already been used in our previous studies, for instance, in the analysis of NLTE stellar parameters and metallicities (Ruchti et al. 2013), ages (Serenelli et al. 2013), and NLTE Mg abundances (Bergemann et al. 2017a,b).We adopted the 1D-LTE and 1D-NLTE atmospheric parameters from Ruchti et al. (2013).
In order to derive chemical abundances of Ba ii, Y ii, and Sr i, we used the spectral fitting code TSFitPy1 , based on the LTE version of TurboSpectrum (Plez 2012) as well as its NLTE extension2 (Gerber et al. 2023).TSFitPy allows for radial velocity corrections to be applied to the data and to simultaneously fit the abundance as well as the micro-and macro-turbulence, which are typically needed owing to the lack or realistic convection and turbulent flows in 1D hydrostatic models (see e.g.Dravins 2008; Nordlund et al. 2009;Meunier et al. 2017).
The model atom of Sr used in this work is based on the model described in Bergemann et al. (2012); however, it has been updated with new quantum-mechanical data for inelastic transitions in Sr+H collisions (Gerber et al. 2023).The Ba model comes from Gallagher et al. (2020) and the Y model from Storm & Bergemann (2023).The atomic transition probabilities come from Davidson et al. (1992) for the Ba ii lines, García & Campos (1988) for the Sr i lines, and Biémont et al. (2011) for Y (see Heiter et al. 2021 for more details).Ba ii lines suffer significantly from hyperfine splitting (HFS) and isotopic shifts and these effects have been included in the calculations, as described in Gallagher et al. (2020).Overall, HFS is negligible for Y ii (<0.5 mÅ) and is not included in the linelist.For Ba ii, we adopted the lines at 5853.67, 6141.71,6496.90Å that show rather strong features even down to [Fe/H] = −3.For Sr, we used the strong and unblended spectral line of Sr i at 4607.33 Å, while two Y ii lines were adopted for the Yttrium measurements (4883.68 and 5087.42Å).It was already demonstrated in Bergemann et al. (2012) that NLTE provides a robust ionization balance for Sr I and Sr II-based abundances for dwarfs and red giants over the metallicity range relevant to the present work.For Y, the standard validation tests of the NLTE model atom, including validation on metal-poor red giant atmospheres, were presented in Storm & Bergemann (2023).For the atomic and molecular blends, we took advantage of the comprehensive Gaia-ESO survey linelist (Heiter et al. 2021).We adopted the extensively used 1D MARCS model atmospheres from Gustafsson et al. (2008).The solar abundances are taken from Magg et al. (2022).
We carefully checked by eye the quality of the fitted spectral lines to ensure the robustness of the abundance measurements.Examples of Ba ii and Y ii best-fit profiles are showed in Fig. 2 for two red giants with different metallicities.For a given element, the error budget σ was computed by quadratically summing the line-to-line scatter (σ sc ) to the propagated errors from the three atmospheric parameters (T eff , log(g), and [Fe/H]) (σ atm ).
Chemical abundance trends of [Sr/Fe], [Y/Fe], and [Ba/Fe]
In Fig.We notice that the overall star-to-star [Y/Fe] scatter is equal to 0.17 dex in both LTE and NLTE; this scatter slightly increases with [Fe/H] and ranges from 0.14 to 0.18 in LTE and 0.12 to 0.17 in NLTE.Such an increase is likely due to the presence of [Y/Fe]-rich and poor stars (see below).On average, NLTE [Y/Fe] ratios are higher than LTE [Y/Fe] by ∼0.15 dex at [Fe/H] ≈ −2, while the difference between NLTE and LTE decreases to 0.04 for [Fe/H] −1.This result is similar, but less pronounced than for [Sr/Fe].The overall behaviour of NLTE effects in Y with metallicity is consistent with the results of Storm & Bergemann (2023).
In the top-right panel of Fig. 3, we show that the LTE and NLTE [Ba/Fe] abundances follow a similar, albeit not the same, trend.As metallicities above ∼−1, NLTE [Ba/Fe] is slightly lower than LTE [Ba/Fe] by about 0.07 dex, consistent with past studies, for instance, our previous work in Gallagher et al. (2020), as we expect the equivalent widths of
Confronting chemical evolution model with heavy-to-light s-process element ratios
Here, we investigate the [Ba/Y] ratio, which is a proxy of the heavy-to-light s-process elements (e.g.Lian et al. 2023).We compare our observations to simple one-zone and inhomogeneous (stochastic) Galactic chemical evolution models, with the former being primarily relevant with respect to the understanding of the chemical enrichment of the disc and the latter being qualitatively consistent with the present understanding of the formation of the Galactic halo (see for instance Matteucci 2021 and references therein).
In the left panel of Fig. 6, we present the LTE (blue contours) and NLTE (red contours) distributions of [Ba/Y] ratios for the 187 stars of our sample with available Ba and Y abundances A73, page 3 of 7 2023).Even though the abundances between this work and the Gaia-ESO were computed with different spectral analysis pipelines, the data is rather complementary3 .
One-zone GCE models
As in Lian et al. (2023), we made of the OMEGA+ Galactic chemical evolution (GCE) model (Côté et al. 2017(Côté et al. , 2018)), which includes gas inflow and outflows.The basic model includes core-collapse supernova (CCSN) yields from Limongi & Chieffi (2018), as well as Type Ia supernovae with yields from different Chandrasekhar-and sub-Chandrasekhar mass explosions as described in Eitner et al. (2023).The GCE model also includes AGB yields from Cristallo et al. (2015).This basic GCE model is displayed in orange in Fig. 6.For comparison, we also display a GCE model that includes recent AGB yields by Karakas (2010), which account for n-capture elements nucleosynthesis for metallicites down to −2 (see Cinquegrana & Karakas 2022 and references there-in for more details).We also show one GCE model with no AGB contribution (in purple) and one with metallicity-independent AGB yields (in green).Finally, we added a GCE model that only includes non-rotating massive stars.Lian et al. (2023) concluded that the shape of [Ba/Y] in the metal-rich regime ([Fe/H] −0.6) is driven by the metallicity dependence in the neutron-capture efficiency in AGB stars.The mismatch between the GCE models and observations in this [Fe/H] regime is likely due to an overestimation of the s-process efficiency of low mass AGB stars (Magrini et al. 2021).
In the metallicity range of −2 [Fe/H] −0.8, the model without massive star yields shows a strong underproduction of [Ba/Y] and it is not consistent with the data.The large scatter in [Ba/Y] at a given metallicity could be a sign of chemical enrichment from AGBs with masses between 2 and 6 solar A73, page 4 of 7 Fig. 4. LTE and NLTE metallicity distribution of our stellar sample probing the metal-weak Galactic disc and the halo (see Ruchti et al. 2013).The distribution is not uniform and not statistically complete because of the observational selection function (Ruchti et al. 2011).masses (their Fig. 5 Lian et al. 2023).We also find that the GCE track computed with non-rotating CCSN yields underpredicts our observations, which supports evidence from the literature that CCSN resulting from the evolution of rapidly rotating massive stars are important sources of s-process elements (e.g.Limongi & Chieffi 2018).In conclusion, such chemical evolution models with different nucleosynthesis prescriptions are not able to reproduce the data, mainly due to the large scatter in [Ba/Y] at a given [Fe/H].
Stochastic GCE models
Substantial efforts have been made in the GCE model community in trying to reproduce the abundance patterns measured in the Galactic halo stars.Cescutti & Chiappini (2014) and Rizzuti et al. (2021) developed stochastic GCE models.Such models are meant to reproduce the chemical evolution of the Galactic halo, implying a series of nucleosynthesis events, overall on a time scale of 1 Gyr.Their model MRD+s B2 includes r-process contribution from magneto-rotational (MRD) supernovae and s-process nucleosynthesis from two channels: low-mass AGB stars and rotating massive stars (see Cescutti & Chiappini 2014 for more details).In this instance, we adopted the MRD+s B2 model.Here, we explore whether such models can reproduce the scatter we measure in our observations of [Ba/Y].We notice that contrary to the model of Lian et al. (2023), the models from Cescutti & Chiappini (2014) do not include neutron star mergers.
In the top panel of Fig. 7, we present the LTE and NLTE [Ba/Y] abundance ratios as a function of NLTE [Fe/H] (blue and red contours, respectively).Additionally, we present stochastic GCE (colour-coded with number of stars in the model, i.e.SFR tracer).For [Fe/H] −2.5, the GCE model shows a large scatter in the [Ba/Y] ratios, ranging from ∼−1 to +0.3.Such behaviour is directly attributed to the stochastic sampling of the IMF during the phase of halo formation (Cescutti & Chiappini 2014).The predicted [Ba/Y] trend flattens out for metallicities [Fe/H] −2.5 and slightly rises up to [Ba/Y] ≈ 0.25 for [Fe/H] −1.This GCE model matches rather well our LTE [Ba/Y] ratios, however, it overpredicts [Ba/Y] when compared to NLTE [Ba/Y].This mismatch is simply the consequence of the fact that in this GCE model the yttrium yields were modified to match the LTE observations.Specifically, the r-yields were scaled the LTE pattern of r-process rich stars.This pattern differs by a factor of 3 for Y, whereas it is consistent with the r-process solar residual for the remaining elements (see Cescutti & Chiappini 2014 for more details).Hence, the GCE matches rather well our LTE [Ba/Y] pattern.Such results show that taking into account NLTE effects is key for achieving accurate comparisons between GCEs and observations.
In the bottom panel of Fig. 7, we show similar plots but for the [Ba/Sr] ratios.The GCE model shows a similar trend with [Ba/Y].Contrary to [Ba/Y], the GCE model matches the NLTE [Ba/Sr] ratios better, while the GCE model underpredicts our LTE [Ba/Sr] ratios.This could be due to the large NLTE effect when measuring the Sr line at 4607 Å.Again, taking properly into account NLTE effects is key when comparing chemical evolution models to observations, especially in the metal-poor regime.
Considering that we provide new NLTE abundances of neutron-capture elements for our stellar sample, it is necessary to confront our data to a stochastic chemical evolution model that is not scaled to reproduce the LTE abundance patterns.It corresponds to the model MRD+s B from Cescutti & Chiappini (2014), which is similar to the model MRD+s B2; however, the r-process contribution to Y production is scaled to the solar residual, as in the case of the other elements, and therefore they are not divided by a factor of 3. We show such a model in Fig. 8, together with the LTE and NLTE abundances of our metal-poor stars.Naturally, the predicted ratio of [Ba/Y] is lower by 0.3 dex compared to the model MRD+s B2.Interestingly, the GCE model based on r-process solar residual is indeed closer to the NLTE observational distributions of [Ba/Y] and [Ba/Sr] in our stellar sample.It is important to remind the reader that our abundances are computed using 1D model atmospheres and we expect the [Ba/Y] ratio to be lower when adopting an updated model atom (Storm et al. 2024), with Y+H collisional processes updated to new quantum-mechanical values.Also, adopting 3D model atmospheres (Storm et al. 2024) can induce larger and more positive 3D NLTE effects for Y ii lines.As a result, we do not see evidence for re-scaling the MRD yields for Y to the pattern of the r-process rich stars as used in the model MRD+s B2 of Cescutti & Chiappini (2014); moreover, the r-process solar residuals appear to be more reliable, as expected: they are not affected by the NLTE corrections.
A73, page 5 of 7 12 dex relative to the solar values even at metallicities close to solar.6. Single-zone chemical evolution models are unable to reproduce the [Ba/Y] scatter observed at a given metallicity.Such a scatter can, however, be more captured by stochastic GCE models.7. Most importantly, we find a better agreement of the NLTE abundance ratios of light (Sr, Y) and heavy (Ba) element ratios, as compared to the GCE tracks from stochastic chemical evolution models with r-yields scaled with an r-process solar residual.There is no longer any need for modifications to the r-process yields of yttrium following the pattern of r-process rich stars, as done in Cescutti & Chiappini (2014), for instance.Therefore, we conclude that properly taking into account NLTE effects when measuring abundances directly impacts comparisons among galactic chemical evolution models and observations, thereby affecting yield prescriptions and nucleosynthesis channels.
Conclusions
The sample studied here is still rather limited in terms of the number of stars and in the metallicity coverage.Indeed, going to low metallicity, typically down to [Fe/H] of ∼−4 or −5, will allow us to probe the early neutron-capture enrichment of the Milky Way in greater detail.In the near future, 4MOST will deliver hundreds of thousands of high-resolution (R ∼ 20 000) optical spectra of the Milky Way disc, halo, and bulge stars (de Jong et al. 2019;Bensby et al. 2019;Christlieb et al. 2019), opening up a new era for NLTE abundances exploration down to very low metallicities.Substantial efforts will have to be made to provide the community with precise and accurate neutroncapture abundances from such facilities.
Fig. 2 .
Fig. 2. Examples of Ba ii (left) and Y ii (right) lines in the spectra of two red giants with [Fe/H] NLTE = −1.65 (top) and [Fe/H] NLTE = −0.77(bottom).The red shaded area represents the spectral range over which the line is fitted.The orange curve corresponds to the best line-fit.The black vertical corresponds to the central wavelength of the line.
the
Ba ii lines to increase due to NLTE effects.NLTE [Ba/Fe] is rather flat for [Fe/H] −1.25, in agreement with previous studies (e.g.Delgado Mena et al. 2017 in LTE and Korotin et al. 2011 in NLTE).The star-by-star standard deviation of NLTE [Ba/Fe] abundances is 0.16 dex, while it reaches 0.21 dex for LTE [Ba/Fe].This shows that NLTE abundances have less intrinsic scatter, which has implications for the chemical enrichment of the elements in the Galaxy, as we show in Sect. 4 below.We notice the presence of stars deficient in [Y/Fe], compared to the main distribution at a given metallicity, as well as some stars with large [Ba/Fe] and [Y/Fe] values.To search for possible correlations between these low-and high-abundance stars, we present in Fig. 5 the NLTE abundances of [Y/Fe] as a function of [Ba/Fe], colour-coded with [Sr/Fe].Firstly, we found ten stars with [Y/Fe] < −0.3, showing also both solar or sub-solar (<+0.1)[Ba/Fe] and [Sr/Fe].Secondly, five stars have large [Y/Fe] > 0.2 together with large [Ba/Fe] ([Ba/Fe] > 0.3) and [Sr/Fe] ([Sr/Fe] > 0.15).We investigated on the origin of such enhanced (deficient) stars by checking for potential common membership with the main Milky Way components.We adopted the thin disc, thick disc, and halo kinematics-based membership classification ofRuchti et al. (2011).We find that these enhanced (deficient) stars do not preferentially belong to one particular Galactic component.For instance, among the [Y/Fe]-deficient stars, four stars belong to the thin disc, five stars to the thick disc, and one star to the halo.For the dwarfs and turn-off stars present in this sample, we checked for potential age signatures by adopting the isochrone-based stellar ages fromSerenelli et al. (2013).The stars enhanced (deficient) in [Y/Fe] span stellar ages of between 6 and 13 Gyr, with no apparent correlation visible between the stellar ages and enhanced (deficient) n-capture abundances.
Fig. 3 .
Fig. 3.Chemical abundances of [Sr/Fe] (left), [Y/Fe] (center), and [Ba/Fe] (right) in LTE as a function of LTE [Fe/H] shown in the top panel.We display both the individual stars and contour-plot.Black error bars correspond to mean uncertainties σ .Bottom panel is the same as top, but in NLTE.The number of stars is indicated in the top right corner in each panel, with both rows having the same number of stars.
Fig. 6 .
Fig. 6.Chemical abundance ratios [Ba/Y] in both LTE (blue contours) and NLTE (red contours) as a function of [Fe/H] (LTE and NLTE, respectively), for 187 stars (left).Error bars correspond to mean uncertainties in LTE and NLTE.Only NLTE [Ba/Y] (red contours) together with Gaia-ESO sample used by Lian et al. (2023), as well as one-zone chemical evolution models with different yields prescriptions (right).
In this work, we focus on constraining the chemical enrichment of [Ba/Fe], [Sr/Fe], [Y/Fe], and [Ba/Y] ratios of Milky Way stars in the domain of −2.5 [Fe/H] −0.5There is lack of abundance measurements in this [Fe/H] range that makes it challenging to set direct constraints of Galactic chemical evolution.
3. We showed that the bulk of NLTE[Ba/Fe]ratios decreases with increasing [Fe/H], while NLTE [Sr/Fe] is rather constant with [Fe/H], and NLTE [Y/Fe] decreases with [Fe/H].The combined NLTE effects are of the order of −0.07 dex for [Ba/Fe], +0.18 dex for [Sr/Fe], and +0.10 dex for [Y/Fe] that also includes the NLTE effect on [Fe/H].4. Focusing on NLTE abundances, we find that stars enhanced (deficient) in [Ba/Fe] and [Y/Fe] are enhanced (deficient) in [Sr/Fe]. 5. We showed that the NLTE ratios of [Ba/Y] are centred around solar values and the behaviour of the trend is rather flat with NLTE metallicity [Fe/H], implying that [Ba/Y] is not sensitive to [Fe/H].The star-to-star scatter is substantial and is of the order of 0.2 dex.LTE [Ba/Y] ratios show a similar dispersion as NLTE [Ba/Y], but are shifted by +0. | 5,292 | 2023-11-09T00:00:00.000 | [
"Physics"
] |
The UTfit Collaboration Average of D meson mixing data: Spring 2012
We derive constraints on the parameters $M_{12}$, $\Gamma_{12}$ and $\Phi_{12}$ that describe $D$ meson mixing using all available data, allowing for CP violation. We also provide posterior distributions and predictions for observable parameters appearing in $D$ physics.
We derive constraints on the parameters M12, Γ12 and Φ12 that describe D meson mixing using all available data, allowing for CP violation. We also provide posterior distributions and predictions for observable parameters appearing in D physics.
Meson-antimeson mixing in the neutral D system has been established only in 2007 [1][2][3]. Early combinations of available data allowed to put stringent constraints on New Physics (NP) contributions, although the possibility of non-standard CP violation remained open [4][5][6][7][8]. More recently, CP violation in the D system received considerable attention after the measurement at hadron colliders of large direct CP violation in D → ππ and D → KK decays [9,10], which may signal the presence of NP [11][12][13][14][15][16]. It then becomes crucial to extract updated information on the mixing amplitude in order both to disentangle more precisely indirect and direct CP violation in D → ππ and D → KK, and to obtain up-to-date constraints on NP in ∆C = 2 transitions that can be used to constrain NP contributions to ∆C = 1 processes in any given model.
In this letter, we perform a fit to the experimental data in Table I following the statistical method described in ref. [39]. We assume that all Cabibbo allowed (and doubly Cabibbo suppressed) decay amplitudes in the phase convention CP|D = |D and CP|f = η f CP |f satisfy the relation A(D → f ) = η f CP A(D →f ), which is expected to hold in the SM (in the standard CKM phase convention) with an accuracy much better than present experimental errors. In the same approximation this implies Γ 12 real. For singly Cabibbo suppressed decays D 0 → K + K − and D 0 → π + π − we allow for direct CP violation to be present. We assume flat priors for x = ∆m D /Γ D , y = ∆Γ D /(2Γ D ) and |q/p|, with |D L,S = p|D 0 ± q|D 0 and |p| 2 + |q| 2 = 1. We can then express all mixing-related observables in terms of x, y and |q/p| using the following formulae [4,[40][41][42][43]: x . Asymmetric errors have been symmetrized. We do not use measurements that do not allow for CP violation in mixing, except for ref. [27] (as shown in ref. [3], the results for x and y from the Dalitz analysis of D → Ksππ are not sensitive to the assumptions about CP violation in mixing).
with δ f a strong phase and A D forced to vanish in the fit. In addition, for the CP asymmetries we have where D f (t) is the observed distribution of proper decay time and τ D 0 is the lifetime of the neutral D mesons.
For the purpose of constraining NP, it is useful to express the fit results in terms of the ∆C = 2 effective Hamiltonian matrix elements M 12 and Γ 12 : with Φ 12 = arg Γ 12 /M 12 . Consistently with the assumption A(D → f ) = A(D →f ), Γ 12 can be taken real with negligible NP contributions, and a nonvanishing Φ 12 can be interpreted as a signal of new sources of CP violation in M 12 . For the sake of completeness, we report here also the formulae to compute the observables x, y and δ from M 12 and Γ 12 : in agreement with [42] up to a factor of √ 2. The results of the fit are reported in Table II. The corresponding p.d.f are shown in Figs. 1 and 2. Some twodimensional correlations are displayed in Fig. 3.
A direct comparison with the HFAG results [38] is not straightforward, as our fit does not fall into any of the HFAG categories (no CPV, no direct CPV, direct CPV), since we allow for direct CP violation only in singly Cabibbo suppressed decays. However, our fit results should be close to the "no direct CPV" HFAG fit. Indeed, we find compatible results within errors. We notice, however, that HFAG performs a fit with four independent parameters (x, y, φ and |q/p|), while only three of these parameters are independent, as can be seen from eq. (1). In particular, φ should vanish for |q/p| = 1. This feature can be seen in Fig. 3 (up to the smoothing of the p.d.f) but not in the equivalent plot from HFAG, which displays completely different 2-dimensional contours. We can but recommend that in the future HFAG takes the relation φ = arg(y + iδx) always into account. The results in Table II can be used to constrain NP contributions to D −D mixing and decays. M.C. is associated to the Dipartimento di Fisica, Università di Roma Tre. E.F. and L.S. are associated to the Dipartimento di Fisica, Università di Roma "La Sapienza". We acknowledge partial support from ERC Ideas Starting Grant n. 279972 "NPFlavour" and ERC Ideas Advanced Grant n. 267985 "DaMeSyFla". We thank B. Golob and A. Schwartz for clarifications about the HFAG averages. | 1,243.2 | 2012-06-27T00:00:00.000 | [
"Physics"
] |
Surface Crack Monitoring by Rayleigh Waves with a Piezoelectric-Polymer-Film Ultrasonic Transducer Array
This paper presents a method for measuring surface cracks based on the analysis of Rayleigh waves in the frequency domain. The Rayleigh waves were detected by a Rayleigh wave receiver array made of a piezoelectric polyvinylidene fluoride (PVDF) film and enhanced by a delay-and-sum algorithm. This method employs the determined reflection factors of Rayleigh waves scattered at a surface fatigue crack to calculate the crack depth. In the frequency domain, the inverse scattering problem is solved by comparing the reflection factor of the Rayleigh waves between the measured and the theoretical curves. The experimental measurement results quantitatively matched the simulated surface crack depths. The advantages of using the low-profile Rayleigh wave receiver array made of a PVDF film for detecting the incident and reflected Rayleigh waves were analyzed in contrast with those of a Rayleigh wave receiver using a laser vibrometer and a conventional lead zirconate titanate (PZT) array. It was found that the Rayleigh waves propagating across the Rayleigh wave receiver array made of the PVDF film had a lower attenuation rate of 0.15 dB/mm compared to that of 0.30 dB/mm of the PZT array. Multiple Rayleigh wave receiver arrays made of the PVDF film were applied for monitoring surface fatigue crack initiation and propagation at welded joints under cyclic mechanical loading. Cracks with a depth range of 0.36–0.94 mm were successfully monitored.
Introduction
The fatigue crack in metals is the most common cause of failure in industry and has caused many catastrophic disasters. The fatigue crack usually develops from the surface of a structure, where fatigue damage typically initiates as shear cracks on crystallographic slip planes [1][2][3][4]. The surface fatigue crack growth proceeds in two steps: crack initiation and crack propagation, both of which may not be noticed macroscopically. In offshore and marine structures, the fatigue of welded joints is a common problem [5,6]. Surface fatigue cracks appear in welded structures mostly at the welded joints rather than in the base metal [7]. This is because the welding process includes heating and subsequent cooling as well as a fusion process with additional filler material, resulting in different materials and inherent metallurgical geometrical defects. Therefore, the fatigue behavior of welded joints has attracted great attention, and surface fatigue crack growth monitoring is considered one of the most effective ways to study the fatigue behavior and monitor the structural health of a welded structure [8].
To meet the safety requirement for structures, the detection of surface fatigue cracks before they reach a critical length is necessary. Ultrasonic testing is now widely used for its high sensitivity, high penetrating capability, high accuracy, and fast response [9]. Rayleigh waves, which are surface acoustic waves, are effective for surface crack detection. This is because when Rayleigh waves propagate along a surface, their amplitude decreases exponentially with the depth of surface irregularities, making them more sensitive to surface defects compared to other wave types. In this case, a crack depth and location can be estimated simultaneously by monitoring the Rayleigh waves scattered from the crack. The detailed characteristics of the crack can be obtained from the traveling time and amplitudes of the incident, reflected, and transmitted Rayleigh waves [10].
Because Rayleigh waves are sensitive to surface discontinuities, non-contact methods to detect the scattered Rayleigh waves are preferred, such as a laser interferometer and the EMAT (Electro Magnetic Acoustic Transducer) [11][12][13][14]. However, it is difficult to place a bulky equipment at welded joints with a complex structure. To detect surface fatigue cracks on welded joints, ultrasonic transducers with simplified structure, high accuracy, and low profile on the surface conditions are required.
In this study, a Rayleigh wave receiver array made of a thin film polyvinylidene fluoride (PVDF) ultrasonic transducer array comprising nine PVDF ultrasonic transducers is proposed to meet the above stated requirements for monitoring surface fatigue crack growth at welded joints. The depth of the surface fatigue cracks was estimated from Rayleigh waves generated and detected by the ultrasonic transducers, based on a reference reflection factor curve and an improved measurement procedure. The reference curve was established from analytical results, and a delay-and-sum algorithm was deployed in the measurement procedure to average out the unwanted modes. The proposed Rayleigh wave receiver array is made of a flexible and thin PVDF film bonded on the structure. Compared to the traditional ultrasonic transducer made of lead zirconate titanate (PZT), the PVDF film is lightweight, conformal to the surface of the structure, and low-profile, allowing the Rayleigh waves to propagate over the surface with low attenuation and the array receiver to detect the Rayleigh waves. This work presents novel methods for monitoring the depth of surface defects on a welded structure with a Rayleigh wave receiver array made of the PVDF film and a delay-and-sum algorithm, enabled by the low-attenuation Rayleigh wave receiver array design allowing the significant enhancement of incident and reflected Rayleigh waves.
The monitoring procedure was demonstrated experimentally with actual surface fatigue cracks. The incident and reflected Rayleigh waves propagating near the crack were separated from the other wave types by an enhanced delay-and-sum algorithm. The experimental results were similar to the simulation results when the crack depth ranged from 0.36 mm to 0.94 mm.
Scattering of Rayleigh Waves by a Surface-Breaking Crack
The interaction between Rayleigh waves and cracks has been widely studied since the 1970s [15]. When Rayleigh waves are scattered at a crack, information in the scattered Rayleigh wave including arrival time, signal amplitude, and signal frequency can be used to estimate the crack depth. For example, the crack depth can be estimated from the propagating time of the Rayleigh wave along the cracks. This method, however, is effective only when the crack depth is greater than 0.8 times the Rayleigh wavelength, else there will be a time delay fluctuation. For shallow cracks, the relative amplitudes of the incident, reflected, and transmitted Rayleigh waves are more useful indicators.
Reflection and transmission coefficients have been studied with the numerical simulations of theoretical models. The reflection and transmission coefficients are obtained by comparing the Rayleigh wave reflected from a crack and the Rayleigh wave transmitted to the other side of the crack. Using the elastodynamic ray theory, Achenbach et al. derived exact and approximate solutions for high-frequency waves scattered at surface-breaking cracks and cracks near a free surface [16]. The incident surface wave scattered at a surfacebreaking crack in two-dimensional geometry was also studied by Mendelsohn et al. [17].
With the development of the Finite Element Method (FEM), the scattering behavior can be investigated more accurately in more detail. Based on the theory developed by Mendelsohn, Masserey et al. successfully measured the surface crack depth on thick steel plates with good accuracy and repeatability, down to the smallest available ratio of crack depth to Rayleigh wavelength a/λ = 0.15 [18]. For welded joints, as in our study, it is not practical to use the transmission coefficient for crack depth measurement. This is because of the required complex structure that prevents its installation on the other side of the welding line for welded joint surface crack monitoring. Therefore, the reflection coefficient is used in this work. The reflection coefficient is defined as the ratio of the reflected Rayleigh wave signal to the incident Rayleigh wave signal. All parameters and abbreviations used in this paper are listed in Table 1. A delay-and-sum method is useful to increase the signal-to-noise ratio of a Rayleigh wave by averaging out the unwanted wave modes [19]. The process is conducted by: (i). Selecting the first Rayleigh wave receiver as a reference point (ii). Calculating the time delay caused by the additional propagation time for the Rayleigh wave to travel to the subsequent Rayleigh wave receivers from the reference point (iii). Adding the time delay to the time domain signals collected from the Rayleigh wave receivers so that the Rayleigh waves are in phase (iv). Summing the delayed time domain signals (v). Using the enhanced Rayleigh waves for the determination of the crack depth.
In this work, with the delay-and-sum algorithm, a parameter representing reflection, called reflection factor (F r ) was used and corresponds to where R i,n is the gated ultrasonic signal of the incident Rayleigh wave received by the n-th Rayleigh wave receiver, R r,n is the gated ultrasonic signal of the Rayleigh wave reflected from the crack and then received by the n-th Rayleigh wave receiver, and N is the total number of Rayleigh wave receivers. The gated ultrasonic signals were obtained by isolating the Rayleigh waves from unwanted ultrasonic signals in the time domain, collected by the Rayleigh wave receivers. The gated ultrasonic signals were then converted to the frequency domain using the Fast Fourier Transform (FFT). Ultrasonic signals attenuate the further they propagate. In order to prevent the unwanted wave types detected by the first Rayleigh wave receiver from overshadowing the Rayleigh wave detected by the subsequent Rayleigh wave receivers, each frequency spectrum of the gated ultrasonic signal was normalized before summation. As a result, the reflection factor F r used in this study could be larger than 1. Then, 2-D finite element models were applied to obtain the reflection coefficient for a notch with a certain depth at different central frequencies.
The results were plotted with respect to the ratio of the crack depth to the wavelengt, and were in agreement with the prediction from Masserey et al. [17]. Note that this reflection coefficient was simulated without normalization, thus Cr < 1.
Characterization in the Frequency Domain
According to Figure 1, the reflection coefficient Cr reaches the maximum when a/λ = 0.45. By measuring the maximum Cr and the corresponding frequency, we can obtain the wavelength and then calculate the crack depth. We have where a is the crack depth, λ is the wavelength, v is the speed of sound in the medium, and f is the frequency corresponding to the maximum Cr. Since the Rayleigh wave velocity here is a constant, the surface defect depth can be rewritten as a function of the frequency. The relationship between the surface defect depth and the optimal frequency is shown in Figure 2. The relationship between the surface defect depth and the frequency that corresponds to the maximum Cr is shown in Figure 2.
the subsequent Rayleigh wave receivers, each frequency spectrum of the gated ultrasonic signal was normalized before summation. As a result, the reflection factor used in this study could be larger than 1. Then, 2-D finite element models were applied to obtain the reflection coefficient for a notch with a certain depth at different central frequencies. The results were plotted with respect to the ratio of the crack depth to the wavelengt, and were in agreement with the prediction from Masserey et al. [17]. Note that this reflection coefficient was simulated without normalization, thus < 1.
Characterization in the Frequency Domain
According to Figure 1, the reflection coefficient reaches the maximum when / = 0.45. By measuring the maximum and the corresponding frequency, we can obtain the wavelength and then calculate the crack depth. We have where is the crack depth, is the wavelength, v is the speed of sound in the medium, and is the frequency corresponding to the maximum . Since the Rayleigh wave velocity here is a constant, the surface defect depth can be rewritten as a function of the frequency. The relationship between the surface defect depth and the optimal frequency is shown in Figure 2. The relationship between the surface defect depth and the frequency that corresponds to the maximum is shown in Figure 2. study could be larger than 1. Then, 2-D finite element models were applied to obtain the reflection coefficient for a notch with a certain depth at different central frequencies.
The results were plotted with respect to the ratio of the crack depth to the wavelengt, and were in agreement with the prediction from Masserey et al. [17]. Note that this reflection coefficient was simulated without normalization, thus < 1.
Characterization in the Frequency Domain
According to Figure 1, the reflection coefficient reaches the maximum when / = 0.45. By measuring the maximum and the corresponding frequency, we can obtain the wavelength and then calculate the crack depth. We have where is the crack depth, is the wavelength, v is the speed of sound in the medium, and is the frequency corresponding to the maximum . Since the Rayleigh wave velocity here is a constant, the surface defect depth can be rewritten as a function of the frequency. The relationship between the surface defect depth and the optimal frequency is shown in Figure 2. The relationship between the surface defect depth and the frequency that corresponds to the maximum is shown in Figure 2.
Ultrasonic Transducers' Design
A schematic of the active ultrasonic transducer design for crack depth measurement using Rayleigh waves is shown in Figure 3.
For this design, the Rayleigh waves were generated with a Rayleigh wave transmitter. The Rayleigh wave transmitter consisted of an ultrasonic transducer installed on an ultrasonic wedge with a critical angle for Rayleigh wave generation, and the ultrasonic wedge was bonded on the surface of the structure with adhesive. Meanwhile, a Rayleigh wave receiver array made of a PVDF film with three discrete electrodes was bonded on the surface of the structure in front of the crack. A longitudinal wave emitted from the ultrasonic transmitter was converted into a Rayleigh wave at the interface of the structure and the wedge. As the Rayleigh wave traveled past the Rayleigh wave receiver array, an incident Rayleigh wave was detected by the Rayleigh wave receiver array. As the Rayleigh wave traveled farther, it was scattered at the crack when it reached the crack. Thereafter, the Sensors 2023, 23, 2665 5 of 13 scattered wave was received by the Rayleigh wave receiver array. Information about the crack was contained in the scattered wave. Subsequently, the delay-and-sum algorithm of the detected received ultrasonic waves was applied. By repeating the process and analyzing the incident and reflected Rayleigh waves in the frequency domain, the depth and location of the crack could be monitored.
Ultrasonic Transducers' Design
A schematic of the active ultrasonic transducer design for crack depth measurement using Rayleigh waves is shown in Figure 3. For this design, the Rayleigh waves were generated with a Rayleigh wave transmitter. The Rayleigh wave transmitter consisted of an ultrasonic transducer installed on an ultrasonic wedge with a critical angle for Rayleigh wave generation, and the ultrasonic wedge was bonded on the surface of the structure with adhesive. Meanwhile, a Rayleigh wave receiver array made of a PVDF film with three discrete electrodes was bonded on the surface of the structure in front of the crack. A longitudinal wave emitted from the ultrasonic transmitter was converted into a Rayleigh wave at the interface of the structure and the wedge. As the Rayleigh wave traveled past the Rayleigh wave receiver array, an incident Rayleigh wave was detected by the Rayleigh wave receiver array. As the Rayleigh wave traveled farther, it was scattered at the crack when it reached the crack. Thereafter, the scattered wave was received by the Rayleigh wave receiver array. Information about the crack was contained in the scattered wave. Subsequently, the delay-and-sum algorithm of the detected received ultrasonic waves was applied. By repeating the process and analyzing the incident and reflected Rayleigh waves in the frequency domain, the depth and location of the crack could be monitored.
Structure to Be Monitored
In our experiments, six sets Rayleigh wave receiver arrays (labeled as 'A', 'B', 'C', 'D', 'E', and 'F') were bonded on the two surfaces of the structure to be monitored. Each of the Rayleigh wave receiver array contained three electrodes (named '1′, '2′, and '3′) that enabled the detection of Rayleigh waves in three different positions. The Rayleigh waves collected at each of the three positions were processed according to Equation 1 for signal enhancement. The schematic drawing of the transducers and a photo of the experimental setup with a welded joint to be monitored are presented in Figure 4.
Structure to Be Monitored
In our experiments, six sets Rayleigh wave receiver arrays (labeled as 'A', 'B', 'C', 'D', 'E', and 'F') were bonded on the two surfaces of the structure to be monitored. Each of the Rayleigh wave receiver array contained three electrodes (named '1 , '2 , and '3 ) that enabled the detection of Rayleigh waves in three different positions. The Rayleigh waves collected at each of the three positions were processed according to Equation (1) for signal enhancement. The schematic drawing of the transducers and a photo of the experimental setup with a welded joint to be monitored are presented in Figure 4.
The structure used in this study consisted of 38 mm thick cruciform welded S550 high-strength steel joints with good welding properties [20]. The structure was subjected to three-point bending on the top of the attachment plate. The maximum load applied was 50 kN. with a load ratio of 0.1, and the loading frequency was 3 Hz. As shown in Figure 4b, potential cracks occurred in the two bottom areas in the plate near the weld toe. Two Rayleigh wave transmitters were placed on two sides of the structure, as shown in Figure 4. Three sets of the Rayleigh wave receiver arrays made of the PVDF film were placed in front of each of the two Rayleigh wave transmitters.
As shown in Figure 4a, each Rayleigh wave receiver array comprised a PVDF film with three discrete linear electrodes that were equally spaced. The width of the electrodes was smaller than half of the Rayleigh wavelength, which was determined by the smallest crack depth to be monitored. If the width of the electrodes were larger than the half wavelength of the Rayleigh wave travelling across the width direction of the electrode, the Rayleigh wave signal collected by each electrode would destructively cancel out. To avoid this, the width of the transducers was no more than half of the Rayleigh wavelength. Sensors 2023, 23, x FOR PEER REVIEW 6 of 14 The structure used in this study consisted of 38 mm thick cruciform welded S550 high-strength steel joints with good welding properties [20]. The structure was subjected to three-point bending on the top of the attachment plate. The maximum load applied was 50 kN. with a load ratio of 0.1, and the loading frequency was 3 Hz. As shown in Figure 4b, potential cracks occurred in the two bottom areas in the plate near the weld toe. Two Rayleigh wave transmitters were placed on two sides of the structure, as shown in Figure 4. Three sets of the Rayleigh wave receiver arrays made of the PVDF film were placed in front of each of the two Rayleigh wave transmitters.
As shown in Figure 4a, each Rayleigh wave receiver array comprised a PVDF film with three discrete linear electrodes that were equally spaced. The width of the electrodes was smaller than half of the Rayleigh wavelength, which was determined by the smallest crack depth to be monitored. If the width of the electrodes were larger than the half wavelength of the Rayleigh wave travelling across the width direction of the electrode, the Rayleigh wave signal collected by each electrode would destructively cancel out. To avoid this, the width of the transducers was no more than half of the Rayleigh wavelength.
Materials and Methods
An ultrasonic transducer (V106, Olympus Scientific Solutions Americas Inc. Waltham, MA, USA) with a central frequency of 2.25 MHz was used as the ultrasonic transducer for the Rayleigh wave transmitter. The ultrasonic transducer was bonded to the wedge using a conductive silver epoxy adhesive (Polytec PT EC244, Waldbronn, Germany), followed by curing at 70 °C for 1 h. The wedge was then bonded to the structure to be monitored by an epoxy adhesive layer (Araldite 2011) and cured overnight at room temperature.
For the Rayleigh wave receiver array, a PVDF film (PolyK, Philipsburg, PA, USA) with a thickness of 50 μm was bonded to the structure to be monitored using the conductive silver epoxy adhesive, followed by curing at 70 °C for 1 h. Afterward, a sticker mask was used to pattern nine discrete top electrodes on the bonded PVDF film. Silver electrodes were deposited by spraying, followed by curing at 70 °C for 10 min. The cured silver electrodes had a thickness of 5 μm. A waterproof layer was coated on top of the
Materials and Methods
An ultrasonic transducer (V106, Olympus Scientific Solutions Americas Inc. Waltham, MA, USA) with a central frequency of 2.25 MHz was used as the ultrasonic transducer for the Rayleigh wave transmitter. The ultrasonic transducer was bonded to the wedge using a conductive silver epoxy adhesive (Polytec PT EC244, Waldbronn, Germany), followed by curing at 70 • C for 1 h. The wedge was then bonded to the structure to be monitored by an epoxy adhesive layer (Araldite 2011) and cured overnight at room temperature.
For the Rayleigh wave receiver array, a PVDF film (PolyK, Philipsburg, PA, USA) with a thickness of 50 µm was bonded to the structure to be monitored using the conductive silver epoxy adhesive, followed by curing at 70 • C for 1 h. Afterward, a sticker mask was used to pattern nine discrete top electrodes on the bonded PVDF film. Silver electrodes were deposited by spraying, followed by curing at 70 • C for 10 min. The cured silver electrodes had a thickness of 5 µm. A waterproof layer was coated on top of the ultrasonic sensors as a protective layer. The electrodes were connected to a customized flexible printed circuit (MFS Technology, Singapore) and terminated to a D-Subminiature (DB9) connector, which was then connected to the ultrasonic testing system (Vantage 64, Verasonics Inc., Kirkland, WA, USA).
The Rayleigh wave receiver array made of the PVDF film with three discrete electrodes was compared with a laser interferometer (UHF 120, Polytec, Waldbronn, Germany) and a Rayleigh wave receiver array made of three discrete PZTs. The experimental setups of the Rayleigh wave receivers made of the piezoelectric polymer film ultrasonic transducer, the piezoelectric ceramic ultrasonic transducer, and the laser interferometer are shown in Figure 5. An excitation signal using a −13 Vp pulse with a pulse width of 385 ns was applied to the Rayleigh wave transmitter. A surface defect was simulated by machining a slot with 1 mm depth on a 40 mm thick aluminum block.
trodes was compared with a laser interferometer (UHF 120, Polytec, Waldbronn, Ger-many) and a Rayleigh wave receiver array made of three discrete PZTs. The experimental setups of the Rayleigh wave receivers made of the piezoelectric polymer film ultrasonic transducer, the piezoelectric ceramic ultrasonic transducer, and the laser interferometer are shown in Figure 5. An excitation signal using a −13 Vp pulse with a pulse width of 385 ns was applied to the Rayleigh wave transmitter. A surface defect was simulated by machining a slot with 1 mm depth on a 40 mm thick aluminum block.
Results and Discussion
The generated Rayleigh wave would propagate along the surface, reach the Rayleigh wave receiver and be detected by the Rayleigh wave receiver showing the incident Rayleigh wave. The Rayleigh wave then would continue propagating to the crack, be reflected by the crack, and be received by the Rayleigh wave receiver array as a reflected Rayleigh wave. The incident and reflected Rayleigh waves detected by the Rayleigh wave receiver made of the PVDF film on the machined slot with a depth of 1 mm are presented in Figure 6. The received ultrasonic signals were analyzed using the delay-and-sum algorithm. The
Results and Discussion
The generated Rayleigh wave would propagate along the surface, reach the Rayleigh wave receiver and be detected by the Rayleigh wave receiver showing the incident Rayleigh wave. The Rayleigh wave then would continue propagating to the crack, be reflected by the crack, and be received by the Rayleigh wave receiver array as a reflected Rayleigh wave. The incident and reflected Rayleigh waves detected by the Rayleigh wave receiver made of the PVDF film on the machined slot with a depth of 1 mm are presented in Figure 6. The received ultrasonic signals were analyzed using the delay-and-sum algorithm. The time window gating was set to be narrow to exclude noise and unwanted wave types. The gated ultrasonic signal was then processed with zero padding to ensure sufficient FFT points. Throughout the whole experiment, the total time period of the gated ultrasonic signal was set to 3.5 µs for both incident and reflected Rayleigh waves.
The performance of the Rayleigh wave detection system with the Rayleigh receiver array made of the PVDF film was compared with those of the Rayleigh wave receiver array made of PZT and the laser interferometer. Figure 7 presents the frequency spectra of the incident and reflected Rayleigh wave signals after applying the delay-and-sum algorithm for the three types of Rayleigh wave receivers. The reflection factor (F r ) was calculated by applying Equation (1), shown in Figure 7. For the defect depth determination, the F r peak was searched within the −6 dB frequency bandwidth of the incident Rayleigh wave. time window gating was set to be narrow to exclude noise and unwanted wave types. The gated ultrasonic signal was then processed with zero padding to ensure sufficient FFT points. Throughout the whole experiment, the total time period of the gated ultrasonic signal was set to 3.5 μs for both incident and reflected Rayleigh waves. The performance of the Rayleigh wave detection system with the Rayleigh receiver array made of the PVDF film was compared with those of the Rayleigh wave receiver array made of PZT and the laser interferometer. Figure 7 presents the frequency spectra of the incident and reflected Rayleigh wave signals after applying the delay-and-sum algorithm for the three types of Rayleigh wave receivers. The reflection factor ( ) was calculated by applying Equation 1, shown in Figure 7. For the defect depth determination, the peak was searched within the −6 dB frequency bandwidth of the incident Rayleigh wave. No peaks were detected for the using the Rayleigh wave receiver array made of three discrete PZTs within the effective frequency bandwidth. This was due to the low reflected Rayleigh wave signal amplitude, which resulted from the high attenuation rate Figure 7. Frequency spectra of the incident Rayleigh wave and reflected Rayleigh wave and reflection factor (F r ) detected by Rayleigh wave receivers made of (a) the Rayleigh wave receiver array made of the PVDF film and three discrete electrodes; (b) the Rayleigh wave receiver array made of three discrete PZTs; and (c) the laser interferometer. No peaks were detected for the F r using the Rayleigh wave receiver array made of three discrete PZTs within the effective frequency bandwidth. This was due to the low reflected Rayleigh wave signal amplitude, which resulted from the high attenuation rate when the Rayleigh wave propagated past each PZT. For comparison, the amplitude of the incident Rayleigh waves detected by different types of Rayleigh wave receivers was recorded. The performance comparison for the three Rayleigh wave receiver array designs is presented in Table 2. Table 2. Performance benchmark for using the PVDF film, the discrete PZT, and the laser interferometer as Rayleigh wave receivers to measure 1 mm deep surface defects. In Table 2, the Rayleigh wave receiver array made of the three discrete PZTs had the highest attenuation rate, while the Rayleigh wave receiver array made of the PVDF film with three discrete electrodes had an attenuation rate just slightly higher than that of the laser interferometer. The reason for the higher attenuation rate when using the Rayleigh wave receiver array made of discrete PZTs was the attenuation of the surfacesensitive Rayleigh wave when travelling across the bulky PZTs. Furthermore, due to the low mechanical damping properties of PZT, the frequency bandwidth of the detected Rayleigh waves was narrower. This led to a narrower surface defect depth measurement range. Therefore, the Rayleigh wave receiver array made of three discrete PZT strips bonded on the structure was not able to measure the depth of the defect. On the other hand, the feasibility of applying the PVDF film as a Rayleigh wave receiver for determining the depth of surface crack was successfully demonstrated via the experimental results. It was also demonstrated that the Rayleigh wave receiver array made of the PVDF film had a comparable incident Rayleigh wave frequency bandwidth as the non-contact laser interferometer. Despite showing a relatively lower crack depth measurement accuracy when compared to the laser interferometer, the Rayleigh wave receiver array made of a piezoelectric polymer layer has a much lower cost and does not require a line of sight to perform structural health monitoring.
Rayleigh Wave Receiver
The Rayleigh wave receiver array made of the PVDF film that was fabricated using the method described in the Section 3.3 was subsequently applied for surface fatigue crack monitoring, as shown in Figure 4 and as described before. The crack depth measurement range was determined from the −6 dB cutoff frequencies of the incident Rayleigh wave frequency spectra according to the delay-and-sum algorithm for the respective positions ( Figure 8). After the lower and the upper cutoff frequencies were determined, the crack depth measurement range for each position was calculated using Equation (2), as summarized in Table 3. the method described in the Materials and Method section was subsequently applied for surface fatigue crack monitoring, as shown in Figure 4 and as described before. The crack depth measurement range was determined from the −6 dB cutoff frequencies of the incident Rayleigh wave frequency spectra according to the delay-and-sum algorithm for the respective positions (Figure 8). After the lower and the upper cutoff frequencies were determined, the crack depth measurement range for each position was calculated using Equation (2), as summarized in Table 3. For every 5000 fatigue loading cycles, ultrasonic signals were generated and received using the ultrasonic testing system. The collected ultrasonic signals were processed by applying the delay-and-sum algorithm to the incident and reflected Rayleigh waves. Thereafter, the peak of the F r was recorded, so that crack depth could be calculated. Figure 9 shows the Rayleigh wave spectral method with the delay-and-sum algorithm for position B at cycle 25,669. The incident and reflected Rayleigh wave signals detected by the Rayleigh wave receiver array in position 'B' are shown in Figure 9a,b. The signals were then processed using the delay-and-sum algorithm according to Equation (1), and the calculated F r is shown in Figure 9c. Thus, the optimal frequency was 2.33 MHz, and the crack depth was calculated as 0.595 mm using Equation (2).
The crack depth measured at each position for different fatigue loading cycles is presented in Figure 10. Figure 10a shows the crack depth monitored by the Rayleigh wave receiver array in positions 'A', 'B', and 'C'; Figure 10b shows the crack depth monitored by the Rayleigh wave receiver array in positions 'D', 'E', and 'F'. As shown in Table 2, the measurement range of each receiver array was limited by the −6 dB frequency bandwidth of the incident Rayleigh wave. For the Rayleigh wave receiver array 'A', the measurement range was 0.36 mm-0.94 mm, and the actual crack depth measured was 0.42 mm-0.92 mm. The crack depths measured from the six Rayleigh wave receiver arrays were different. This indicated that the cracks had a different growth behavior at different positions. With the six receiver arrays, crack information over this area was obtained. The crack depth was also simulated with the same method as in [21]. The theoretical analysis simulated crack growth of the weldline, i.e., positions 'B' and 'E'. As the simulation was ideal, the simulation results of the two sides were symmetrical. Figure 10 shows that the simulation results had the same trend as the measured results of the crack depth. The numerical simulation, however, did not reflect the exact unsymmetrical cracks in the two sides of the welded joints, due to the simplified model of the weld geometry and boundary conditions. As a result, the simulation result tended to overestimate the crack growth due to the higher stress concentration in the finite element model in comparison to that in the experimental tests. Nonetheless, the results of the numerical simulation provided a reference for the crack measurement by the Rayleigh wave receiver arrays. ure 9 shows the Rayleigh wave spectral method with the delay-and-sum algorithm for position B at cycle 25,669. The incident and reflected Rayleigh wave signals detected by the Rayleigh wave receiver array in position 'B' are shown in Figure 9a,b. The signals were then processed using the delay-and-sum algorithm according to Equation 1, and the calculated is shown in Figure 9c. Thus, the optimal frequency was 2.33 MHz, and the crack depth was calculated as 0.595 mm using Equation (2). The crack depth measured at each position for different fatigue loading cycles is presented in Figure 10. Figure 10a shows the crack depth monitored by the Rayleigh wave receiver array in positions 'A', 'B', and 'C'; Figure 10b shows the crack depth monitored by the Rayleigh wave receiver array in positions 'D', 'E', and 'F'. As shown in Table 2, the measurement range of each receiver array was limited by the −6 dB frequency bandwidth of the incident Rayleigh wave. For the Rayleigh wave receiver array 'A', the measurement range was 0.36 mm-0.94 mm, and the actual crack depth measured was 0.42 mm-0.92 mm. The crack depths measured from the six Rayleigh wave receiver arrays were different. This indicated that the cracks had a different growth behavior at different positions. With the six receiver arrays, crack information over this area was obtained. The crack depth was also simulated with the same method as in [21]. The theoretical analysis simulated crack growth of the weldline, i.e., positions 'B' and 'E'. As the simulation was ideal, the simulation results of the two sides were symmetrical. Figure 10 shows that the simulation results had the same trend as the measured results of the crack depth. The numerical simulation, however, did not reflect the exact unsymmetrical cracks in the two sides of the welded joints, due to the simplified model of the weld geometry and boundary conditions. As a result, the simulation result tended to overestimate the crack growth due to the higher stress concentration in the finite element model in comparison to that in the experimental tests. Nonetheless, the results of the numerical simulation provided a reference for the crack measurement by the Rayleigh wave receiver arrays. In recent years, piezoelectric ultrasonic transducers can be fabricated in situ on the surface of a structure to conduct structural health monitoring (SHM). These low-profile, lightweight and highly conformable piezoelectric ultrasonic transducers are known as direct-write ultrasonic transducers and have been demonstrated to be efficient for SHM, such as for detecting the presence of various defects and plastic deformation [22,23]. By combining the scalable direct-write ultrasonic transducer technology, an active ultrasonic In recent years, piezoelectric ultrasonic transducers can be fabricated in situ on the surface of a structure to conduct structural health monitoring (SHM). These low-profile, lightweight and highly conformable piezoelectric ultrasonic transducers are known as direct-write ultrasonic transducers and have been demonstrated to be efficient for SHM, such as for detecting the presence of various defects and plastic deformation [22,23]. By combining the scalable direct-write ultrasonic transducer technology, an active ultrasonic SHM system with edge computing capability, and the methods proposed in this work, it will be possible to realize a scalable quantitative crack size monitoring over a large area [24][25][26].
Conclusions
Surface crack depth measurement using piezoelectric polymer film ultrasonic transducer arrays was successfully demonstrated by analyzing the detected Rayleigh waves in the frequency domain. A delay-and-sum algorithm was adopted for enhancing the detected Rayleigh wave signals. The proposed method was compared with Rayleigh wave detection with a Rayleigh wave receiver made of piezoelectric ceramic and a laser interferometer. Both methods using laser without physical contact and the low-profile PVDF film transducer array with minimized interference with the surface conditions were able to determine the crack depth because of the corresponding lower attenuation of the surface-sensitive Rayleigh waves (0.15 dB/mm). Meanwhile, the method using the bulky piezoelectric ceramic Rayleigh wave receiver arrays failed due to the significant attenuation of the Rayleigh waves (0.30 dB/mm). This method based on the frequency spectra of reflected Rayleigh waves is very sensitive for measuring crack depths below 1 mm, which makes it suitable for monitoring crack initiation and early-stage propagation. Furthermore, this method does not require the transmission of the ultrasonic signal across the structure and is thus applicable to measure cracks present in complex structures such as welded joints. Compared to the laser interferometer, the Rayleigh wave receiver array made of a piezoelectric polymer layer is of much lower cost and does not require a line of sight to perform crack monitoring.
The crack depth monitoring procedure using six PVDF Rayleigh wave receiver arrays was further demonstrated by measuring real fatigue cracks induced at two welded joints of a 38 mm thick steel cruciform structure under cyclic mechanical loading test. The maximum load applied was 50 kN with a load ratio of 0.1, and the loading frequency was 3 Hz. Realtime monitoring was realized with the six PVDF Rayleigh wave receiver arrays bonded to the structure. The measurement range was determined by the −6dB frequency bandwidth of the incident Rayleigh wave. We showed that the Raleigh wave receiver arrays worked efficiently from 7140 to 36,700 fatigue loading cycles. Crack initiation and propagation along the two welded joints with a depth range between 0.36 and 0.94 mm were determined quantitatively during the cyclic fatigue loading process. Data Availability Statement: Not applicable.
Conflicts of Interest:
The authors declare no conflict of interest. | 8,820 | 2023-02-28T00:00:00.000 | [
"Physics"
] |
Heat Transfer and Entropy
indicating that the (process) quantity heat (δQ) is obviously closely linked to the (state) quantity entropy (dS ), here both written as infinitesimal quantities. If, however, you do the same with a standard textbook on heat transfer (like [4] with 1024 pages or [5] with 1107 pages), you will find entropy neither in the index of these books, nor in the text. There may be two reasons for that: Either entropy has turned out to be irrelevant for a heat transfer analysis or entropy is ignored deliberately in the heat transfer community in spite of its relevance. What is true is a yet open question and can only be answered when thermody‐ namic considerations are taken into account. In thermodynamics the relevance of entropy with respect to heat transfer is beyond any controversy, it is the heat transfer community that has to be persuaded of its relevance. This can best be done by showing the advantages of including entropy in a heat transfer analysis as well as showing the disadvantages one has to face when entropy is ignored.
Introduction
When you read a standard textbook on thermodynamics (like [1][2][3]) as one of the most fundamental formulae you will find δQ T dS = (1) indicating that the (process) quantity heat (δQ) is obviously closely linked to the (state) quantity entropy (dS ), here both written as infinitesimal quantities.
If, however, you do the same with a standard textbook on heat transfer (like [4] with 1024 pages or [5] with 1107 pages), you will find entropy neither in the index of these books, nor in the text.
There may be two reasons for that: Either entropy has turned out to be irrelevant for a heat transfer analysis or entropy is ignored deliberately in the heat transfer community in spite of its relevance. What is true is a yet open question and can only be answered when thermodynamic considerations are taken into account.
In thermodynamics the relevance of entropy with respect to heat transfer is beyond any controversy, it is the heat transfer community that has to be persuaded of its relevance. This can best be done by showing the advantages of including entropy in a heat transfer analysis as well as showing the disadvantages one has to face when entropy is ignored.
This line of argument, however, violates at least two principles of thermodynamics and misses the crucial point. From a thermodynamics point of view heat is a process quantity that describes a certain way by which energy can be transferred across the boundary of a system. And of course this quantity cannot be stored, only the energy moved by it can be stored.
And the crucial point is: Transferring energy as heat into a system is fundamentally different from doing the same by work. The energy transferred in form of heat and work, though it may be the same amount, has a very different quality once it is part of the energy of the system. To put it in a simple and not yet precise form for the moment: It is not only the amount of energy that counts in energy transfer processes (like heat transfer) but also the quality of the energy and the change in quality during the transfer process. If that is true, there must be a measure for the quality and its potential degradation in energy transfer processes. This is where entropy comes in and plays a crucial role -even and also in heat transfer considerations.
From the very clear principle of energy conservation (thermodynamically formulated as the first law of thermodynamics) we know that energy given as primary energy never gets lost when used in technical devices but finally ends up as part of the internal energy of the ambient. Then, however, it is of no use anymore. Obviously energy has a certain potential that can get lost on the way from being primary energy to being part of the internal energy of the ambient.
In thermodynamics there is a useful definition by which the quality of an energy can be characterized which was first proposed in [6]. This definition primarily refers to an energy which is subject to transfer processes either by work or by heat. According to this definition energy is composed of two parts, exergy and anergy. Within this concept exergy is the precious part of the energy. It is that part which can be used by work until it is part of the internal energy of the ambient. Sometimes exergy is also called available work. The remaining part of the energy is called anergy. According to the second law of thermodynamics exergy can get lost (can be converted to anergy) in irreversible processes but never can be generated. Any transfer of energy by work or by heat thus can either preserve the exergy part of the energy in a reversible process or reduce it in an irreversible one.
As far as heat transfer is concerned there are two aspects that are important: The first is the amount of energy transferred by heat and the second is the amount of exergy lost in this (heat) transfer process. Ignoring entropy means that only the first aspect can be accounted for. For a complete characterization of a heat transfer process both aspects have to be accounted for, i.e. two physical quantities have to be specified. They can be In a heat transfer process both quantities are independent of each other because a certain amount of energy (q) can be transferred with a different decrease of quality, i.e. with a different degree of irreversibility (ΔT ). Here ΔT is an indirect measure of the quality decrease of the energy in the transfer process since ΔT = 0 is the reversible limit of an irreversible process with ΔT > 0. When two independent quantities are required then two nondimensional parameters are needed in the context of describing heat transfer processes nondimensionally. In section 3 it will be discussed what is missing when the Nusselt number Nu alone is used in order to characterize a heat transfer process.
In thermodynamics the two aspects of energy transfer and its devaluation by irreversible processes are quantified by introducing the entropy and its generation in the course of irreversible processes. In this context entropy is a measure of the structure of the system storing the energy under consideration, i.e. energy can be stored in a more or less ordered way. This again can be expressed in terms of exergy versus anergy of the energy transferred and stored.
Change of entropy in energy transfer processes
For most considerations the absolute value of entropy is not of interest but its change during a certain process like a heat transfer process. This change of entropy in a transfer process generally is twofold: Transfer -change of entropy in a reversible process,
ii.
Generation -change of entropy when the transfer process is not reversible, i.e. irreversible.
In a real (irreversible) process the change of entropy thus always is the sum of both, i.e. (i) + (ii).
For a heat transfer process between two temperature levels T a and T b the two parts (i) and Equation (2) corresponds to eq. (1) in the introduction, now in terms of rates for a continuous process. Equation (3) states that entropy generation leads to an increase of entropy when the energy is transferred from one system (a) with high temperature (i.e. low entropy) to another system (b) with low temperature (i.e. high entropy). Thus the overall change of entropy in such a process is In figure 1 such a process is illustrated for the convective heat transfer from a flow in system (a) with ṁ a to a flow in system (b) with ṁ b . The wall between both flows is diabatic, walls to the ambient are adiabatic.
The generation-change of entropy in eq. (3) strictly speaking is an approximation only. It is based on the assumption that in (a) and in (b) the real temperature distributions can be approximated by their (constant) mean values and that the temperature drop from (a) to (b) completely happens in the wall between both systems, see figure 1 for an illustration of this approximation. In section 4 the real temperature distribution is accounted for in order to determine the generation-change of entropy without approximation.
Though it is not the topic of this chapter it should be mentioned what (i) and (ii) are for an energy transfer by work: with δΦ as dissipation rate of mechanical energy in the flow field involved in the transfer process. That always d t Ṡ = 0 holds for a work transfer of energy shows the fundamental difference of the two ways to transfer energy, i.e. by heat or by work, c.f. eq. (2) for the energy transfer by heat.
Energy devaluation in a heat transfer process and the entropic potential concept
When in an energy transfer process exergy gets lost the "value" of the energy is reduced, since exergy as the precious part of the energy is reduced. This is called energy devaluation during a transfer process and is immediately linked to the generation-change of entropy, c.f. eq. (3).
Exergy lost and entropy generated are interrelated by the so-called Gouy-Stodola theorem, see for example [7]. It reads Here T ∞ is the ambient temperature and Ė l e is the loss of the exergy rate Ė e of the energy rate Ė , after subdividing Ė into an exergy and an anergy part, Ė e and Ė a , respectively.
For a single transfer operation indicated by i then there is the finite exergy loss , , with Ṡ g,i as entropy generation in the transfer operation i. This entropy generation can and should be seen in the context of those devaluations of the energy transfer rate Ė that happened prior to the transfer operation i and that will happen afterwards. This idea takes into account that a certain energy (rate) always starts as primary energy being exergy as a whole and finally ends up as part of the internal energy of the ambient, then being anergy as a whole. In [8] this has been described as the "devaluation chain" with respect to the energy transfer rate Ė with the process i being one link of this chain.
For the sum of all single transfer operations that completely devaluates the energy from 100% exergy to 100% anergy then holds. Here Ṡ g is the overall entropy generation (rate), i.e. the entropy increase of the ambient, when Ė becomes part of its internal energy.
In [8] this quantity is called the entropic potential: of the energy Ė involved in an energy (here: heat) transfer process. Taking this as a reference quantity the so-called energy devaluation number , , indicates how much of the entropic potential of the energy is used in a certain transfer process i with N i = 0 for a reversible process. Examples will be given afterwards.
An engineering view on heat transfer
As mentioned before, engineers trained to solve heat transfer problems with books like [4] care little or not at all about entropy. They characterize heat transfer situations by the heat transfer coefficient or in a more systematic way by the Nusselt number In both cases q w and ΔT are combined within one assessment quantity so that the two independent aspects of heat transfer • the amount, associated with q w and • the change of quality, associated with ΔT are not captured separately. A second assessment quantity is required for a comprehensive characterization of a heat transfer situation. This can be the energy devaluation number N i according to eq. (11).
When N i accounts for the quality of heat transfer the Nusselt number Nu covers the quantitative aspect in the following sense. Often either ΔT or q w are prescribed as a thermal boundary condition. Then the Nusselt number quantifies the heat transfer by providing the heat flux that occurs or the temperature difference that is required, respectively. Both are quantitative aspects leaving the question about the quality still open. This then is addressed by the energy devaluation number N i .
Since the Nusselt number Nu is well established in the heat transfer community, but the energy devaluation number N i is not, N i will be further explained with respect to its physical background in the following section.
The physics behind the energy devaluation number
According to Fourier's law of heat conduction, see for example [4] or [9], i.e. a heat flux occurs along the (negative) gradient of temperature. The energy transferred in this way reduces its exergy part because this exergy part is with the Carnot factor Here again T ∞ is the ambient temperature, so that the exergy part of Q once its temperature level T has reached the ambient temperature, is zero.
This permanent exergy loss when heat transfer occurs with gradT > 0 (irreversible heat transfer) according to the Gouy-Stodola theorem (7) is accompanied by entropy generation which here can be written as or after integrating the local entropy generation rate Ṡ g ''' as ( ) which in Cartesian coordinates reads Note that this eq. (19) reduces to eq. (3) when there is a linear temperature distribution in xdirection only so that ∂ T / ∂ x = ΔT / Δx, dV = dAΔx and ∂ Q = − k(ΔT / Δx)dA.
Comparing eqs. (3) and (19) shows that in the mean temperature model according to eq. (3) and figure 1(2) is an integration with respect to δQ while with the real temperature distribution according to eq. (19) and figure 1 (1) it is an integration with respect to the volume accounting for the local entropy generation rate.
In both cases Ṡ g ,i is determined which is the overall entropy generation due to heat conduction in a transfer process i. The energy devaluation number refers this to the entropic potential of is that percentage used of the entropic potential of the energy Ė which in a process i is transferred as heat Q . Note that part of the entropic potential has been used already on the way of Ė starting as primary energy to the situation in which it is transferred as heat and that the remaining part of the entropic potential after the heat transfer process i can be used in subsequent energy transfer processes. This may illustrate why it is important to see a certain transfer process i in the context of the overall devaluation chain of an energy starting as primary energy and ending as part of the internal energy of the ambient, for more details of this concept see [8].
Convective heat transfer
Often convective heat transfer occurs in technical applications like power plants and heating or cooling systems. Then a second energy flux is involved which is the flow work rate that is needed to maintain the flow into which or out of which the heat transfer occurs. This energy flux applied as work is pure exergy which gets lost in the dissipation process during the convective heat transfer.
Losses due to dissipation of mechanical energy
In fluid mechanics losses in a flow field usually are characterized by a drag coefficient c D for external flows and a head loss coefficient K for internal flows, which are a nondimensional drag force F D and a nondimensional pressure loss Δ p, respectively. In table 1 both definitions are shown together with an alternative approach based on the entropy generation rate Ṡ g ,D due to the dissipation of mechanical energy (index: D). For details of this alternative approach see [10]. Since both coefficients, c D and K , account for the dissipation rate in the flow field and according to eq. (6) δΦ = T d g Ṡ the dissipation of mechanical energy corresponds to the loss of exergy only when T = T ∞ , c.f. eq. (7). Whenever the flow occurs on a temperature level which is not that of the ambient temperature T ∞ , c D and K account for the dissipation but not for the lost exergy in the flow.
Then a second coefficient is needed which best is defined as an exergy destruction number N E analogous to the energy devaluation number, eq. (11), i.e.
Note that N E is not an energy devaluation number in the sense of its definition in eq. (11) because the reference quantity Ė in eq. (22) is not an energy transfer rate (that might be devaluated during the transfer process). Instead it is the kinetic energy involved in the convective process. It serves as a reference quantity for the flow work required to maintain the flow.
Different from N i according to eq. (11), for which by definition always 0 ≤ N i ≤ 1 holds, N E is not restricted to this range. For example N E = 3 for an internal flow means that the exergy loss (exergy destructed) during this process is three times higher than the kinetic energy involved in the convective process. Note that it is not the kinetic energy that is devaluated but the energy that enters the system as flow work, being pure exergy at the beginning and partly or totally converted to anergy by the dissipation process.
Assessing convective heat transfer
Since both energies in a convective heat transfer process (flow work needed and thermal energy transferred) are subjected to devaluation they should both be accounted for when a convective heat transfer process is assessed, for example for the purpose of its optimization.
In terms of losses what counts is the lost exergy in both energies that are involved in the convective heat transfer process. These exergy losses are characterized by the corresponding entropy generation rates Ṡ g ,i in eq. (11) and Ṡ g ,D in eq. (22). They can be added to provide the overall entropy generation rate in a convective heat transfer process and serve as a target quantity in an optimization procedure. This is a reasonable criterion for all those cases in which the exergy part of energy transfer process counts like for a power cycle. In such a process exergy lost ahead of the turbine cannot be converted to mechanical energy in the turbine and thus reduces the efficiency of the power cycle.
When the entropy generation rates should be determined from detailed numerical solutions of a convective heat transfer process, Ṡ g ,i follows from eqs.
When the flow is turbulent, d g Ṡ according to eqs. (19) and (26) are adequate only for a direct numerical simulation (DNS) approach with respect to the turbulence, as for the example shown in [11]. Since DNS solutions with their extraordinary computational demand cannot be used for solving technical problems, the time-averaged equations (Reynolds-averaged Navier-Stokes: RANS) are solved instead. Then, also d g Ṡ has to be time averaged, leading to: with d g Ṡ C and d g Ṡ D for the entropy generation in the time-averaged temperature and velocity field as well as d g Ṡ C ' and d g Ṡ D ' for the time averaged contributions of the corresponding fluctuating parts.
All four parts are with the results for a turbulent flow field from RANS equations, d g Ṡ C and d g Ṡ D can be determined, but not d g Ṡ C ' and d g Ṡ D ' . For these terms turbulence models are needed, as for examples discussed in [12].
Nondimensional parameters
When the whole process of a convective heat transfer should be assessed (comprising the exergy loss in the temperature and in the flow field) that again should be done by means of nondimensional parameters. The nondimensional parameters introduced so far are: • Nusselt number Nu / eq. (13), indicating the strength of heat transfer versus its irreversibility; • Energy devaluation numberN i / eq. (11), indicating the loss of entropic potential of the transferred energy; • Head loss coefficient K / table 1, indicating the dissipation rate in the flow field; • Exergy destruction number N E / eq. (24), indicating the loss of exergy in the flow field. If now the overall exergy loss for a convective heat transfer process is of interest this basically is the sum of the effects covered by N i and N E . Since both parameters are not nondimensionalized in the same way, however, they cannot simply be added. Note that N i refers to the transferred energy which for the convective heat transfer is Q , whereas in N E the kinetic energy of the fluid flow is used as a reference quantity.
For an overall assessment of a convective heat transfer process we now refer the sum of the exergy losses (in the temperature and in the flow field) to the exergy transferred in the process, which is η c Q , c.f. eq. (15), and thus introduce the ( ) , , overall exergy loss number : N With the help of eq. (33) it can be decided whether the increase of the Nusselt number by a certain technique to improve the heat transfer, like adding turbulence promoters, roughening of the wall or simply increasing the flow rate, is beneficial from the perspective of exergy conservation. When N E is decreased, more available work is left and the increase of Nu is beneficial.
Since a device with a small N E obviously is more efficient than one with a larger N E , an overall efficiency factor :1 was introduced in [13] which is η E = 1 for a perfect (thermodynamically reversible) process without any exergy loss and η E = 0 for a process in which all exergy gets lost because it is converted to anergy.
Examples
Two examples will be given in which the parameters that were introduced above will be used in order to characterize the heat transfer situation. With these examples it should become obvious that entropy and/or its generation should not be ignored when heat transfer processes are considered in practical industrial applications.
Fully developed pipe flow with heat transfer
This simple example may illustrate how important it is to account for entropy generation which is the crucial aspect in the energy devaluation number N i according to its definition (11).
What usually can be found as the characterization of the heat transfer performance of a fully developed pipe flow is the Nusselt number Nu. Let's assume it is Nu = 100 and it occurs on the upper temperature level of a power cycle, i.e. ahead of the turbine of this energy conversion device. Let's also assume that this heat transfer situation with Nu = 100 and a heat flux q w = 10 3 W / m 2 on a length L = 0, 1 m occurs in two different power cycles: • A steam power cycle (SPC) with water as the working fluid and an upper temperature level T m,u = 900 K.
• An organic Rankine cycle (ORC) with ammonia NH 3 as working fluid and an upper temperature level T m,u = 400 K.
When in both cycles Nu, q w and L are the same, the temperature difference ΔT in Nu according to eq. (13) is larger by a factor 2.6 for ammonia compared to water. This is due to the different values of the thermal conductivity k of water (at T m,u = 900 K and p = 250 bar) and ammonia (at T m,u = 400 K and p = 25 bar), assuming typical values for the temperature and pressure levels in both cycles.
For a further comparison note that the energy devaluation number according to eq. (11) in this case with d g Ṡ i according to eq. (3) and integrated to obtain , , , (36) Table 2 shows the energy devaluation number N i for both cases according to this approximation.
It shows that only 0.37 % of the entropic potential is used for the heat transfer in the SPC-case, but almost 5% in the ORC-case "though" both heat transfer situations have the same Nusselt number Nu = 100 and the same amount of energy is transferred. Note that only that part of the entropic potential that is not yet used is available for further use after the process under consideration.
Using CFD to assess a heat exchanger
In the previous example, two similar processes at two different temperature levels were considered. Such a pipe flow with heat transfer is part of the heat transfer situation illustrated in figure 1: the cold side (b) is heated.
In the second example computational fluid dynamics (CFD) is used to assess the heating of a fluid in a passage within a plate heat exchanger, trying to find the best point of operation for the device. We will first describe the device and how it is modeled, and then discuss the results and how to use them. Further details can be found in [14].
Geometry of the device
Plate heat exchangers are made of corrugated plates which are arranged in a plate stack, forming channels between the plates. The plates are designed in such a way that two fluids are separated from each other on their way through adjacent channels.
Depending on the plate corrugation the channels have constantly changing cross sections, but there is a repeating geometric pattern. Figure 2 (left) shows part of a plate with such a pattern; in this case it is a symmetric fish-bone pattern with a sinusoidal corrugation (see figure 2, right).
Modeling of the device
The first simplification made in order to facilitate the simulations is that the plate (and therefore the heat exchanger) is assumed to have an infinite length. Thus effects on the flow caused by the inlet or outlet areas can be neglected: the flow is hydraulically developed. This has two consequences: • the channel can be modeled as an endlessly repeating stripe of finite length, see figure 3 (a), • only half of the channel must be simulated, see figure 3 (b).
The resulting domain geometry is shown in figure 4. The second simplification made here is that the heat exchanger is operated with a balanced counter-flow: The capacity flow rate ṁ c p is the same on the hot and the cold side, so that the temperature difference between them as well as the heat flux q w are the same at every point between the inlet and the outlet.
Boundary conditions
Based on the assumptions made above, periodic boundary conditions can be applied to the flow field in main flow direction x (see figure 3). The boundary condition applied with respect to the pressure field is a so-called "fan" boundary condition that sets a constant pressure drop between the inlet and outlet patch. In the symmetry plane a symmetry boundary condition is imposed, and no-slip boundary conditions hold at all walls.
The temperature field has a fan boundary condition with a positive temperature difference ΔT io between the inlet and the outlet patch. This results in a heating of the fluid as it passes through the simulated passage. The boundary condition used for the top and bottom walls is a linearly increasing temperature profile in mean flow direction. The increase in temperature ΔT ω,io is the same as ΔT io . Together, these two boundary conditions model the balanced counter-flow configuration of the heat exchanger. A zero-gradient boundary condition is used for the gasket, which is modeled as an adiabatic wall.
Changing the pressure drop leads to different mean flow velocities. In order to keep the heat flux q w fixed, it was necessary to adjust the temperature difference between inlet and outlet (ΔT w,io = ΔT io = q w A / ṁ c p ) accordingly.
Simulation results
The results obtained from CFD simulations give access to the velocity, pressure and temperature fields u, p and T . They can be used to calculate the heat transfer coefficient and the head loss coefficient for the convective heat transfer under consideration.
Calculating the pressure and velocity fields is the computationally expensive part of the simulation. When all fluid properties are assumed to be constant, i.e. pressure and temperature independent, the temperature field can even be modeled as a passive scalar, which comes at very little computational cost. The four parts of the entropy generation (Ṡ g ,C , Ṡ g ,C ' , Ṡ g ,D , Ṡ g ,D ' , see eqs. (29) to (32) in section 5.2.) are post-processing quantities: they can be obtained from the u -, p -and T -fields without solving further differential equations. This is beneficial for the assessment of a certain process operating on different temperature levels.
The entropy generation rates due to dissipation, conduction and the sum of both are shown in figure 5 for different Reynolds numbers. For increasing Reynolds numbers, Ṡ g ,D increases, while Ṡ g ,C decreases. An optimal point of operation can be identified at about Re = 2000. The same optimum can be identified in figure 6 for the energy devaluation number of the heat exchanger, N he , since in eq. (11) the heat flux, wall area and ambient temperature are the same for all calculations.
Note that the curves for Ṡ g ,C and Ṡ g ,D in figure 5 are almost straight lines, especially for higher Reynolds numbers. Therefore only two simulations are necessary in order to roughly estimate Figure 5. Overall entropy generation rate Ṡ g , entropy generation rate due to dissipation Ṡ g ,D and entropy generation rate due to conduction Ṡ g ,C (normalized with the minimum entropy generation rate at Re ≈ 2000) at varying Reynolds numbers, for the simulated heat exchanger passage.
an optimum point of operation. From the two straight lines for Ṡ g ,C and Ṡ g ,D the sum of both results as a curve with the minimum at the optimal Reynolds number.
As mentioned before the entropy generation is a post-processing quantity. This can be leveraged to assess the simulated heat transfer situation at different temperature levels. If the overall change in temperature between inlet and outlet is not too large, an approximation can be done by simply scaling the results accordingly. The entropy generation due to dissipation Ṡ g ,D,new at the temperature level T new is (compared to the entropy generation in an existing simulation result) Ṡ g ,D,new / Ṡ g ,D,sim = T sim / T new . If the new temperature level is higher, Ṡ g ,D,new will be smaller than Ṡ g ,D,sim . Similarly, for entropy generation due to conduction, the relationship is Ṡ g ,C ,new / Ṡ g ,C ,sim = (T sim / T new ) 2 . Again, if the new temperature level is higher, Ṡ g ,C ,new will be smaller thanṠ g ,C ,sim . The optimum point of operation shifts to a lower Reynolds number (see figure 7), because the effect of a temperature level change on Ṡ g ,C is larger than the effect on Ṡ g ,D . Heat Transfer and Entropy http://dx.doi.org/10.5772/60610
Conclusions
Despite its apparently low popularity, entropy generation is a crucial aspect of every heat transfer process. Every real technical process includes the generation of entropy, which at some point has to be discharged to the ambient. It has been shown that every energy flow has an entropic potential, which is the amount of entropy that can be discharged to the ambient along with the energy flow. It therefore sets the limit for all wanted processes associated with this energy flow. Based on this, the energy devalution number has been introduced, which quantifies the part of the entropic potential which is lost in a transfer process. The energy devalution number is applicable to all processes in which energy is transferred and is recommended for their assessment especially with regard to sustainability.
In the examples it has also been shown how different heat transfer situations can be compared with each other. Such comparisons can be made on very different levels, reaching from system assessment (i.e. to compare different systems) to more detailed studies regarding the optimization of subsystems which are part of an overall heat transfer system. It has also been shown how existing simulation results can be reused at different temperature levels, effectively lowering the cost of CFD simulations.
Author details
Heinz Herwig and Christoph Redecker *Address all correspondence to<EMAIL_ADDRESS>Institute for Thermo-Fluid Dynamics, Hamburg University of Technology, Germany | 7,596.4 | 2015-07-29T00:00:00.000 | [
"Physics"
] |
Rolling Element Bearing Fault Diagnosis based on Deep Belief Network and Principal Component Analysis
Rolling element bearings are critical components in industrial rotating machines. Faults and failures of bearings can cause degradation of machine performance or even a catastrophe. Bearing fault diagnosis is therefore essential and significant to the safe and reliable operation of systems. For bearing condition monitoring, acoustic emission (AE) signals attract more and more attention due to its advantages on sensitivity over the extensively used vibration signal. In bearing fault diagnosis and prognosis, feature extraction is a critical and tough work, which always involves complex signal processing and computation. Moreover, features greatly rely on the characteristics, operating conditions, and type of data. With consideration of changes in operating conditions and increase of data complexity, traditional diagnosis approaches are in-sufficient in feature extraction and fault diagnosis. To address this problem, this paper proposes a Deep Belief Network (DBN) and Principal Component Analysis (PCA) based fault diagnosis approach using AE signal. This proposed approach combines the advantages of deep learning and statistical analysis, DBN automatically extracts features from AE signal, PCA is applied to dimensionality reduction. Different bearing fault modes are identified by least squares support vector machine (LS-SVM) using the extracted features. An experimental case is conducted with a tapered roller bearing to verify the proposed approach. Experimental results demonstrate that the proposed approach has excellent feature extraction ability and high fault classification accuracy.
INTRODUCTION
Rolling element bearings are key components in mechanical systems.They are subject to various stresses, transmissions and shocks, which may cause bearing fault, and eventually lead to system breakdown.The degradation of bearing condition will definitely affect the performance of the systems.To prevent unexpected system failure and reduce the maintenance cost, bearing fault diagnosis is desired to detect fault as early as possible.
A rolling element bearing is composed of rolling elements, an inner race, an outer race, and a cage.The faults can appear on any component, and these faults can be roughly divided as local faults and distributed faults (Zhang et al., 2008;Cerrada et al., 2018).Local faults are defined as a single localized fault, such as pitting, scratch, crack, hole, etc. Distributed faults are defined as irregularities of bearing structure, such as misalignment of shaft or races, eccentric races, off-size rolling elements, roughness, etc.These faults can be caused by many reasons, such as, overheating and load, improper installation, imperfect manufacturing.These distributed faults will cause excessive contact force and friction, which will finally lead to local faults.When a bearing operates under fault conditions, they cause certain characteristic signals in the form of sound, vibration, energy, or acoustic emission.
With the advancement of machine condition monitoring techniques, many different types of signals such as vibration, acoustic emission, ultrasound have been used for diagnosis (Rai & Upadhyay, 2016;Zhang et al., 2010;Li et al., 2018).Among these signals, acoustic emissions are the transient elastic waves, which are generated from a rapid release of localized stress energy caused by deformation or defect within or on the surface of a material (Al-Ghamd & Mba, 2006).Compared with most widely used vibration signals, AE signals have many advantages: 1) insensitive to mechanical disturbances and noises caused by different operating conditions; 2) sensitive to fault size, which can offer earlier fault detection than vibration signals.These advantages make AE signals promising in bearing fault diagnosis.
Over the past decades, a lot of efforts have been presented for bearing fault diagnosis.These existing works are mainly divided into signal processing based approach and learning based approach (Cerrada et al., 2018;S. Guo, Yang, Gao, Zhang, & Zhang, 2018).For signal processing based approaches, feature extraction is needed to extract a fault indicator that is related to fault modes and fault state.Zhao et al. (S. Zhao, Liang, Xu, Wang, & Zhang, 2013) applied Empirical Mode Decomposition and Approximate Entropy based approach to detect different fault modes.Khanam et al. (Khanam, Tandon, & Dutt, 2014) employed Discrete Wavelet Transform (DWT) to decompose signals and estimate ball bearing faults.Hilbert transform (Bujoreanu, Monoranu, & OLARU N, 2014), matching pursuit method (Cui, Zhang, Zhang, Zhang, & Lee, 2016), spectral analysis and statistical analysis (Gerber, Martin, & Mailhes, 2015) and envelop analysis (Sun, Guo, & Gao, 2015) are also very effective signal processing techniques in bearing monitoring.
In practical applications, however, fault characteristic signals are often corrupted by noises, which makes feature extraction and fault diagnosis difficult and challenging.For different monitoring signals and different fault modes, no generic feature extraction method is available.As a result, feature extraction is ad-hoc for different systems and this process is time-consuming, requires complex signal processing techniques, and needs extensive human involvement.All these limitations severely hinder the development of applications of signal processing based diagnosis approaches.
Learning-based approach, on the other hand, aims to learn potential signal patterns that are related to different fault modes or fault levels (Wang, Xiang, Zhong, & Zhou, 2018).Moreover, learning-based approaches, as a supervised learning process, require data including fault samples and their labels.The process involves feature extraction and feature classification.Feature extraction can be conducted in the time domain, the frequency-domain, and transform-domains, such as statistical parameters, signal energy of Intrinstic Mode Functions (IMFs) from Empirical Mode Decomposition (EMD), Discreet Wavelet Transform (DWT), Hilbert-Huang transform, etc.With feature extracted, a classifier is designed to classify features under different fault conditions for fault detection.Some widely used classifiers include neural networks, Support Vector Machines (SVM), and Bayesian estimation, among others.
Recently, with the successes of deep learning in image recognition and speech processing, many deep learning based fault diagnosis approaches were proposed for many applications (Cococcioni, Lazzerini, & Volpi, 2013;Tang et al., 2018;Chen & Li, 2017).Guo et al. proposed a continuous wavelet transform scalogram (CWTS) and convolutional neural network (CNN) based approach for rotating machinery fault diagnosis (S.Guo, Yang, Gao, & Zhang, 2018) .Qin et al. presented an optimized DBN and improved logistic sigmoid unit based fault diagnosis for planetary gearboxs of wind turbines (Qin, Wang, & Zou, 2019).These applications show that deep learning has great potentials in feature extraction and data mining.
These reported learning based approaches, although achieved good performance in some aspects, are insufficient in dealing with bearings under complex operating conditions and the continuously increase of volume and complexity of monitoring data.As a result, diagnosis accuracy can be affected.Another limitation of these proposed approaches is that signal transformation or feature extraction are also involved.Thus, the strong feature extraction and learning ability of deep learning cannot be fully exploited.Inspired by these limitations, a deep learning and statistics based approach is proposed in this paper.This proposed approach integrates DBN and PCA to extract features from raw data and, therefore, can avoid complex signal processing and corresponding feature extraction.LS-SVM is an effective pattern recognition approach, which is an extension and improvement of SVM.It has been widely used in fault diagnosis, and has shown excellent fault identification capability.Due to this feature, it is employed to process the extracted features for diagnosis in this paper.Experimental result shows that it can achieve high accuracy.
This paper is organized as follows.A brief introduction of DBN, PCA and LS-SVM is presented in Section 2. Section 3 describes the fault diagnosis steps of the proposed approach.Experiments are presented and results are analyzed and visualized in Section 4 to demonstrate the performance of the proposed approach.Finally, Section 5 provides concluding remarks and some future research directions.
DBN principle
DBN can be regarded as a special neural network constructed from multiple Restricted Boltzmann Machines (RBMs) (G.Zhao et al., 2017).Fig. 1 shows the schematic representation of a two hidden layer DBN.DBN has a strong capability in capturing representative information from raw time series data.The output of the learning information is extracted features, which can be utilized as the input of supervised learning algorithms in classification or regression for fault diagnosis.
RBM is a special probabilistic model of Boltzmann machine, The joint configuration (v, h) can be given by the energy function ( 1).
where v j and a j are the binary states and bias of the j-th element of the visible vector, h i and b i are the binary states and bias of the i-th element of the hidden vector, w ij is the weight of the connection between the visible layer and the hidden layer.The joint distribution over the visible layer and hidden units is defined as where Z is a partition function, which can be described as In DBN structure, the connections just exist between the visible layer and the hidden layer.The neurons in the same layer are independent with each other.The conditional probabilities of the hidden layer and the visible units are given as The learning process of DBN can be divided into two stages: pre-training and fine-tuning (Hinton, Osindero, & Teh, 2006).
In the pre-training process, the RBMs are trained layer by layer with an unsupervised manner.The forward pre-training process can be regarded as a construction and reconstruction process using Eq. ( 1).After all the RBMs in the DBN are pre-trained, the fine-tuning step will be applied to DBN using backpropagation algorithm (G.Zhao et al., 2018).In this fine-tuning process, the weights and biases of every layer are adjusted continuously until the error becomes smaller than predefined threshold.The trained DBN model is obtained after the fine-tuning step and can be used in describing the fault dynamics.
As mentioned earlier, the training procedure includes pretraining and fine-tuning.Pre-training stage aims to extract features based on its learning rules automatically.In pretraining, the stacked RBMs are trained layer by layer using greedy learning algorithm (Hinton et al., 2006).This is an unsupervised training process.
Given training input data and the initialization parameters, the first hidden layer can be trained greedily by ( 4) and ( 5).This process is a positive phase, in which the gradient of the log probability of the given training data can be described as: The learning rule aims at maximizing the log probability of the data, which is equal to minimizing the divergence of the distribution defined by the model and the given training data.
Based on the Contrastive Divergence (CD) algorithm (Hinton et al., 2006), in the training process, the parameters of DBN can be adjusted by where γ ∈[0,1] denotes the learning rate, which can be used to adjust the learning speed.
The fine-tuning process is conducted to optimize the pretrained network parameters and this supervised learning process will further adjust the structure to improve the classification accuracy.Conjugate gradient algorithm is applied to fine-tune the trained parameters using the labeled data.In this step, all parameters are updated at the same time until the fine-tuning threshold is reached.The trained DBN model can be got after these two steps are finished.
PCA principle
Principal component analysis is a traditional statistical analysis approach which can be used to get principal components.
PCA can be assumed as a transformation that projects original data to a new space with lower dimension (Chang et al., 2008).Given original data vector x i (i = 1, ..m), the covariance matrix of the data vector can be calculated as: where µ is the mean value of the vector, µ = 1 m m i=1 x i .Assume that the origin data vector is a n dimensional data, the eigenvalue of the covariance matrix can be described as: where λ j are the eigenvalues of the covariance matrix, which are sorted in descending order and u j are the corresponding eigenvectors.
To get the first k eigenvectors (k < n) that corresponding to the k largest eigenvalues, let The principal components of the original data can be computed as the orthogonal transformations of x i : The obtained components are named as principal components.Dimensional reduction can be achieved by using the first several eigenvectors of the eigenvectors.In this paper, the distribution of the extracted features are assumed as Gaussian, this work mainly uses the characteristic of dimensional reduction of PCA.
LS-SVM principle
LS-SVM is an extension of SVM.It changes the inequality constraints in SVM to equality constraints, which transforms the quadratic problems in SVM into linear equations problems.Compared with traditional SVM, LS-SVM has higher operation efficiency and solution accuracy.
Given training dataset (x i , y i ) with x i being the input vector and y i being its corresponding output label, we define χ as the corresponding feature vector that can be used to map the input vector into a new feature space.Then a hyperplane can be described as: where w denotes the weight of the orientation of the hyperplane, b is the bias.LS-SVM based identification problem can be regarded as the following optimization problem (Liu, Bo, & Luo, 2015): where J is the objective function, γ is the tradeoff coefficient.Sample x i can be projected into high-dimensional space by nonlinear mapping χ.To minimize the objective function, the first step is to define the corresponding Lagrange function: ) where β i is a Lagrange multiplier.The conditions for optimality are given as: Eliminate w and e, a linear equation can be obtained as: where y = [y i , y 2 , ..., y N ] T ; l = [1, 1, ..., 1] T ; β = [β 1 , β 2 , ..., β N ] T ; Φ i,j = (x i ) T (x j ), I is the unit matrix.Finally, LS-SVM classification decision-making model can be described as: is the Radial Basis Function (RBF) kernel function to be used in this paper, and σ is the kernel bandwidth.
Bearing fault diagnosis is an multi-classification problem in which the classification model is actually constructed by combining multiple two-class SVM classifiers.In this paper, one-against-one SVM is applied to identify different fault modes.
DBN-PCA-LSSVM BASED BEARING DIAGNOSIS
This research presents a bearing diagnosis using AE signals.The proposed approach includes offline modeling and online testing processes.In the modeling process, acoustic emission signals collected from bearings are pre-processed and fed into the initialized DBN structure, through which features can be extracted automatically layer by layer.
The detailed implementation diagnostic procedure steps are described as follows: Step 1: Partition the time series data into segments based on the data sampling rate and roller bearing operation state, and divide the data into training data and testing data.
Step 2: Define the DBN structure, and train the DBN using the training data set.In this step, the number of hidden layers, the number of neurons in each hidden layer, the learning rate, and the initial weights should be defined.The training process is finished when the performance meets pre-defined requirements or iteration number reaches the threshold.
Step 3: PCA is applied on the extracted features ([x 1 , x 2 , ..., x n ]) from DBN to reduce dimensionality.Lowdimensional training features ([z 1 , z 2 , ..., z m ], m < n) can be obtained in this step.Besides, a projection matrix, which will be used in the testing process, is also obtained.
Step 4: Optimize LS-SVM by using training labels and the low-dimensional features obtained in Step 3 to identify different bearing fault modes.
Step 5: Test the trained model with the testing data set, trained DBN model, eigenvector of PCA, and trained LS-SVM.Analyze the performance on test data.
This proposed DBN-PCA-LSSVM based bearing diagnostic approach can extract features from raw data automatically, classify the fault mode, and estimate the fault severity.It avoids complex signal processing and human involvement in feature selection and extraction, which makes it more applicable, and easier to be extended to other applications.
Acoustic emission data preparation
The bearing used for the verification of the proposed approach is a tapered roller bearing: Timken LM501310 cup and LM501349 cone.The structure of the rolling bearing is described in Fig. 4 (Zhang et al., 2008) and the main geometric parameters are listed in Table 1.The data was collected from the AE sensors with the sampling rate of 50kHz, and the experimental test was conducted under different fault sizes with three different rotating speeds and three different loads, which makes nine different data sets for each fault size.The details of the collected AE data are described in Table 2.For each test, the fault size is given by depth and width measured by microns to show fault severity.To utilize the data efficiently, the fault size is defined as the sum of width and 3. Based on this fault size definition, the fault mode is defined from F-1 (Health) to F-6 as shown in Table 3.To show the feature extraction performance, principle component analysis (PCA) is applied on the output of each layer.
Only the first three main components are visualized in the 3-D space to make the performance of feature extraction clear.Fig. 5 is the visualization of raw AE data while Fig. 6 is the visualization of the extracted features by DBN.The misclassification samples mainly appear on F-4 and F-6, 104 samples from F-4 are misclassified as F-6, and 75 samples from F-6 are misclassified as F-4.These results are also consistent with the results in Fig. 6, in which the degrees of overlapping of F-6 (cyan samples) and F-4 (black samples) are larger than others.Here is an example: One sample of F-6 is incorrectly classfied as F-4.Based on the outputs of DBN, the probabilities of this sample belongs to F-4 and F-6 are 0.5909 and 0.4087, respectively.Both of the probabilities are not large enough for the classifier to make a strong decision.In this case, misclassification occurs.The potential causes and advanced approach to make correct classification will be further investigated in the future work.
CONCLUSIONS AND FUTURE WORK
This paper presents a DBN-PCA-LSSVM based rolling element bearing fault diagnosis approach.In the proposed approach, DBN is developed to extract feature automatically from raw sensor data, PCA is applied to reduce the dimensionality of the extracted features, and LS-SVM is performed to identify different fault modes.The rolling bearing fault diagnosis experiment is presented to validate the proposed approach.
The contributions of this paper are as follows: 1) By combining PCA with DBN, an integrated, accurate and intelligent fault diagnosis is proposed, in which DBN and PCA are used for bearing feature extraction, and LS-SVM is used for fault diagnosis.This integration takes full advantages of strong feature learning ability of DBN and statistic analysis of PCA.
2) Features with different dimension sizes are analyzed to find the optimal feature size for LS-SVM, which can achieve the highest classification accuracy.
With a DBN structure designed, the raw AE data are fed into the DBN and features are extracted automatically for fault diagnosis.PCA is applied to reduce the dimension of the extracted, then improve the accuracy and efficiency of fault classification.The experimental results show that this approach can achieve high diagnostic accuracy.From this perspective, the proposed DBN-PCA-LSSVM based approach provides a generic solution that can be applied to a variety of systems.
Compared with the traditional signal processing and machine learning based approaches, the proposed method does not require complex signal processing techniques and human involvement.
The future research work will mainly focus on optimizing the structure and analyzing the misclassification causes of the proposed approach to enhance fault diagnosis accuracy and efficiency.
Table 5. Fault diagnosis results
Figure 1 .
Figure 1.The structure of a 2 hidden layer DBN
Figure 2 .
Figure 2. Structure of Restricted Boltzmann Machine
Fig. 5
Fig.5shows that the raw data of all the fault modes have severe degrees of overlapping.In other words, it will be very difficult to classify different fault modes and severity from raw data.With DBN learning outputs at different layers, the degrees of overlapping of the outputs from each DBN layer is decreasing.At the output layer, the extracted features are almost separated, as visualized in Fig.6.
Figure 8 .
Figure 8. Diagnosis results obtained by DBN-PCA-LSSVM with different dimension sizes for PCA
Table 1 .
The geometric parameters of bearing
Table 2 .
AE testing data description For example, for C1 in Table2with fault width and depth of 35.33 and 2.46, respectively, the fault dimension is measured as 35.33+2.46=37.79,as shown in Table
Table 4 .
Training parametersFor bearing fault diagnosis, the information in one cycle of rotation should be included in the input vector of DBN.For this reason, consider the lowest rotating speed, the input vector size is set as 3750.The DBN structure is given as 3750-1500-600-200.Other training parameters are given in Table4.Each fault mode has 2250 samples in which 60% are used for training and the remaining 40% are used for testing.To train the DBN with a fair way, each raw data set is separated into several segments, which are randomly selected to construct the training set and testing set.
Table 5
analyzed the misclassification results of each fault mode. | 4,776.8 | 2019-09-22T00:00:00.000 | [
"Engineering",
"Materials Science",
"Computer Science"
] |
iTRAQ-based quantitative analysis of age-specific variations in salivary proteome of caries-susceptible individuals
Background Human saliva is a protein-rich, easily accessible source of potential biomarkers for the diagnosis of oral and systemic diseases. However, little is known about the changes in salivary proteome associated with aging of patients with dental caries. Here, we applied isobaric tags for relative and absolute quantitation (iTRAQ) in combination with multiple reaction monitoring mass spectrometry (MRM-MS) to characterize the salivary proteome profiles of subjects of different ages, presenting with and without caries, with the aim of identifying age-related biomarkers for dental caries. Methods Unstimulated whole saliva samples were collected from 40 caries-free and caries-susceptible young adults and elderly individuals. Salivary proteins were extracted, reduced, alkylated, digested with trypsin and then analyzed using iTRAQ-coupled LC–MS/MS, followed by GO annotation, biological pathway analysis, hierarchical clustering analysis, and protein–protein interaction analysis. Candidate verification was then conducted using MRM-MS. Results Among 658 salivary proteins identified using tandem mass spectrometry, 435 proteins exhibited altered expression patterns in different age groups with and without caries. Of these proteins, 96 displayed age-specific changes among caries-susceptible adults and elderly individuals, and were mainly associated with salivary secretion pathway, while 110 age-specific proteins were identified among healthy individuals. It was found that the age factor caused significant variations and played an important role in both healthy and cariogenic salivary proteomes. Subsequently, a total of 136 target proteins with complex protein–protein interactions, including 14 age-specific proteins associated with caries, were further successfully validated using MRM analysis. Moreover, non-age-specific proteins (histatin-1 and BPI fold-containing family B member 1) were verified to be important candidate biomarkers for common dental caries. Conclusions Our proteomic analysis performed using the discovery-through-verification pipeline revealed distinct variations caused by age factor in both healthy and cariogenic salivary proteomes, highlighting the significance of age in the great potential of saliva for caries diagnosis and biomarker discovery. Electronic supplementary material The online version of this article (10.1186/s12967-018-1669-2) contains supplementary material, which is available to authorized users.
Page 2 of 14 Wang et al. J Transl Med (2018) 16:293 Background Human saliva is mainly composed of the secretions from the parotid, submandibular, sublingual and minor salivary glands, with functional roles in protecting against tooth demineralization and microbial infection, participating in acquired enamel pellicle formation, and maintaining of the normal equilibrium buffer state [1][2][3]. Salivary proteins are a smaller component but are still crucial for reflecting the health status or disease susceptibility to oral and systemic pathologies. Alterations in salivary protein composition can be monitored using diagnostics techniques and compared with other clinical parameters. It is known that the composition of saliva varies with the human physiological states [4]. Changes in the production and concentration of saliva with aging have been reported [5]. Age-related variations in the salivary composition and gland morphology have been reported in healthy individuals [6]. Additionally, animal studies have revealed a reduction in salivary protein synthesis with aging [7]. A previous study compared the differences in the composition of the salivary proteome in healthy subjects stratified according to age by means of 2D-SDS-PAGE [8]. However, only limited and conflicting age-related differences have been noted. By contrast, another study reported no significant age-related changes in the salivary composition [9]. Therefore, a thorough understanding of whole saliva is a prerequisite for its diagnostic utility. Dental caries is by far the most common multifactorial infectious oral disease, caused by complex interactions among cariogenic microorganisms, fermentable carbohydrates and many host factors, including saliva. As the host-associated factor, saliva plays an essential role in the dynamic equilibrium between demineralization and remineralization, and has been suggested to predict the development of caries [10]. Efforts to characterize whole saliva using two-dimension gel electrophoresis, HPLC combined with mass spectrometry, and immunoblotting have resulted in the identification of several salivary proteins associated with caries susceptibility [11,12]. Vitorino et al. previously identified a strong correlation between salivary phosphopeptides and the absence of dental caries using HPLC-MS [13]. More recently, Castro et al. showed higher total protein concentration and salivary IgA level in caries-free adults compared to adults with high caries activity [14]. Nevertheless, as we know, the sensitivity and evolution of caries also depends on the influence of independent risk factors, including age, hygiene practices, education and income, which interact with the salivary components in a protective or a riskincreasing manner [15]. A previous study attempted to explore the relationship between several salivary components and dental caries, concluding that changes in salivary component output during aging are associated with a high caries prevalence [16]. However, limited studies identified only a few differentially expressed proteins without providing a comprehensive understanding of the effect of age on the relationship between changes in the salivary proteome and caries. To our knowledge, a comparative analysis of the human cariogenic salivary proteome along with aging has not yet been established.
With the rapid development of proteomics technology and application of high resolution MS, in-depth proteomic analyses have recently been achievable [17]. Isotope labeling techniques such as iTRAQ (isobaric tags for relative and absolute quantification) have been applied to the biomarker discovery and are particularly useful for quantitatively comparing proteomes between samples obtained from human. Moreover, the significantly shorter lead-time and reduced costs of the multiple reaction monitoring (MRM) assay make it a better alternative to immunoassays in protein biomarker validation to support preclinical and clinical studies [18,19]. As a result of this proteomic technology, our group has already established a salivary proteome profile with a potential therapeutic use in preventing childhood dental caries [20]. Furthermore, to obtain an unrivalled understanding of the role of salivary proteins involved in caries resistance or cariogenicity, we performed a comparative analysis of salivary proteomes from caries-free to cariessusceptible subjects of different ages using iTRAQ coupled with MRM approach in this study.
In the present study, we aimed to (1) identify the salivary proteomic profiles of individuals of different ages presenting with and without dental caries; (2) characterize the changes in salivary proteome influenced by age and caries susceptibility; and (3) seek for age-specific and non-age-specific proteins associated with dental caries. For the first time, comparative salivary proteomics data were constructed for caries-susceptible young adults and the elderly, providing age-specific and non-age-specific candidates with diagnostic or protective value for caries susceptibility and caries prevention.
Subjects and saliva sampling
Written informed consent was obtained from all volunteers participating in this study, and the procedures were approved by the ethics committee of West China Hospital of Stomatology, Sichuan University (NO. WCHSIRB-D-2017-047), and conducted in accordance with the ethical guidelines. Saliva samples were randomly collected during follow-up clinical examinations at West China Hospital of Stomatology, according to the criteria defined by the World Health Organization [21], and then divided into four groups: 20 young adults aged between 19 and 24 years (mean age of 20.5 years) including caries-free (ACF, n = 10, DMFT = 0) and caries-susceptible (ACS, n = 10, DMFT ≥ 5) individuals, and 20 elderly subjects aged between 62 and 89 years (mean age of 82.8 years) including caries-free (ECF, n = 10, DMFT = 0) and caries-susceptible (ECS, n = 10, DMFT ≥ 5) individuals. A significant difference in the gender distribution was not observed among different groups. Inclusion criteria for all participating subjects with permanent dentition were an absence of severe systemic disorders and other detectable oral diseases, and no use of systemic antibiotics or antibacterial mouth rinse within the past 1 month.
Saliva collection was performed between 9:00 and 11:00 a.m. Subjects were informed in advance not to eat or to drink for at least 2 h before sampling [22]. A total of 3 ml spontaneous, whole unstimulated saliva was collected from each donor in a sterile enzyme-free conical tube according to the standard techniques [23]. After collection, all saliva samples were immediately transferred to the laboratory on ice. Supernatants were obtained through centrifugation at 12,000 rpm for 5 min at 4 °C, and then a protease inhibitor cocktail (Sigma-Aldrich, St Louis, MO, USA) was added to prevent proteolytic degradation within 2 h of collection [20]. After aliquoting, samples were stored at − 80 °C until further analyses.
Extraction and trypsin digestion of whole salivary proteins
The salivary proteins from each group were pooled, reduced by adding 10 mM dithiothreitol and incubating at 56 °C for 60 min, and alkylated with 55 mM iodoacetamide at room temperature in the dark for 60 min. Afterwards, the treated proteins were precipitated in 80% acetone at − 20 °C for 3 h, and were then centrifuged at 20,000g for 30 min at 4 °C. The pellets were resuspended in 500 mM triethyl ammonium bicarbonate buffer containing 0.1% SDS. Each saliva pool was prepared using equal amounts of total protein from each group, and analyzed using SDS-PAGE. Duplicate aliquots of 100 µg of treated proteins were digested with trypsin (1:30 w/w, Promega, Madison, USA) overnight at 37 °C.
iTRAQ labeling and SCX fractionation
For iTRAQ analysis, the tryptic peptides in each group of technical duplicates were labeled with iTRAQ reagents for 8-plex reaction according to the manufacturer's instructions (Applied Biosystems, Foster City, USA), using 115 and 116 tags for the ACF group, 113 and 114 tags for the ACS group, 117 and 118 tags for the ECF group, and 119 and 121 tags for the ECS group, respectively. After 2 h of labeling reactions, each labeled peptide segments were mixed, further purified using Strata-X-C (Phenomenex, Torrance, USA), and then lyophilized with a Speed-vacuum to remove the reaction solvents. A detailed description of strong cation-exchange chromatography (SCX) fractionation is provided in Additional file 1.
Identification of peptides using LC-MS/MS
Each SCX fraction was loaded twice onto a nano-RP column mounted on a Dionex ultimate 3000 nano-HPLC system (Shimadzu, Kyoto, Japan), and then eluted using an ACN gradient from 5 to 80% (v/v) containing 0.1% formic acid over 45 min at a flow rate of 300 nl/min. The eluates were directly injected into a Q-Exactive mass spectrometer (Thermo Fisher Scientific, Waltham, MA, USA), run in a positive ion mode with a full MS scan from 350 to 2000 m/z. The MS/MS spectra were acquired in a data-dependent mode and a high-sensitivity manner using the following parameters: full scans acquired at a resolution of 70,000 and MS/MS scans at a resolution of 17,500 with a minimum signal threshold of 1E+5.
iTRAQ data processing and bioinformatics analyses
For iTRAQ-based protein identification, the original mass data were processed with Proteome Discover 1.3 (Thermo Fisher Scientific, Waltham, MA, USA; version 1.3) and searched with the Mascot search engine (Matrix Science, Boston, MA, USA; version 2.3.01) against the Uniprot protein database (http:// www.unipr ot.org) for Homo sapiens containing 20,199 sequences (release date 15.03.2016). Carbamidomethyl cysteine was specified as a fixed modification, with a tolerance of one missed cleavage site in the trypsin digests. Gln → pyro-Glu (N-term Q), oxidation (M), iTRAQ 8-plex (K), iTRAQ 8-plex (Y), and iTRAQ-8 plex (N-term) for methionine were selected as the potential variable modifications. The precursor mass tolerance was 15 ppm, and the product ion tolerance was 20 mmu. For protein identification, the following filters were used: significance threshold P < 0.05 (with 95% confidence) and ion score or expected cutoff less than 0.05 (with 95% confidence). For protein quantification, proteins for which at least one unique peptide was detected and the overall false discovery rate (FDR) was less than 1% were qualified for further analysis. The quantitative protein ratios were weighted and normalized to the median ratio in Mascot. Student's t-test was performed to determine the significance of the differences in the levels of each protein when two groups were compared in each repetition. To be identified as being significantly differentially expressed, proteins were quantified in two biological replicates, along with a Fisher's combined probability of < 0.05 and a fold change ± 1.2 (the average ratio of two repeat experiments). Additional filtering was performed using Bonferroni's correction for multiple comparisons as necessary (P < 0.0125). The use of a conservative criterion was motivated by the goal of selecting a small subset of putative but reliable biomarkers.
Functional annotations of the identified proteins were conducted by performing gene ontology (GO) analysis of biological processes, molecular functions and cellular components. The Kyoto Encyclopedia of Genes and Genomes database (KEGG; http://www. genom e.jp/kegg/pathw ay.html) was used to identify the majority of the important proteins involved in biological metabolic and signal transduction pathways. P values less than 0.05 were considered statistically significant using a two-tailed Fisher's exact test. A hierarchical clustering (HCL) analysis of the quantitative data in the four comparative groups was performed using Cluster 3.0 software (Stanford University, USA) and visualized using Java Treeview software. The analysis of the protein-protein interaction (PPI) network was analyzed using the STRING online database (http://strin g-db.org) [24].
Candidates verification using LC-MRM-MS
MRM assays were used to validate the differentially expressed proteins identified in the iTRAQ analysis. Details of the MRM analysis were referred to the procedure in our previous study [20] with some modifications as well as described in Additional file 1.
Statistical analysis
Statistical calculations were performed using SPSS software version 19.0 (Chicago, IL, USA) and Graph-Pad Prism version 6.0 (San Diego, CA, USA). The unpaired Student's t-test was employed to evaluate the differences between groups, which were considered statistically significant at P values less than 0.05.
Overall workflow and iTRAQ-based quantification salivary proteomics
Four pooled saliva samples from the ACF, ACS, ECF, and ECS groups were used for this study. The demographic and clinical characteristics of all subjects are shown in Table 1 (Additional file 2: Table S1). The mean DMFT for two different aged groups showed no significant difference between males and females (P > 0.05). Quantitative proteomic analysis of whole saliva samples was performed using the iTRAQ-coupled LC-MS/MS method. The workflow of this study is illustrated in Fig. 1a. The protein composition of saliva samples from subjects of different ages presenting with and without caries showed visibly distinct band patterns via gel electrophoresis (Additional file 2: Figure S1), indicating the significance of the research regarding age-related changes in healthy and cariogenic human salivary proteomes.
Equal amounts of salivary proteins from four groups (100 μg for each group) with technical duplicates were pooled for the iTRAQ analysis. For protein quantification, the Pearson correlation analysis of the normalized tag intensities of spectra revealed a high reproducibility, with correlation coefficients exceeding 0.93 between technical duplicates from the four groups (Additional file 2: Figure S2). Thus, the spectra from technical duplicates were combined for further analysis. A total of 4564 unique peptides corresponding to 658 proteins (unique peptides ≥ 1) were identified, with a 1% false-positive rate at the protein level (Additional file 3). The distribution of the protein sequence coverage was analyzed for all proteins identified by iTRAQ (Fig. 1b). Based on these results, iTRAQ was able to cover the majority of the expressed salivary proteins. As for defining differentially expressed proteins, the criteria were established by P value < 0.05 and fold change > 1.2. Overall, 435 differentially expressed proteins were identified, 386 of which were significant after Bonferroni's correction (P < 0.0125) (Additional file 4). For the quantitative analysis depicted in Fig. 1c, a Venn diagram was used to view the distribution of differentially expressed proteins and their overlaps among the four comparison groups. Of these, 17 proteins were commonly present in all comparisons, whereas 20, 28, 110, and 24 differentially expressed proteins were exclusively identified in the comparison groups of ACF vs ACS, ECF vs ECS, ACF vs ECF, and ACS vs ECS, respectively (Additional file 5). Importantly, the greatest number of differentially expressed proteins were identified in ACF vs ECF, followed by ACS vs ECS and ECF vs ECS, and the fewest number was identified in ACF vs ACS (Fig. 1d, Additional file 6). Compared with ECF group, 188 up-regulated proteins and 145 down-regulated proteins were identified in the ACF group, whereas 50 proteins displaying increased expression and 94 proteins exhibiting decreased expression were detected in the ECS group (Fig. 1d). Meanwhile, 79 up-regulated and 34 down-regulated proteins were identified in ACF compared to ACS group. Regarding the comparison between caries-susceptible young adults and elderly individuals, a total of 203 differentially expressed salivary proteins, including 155 overexpressed and 48 underexpressed proteins, were found in ACS group compared to ECS group (Fig. 1d).
Comparative analysis of age-associated and caries-associated salivary proteins
The influences of age and caries susceptibility on the human salivary proteome were then evaluated more comprehensively. According to the volcano plots of differentially expressed proteins, more significant variations in the salivary proteomes were observed between both age groups than between groups with and without caries (Fig. 2). Second, a far greater number of differentially expressed proteins was identified in both comparisons of different aged healthy groups and different aged cariessusceptible groups than that in the other two comparison groups. Furthermore, 110 specific differentially expressed proteins were identified between young adults and elderly individuals without caries, a number that was much more than the other three comparison groups (Fig. 1c). Therefore, age caused more significant alterations and played an important role in determining the caries-free and caries-susceptible human salivary proteomes.
Comparative analysis of age-specific and non-age-specific salivary proteins associated with dental caries Next, we conducted the comparison between ACF vs ACS and ECF vs ECS after mass spectrometry-based identification to further understand the age-specific alterations in salivary proteome of caries-susceptible individuals. Of the 215 differentially expressed proteins, 42 non-age-specific proteins overlapped between ACF vs ACS and ECF vs ECS. Among these proteins, 18 were detected in low levels in all patients of different ages with caries, such as histatin-1, BPI fold containing family B member 1, lipocalin-1, and protein S100-A9. The other 24 overlapping proteins showed different trends for changes in expression in the two comparison groups (Fig. 3a, Additional file 7). For example, cystatin B was detected at higher levels in saliva from ACF than ACS group, although it was present in lower amounts in ECF compared with ECS group. On the other hand, 71 specific differentially expressed proteins (46 up-regulated and 25 down-regulated) were identified in ACF vs ACS comparison group, and 102 unique differentially expressed proteins (67 up-regulated and 35 downregulated) were identified in ECF vs ECS comparison group (Fig. 3a, Additional file 7). The log ratio of the relative intensity was illustrated to better visualize the salivary proteins that were differentially influenced by dental caries and aging (Fig. 3b, Additional file 2: Figure S3). Specifically, we also performed comparative analyses among ACF vs ACS, ECF vs ECS, and ACS vs ECS groups after excluding the proteins that overlapped with ACF vs ECF group. Eventually, 96 age-specific and 6 non-age-specific proteins were associated with dental caries, which were then selected for further validation (Fig. 3c, Additional file 8).
Functional assessment of differentially expressed proteins among different comparison groups
Gene ontology (GO) terms were further assigned to differentially expressed proteins according to the cellular components, molecular functions and biological processes (Fig. 4, Additional file 9). From the cellular component perspective, it can be noticed that the majority differentially expressed proteins in all comparison groups were located in the extracellular region (56.6% in ACF vs ACS, 29.2% in ECF vs ECS, 61.3% in ACS vs ECS, and 43.1% in ACF vs ECF). Regarding the molecular function, the differentially expressed proteins in both comparisons of different aged healthy groups and different aged caries-susceptible groups (ACF vs ECF, and ACS vs ECS) were involved in antigen binding (9.3%, 14.2%). Molecular function regulator (P value 0.036) and enzyme regulator activity (P value 0.026) were the top two significantly enriched terms in ACF vs ACS group, while lipid binding (P value 0.0004) and serine-type endopeptidase inhibitor activity (P value 0.014) were the top two significantly enriched terms in ECF vs ECS group. From the perspective of biological process, the most enriched terms were wound healing (P value 0.025) in ACF vs ACS, inflammatory response (P value 0.000059) in ECF vs ECS, extracellular matrix organization (P value 0.032) in ACF vs ECF, and defense response (P value 0.0057) in ACS vs ECS, respectively. Noticeably, in the KEGG pathway enrichment analysis, all the three comparison groups of ACF vs ACS, ACF vs ECF, and ACS vs ECS shared the same most significantly enriched pathway: salivary secretion. In addition, the top pathway in which differentially expressed proteins in ECF vs ECS group was involved was the gluconeogenesis pathway (Fig. 5, Additional file 10). Afterwards, a hierarchical clustering (HCL) analysis was used to reveal different features of age-and caries-associated salivary proteomes, nicely separating the experimental groups and their replicates into four comparison groups (Additional file 2: Figure S4). Moreover, the ACF vs ECF and ACS vs ECS groups were clustered together, while the ACF vs ACS and ECF vs ECS groups were grouped into a separate cluster. These results directly confirmed the visible difference between age and caries-associated salivary proteome profiling. An integrated analysis of proteins expressed at different levels among the four comparison groups with successful validation was performed using the STRING online database, excluding proteins without information in the STRING database. The protein-protein interaction (PPI) network contained 115 proteins and 388 protein-protein interactions (Fig. 6, Additional file 11), in which alpha-1-antitrypsin and lysozyme C were key proteins and interacted with 24 and 19 proteins, respectively.
Verification of candidate salivary proteins using MRM-MS
To further verify the reliability of the iTRAQ results, MRM analysis was performed. Consistent with the reported data [25,26], as well as the differentially expressed proteins analyses, a total of 136 candidate proteins, including 36, 30, 56, and 113 proteins in comparison groups of ACF vs ACS, ECF vs ECS, ACS vs ECS, and ACF vs ECF, were selected and then successfully verified using an established MRM method (Additional file 12). Based on the results of MRM assay, the expression levels of these target proteins in different comparison groups were consistent with the iTRAQ expression patterns (Additional file 2: Figure S5, S6). The difference between the expression levels may have been due to the use of different detection methods.
Regarding the age-specific proteins in caries-free individuals, the MRM analysis validated 113 differentially expressed proteins in the ACF vs ECF group. Among them, 29 unique proteins, including 10 up-regulated and 19 down-regulated proteins, were further confirmed (Additional file 2: Figure S6). Compared with orally healthy elderly subjects, the MRM results revealed that the FAM3D and poly(U)-specific endoribonuclease proteins were up-regulated 3.40-and 2.67-fold, whereas apolipoprotein A-I and haptoglobin was down-regulated 12.76-and 9.01-fold in the saliva of young adults without caries, consistent with their expressed trends in the iTRAQ results (Additional file 2: Figure S6; Additional file 12). Additionally, the functional assessment showed that the up-regulated proteins in the ACF group were 16:293 primarily involved in the immune response, complement activation, and serine-type endopeptidase activity, while the up-regulated proteins in the ECF group were mainly associated with neutrophil degranulation, metal binding, lipid metabolism, protein stabilization, and actin binding. For the analysis of age-specific and non-age-specific proteins in caries-susceptible individuals, MRM analysis verified 17 specific proteins among ACF vs ACS, ECF vs ECS, and ACS vs ECS groups after excluding proteins that overlapped with ACF vs ECF group. Fourteen of these age-specific proteins, such as cornulin, myeloblastin, keratin type II cytoskeletal 2 epidermal, keratin type II cytoskeletal 5, and keratin type I cytoskeletal 10, were confirmed to be associated with dental caries (Fig. 7, Additional file 13). The functional analysis showed that these age-specific proteins associated with dental caries were mainly involved in calcium ion binding, protein domain specific binding, cellular response to oxidative stress, keratinization, serine-type endopeptidase activity, antimicrobial humoral response, and regulation of immune response. On the other hand, 3 non-age-specific proteins, including histatin-1, BPI fold-containing family B member 1, and alpha-enolase were determined to be associated with dental caries (Fig. 7, Additional file 13). Importantly, histatin-1 and BPI fold-containing family B member 1 were down-regulated in both caries-susceptible young adults and elderly subjects compared to orally healthy controls, and were mainly associated with antimicrobial humoral response. By contrast, alpha-enolase showed different expression trends between the two comparison groups of ACF vs ACS and ECF vs ECS.
Discussion
In this study, we analyzed the impact of age on the variations in caries-free and caries-susceptible human salivary proteomes based on a quantitative iTRAQ analysis. The proteomics data were constructed for four comparison groups of different ages and different caries-susceptibilities, and a total of 435 differentially expressed proteins were identified. These proteins exhibited a broad range of biological functions, with most involved in salivary secretion. In aspects of salivary gland function, flow rates of unstimulated whole saliva, as well as unstimulated and stimulated submandibular/sublingual saliva decreased with aging [27]. As we know, saliva serves multiple functions in the oral cavity, and its anti-caries activity depends on the remineralization, buffering, rinsing and anti-bacterial capacities. Decreased saliva secretion is considered a major problem related to caries prevalence [16]. Our results confirmed the consensus that human salivary secretion changes during aging and caries processes. In addition, we also compared the influences of age and caries susceptibility on the salivary proteome variations. Our finding implied that the effect of age on the salivary proteome was more significant than the caries status, highlighting an important effect of age on both healthy and cariogenic salivary proteomes.
During normal aging, the physiological states of the human body and oral microbial communities may change significantly, which might be conceivably cause variations in salivary proteome [28]. In the comparison between caries-free young adults and the elderly (ACF vs ECF), 110 unique proteins were identified from the iTRAQ results. Twenty-nine of these proteins were further verified using MRM analysis and were mainly associated with the immune response and complement activation. Our results were consistent with Sun et al. [29] who showed that salivary glycoproteins associated with aging were involved in the immune response and oral cavity protection. Therefore, these 29 age-related proteins might play a dominant role in the maintaining of oral health and homeostasis. In particular, apolipoprotein A-I showed the highest MRM relative abundance in the caries-free elderly individuals relative to young adults. Apolipoproteins have recently been suggested to be particularly relevant to the aging process and longevity by playing crucial roles in human immune functions [30]. When comparing the two groups between ACF vs ACS and ECF vs ECS, 18 common proteins with lower relative abundances in both caries-susceptible young adults and the elderly were identified, such as mucin-5B, histatin-1, BPI fold-containing family B member 1, protein S100-A9, protein S100-A8 and lipocalin-1, indicating their potential protective effects on dental caries. For example, mucin-5B has been implicated in the clearance of cariogenic bacteria in the oral cavity through reducing the attachment and biofilm formation of Streptococcus mutans [31]. Protein S100-A9 is a calcium-and zincbinding protein with a prominent role in regulating the immune response and antimicrobial humoral response, and has also been reported to be associated with dental caries [32]. Protein-protein interactions are a common physiological mechanism for the protection and function of proteins in saliva. The STRING protein database was found to be useful for studying and predicting protein-protein associations [33]. In our previous study, the STRING online database, we identified 63 interactions in saliva samples from children with and without dental caries, and reported associations among histatin-1, mucin-5B, mucin-7, and cystatin S [20]. Consistent with these findings, the protein-protein interaction networks identified in the present study also corroborated this biological framework, highlighting their important roles in Fig. 7 MRM verification of age-specific and non-age-specific proteins related to dental caries. a Heatmap illustrating the changes in the expression of age-specific and non-age-specific proteins in ACF vs ACS, ECF vs ECS, and ACS vs ECS groups measured by MRM and iTRAQ. b Venn diagram showing the differentially expressed proteins verified by MRM among ACF vs ACS, ECF vs ECS, and ACS vs ECS after excluding the proteins that overlapped with ACF vs ECF protecting the oral cavity across all ages. Therefore, the PPI network predicted from the STRING database in this study could provide a potentially useful platform for further exploration of the molecular mechanism underlying the complex interplay among different salivary proteins, which might be a more promising method for identifying caries-susceptible individuals. Notably, a separate network was predicted that contained the interactions of keratin type II cytoskeletal 1, keratin type II cytoskeletal 2 epidermal, keratin type II cytoskeletal 5, keratin type I cytoskeletal 9, keratin type I cytoskeletal 10, and desmoglein-3, which were mainly involved in the biological process of cornification and keratinization. Moreover, the down-regulation of keratin type II cytoskeletal 2 epidermal, keratin type II cytoskeletal 5, and keratin type I cytoskeletal 10 in caries-susceptible elderly individuals was also confirmed in the MRM analysis, potentially indicating an abnormal oral condition of those elderly subjects susceptible to dental caries. According to recent studies, a set of keratins was incorporated into mature enamel, and keratin 75 mutations are associated with increased susceptibility to dental caries [34,35].
Keratins have the ability to spontaneously self-assemble and polymerize, facilitating the development of various types of biomaterials, such as porous scaffolds, films and hydrogels [35]. Combined with these supporting findings, our results indicated that keratins might potentially be used as novel tools for enamel repair and caries prevention, particularly for senile caries. However, additional studies are needed to validate these key screened proteins in a larger sample size, to further investigate the mechanism by which keratins protect against dental caries, and to translate these proteins from the laboratory level into clinical applications.
To further confirm the age-specific and non-age-specific salivary proteins related to dental caries, we narrowed the comparisons among ACF vs ACS, ECF vs ECS, and ACS vs ECS by excluding the differentially expressed proteins that overlapped with ACF vs ECF group. As a result of MRM, 14 age-specific proteins were verified to be associated with dental caries, among which glutathione S-transferase P, peroxiredoxin-6, WD repeatcontaining protein 1, and glucose-6-phosphate isomerase exhibited complex interactions with each other. Their biological activities in the context of dental caries in subjects of different ages warrant future investigations. Additionally, as a serine protease involved in the antimicrobial humoral response, myeloblastin interacted with lysozyme C and mucin-5B, and was expressed at lower levels in caries-susceptible young adults than in the elderly. These results implied that the complex interaction among several salivary proteins and their functions associated with dental caries might differ in subjects of different ages in the way they act or in their degrees of importance, which should be considered distinct markers for adult and elderly population. In an attempt to put our results to good use, we propose that these age-specific proteins determined from an analysis of proteome variations in whole saliva could provide suitability for caries biomarker screening among different age groups. Of those non-age-specific proteins, histatin-1 and BPI foldcontaining family B member 1, which are involved in the antimicrobial humoral response, were down-regulated in caries-susceptible young adults and the elderly compared to healthy controls. This result highlighted strong correlations between the absence of dental caries and high levels of histatin-1 and BPI fold-containing family B member 1. Histatin-1 is a major factor present in the protective proteinaceous structure on the tooth surface with antibacterial and antifungal activity, and displays a significant role in maintaining tooth integrity and protection against cariogenic bacteria [36,37]. Interestingly, histatin-1 also showed decreased salivary abundance in caries-positive children in our previous study, and histatin-1 was suggested to be an important candidate biomarker of childhood caries [13,20,36]. To further provide stronger evidence for histatin-1 as a candidate biomarker applicable for detecting dental caries in all age groups, more indepth studies on the intrinsic mechanisms underlying the functions of histatin-1 and the occurrence and development of dental caries will be performed in larger patient cohorts in the future.
Conclusions
In summary, this study applied the discovery-throughverification pipeline to construct the first salivary proteomics map for individuals of different ages presenting with and without dental caries by means of iTRAQ/MRM technology. Our results indicated that age-specific differences existed in the unstimulated salivary proteome, and caused more significant variations in the salivary proteome than caries status. The obtained protein data from the present study contribute to improving our understanding of the effect of aging on the healthy and cariogenic salivary proteomes, highlighting the importance of age in the great potential of saliva for caries diagnosis and biomarker discovery. And the 14 age-specific proteins identified in this dataset hold not only important salivary candidates correlated with caries susceptibility in different age groups, but also serve as potential targets for preventive strategies against dental caries in the future. Moreover, two differentially expressed proteins, histatin-1 and BPI fold-containing family B member 1, were validated to be non-age-specific candidate biomarkers of | 7,606.2 | 2018-10-25T00:00:00.000 | [
"Medicine",
"Biology"
] |
Low-cost and clinically applicable copy number profiling using repeat DNA
Background Somatic copy number alterations (SCNAs) are an important class of genomic alteration in cancer. They are frequently observed in cancer samples, with studies showing that, on average, SCNAs affect 34% of a cancer cell’s genome. Furthermore, SCNAs have been shown to be major drivers of tumour development and have been associated with response to therapy and prognosis. Large-scale cancer genome studies suggest that tumours are driven by somatic copy number alterations (SCNAs) or single-nucleotide variants (SNVs). Despite the frequency of SCNAs and their clinical relevance, the use of genomics assays in the clinic is biased towards targeted gene panels, which identify SNVs but provide limited scope to detect SCNAs throughout the genome. There is a need for a comparably low-cost and simple method for high-resolution SCNA profiling. Results We present conliga, a fully probabilistic method that infers SCNA profiles from a low-cost, simple, and clinically-relevant assay (FAST-SeqS). When applied to 11 high-purity oesophageal adenocarcinoma samples, we obtain good agreement (Spearman’s rank correlation coefficient, rs=0.94) between conliga’s inferred SCNA profiles using FAST-SeqS data (approximately £14 per sample) and those inferred by ASCAT using high-coverage WGS (gold-standard). We find that conliga outperforms CNVkit (rs=0.89), also applied to FAST-SeqS data, and is comparable to QDNAseq (rs=0.96) applied to low-coverage WGS, which is approximately four-fold more expensive, more laborious and less clinically-relevant. By performing an in silico dilution series experiment, we find that conliga is particularly suited to detecting SCNAs in low tumour purity samples. At two million reads per sample, conliga is able to detect SCNAs in all nine samples at 3% tumour purity and as low as 0.5% purity in one sample. Crucially, we show that conliga’s hidden state information can be used to decide when a sample is abnormal or normal, whereas CNVkit and QDNAseq cannot provide this critical information. Conclusions We show that conliga provides high-resolution SCNA profiles using a convenient, low-cost assay. We believe conliga makes FAST-SeqS a more clinically valuable assay as well as a useful research tool, enabling inexpensive and fast copy number profiling of pre-malignant and cancer samples. Supplementary Information The online version contains supplementary material available at (10.1186/s12864-022-08681-8).
Next-generation sequencing
We calculated the per sample cost based on using an Illumina HiSeq 4000 sequencer which, for our purposes, produces 350 million single end (SE) 150 base pair (bp) reads from a single lane of sequencing. We factored in that our library would include 20% PhiX to increase diversity for sequencing, and as such, we would expect 280 million reads per lane to originate from our FAST-SeqS amplicons. Aiming for approximately 2 million reads per sample, this would mean multiplexing 140 FAST-SeqS on a single lane.
There is considerable variation in the cost of sequencing services, depending on sector, location, and relationship with the customer. Moreover, of those services that display their costs up front, extremely few provide a direct comparison of prices for Single-End 50bp reads and Single-End 150bp reads on an Illumina HiSeq 4000 machine. Thus, we will make use here of the Stanford Medicine Genome Servicing Sequence Centre prices, roughly converted to Sterling, obtained from http://med.stanford.edu/gssc/rates.html on 17/08/18. These costs do not differ substantially from our own experience. Thus, the cost of a single lane 150 bp SE sequencing on the HiSeq 4000 we take to be approximately £1400 at the time of writing. As such, the sequencing cost equates to £10 per sample.
DNA Shearing
Prior to library preparation, the input DNA needs to be sheared to a desired length distribution. This is often achieved by the use of sonification, for example using Covaris microTUBE strips. At the time of writing, 12 x 8 microTUBE strips (i.e. for 96 samples) can be purchased for £413.10 and is therefore approximately £4.30 per sample.
Library preparation
To process the DNA and prepare the library for sequencing, library preparation is required. This generally consists of end-repair, adapter ligation, and is sometimes followed by PCR amplification to generate sufficient quantities of the library for sequencing. Library preparation kits can be purchased from a variety of manufacturers, with varying costs and time to prepare each sample. Examples of library preparations include:
DNA Quantification and Quality Control
Similarly to FAST-SeqS, quantification of DNA is performed using Bioanalyzer 1000 DNA kit on an Agilent 2100 Bioanalyzer instrument, for example. 300 Bioanalyzer 1000 DNA chips can be purchased at approximately £500, which equates to £1.67 per sample.
Next-generation sequencing
We calculated the per sample cost based on using an Illumina HiSeq 4000 sequencer, which can be used for lowcoverage WGS to produce 350 million single end (SE) 50 base pair (bp) reads from a single lane of sequencing.
PhiX should not be required as the library should not be low complexity. To achieve approximately 9 million reads per sample in order to obtain approximately 0.1X coverage as per Scheinin et al. [1], would mean multiplexing 38 samples on a single lane. The cost of a single lane 50 bp SE sequencing on the HiSeq 4000 we take to be £1000 (justification as in the previous section). As such, the sequencing cost equates to ∼£26 per sample.
Supplementary Note 2: Aspects of FAST-SeqS data
We explored the loci counts of normal samples (which were assumed to be predominantly diploid) and observed various aspects of the data which led to the model. We observed (1) a technical bias in the number of reads This could be extended to include all J non-control samples, so that β, π 0 , π u ,ĉ u , z r,l ,s,θ r,l , y r,l andñ are sample specific and include an index j. However, here we drop the j index and consider only one non-control sample for simplicity.
m r,l | ϕ c,r,l , ϕ d,r,l ∼ Beta(ϕ c,r,l , ϕ d,r,l ) θ r,l,k | s k , m r,l ∼ Beta(s k m r,l , s k (1 − m r,l )) x r,l,k | θ r,l,k , n k ∼ Binomial(n k , θ r,l,k ) θ r,l | {ĉ u } ∞ u=1 , z r,l ,m r,l ,s ∼ Beta(sĉ z r,lm r,l ,s(1 −ĉ z r,lm r,l )) y r,l |θ r,l ,ñ, ∼ Binomial(ñ,θ r,l ) See Supplementary Table 1 and Methods for an explanation of the variables. Note that this model is not implemented but is shown for completeness (see below for how we split this generative model into two separate generative models in practice). Notice that we assume that the sample inverse dispersion parameters are drawn from the same distribution, reflecting our belief that normal and tumor count observations should have the same level of noise. Here we assume fixed values for ω. If we were to use this model as a basis for inference of the latent variables, we may wish to place priors over the values of ω and infer them from the data.
Split generative model (for more efficient inference)
We decided to split the full model in two parts. The first part describes the generation of the data for the control samples. The second part describes the generation of the copy number profile and loci count observations for a non-control sample, using the maximum a prior (MAP) estimate of m. We did this to allow for simpler implementation of the inference algorithms. In this way, we could infer the MAP estimates of m and the nuisance parameters s using the counts of the control samples. Once MAP estimates were obtained, we could infer the copy number profile for each non-control sample in independent MCMC chains, allowing the inference of each sample to be run in parallel.
Part 1: Generative model for control counts
x r,l,k | θ r,l,k , n k ∼ Binomial(n k , θ r,l,k ) (2) Part 2: Generative model for the counts of a sample with a relative copy number profile , z r,l ,m r,l ,s ∼ Beta(sĉ z r,lm r,l ,s(1 −ĉ z r,lm r,l )) y r,l |θ r,l ,ñ, ∼ Binomial(ñ,θ r,l ) Note that here we allow the distribution of sample specific parameters to vary between the normals (in part 1) and the sample with relative copy number profile z (in part 2). This distinction is made so that we can use the posterior distribution of s k to update our prior distribution overs.
Supplementary Note 4: Notation used in MCMC algorithms
We denote the probability mass function (pmf) of the compound Beta-Binomial distribution as follows: where B represents the Beta function, n represents the total number of Bernoulli trials (counts), k represents a count observation (k ∈ { 0, . . . , n }), a and b are parameters (a > 0, b > 0). This is used as our likelihood function in algorithm 1 where k = x r,l,k , n = n k , a = s k m r,l , and b = s k (1 − m r,l ). It is also used as a likelihood function in algorithm 2 where k = y r,l , n =ñ, a =sm r,l , and b =s(1 −m r,l ).
We denote the probability density function (pdf) of the Beta distribution as follows: where x represents an observation (x ∈ [0, 1]), and c and d are the shape parameters of the Beta distribution We denote the pdf of the Gamma distribution as: where Γ represents the Gamma function, k is the shape parameter (k > 0), θ is the scale parameter (θ > 0) and observation x (where x ≥ 0).
The normal distribution is denoted N (µ, σ) and the uniform distribution is denoted U (a, b). We use the follow notation: M·,·+γ η ∼ Beta γ + 1,M ·,· Then sample γ as follows: If not provided as a fixed value, sample ρ: | 2,293.2 | 2022-08-17T00:00:00.000 | [
"Biology"
] |
Gene discovery and virus-induced gene silencing reveal branched pathways to major classes of bioactive diterpenoids in Euphorbia peplus
Significance Euphorbia peplus, a member of the Euphorbia genus, is rich in jatrophane and ingenane diterpenoids. Using a metabolomics-guided transcriptomic approach to gene candidate identification, we have discovered a short-chain dehydrogenase gene involved in the production of the lathyrane jolkinol E. We have developed a virus-induced gene-silencing method in E. peplus that has allowed us to demonstrate the direct relationship between casbene and polycyclic diterpenoids and that jolkinol C acts as a key branch point intermediate in the production of ingenanes and jatrophanes. This work contributes both knowledge and tools for engineering production of bioactive diterpenoids in heterologous host systems, thus enabling their further evaluation and development.
Most macro-and polycyclic Euphorbiaceae diterpenoids derive from the common C 20 precursor casbene. While the biosynthetic pathway from casbene to the lathyrane jolkinol C is characterized, pathways to other more complex classes of bioactive diterpenoids remain to be elucidated. A metabolomics-guided transcriptomic approach and a genomics approach that led to the discovery of two casbene-derived diterpenoid gene clusters yielded a total of 68 candidate genes that were transiently expressed in Nicotiana benthamiana for activity toward jolkinol C and other lathyranes. We report two shortchain dehydrogenases/reductases (SDRs), identified by RNA sequencing to be highly expressed in Euphorbia peplus latex. One of these, EpSDR-5, is a C3-ketoreductase, converting jolkinol C to the lathyrane jolkinol E. Gene function of EpSDR-5 was further confirmed by heterologous expression in Saccharomyces cerevisiae. To investigate the in vivo role of EpSDR-5, we established virus-induced gene silencing (VIGS) in E. peplus, resulting in a significant reduction in jatrophanes and a corresponding increase in ingenanes. VIGS of Casbene Synthase results in a major reduction in both jatrophanes and ingenanes, the two most abundant classes of E. peplus diterpenoids. VIGS of CYP71D365 had a similar effect, consistent with the previously determined role of this gene in the pathway to jolkinol C. These results point to jolkinol C being a branch point intermediate in the pathways to ingenanes and jatrophanes with EpSDR-5 responsible for the first step from jolkinol C to jatrophane production.
terpenoids j oxidation j cytochrome P450s j short-chain dehydrogenases/reductases j virus-induced gene silencing The Euphorbiaceae family of flowering plants produces a diverse range of 20-carbon casbene-derived diterpenoids (1) including the lathyranes, which are inhibitors of ATP-binding cassette transporters. These transporters are responsible for the efflux of chemotherapy drugs in multidrug-resistant cancers (2) as well as an efflux of drugs for the treatment of fungal (3) and protozoal (4) pathogens. The lathyranes are also believed to serve as precursors of many other bioactive diterpenoids including ingenol mebutate (IM), a licensed pharmaceutical used for the treatment of actinic keratosis, which is extracted from the aerial parts of Euphorbia peplus (5); tigilanol tiglate, an antitumor compound that is extracted from seeds of Fontainea picrosperma (6); and resiniferatoxin, a capsaicin analog currently in phase 1b clinical trials for the treatment of cancer-related intractable pain, which can be extracted from the latex of Euphorbia resinifera, Euphorbia poissonii, and Euphorbia fischeriana (7). Several casbene-derived phorbol esters exhibit in vitro antiviral activities including prostratin, a lead compound for the treatment of latent HIV infections (8), and others that exhibit activity against chikungunya virus and HIV (9). With over 500 isolated structures, jatrophanes make up a particularly large class with members exhibiting various biological activities including a reversal of multidrug resistance in cancer cell lines overexpressing P-glycoprotein (10,11). A low abundance of many of these compounds in their natural hosts (12,13) together with challenging chemical synthesis due to high structural complexity (14)(15)(16) means that alternative production platforms are needed if the full potential for industrial applications is to be realized. Metabolic engineering of microbial, algal, or plant-based production platforms offers such an alternative once the gene toolkit becomes available.
Jolkinol C [1] biosynthesis has been determined in several Euphorbiaceae species including Jatropha curcas (17), Euphorbia lathyris (18), and E. peplus (18). Two P450mediated oxidations introduce keto-and hydroxy-groups at positions 5-, 6-, and 9-, of casbene, thereby enabling a spontaneous intramolecular aldol reaction that forms a new carbon-carbon bond between the 6-and 10-positions. The introduction into Saccharomyces cerevisiae of J. curcas casbene synthase (JcCAS) and two cytochrome P450 Significance Euphorbia peplus, a member of the Euphorbia genus, is rich in jatrophane and ingenane diterpenoids. Using a metabolomics-guided transcriptomic approach to gene candidate identification, we have discovered a short-chain dehydrogenase gene involved in the production of the lathyrane jolkinol E. We have developed a virus-induced genesilencing method in E. peplus that has allowed us to demonstrate the direct relationship between casbene and polycyclic diterpenoids and that jolkinol C acts as a key branch point intermediate in the production of ingenanes and jatrophanes. This work contributes both knowledge and tools for engineering production of bioactive diterpenoids in heterologous host systems, thus enabling their further evaluation and development.
oxidases (CYP726A20 and CYP71D495) along with an alcohol dehydrogenase (JcADH1) results in jolkinol C [1] production at 800 mg/L culture medium (19). Casbene synthesis has also recently been achieved in the green algae Chlamydomonas reinhardtii at a 19-mg/L culture (20). Lathyranes, such as jolkinol C [1], have been proposed as advanced precursors for the biosynthesis of several classes of diterpenoids including ingenanes and tiglanes (21). Recent work has identified several candidate acyl-coenzyme A ligases potentially involved in angeloylation of ingenol to IM (22). However, the biosynthetic pathways leading from casbene to jatrophanes, ingenanes, and other polycyclic diterpenoids remain hypothetical. and the present study addresses this knowledge gap.
Results and Discussion
A Combined Metabolomics and Transcriptomics Approach to Diterpenoid-Related Gene Discovery in E. peplus. Metabolomic and NMR analysis were performed to establish the diterpenoid composition of various tissues of E. peplus and to guide subsequent RNA sequencing (RNAseq) analysis aimed at the discovery of candidate genes involved in the biosynthesis of IM ( Fig. 1 and SI Appendix, Figs. S1 and S2 A and B and Table S1). Three of the ingenanes characterized by NMR, namely, ingenol-3angelate (IM), ingenol-3-angelate-20-acetate, and 20-deoxyingenol-3-angelate, have been described previously (23,24). These ingenanes were most abundant in latex and latex-containing tissues such as main stems and side stems and to a lesser extent in leaves and pods but were absent from latex-free roots ( Fig. 1 and Table S1). The 20-deoxyingenol-3-angelate accumulates in dry seeds ( Fig. 1 and Table S1). IM was only detectable in latex as a very minor constituent (0.11 μg/mg of fresh tissue), while the concentration of its 20-acetylated derivative (ingenol-3-angelate-20-acetate), was 22-fold higher ( Fig. 1 and Table S1) and detectable in other latex-containing tissues and dry seeds. In agreement with previously published data (23,24), we have also found a number of heavily modified jatrophanes (Jatrophanes 1 to 4), carrying between three to six acyl groups in addition to other functional groups, such as a benzoyl group at the 3-position, an isobutanoyl group at the 7-position, and a nicotinic acid ester at the 9-position (SI Appendix, Figs. S1 and S2A). We have identified three additional jatrophanes (Jatrophanes 5 to 7) with mass-to-charge ratio (m/z) spectra that match previously published jatrophanes from E. peplus latex (24) (SI Appendix, Fig. S2B). All seven jatrophanes were most abundant in latex and latex-containing main stem, side stem, and leaf tissues and, except for Jatrophane 7, were absent from latex-free roots ( Fig. 1 and Table S1). Peplusol is a triterpene alcohol with strong antifungal activities (24) that was previously described as being responsible for the physical properties of E. peplus latex (25), but we have now identified it to be also present in pods and latex-free roots ( Fig. 1 and Table S1). It is noteworthy that we only found trace amounts of casbene in seed tissue ( Fig. 1) and lathyranes including jolkinol C were not detected in any of the tissues analyzed, suggesting that the proposed intermediates for IM biosynthesis are rapidly converted to pathway end-products.
To identify candidate genes associated with the biosynthesis of specific metabolites, we performed RNAseq analysis on messenger RNA extracted from both latex-containing tissues (main stems, leaves and pods) and latex-free tissues (roots), as well as isolated latex (SI Appendix, SI Materials and Methods and Table S4). RNAseq data were de novo assembled into 201,887 contigs with an average contig length of 2 kb (1.3-kb median). Further analysis revealed that 1,453 contigs were expressed at a significantly higher level in latex and/or stem tissue (out of a total of 106,578 expressed contigs). Functional annotations were assigned for the selected 1,453 contigs using the SwissProt database. The number of candidate genes was reduced to 46 by focusing on those predicted on the basis of homology to encode enzymes expected to be involved in ingenol synthesis and modification, including cytochrome P450 monooxygenases, dioxygenases, alkenal reductases, hydroxylases, dehydratases, dehydrogenases, and epoxidases (SI Appendix, Fig. S3).
Discovery of Two Gene Clusters Involved in Diterpenoid
Metabolism in E. peplus. Our previous work indicated that the E. peplus CAsbene Synthase (EpCAS) and casbene-5-oxidase (EpCYP726A19) genes are physically linked in the E. peplus genome (26). Further to this, Luo et al. (18) also reported the characterization of jolkinol C biosynthetic genes from E. peplus, in which CYP726A4 appeared to be a casbene-5-hydroxylase, and CYP71D365 was a casbene-9-oxidase (18). We constructed a 2.36-Gbp bacterial artificial chromosome (BAC) library from E. peplus genomic DNA (equivalent to 7× genome coverage) (27) and screened this initially using primers for CYP726A4 and EpCAS. Subsequent rounds of screening, which were performed using primers designed against terminal regions of the BAC ends, led to the identification of two gene clusters containing known genes for casbene synthesis and casbene modification, surrounded by several other genes that could potentially be involved in diterpenoid biosynthesis (SI Appendix, Fig. S4). Gene cluster 1 is 447 Kbp long and contains a casbene synthase sequence next to CYP726A19, confirming our previous results (26). These genes are in close proximity to the previously (Table S1).
published EpADH1 sequence (18) (SI Appendix, Fig. S4), which is adjacent to EpADH2 with 81% identity at the nucleotide level. This gene cluster, composed of 53 genes and 1 retrotransposon, also contains 14 P450 oxidase homologs, mostly from the CYP726A clan, as well as gene homologs of other enzymes potentially involved in diterpenoid biosynthesis. These include dioxygenases, an oxido-reductase, a ketoreductase, an alkenal-reductase, and a crotonase (SI Appendix, Fig. S4). Three of the gene cluster 1 P450 oxidases (CYP726A3, CYP726A5, and CYP726A6) have been previously reported (18). Gene cluster 2 contains functionally characterized CYP726A4 and CYP71D365 (18) surrounded by nine genes potentially involved in diterpenoid oxidation and other modifications, including seven P450 oxidases from the CYP71D and CYP726A clans, a crotonase, and a carboxylesterase (SI Appendix, Fig. S4).
RNAseq-based gene expression profiling of the 5 functionally characterized genes from the 2 gene clusters together with 32 other candidate diterpenoid genes revealed that the Casbene synthase expression pattern broadly overlaps with that of the 3 known casbene oxidases as well as EpADH1, with high expression levels in roots and stems and intermediate levels in developing pods (Fig. 2) Interestingly, Casbene synthase and CYP726A19 expression were extremely low compared to CYP726A4, CYP71D365, and ADH1 in diterpenoid-rich latex tissue (Fig. 2). The coordinate expression of genes associated with these two clusters provides further evidence that they are functionally related, as is the case with other plant gene clusters (28). The majority of cluster 1 genes are expressed highly in stems and at lower levels in roots, but their expression pattern varies among the other tissues (Fig. 2). Crotonase-1, Dioxygenase-1, and Oxido-Reductase from gene cluster 1 are highly expressed in latex, whereas other genes, including EpADH2, Dioxygenase 4, and CYP71D627, are expressed preferentially in roots (Fig. 2). CYP80C15 is the only gene highly expressed in leaves. The majority of cluster 2 genes including the functionally characterized CYP726A4 and CYP71D365 are expressed most highly in stem and pods (Fig. 2). Crotonase 2 and CYP71D626 are the only two genes expressed highly in latex (Fig. 2). A few genes from gene clusters 1 and 2, such as Dioxygenase-2 and Dioxygenase-3, and CYP726A40, were not expressed in any of the tissues analyzed (Fig. 2).
Identification of E. peplus Gene Products That Utilize Jolkinol C [1]/epi-Jolkinol C [2] as Reaction Substrates. A total of 28 E. peplus genes from the 2 gene clusters and 40 candidate genes identified by RNAseq were cloned into pEAQ-HT vectors and transiently expressed in N. benthamiana to test for activity using jolkinol C [1] and epi-jolkinol C [2] as substrates. In all cases, the coinfiltration mixture contained either a candidate gene in the pEAQ-HT vector or an empty vector control together with three isoprenoid precursor-supply genes from Arabidopsis thaliana, namely, AtDXS, AtHDR, and AtGGPPS, in combination with three genes from the previously published jolkinol C biosynthetic gene cluster from J. curcas (17), namely, JcCAS, CYP726A20, and CYP71D495 (SI Appendix, SI Materials and Methods). This particular combination of six genes results in the production of [1] when expressed transiently in N. benthamiana (17,29). Of the 68 genes tested, only 2 members of a 7-gene family of short-chain dehydrogenases/reductases (SDRs), identified by RNAseq to be expressed highly in latex and/or stems (Fig. 2) were found to have activity when transiently expressed in N. benthamiana with the gene combination that produces [1] (Fig. 3). EpSDR-1 produced a peak eluting at 9.4 min (peak 4, Fig. 3A Fig. S4). A peak with a similar retention time and an identical molecular ion had previously been identified as 6,9-dihydroxy-5-ketocasbene (29), which suggested that the product of EpSDR-1 might be structurally related. Production of this peak was accompanied by a slight decrease in the accumulation of [1] and [2] (peaks 1 and 2, Fig. 3A) when compared to the control. Expression of EpSDR-1 also led to a very strong decrease in the level of (3E, 6E, 11E)-8-hydroxy-casba-3,6,11-trien-5,9-dione (peak 3, Fig. 3A).
Expression of codon-optimized EpSDR-5 in the jolkinol-C-producing S. cerevisiae strain did yield jolkinol E, further confirming the functional characterization of this gene. It is noteworthy that EpSDR-5 appears to accept both jolkinol C [1] and epi-jolkinol C [2] as substrates when reducing the 3-keto group to form the two stereoisomers, namely, jolkinol E [5] and epi-jolkinol E [6], in N. benthamiana. However, we were unable to detect epi-jolkinol E [6] while heterologously expressing EpSDR-5 in S. cerevisiae (Fig. 3A). Although engineered S. cerevisiae strains are able to produce epi-jolkinol C, levels are considerably lower than in N. benthamiana (Fig. 3A), which may cause epi-jolkinol E production to fall below detection limits. Alternatively, EpSDR-5 function may be different in S. cerevisiae compared to the plant host with epi-jolkinol C not acting as the substrate. In any case, it is likely that the epijolkinol C conversion represents a promiscuous activity not relevant in the native host, as the vast majority of presumably lathyrane (jolkinol C)-derived jatrophanes, ingenanes, and tiglanes have the C2β methyl group configuration with the C2-epimer methyl configuration not involved.
EpSDR-1 and EpSDR-5 protein sequences also share very low homology (<20%) with two previously characterized Euphorbiaceae alcohol dehydrogenases, namely, EpADH1 from E. peplus and ElADH1 from E. lathyris, and JcADH1 [4], [5] and [6] were determined by NMR (SI Appendix, SI Materials and Methods). Compound numbering corresponds with the peak numbering in A. Lathyrane ring numbering is shown in blue.
from J. curcas (SI Appendix, Fig. S6). These three ADHs belong to the SDR110C family and have a role in jolkinol C biosynthesis in heterologous hosts (18,19). That work demonstrated that the addition of either JcADH1 or ElADH1 to N. benthamiana or S. cerevisiae resulted in dehydrogenation of the hydroxyl groups introduced by cytochrome P450s from E. peplus and E. lathyris at position C5, C6, and C9 of the casbene ring, resulting in a rearrangement and cyclization via an intramolecular aldol reaction and overall increase in jolkinol C production (18,19). To investigate if similar dehydrogenation had any effect on products downstream of jolkinol C, we included JcADH1 from the J. curcas jolkinol C biosynthetic gene cluster (17) in N. benthamiana transient expression experiments but found no effect on the biosynthesis of (3E, 6E, 11E)-8, 9-dihydroxy-casba-3,6,11-trien-5-one [4], jolkinol E [5], or epi-jolkinol E [6] (SI Appendix, Fig. S8).
Although several derivatives of jolkinol E have been detected in the Euphorbiaceae (38), jolkinol E itself has not previously been described as a natural product. Furthermore, the vast majority of the jatrophanes and ingenanes cited in the literature have undergone similar reduction to a 3β-hydroxy group (1,10) and the introduction of a 3-hydroxy functional group renders the ingenol backbone amenable to Angeloylation in the biosynthesis of IM. In contrast, the majority of tiglanes contain a 3-keto functional group (1). If we assume tiglanes are also derived from jolkinol C, this may indicate they are derived from a distinct biosynthetic route to that involved in the production of jatrophanes and ingenanes.
In Planta Confirmation of Diterpene Biosynthetic Activities of E. peplus Genes Using VIGS. We next established virus-induced gene silencing (VIGS) (39) in E. peplus seedlings to directly investigate the in planta role of selected diterpenoid-related genes. This was facilitated by the identification of an E. peplus gene encoding a subunit of Mg chelatase (EpCH42; SI Appendix, Fig. S9), the homolog of which was shown to act as a visual marker for VIGS in J. curcas (40,41). The two genes share 82% nucleotide identity and EpCH42 is expressed highly in leaves and stems (SI Appendix, Fig. S9 A and B). First, chlorosis in cotyledons was seen 5 to 6 d after infiltration of 9-d-old seedlings, progressing to leaves and eventually stems (SI Appendix, Fig. S10). Agrobacterium tumefaciens-based infiltration of pTRV2 VIGS constructs containing EpCH42 either alone or combined with EpCAS, Casbene-9-oxidase (CYP71D365), or jolkinol C 3-ketoreductase (EpSDR-5) into 9-d-old E. peplus seedlings was performed, and chlorotic parts of stems and leaves were harvested around 40 d postinfiltration as described in SI Appendix, SI Materials and Methods. Metabolite analysis revealed that VIGS of EpCAS significantly (over twofold) decreased the level of jatrophanes and ingenanes in stems and leaves ( Fig. 4A and Table S2). Transcript levels of EpCAS were also significantly reduced in stems with a threefold to fourfold reduction compared with EpCH42-infiltrated controls (SI Appendix, Fig. S11A). These in planta results are consistent with the long-held view that jatrophanes and ingenanes are casbene derived in the Euphorbiaceae (10,21). Levels of an abundant triterpene alcohol, peplusol, were not significantly affected in leaves or stems of EpCAS-silenced plants ( Fig. 4A and Table S2), consistent with this natural compound being squalene and not casbene derived.
VIGS of CYP71D365, a key gene in the biosynthesis of jolkinol C resulted in a threefold to fourfold reduction in transcript levels (SI Appendix, Fig. S11 C and D) and over twofold reduction in both jatrophanes and ingenanes in stems with less pronounced effects in leaves (Fig. 4B and Table S3). These Tables S2-S4, and peplusol represents total concentration of the two peaks identified for this compound (Tables S2-S4). Error bars, SEM (n = 5). Statistically significant (t test) changes between control (EpCH42) and diterpenoid-pathway-silenced genes are indicated by asterisks separately for each tissue (*P < 0.05; **P < 0.01). (D) Proposed model for jatrophane and ingenane biosynthetic pathways in E. peplus, based on heterologous expression data (17) and VIGS. Enzymes subjected to VIGS and corresponding reactions are highlighted in red. Solid arrows represent enzymatic reactions; dashed arrows represent proposed nonenzymatic reactions. Note that ingenane and jatrophane structures are presented as consensus molecules that will be subject to further modifications in planta.
results are consistent with the lathyrane jolkinol C being an intermediate in the biosynthetic pathway to both ingenanes and jatrophanes. Biosynthesis of jatrophanes has been postulated to occur either directly from casbene, by the opening of the cyclopropane ring followed by formation of the fivemembered ring between C-6 and C-10, or derived from lathyranes by opening of the cyclopropane ring (10). The results presented in Fig. 4 are consistent with the latter route to jatrophanes in E. peplus. Interestingly, the level of peplusol is also significantly (twofold) reduced by VIGS of CYP71D365 in stems ( Fig. 4B and Table S3). The basis for this reduction is not known, but it could be due to either off-target silencing effects on other P450 oxidases involved in the biosynthesis of peplusol or by direct involvement of CYP71D365 in this process. We have observed a strong accumulation of both 5-ketocasbene and 6-hydroxy-5-ketocasbene in the CYP71D365-silenced stem and leaf tissues, and both of these compounds are on the margins of detectability in control (EpCH42-silenced) plants (Table S3). These in planta results are consistent with the results of a transient expression of CYP71D365 in N. benthamiana that concluded that both 5-ketocasbene and 6-hydroxy-5-ketocasbene are substrates of the corresponding enzyme (18). The VIGS in planta results also indicate that C5-and C6-oxidation of casbene occur before C9-oxidation in the pathway to jolkinol C.
CYP71D365 (casbene-9-oxidase) is present on E. peplus casbene-derived diterpenoids gene cluster 2, and a phylogenetic analysis revealed that it forms a distinct cluster in clade 71D with five other homologs encoded across both gene clusters (SI Appendix, Fig. S12). Very stringent criteria for qRT-PCR primer design (SI Appendix, SI Materials and Methods) revealed that transcript levels of all other CYP71D clade members in CYP71D365-silenced leaf and stem tissue were unchanged (SI Appendix, Fig. S11 C and D). This analysis does demonstrate the high specificity of the VIGS approach, with genes showing up to 70% identity being unaffected. The cause of the decrease in peplusol levels in CYP71D365-silenced leaf and stem tissue remains to be determined.
VIGS of EpSDR-5 resulted in a statistically significant (1.6to 1.8-fold) reduction of jatrophane levels in both leaves and stems ( Fig. 4C and Table S4) and, consistent with this, an over 2-fold reduction in transcript levels (SI Appendix, Fig. S11 E and F). Most interestingly, reduction in jatrophanes was accompanied by a corresponding increase (1.4-to 1.7-fold) in the level of ingenanes in both tissues analyzed. Both the nonacetylated and acetylated forms of IM increase in the EpSDR-5-silenced tissues (Table S4). Levels of peplusol remained unchanged ( Fig. 4C and Table S4). Jolkinol C, casbene, and casbene oxidation products remained undetectable in any of the tissues analyzed.
To check for off-target effects due to VIGS, we measured transcript levels of the other six members of the E. peplus latexspecific SDRs in EpSDR-5-silenced tissue. With very stringent criteria for qRT-PCR primer design (SI Appendix, SI Materials and Methods), we found that transcript levels of the six other SDRs remained unchanged in EpSDR-5-silenced leaf and stem tissue (SI Appendix, Fig. S11 E and F).
Based on these results, we propose a model whereby in E. peplus the biosynthetic pathway to jatrophanes starts with casbene and proceeds via jolkinol C and jolkinol E, involving the action of all three genes targeted by VIGS in the current study (Fig. 4D). According to this model, ingenanes are also derived from casbene and jolkinol C, but the biosynthetic pathway diverges at jolkinol C and does not proceed via jolkinol E (Fig. 4D). A block in the pathway to jatrophanes in EpSDR-5-silenced material results in a redirection of flux from jolkinol C into ingenanes including the medicinal compound IM. Biosynthesis of jatrophanes from jolkinol E requires opening a cyclopropyl ring retained in a latyrane backbone from the casbene precursor. This reaction is almost certainly enzymatic and could be catalyzed by alpha/beta hydrolases, which is an enzyme class that has been involved in the breaking of carbon-carbon bonds (42) and opening of heteroaromatic rings, including epoxides (43,44). Further biosynthetic steps to jatrophanes would require multiple oxidations at position C5, 7, 8, and 9 yielding hydroxyl groups that could be modified further with a range of functional groups present on the backbone molecule (10). Biosynthesis of ingenanes is likely to proceed via a different route, where jolkinol C could be a direct precursor (Fig. 4D). Oxidations at C4, 5, and 20 could occur in conjunction with a Δ12,13-double bond reduction and introduction of a Δ1,2 double bond to form ingenol from jolkinol C. Previous work has suggested that the biosynthesis of ingenanes from a lathyrane precursor may involve a tigiliane intermediate (15,21), which would retain the C3-keto group present in jolkinol C. In any case, the C3-keto reduction that enables further modifications present in E. peplus ingenanes is likely to be catalyzed by an enzyme other than EpSDR-5, as the substrate for such a reaction would be structurally very different to jolkinol C. Although the biosynthetic routes proposed above are speculative and need to be experimentally validated, we have recently reported that JcAlkenalReductase 3 encodes an enzyme with a Δ12,13-double bond reductase activity that converts jolkinol C [1] and epi-jokinol C [2] to 12,13-dihydrojolkinol C and 12,13-dihydro-epi-jolkinol C, respectively (29). It would be interesting to establish if the E. peplus genome encodes a functional equivalent of JcAlkenalReductase 3 and if that gene is involved in the biosynthesis of E. peplus ingenanes.
It is noteworthy that EpSDR-5, which is not associated with either gene cluster 1 or 2, is predominantly expressed in latex, while the genes involved in jolkinol C biosynthesis encoded in gene clusters 1 and 2 (Casbene synthase, CYP726A19, CYP726A4, CYP71D365, and EpADH1), are most highly expressed in roots and/or stems with lower expression in latex. Coordinate gene expression is considered a main driver for clustering of genes associated with plant specialized metabolism (28), and one could speculate that the different expression patterns for the jolkinol C biosynthetic genes and EpSDR-5 could be due to the jolkinol C precursor being synthesized mainly in stems and actively transported to laticifers to undergo conversion to jatrophanes via jolkinol E or to ingenanes via an alternative route. Such compartmentalization of specialized metabolism in internal (resin ducts and laticifers) and external secretory structures (glandular secretory trichomes) has been reported for potentially phytotoxic products or those involved in defense responses against herbivores and pathogens (45).
Conclusions
The short life cycle (around 10 wk), relatively small genome size (27), and rich diversity of the di-and triterpenoids compared to other Euphorbia genus members (46) make E. peplus an attractive model plant for elucidation of the complex pathways to an array of bioactive terpenoids. The 'omics approaches described herein have led to the identification of multiple candidate genes and the functional characterization of EpSDR-5, which encodes a shortchain dehydrogenase/reductase that produces jolkinol E from jolkinol C. We have developed VIGS in E. peplus and deployed this method to show that both ingenanes and jatrophanes are derived from casbene and jolkinol C but their biosynthetic pathways diverge at that point with the biosynthesis of jatrophanes, unlike ingenanes, requiring jolkinol E production. These findings shed light on the biosynthetic pathways to the two most abundant classes of diterpenoids in E. peplus, providing a valuable framework to facilitate the elucidation of the remaining steps in these two pathways.
Materials and Methods
Full details of plant material and GenBank accession numbers for gene and BAC sequences are detailed in SI Appendix, SI Materials and Methods. RNAseq data are available as GenBank BioProject ID PRJNA81996. Liquid chromatographymass spectrometry (MS) and gas chromatography-MS-based metabolomic analysis were conducted on extracts from 8-wk-old E. peplus plants to determine metabolite composition. NMR was conducted to determine the structure of major compounds in E. peplus latex/stems. RNAseq was conducted on five different tissues and used to identify candidate genes associated with diterpenoid biosynthesis. BAC library screening was conducted to identify diterpenoid gene clusters. N. benthamiana and S. cerevisiae were used as heterologous hosts to determine gene function. VIGS was used to confirm in vivo gene function.
Data Availability. Gene and BAC DNA sequence data have been deposited in GenBank (gene accessions MW594404-MW594410, MW594413, MW594414, and MW594418-MW594434 and BAC accessions MW775845-MW775849). RNAseq data are available as GenBank BioProject ID PRJNA81996. All other study data are included in the article and/or supporting information.
ACKNOWLEDGMENTS. This research was funded by the Biotechnology and Biological Sciences Research Council and Innovate UK under Grant BB/ M018210/01 and the Garfield Weston Foundation. We thank Prof. George Lomonossoff (John Innes Centre, Norwich, UK) for providing the pEAQ-HT vector, Dr. Benjamin R. Lichman (Centre for Novel Agricultural Products, University of York, UK) for providing pTRV1 and pTRV2 vectors, and Prof. David Nelson (University of Tennessee Health Science Center, Memphis, TN) for naming the cytochrome P450 proteins. | 6,582.8 | 2022-05-18T00:00:00.000 | [
"Biology",
"Chemistry",
"Environmental Science"
] |
Reversible Data Hiding in JPEG Images Using Quantized DC
Reversible data hiding in JPEG images has become an important topic due to the prevalence and overwhelming support of the JPEG image format these days. Much of the existing work focuses on embedding using AC (quantized alternating current coefficients) to maximize the embedding capacity while minimizing the distortion and the file size increase. Traditionally, DC (quantized direct current coefficients) are not used for embedding, due to the assumption that the embedding in DCs cause more distortion than embedding in ACs. However, for data analytic which extracts fine details as a feature, distortion in ACs is not acceptable, because they represent the fine details of the image. In this paper, we propose a novel reversible data hiding method which efficiently embeds in the DC. The propose method uses a novel DC prediction method to decrease the entropy of the prediction error histogram. The embedded image has higher PSNR, embedding capacity, and smaller file size increase. Furthermore, proposed method preserves all the fine details of the image.
Introduction
JPEG image file format has proved its dominance year after year. Even with the new image standard that supports higher efficiency and compression, it still comes as a default image standard for storing images in smartphones and computers. With unparalleled support for it in variety of devices and software, reversible data hiding JPEG image has become an important topic.
Reversible data hiding is an interoperable data hiding method, which preserves the original file format and has ability to recover the original image from the embedded or watermarked image. But it is different than robust watermarking scheme such as one proposed by Liu et al. [1], which focus on recovery of the embedded message under image processing attacks.
The embedded image should be as close as possible to the original image and the PSNR value is measured against different payload size to compare the performance of the data hiding capability.
On the other hand, reversible data hiding in JPEG has not been extensively researched. There are three main approaches: the first approach modifies the quantization table to artificially increase the quantized DCT coefficients and embed [51,52]. Although this approach has high embedding capacity, the file size increase is much larger than the obtained embedding capacity. The second approach modifies the Huffman table [53][54][55]. Although this approach preserves the file size, the embedding capacity is quite limited. The third approach modifies the quantized DCT coefficients for embedding [56][57][58][59][60][61][62][63][64]. It is most logical approach given that it directly modifies the visual features without modifying other image parameters (such as Huffman table and quantization table).
The proposed method is a third approach, which uses a prediction scheme for quantized DC coefficients. The proposed prediction provide improved accuracy, which decreases the entropy of the quantized DC prediction error histogram to have large embedding capacity with lower distortion. Furthermore, proposed method only modifies the quantized DC values.
The main goal of reversible data hiding in JPEG is to achieve high PSNR without causing much change in the file size, but there are specific cases where quantized AC coefficient preservation is required and is more important than achieving high PSNR. Consider a case where embedded images are used for image data analysis for searching specific patterns or an object. Image data analysis rely on feature extraction of fine image details, which the AC coefficients represent (see Figure 1 for an example). Without the AC coefficient preservation, data analytic may not perform as well.
The proposed method provides a novel reversible data hiding technique which can embed in the quantized DC coefficients. Unlike existing work, all the fine details are preserved since none of the AC coefficients are modified. Quantized DC coefficients preserves the overall intensity, whereas quantized AC coefficients preserve the fine details of the image, making them less ideal for embedding for cases where fine details matter.
Brief Introduction to JPEG Baseline Encoding and Decoding
This section briefly describes the JPEG baseline encoding and decoding steps to aid with understanding of the proposed method. JPEG is a block based lossy compression technique which transforms 8 by 8 pixel blocks into to 8 by 8 quantized DCT coefficient blocks. The transformation consists of normalization by subtracting 128 from each of the pixels, discrete cosine transform (DCT), division by the quantization table, which is usually scaled using a scaling factor called quantization factor (QF) to control the effect of the compression and the image quality, and rounding is applied to make the values integral.
DCT is defined as following: where p i,j represents the pixel value at position (i, j) and DCT u,v represents the DCT value at position (u, v).
Once the quantized DCT coefficients are obtained, they are compressed losslessly. Quantized DCT coefficients consist of quantized DC and quantized AC coefficients. The quantized DC coefficient is the first DCT coefficient value and represents a form of a mean pixel value. The quantized AC coefficients are the rest of the DCT coefficients and represents the fine details of the pixel block. Differential pulse code modulation (DPCM), where the difference between two consecutive values is encoded, is used to compress the quantized DC coefficients in two adjacent blocks. Then, DPCM values are losslessly compressed using a variant of Huffman coding. For the quantized AC coefficients, run length coding is applied, and then encoded using a variant of Huffman coding.
To reconstruct the pixels from the quantized DCT coefficients, the quantized DCT coefficients are multiplied with the quantization table and then, inverse DCT is applied. Then, 128 is added to each value to undo the normalization, and finally, rounding function is used to make the result integral. More information about JPEG encoding and decoding can be found in the ISO document [65].
From here on, the quantized DCT coefficients (including quantized AC and DC coefficients) are denoted by bold font: DCT, AC, and DC.
Proposed Method
The proposed method uses a reversible data hiding technique called histogram shifting, where the performance is highly dependent on the prediction accuracy. The embedding and distortion of histogram shifting is relative to the prediction error; smaller prediction errors mean higher embedding capacity with lower distortion.
Previous work does not utilize advanced prediction in JPEG reversible data hiding. This is because of the assumption that the prediction in the DCT domain is difficult and is not worth the effort. Although the assumption is true in general, it is not true for all DCT. The first DCT in the DCT transformed block, also referred as the DC, represents the 8 Q 1 × mean normalized pixel values in the block, where Q 1 is the quantization table entry for quantizing the DC value. The proposed method builds upon this idea to propose a DC prediction method, which will increase the embedding capacity and decrease the distortion. Figure 2 shows histograms of image Lena (QF = 50). The histogram of DCdoes not have a peak and has the largest entropy, the histogram of differential pulse code modulated (DPCM) DC is better for histogram shifting then DC histogram, because it has a high peak around 0 and lower entropy, and finally, the histogram of proposed DC prediction error histogram has the highest peak and the smallest entropy, making it ideal for histogram shifting. Before explaining the proposed prediction, we define 'T' or 'target block' as the block which we want to predict the DC of. Furthermore, the superscript AC is used to denote that the block is reconstructed only using the AC component.
Then, let T AC denote the partially reconstructed pixel target block using only the AC from the target block (DCvalue is set as 0). Then, because DCT is a linear function, T can be approximately decomposed as following: where Q 1 is the quantization value which divided the DC coefficient to get DC, and DC × Q 1 8 represents the effect of the inverse DCT on DC.
The proposed prediction uses the neighboring blocks and the partially reconstructed blocks using only the AC component. The neighboring DCT blocks are first transformed to pixel blocks of "North", "East", "South", and "West". Figure 4 shows graphical view of the division. The red area represents the parts of neighbors which are closest to the target block, and the yellow area represents the parts of the target block which are closest to the neighboring blocks. Using this setup, we assume that the pixels from the neighboring blocks and the pixels from the target block, which are exactly one position away from each other, should be similarly valued: Pixel red ≈ Pixel yellow (4) where Pixel red , the pixel from the neighboring block, and Pixel yellow , the pixel from the target block, are exactly one position away from each other. In Figure 5, W 8 is exactly one position away from T 1 , but is two positions away from N 57 and T 9 . Combining Equations (3) and (4), we get following approximation: By rearranging the above equation,DC, the predicted value of DC is: where [.] is the rounding function. Finally, since there are multiple Pixel red and Pixel AC yellow , the mean is used as an estimator to evaluateDC:
Embedding
Histogram shifting technique is used to embed in the prediction error values (DC −DC). Embedded DC is denoted by DC , and is obtained using following equation: The histogram shifting technique shifts DC with prediction errors less than −1 by −1, so that DCs valued −1 can be embedded using coefficients valued −1 and −2: the coefficient valued −1 is modified to −2 if the payload bit is "1", and left as −1 if the payload bit is "0". Similar logic applies to DC with prediction error greater than 0. Since the histogram shifting is applied such that none are overlapping, it can be reversed. The next subsection discusses the extraction of the payload and the recovery of the original DC.
Extraction and Recovery
The extraction of the payload and the recovery of the original DC are trivial.
Block Selection
Block selection is important for cases where full embedding capacity is not utilized. In order to have the smallest impact on the PSNR, blocks are sorted by their smoothness and blocks are embedded sequentially only until all the payload is embedded.
To ensure that the smoothest blocks are embedded first, block selection algorithm proposed by Huang et al. [62] is used. In their algorithm, number of zero DCT coefficients are used as a smoothness measure to sort the blocks. The assumption here is that the DCT blocks with more zero DCT coefficients will have less details and thus be smoother.
In the proposed method, zero DC coefficients are not used to measure the smoothness and only the zero AC coefficients are used to measure the smoothness. DC coefficients are not used, because they may change after embedding.
Encoder and Decoder
This section summarizes the encoding and decoding method of the proposed reversible data hiding scheme. Each subsection will describe the implementation steps and include minor implementation details to aid with understanding. 3. Use block selection method to sort the black set of DC . 4. Predict the black set of DC , extract the payload length and the half of the payload, and recover the original DC for the black set. 5. Use block selection method to sort the white set of DC. 6. Predict the white set of DC , extract the first half of the payload, and recover the original DC for the white set. (Prediction uses the original DC recovered from step 4.)
Experiment
The performance of the proposed method is verified using PSNR (between the original JPEG and the embedded JPEG) and the file size gain (due to embedding) comparison. However, there are no existing work that focus only on embedding in DC. Thus, a variant of Huang et al.'s method [62], which is the state of the art algorithm in terms of PSNR and file size gain, is compared with the proposed method.
Methods such as Wang et al. [66], Xuan et al. [58], and Sakai et al. [59] are not compared here, as Quantization factor (QF) values of 50 and 80 are chosen for comparison. QF = 50 based quantization table is the recommended base quantization table written in the standard document, which is scaled to obtain other quantization table, making it a good benchmark for test against. QF = 80 based quantization table is the table which is known to achieve good compression to visual degradation ratio.
The code for the proposed method will be available at https://github.com/suahnkim/jpegrwdc (accessed on 23 August 2019).
Discussion and Analysis
For testing, two image sets are chosen. To see the comparison using the well-known images, the first image set includes 6 images, "Lena", "Boat", "Barbara", "Baboon", "Peppers", and "F16" from USC-SIPI image data set (http://sipi.usc.edu/database/)(accessed on 23 August 2019). The original bmp images are JPEG compressed to the size of 512× 512. These images are chosen specifically for comparing specific unique features. For more general comparison, the second image set includes 1000 images from Alaska image data set (https://alaska.utt.fr/)(accessed on 23 August 2019). The original raw .cr2 images are JPEG compressed to the size of 432 × 648.
Comparison Using USC-SIPI Image Data Set
In this section, USC-SIPI database is used to compare for specific features. PSNR value relative to the size of the embedded payload and the file size gain due to embedding the payload are compared. Both methods preserve the AC coefficients as required, but the proposed method has higher PSNR and embedding capacity for almost all images except the image F16. The proposed method consistently can embed more than 15% of the total blocks, and for few of the images it can embed more than 50%, whereas Huang et al.'s method can only embed between 5% and 25%.
Upon close inspection on the prediction error histograms of F16, DPCM is a better predictor for first few sets of payload. This is not surprising because F16 is a very smooth image. However, this is a single outlier, and the proposed method's prediction is generally better and more consistently accurate than DPCM. More importantly, the proposed method can consistently embed more than Huang et al.'s.
File Size Gain Comparison Using USC-SIPI Image Data Set
File size gain due to embedding is an important measure in JPEG reversible data hiding. JPEG is designed to offer good compression capability with respect to the image quality, thus reversible data hiding should not increase the file size significantly. Ideally, the file size gain due to embedding should be smaller than the embedded payload size. Figure 7 summarizes the comparison result for the file size gain. The file size gain is measured against the size of the embedded payload. To clearly see whether the embedding caused more file size gain than the size of the payload, a straight line through the middle is drawn. The proposed method consistently has smaller file size gain than Huang et al.'s for both QFs. Furthermore, it has smaller file size gain than the size of the payload for all cases. This implies that when proposed method is used for embedding, it will not increase the file size more than the size of the payload.
Comparison Using Alaska Image Data Set
In this section, performance comparison using Alaska image data set is summarized. Unlike the earlier comparison which compared specific images, the comparison here uses 1000 images to compare using more robust statistical results. For the comparison, PSNR gain, file size difference, and payload gain are compared.
Applying reversible data hiding in 1000 JPEG images produces many data points: each image has different maximum payload size, and each payload size gives different PSNR value and file size. Fair comparison is done by only comparing the results for the same image and same payload size.
File Size Difference Comparison Using Alaska Image Data Set
File size difference is the difference between the file sizes of the embedded image using the proposed method and Huang et al.'s. This is used to show that the proposed method produces embedded image with smaller file size. Figure 8b summarizes the result for the average file size difference when different payload sizes are embedded. The negative value means that the file size of the embedded image using the proposed method is smaller than Huang et al.'s, and opposite for the positive values. Clearly, the proposed method has smaller file size gain due to embedding in average.
Payload Gain Comparison Using Alaska Image Data Set
Payload gain is the difference between the maximum payload sizes of the Huang et al.'s and the proposed method. This is compared to show the difference in maximum embeddable payload size for each image. Figure 8c summarizes the result. Positive payload gain means that the proposed method can embed that much more, and opposite for the negative values. For all cases except one, the proposed method embeds more than Huang et al.'s for both QF = 50 and QF = 80. In average, proposed method can embed 1570 bits more for QF = 50, and 1163 bits more for QF = 80.
Effectiveness of the Block Sorting Algorithm in General
In this section, we analyze and discuss the effect of the block sorting algorithm with respect to the prediction error histogram resulting from the proposed method. In reversible data hiding, block sorting algorithm is used to control the rate of embedding such that the smallest number of DC can be used for embedding to minimize the impact on the PSNR.
In the proposed method, only prediction error valued 0 and −1 are used for embedding. However, it can be modified to embed in other prediction error values, such as 1 and −1, or even multiple pairs. Naturally, it is not possible to measure the performance of the block sorting algorithm with respect to all possible modifications.
Instead of measuring the performance for all possible modification, we proposed analyzing the prediction error histogram using the entropy to measure the general effectiveness of the block sorting algorithm. Ideally, block sorting algorithm should sort the blocks such that blocks which are more likely embeddable are prioritized for embedding. In other words, the entropy should increase as more of the less likely embeddable blocks are used for embedding if the block sorting algorithm is well designed. Figure 9 shows the average prediction error entropy of 1000 images from Alaska image data set. Each point is measured for every 10 percentage of the total blocks are used for embedding. From the figure, it is very clear that the entropy is smoothly increasing as a greater number of blocks are used for embedding for both methods. Furthermore, the proposed method has much lower average entropy than the Huang (a) QF = 50 (b) QF = 80 Figure 9. Average prediction error entropy.
Conclusions
Reversible data hiding in JPEG image is becoming an important and highly researched topic. With existing work mostly focusing on embedding only using the quantized AC coefficients, there are no good embedding method only using DC (quantized DC coefficients). This is a problem for data analytic applications where AC (quantized AC coefficients) are used for feature extraction for fine details. The proposed method proposes a novel reversible data hiding in DC. It divides the JPEG blocks into two non-overlapping sets and an accurate predictor is proposed, which uses the four neighboring blocks and the ACs. The experimental results show that the proposed method performs better than the existing work.
Abbreviations
The following abbreviations are used in this manuscript:
DCT
Discrete Cosine Transformation DCT (Bold font) Quantized DCT coefficients DC (Bold font) Quantized DC coefficient AC (Bold font) Quantized AC coefficients PSNR Peak signal-to-noise ratio DPCM JPEG Differential pulse code modulation QF Quantization factor | 4,613 | 2019-08-26T00:00:00.000 | [
"Computer Science"
] |
Testing non-local gravity by clusters of galaxies
Extended theories of gravity have been extensively investigated during the last thirty years, aiming at fixing infrared and ultraviolet shortcomings of General Relativity and of the associated $\Lambda$CDM cosmological model. Recently, non-local theories of gravity have drawn increasing attention due to their potential to ameliorate both the ultraviolet and infrared behavior of gravitational interaction. In particular, Integral Kernel theories of Gravity provide a viable mechanism to explain the late time cosmic acceleration so as to avoid the introduction of any form of unknown dark energy. On the other hand, these models represent a natural link towards quantum gravity. Here, we study a scalar-tensor equivalent model of General Relativity corrected with non-local terms, where corrections are selected by the existence of Noether symmetries. After performing the weak field limit and generalizing the results to extended mass distributions, we analyse the non-local model at galaxy cluster scales, by comparing the theoretical predictions with gravitational lensing observations from the CLASH program. We obtain agreement with data at the same level of statistical significance as General Relativity. We also provide constraints for the Navarro--Frenk--White parameters and lower bounds for the non-local length scales. The results are finally compared with those from the literature.
I. INTRODUCTION
In the last decades, the growing availability of an increasingly larger amount of astrophysical and cosmological data has supposedly led us into a so-called "precision cosmology" era. The effective model that best fits most of the collected observations is the ΛCDM model, which is based on General Relativity (GR) and on the introduction of two exotic fluids, the cold dark matter (DM) and the dark energy (DE). They should represent the ∼ 27% and ∼ 68% of the matter-energy content of the present-day Universe, respectively [1][2][3], and being responsible for the dynamical features of the Universe at all scales. Despite being the best model to explain the collected data, the ΛCDM paradigm is plagued by several problems, both experimental and theoretical [4]. On the one hand we have a huge variety of solutions for DM but we face the complete lack of any detection of any viable particle candidate for DM at fundamental scales [5]. On the other hand, we also have an humongous number of possibilities to describe DE, but also many theoretical shortcomings regarding its nature and behaviour, such as the discrepancy (∼120 orders of magnitude) between the observed value of the cosmological constant and the vacuum energy density calculated via QFT. Other big issues are the presence of singularities in the theory and the completely unsatisfactory description of gravity at quantum level. a<EMAIL_ADDRESS>b<EMAIL_ADDRESS>c<EMAIL_ADDRESS>d<EMAIL_ADDRESS>All these problems led to the idea of developing theories of gravity "beyond GR", aiming at fixing its infrared (IR) and ultraviolet (UV) shortcomings. Several proposal for extended theories of gravity (ETGs) have been made during last thirty years [6,7]. Some of these are based on modifications of the geometrical content of the theory, namely the Hilbert-Einstein Lagrangian; some others are based on modifications of the matter content, for example by adding extra scalar fields. Often these two kind of modifications are introduced together. The most famous and extensively investigated ETGs are f (R) theories [6,[8][9][10][11][12], where the Hilbert-Einstein Lagrangian is replaced by a general function of the Ricci scalar R, and scalar-tensor theories [13][14][15][16][17][18], in which one or more scalar fields are minimally or non-minimally coupled to gravity. These two classes of theories can be made equivalent, since f (R) theories can be recovered by scalartensor ones with some specific changes of variables and viceversa.
Other ETGs approaches replace the Ricci scalar R with the torsion scalar T , instead [19]. In fact, it is possible to build the so called Teleparallel Equivalent of General Relativity (TEGR) by giving up the Equivalence Principle and replacing the Ricci scalar R with the Torsion scalar T . TEGR, firstly introduced by Einstein himself [20], and GR are dynamically equivalent. However, the equivalence does not hold for the teleparallel equivalent of f (R), i.e. f (T ) theories. The latter leads to secondorder field equations, while the field equations derived by f (R) gravity, in metric formalism, are of fourth-order [21].
An interesting approach is the introduction of nonlocal terms [13,22]. Non-locality is one of the main fea-arXiv:2205.03216v2 [gr-qc] 4 Jul 2022 ture of quantum theory, thanks to the Heisenberg Principle, and it automatically arises in quantum field theory (QFT) when one-loop effective actions are considered. Instead, GR is a classical theory, hence local by definition. In order to merge the gravitational interaction with the quantum formalism, it is thus possible to implement an effective approach by adding non-local operators to the gravitational Lagrangian. The procedure can be considered as an effective approach to link gravitation and QFT.
In general, two main different families of non-local theories of gravity can be considered. The first ones are the Infinite Derivatives Theories of Gravity (IDGs), which present, at short range, non-locality caused by terms with entire analytic transcendental functions of a differential operator. The most commonly used terms are the exponential functions of the covariant d'Alembert operator, = g µν ∇ µ ∇ ν . IDGs have been introduced to solve one of the main problems of f (R) theories, namely the lack of unitarity caused by bad ghosts. Moreover, this class of non-local terms weakens gravitational attraction at short length scale. Hence, a natural solution to UV shortcomings of GR is provided [23][24][25][26].
Then, we also have Integral Kernel Theories of Gravity (IKGs), inspired by quantum corrections obtained in QFT on curved spacetime. In IKGs, the Lagrangian is extended by adding transcendental functions of the fields (R, T , G, etc.), which can be always represented by the integral kernels of differential operators, such as Due to its integral nature, this class of terms gives rise to long range non-localities, which can fix the IR shortcomings of GR [27][28][29][30]. Interesting IKG models have been proposed in [31,32]. Subsequent comparisons with cosmological observations [33][34][35][36] showed agreement with data at a level statistically equivalent to ΛCDM and an intriguing reduction of the Hubble tension.
In this paper, we consider a metric IKG proposed in [28] to explain the late-time cosmic acceleration. Nonlocality is introduced by a general function of the inverse d'Alembert operator, Eq. (1.1), the form of which can be found by applying the so-called Noether Symmetry Approach as discussed in [22]. Furthermore, we consider the local representation of the theory, firstly introduced in [37]. Two auxiliary scalar fields emerge as Lagrange multipliers, so that the new scalar-tensor theory is made equivalent to the original non-local theory. The Newtonian limit is finally performed and two Newtonian potentials, φ and ψ, are derived. These point-mass potentials can be generalized to extended spherically symmetric mass distributions which can model gravitational structures like galaxy clusters. Then, the non-local model can be compared to observational data. In other words, signatures of non-locality can emerge from large-scale structure.
Here, we perform an analysis similar to [38][39][40] using a sample of 19 high-mass galaxy clusters, for which strongand weak-lensing data sets from deep Hubble Space Telescope (HST ) and ground-based wide-field observations are available. All data products used in this study are obtained from the Cluster Lensing and Supernova survey with Hubble (CLASH) program [41]. The aim of the paper is to constrain the free parameters of the nonlocal theory and compare the results to those obtained in [42,43], where the same theory has been analyzed using the orbits of S2 stars around the Galactic center. The paper is organised as follow: in section II we present the non-local model and its local scalar-tensor representation. Then, we sketch the Noether Symmetry Approach to derive the form of the non-local terms related to the existence of conserved quantities. Moreover, we perform the weak-field limit in order to find the Newtonian potentials, φ and ψ, and we generalize the results to extended spherically symmetric systems. Finally, our choice for the mass density profile is presented and an overview of the gravitational lensing theory, used to derive the theoretical prediction, is introduced. In Sec. III, the data sets of the CLASH program that we have used in our analysis is presented. Then, we introduce the main points of the statistical analysis we have performed. Furthermore, in Sec. IV, the results of the statistical analysis are discussed and a comparison between them and previous results in the literature is made. In Sec. V, the conclusions are drawn.
II. THE MODEL
The model we are going to study in this paper was firstly introduced in [28]. Here, the Hilbert-Einstein action is extended by adding an extra non-local term characterized by a general function of the inverse d'Alembert operator The function f is called distortion function and GR is immediately restored when f is set to zero. Notice that the theory defined by Eq. (2.1) can be seen as a special case of the Generalized non-local Teleparallel Gravity (GNTG) proposed in [44], from which the above model is recovered by setting the coupling constants equal to 1 and −1, respectively. The model in Eq. (2.1) explains well the current cosmic acceleration. In fact, the non-local terms here introduced allow a delayed response to the transition from radiation to matter dominance, and then avoid fine tunings often introduced to address late time acceleration [28]. Furthermore, using a proper piecewise-defined distortion function, the non-local model may lead to the unification of the early-time inflation with late-time acceleration [37].
A local representation of the non-local model Eq. (2.1) has been proposed in [37], where an equivalent scalar-tensor theory is built by introducing two auxiliary scalar fields, η and ξ, so that the action is rewritten as follows 2) where the term ξ η has been integrated by parts and the boundary term is set to zero. A general procedure to build a local representation of non-local theories is presented in [22]. Varying the action in Eq. (2.2) with respect to ξ and η, we obtain the two Klein-Gordon equations: where the auxiliary fields behave as Lagrange multipliers.
5) A non-trivial form for the distortion function has been reconstructed in [45] in order to reproduce the ΛCDM expansion. The model provided by substituting such form of f in Eq. (2.1) has been analysed in its localized version in [46], using Redshift-Space Distortions (RSD) data: a slightly lower value of σ 8 is derived and, consequently, a better agreement with data results with respect to the ΛCDM model. Moreover, in [47], the author has shown that the same results can be obtained in the original nonlocal version in [45], as long as the initial conditions are set the same. Further analysis have been performed in [48], using Cosmic Microwave Background (CMB), Type Ia supernovae (SNIa) and RSD observations: a deficit of growth of linear structures and a higher lensing power as compared to ΛCDM is derived, so that a significant shift for the parameter σ 8 and τ re results. It follows a CMB-RSD tension and "weak" evidence for the ΛCDM model. The same authors also highlight a modification in the propagation equations for Gravitational Waves (GWs), which provides a powerful way for testing deviations to GR with future third generation GW interferometers. See also [29,30].
A drawback that could arise in the non-local theories of gravitation is the lack of a screening mechanism, which is necessary to avoid any undesired effect at Solar System scale. In [49], it is argued that inside bound objects −1 R acquires positive value, whereas it is negative in cosmology. Thus, as one is free to choose the distortion function, one can set it so that it vanishes for positive values of −1 R, i.e. f ( −1 R) ∼ θ( −1 R) where θ is the Heaviside step function. It follows a perfect screening mechanism which allows the model to reduce to GR at the Solar System scales. However, in [50], has been shown that the value of −1 R is actually negative also at Solar System scale, therefore this procedure cannot be applied. As a consequence, the above model would present a time dependence of the effective Newton constant in the small scale limit and it would thus be ruled out by Lunar Laser Ranging (LLR) observations. This conclusion, drawn in [50], seems to be too strong, since it is still not clear how a Friedman-Lemaître-Robertson-Walker (FLRW) background quantities behave when evaluated from cosmological scales down to Solar System ones, where the system decouples from the Hubble flow. In fact, a full non-linear time-and scale-dependent solution around a non-linear structure would be necessary.
However, some proposals exist in this direction and the so-called Vainshtein mechanism [51] can be considered the paradigm to realize the screening. The main problem is that GR is very well-tested at Solar System scales and then any extension requires fine constraints to be physically viable. For example, f (R) gravity requires an accurate chameleon mechanism to give realistic models ranging from Solar System up to cosmology (see [52] for a discussion). Basically, any screening mechanism require a scalar field coupled to matter, and mediating a "fifth-force" which might span from Solar System up to cosmological scales. For high density, this force has to be suppressed, so that no deviation from GR should emerge. For lower densities, the modification to GR become effective with some observational signature. The screening can be accomplished in several ways: for example, a weak coupling between the field and matter in regions of high density can be considered. This coupling should induce a weak fifth-force. In this situation, the field can acquire a large mass in high density environments, being short-ranged and undetectable. In lower density regions, it should be light and long-ranged, as in the case of chameleon fields [52]. Finally, the field may change the kinetic contribution in the effective Lagrangian, with first or second order derivatives becoming important in a certain range, as in the Vainshtein case. In [38], it has been discussed for clusters of galaxies in presence of galileon fields. In the case we are going to discuss here, non-local terms can be "localized" and they result in an effective scalar field depending on the scale [36]. This feature can naturally give rise to some screening mechanism solving the above reported problems. We will discuss this topic in detail elsewhere.
A. The Noether Symmetry Approach
The action in Eq. (2.2) as well as the two non-trivial field equations Eqs. (2.4) and (2.5), all depend on the specific form of the distortion function f ( −1 R). It is thus possible to use the Noether Symmetry Approach [53] to select a form of the distortion function such that the theory is invariant under point transformations. This method has been extensively used in the literature [44,[53][54][55][56][57], aiming to study modified theories of gravity based on general functions, such as f (R), f (T ), etc. Such theories have to be checked against data in order to be constrained and then obtain physically reliable models. However, it is possible to constraint modified-gravity theories using a theoretical approach rather than a phenomenological one. Specifically, Noether symmetries can be used as a geometric criterion to choose among different models. Moreover, the presence of symmetries imply conserved quantities that, in many cases, have a physical meaning and allow to reduce dynamics and find exact solutions [53].
The Noether Symmetry Approach works as follows: • one first selects a class of background space-time metrics, which, in our case, is spherically symmetric, and one therefore writes the metric; • then, one substitutes the metric into the Lagrangian density Eq. (2.1) and, after integrating out all the total derivative terms, it is possible to obtain a point-like canonical Lagrangian; • one derives the Noether vector X, i.e. the infinitesimal generator of point transformations; • it is then possible to apply the Noether symmetry condition [54] where X [1] is the first prolongation of X, ξ t and ξ r are the coefficients of the Noether vector and h t and h r are two arbitrary functions depending on time and generalized coordinates. Expanding the condition Eq. (2.6), one finds a system of equations with 9 unknown variables, which yields to two possible models that are invariant under point transformations See [22] for details. An overview of the general method is given in [54], while the explicit calculation of the Noether Symmetry Approach applied to the model (2.1) is performed in [42]. It is interesting to note that the two forms Eq. (2.7) and (2.8) of the distortion function correspond to those phenomenologically introduced in [58,59]. Hereinafter, we consider the exponential form Eq. (2.8) for the distortion function and we set all the integration constants to one. Thus, we have (2.9) As reported in [60], this form of coupling is particularly relevant to achieve the so called "superrenormalizability" for effective theories of gravity. Here, it is selected thanks to the existence of related Noether symmetries.
B. The Newtonian limit
Now, let us perform the weak field limit for the above non-local model, in order to derive the Newtonian potentials which will be used to match observations. The gravitational field for a static and spherically symmetric metric is described by (2.10) Notice that the Birkhoff theorem is not guaranteed in non-local gravity, but we expect that static and spherically symmetric solutions are a good approximation when the Newtonian limit is performed. Not even the existence of the solution B(r) = 1/A(r) is guaranteed in modified theories of gravity [61], so it cannot be chosen a priori in Eq. (2.10). It is well known, from GR, that expanding g 00 up to v 2 ∼ O(2), one obtains the Newtonian potential φ for time-like particles. However, for theories beyond GR the Post-Newtonian (PN) limit is necessary, i.e. (2.11) When higher-order corrections are taken into account, two length scales arise, which are related to the scalar degrees of freedom we introduced to localize the theory. The expansion of the metric components as well as the scalar fields therefore gives where η c is a dimensionless constant, which can be set to 1 in order to recover the Newtonian limit for φ. The two parameters r η and r ξ , which arise in the higher-order terms O(4) and O(6), are the length scales related to the the scalar degrees of freedom and thus to the nonlocalities. These length scales are the free parameters of the theory that we want to constrain by observations.
C. Extended spherically symmetric systems
In order to confront the theory against data, it is necessary to generalize the results in Eqs. (2.16) -(2.17) to extended mass distributions. First of all, from Eqs. (2.16) -(2.17) we derive the point-mass expressions for the gravitational (φ) and metric (ψ) potentials, which are, respectively: Before proceeding, it is worth having a look at the orders of magnitude of each of the above contributions, to forecast their weight in the analysis and thus estimate which kind of constraints (if any) it is possible to put on the theory. A rough estimation, using the typical masses and radii of the clusters of galaxies (respectively, M = 10 15 M and r = 3 Mpc), tells us that: It immediately follows that the terms (2.24) are completely negligible in our analysis, and we will not consider them further. However we can also make two additional and more important considerations about these qualitative results. The first one is that, in order to expect a significant contribution from φ 1 and ψ 1 with respect to the standard terms, φ 0 and ψ 0 , we should have r η ∼ r ξ ∼ 10 −5 r.
The second consideration is probably even more decisive: in case the non-local corrections to the potential were not large enough, we would have here a theory which does not reduce to GR. In fact, it is straightforward to see that in that case we would have ψ ∼ φ/3. If such a scenario would be able to fit the data (and if yes, with which implications) is something we are going to check carefully in the following analysis.
The generalization to extended system is based on performing the following integrals (using spherical coordinates) (2.25) with r defined as: where x is the vector position of the point in the space where we want to calculate the potential, and x is the vector position connected to the mass distribution (source of the gravitational potential). Note how the integration over the radial coordinate has to be performed between 0 and ∞ because Newton's theorems are not guaranteed in non-local gravity, so that we cannot apply the Gauss theorem and the effects of external shell of matter cannot be neglected 1 . While the term Ψ 0 (r) is derived as in Eq. (2.25), Φ 1 (r) and Ψ 1 (r) need an intermediate step, as they involve the term M 2 . Since the mass element can be written as 27) and considering that dM 2 = 2M dM , with we get: The same results holds for Ψ 1 (r).
D. The mass density profile
To compute the integrals of the extended potentials, it is necessary to make a choice for the mass density profile describing the mass distribution in galaxy clusters. In our analysis, the matter distribution in galaxy clusters is considered to be dominated by DM. We have chosen to describe the cluster mass distribution with a spherically symmetric Navarro-Frenk-White (NFW) mass density profile [63], where ρ s and r s are the characteristic halo density and radius, respectively. Here, the choice of the NFW density profile is motivated by cosmological N -body simulations [63,64] and observational results based on gravitational lensing [65] (see Section III), both in GR context. It is useful to express the NFW parameters in terms of the overdensity radius r ∆ and the dimensionless concentration parameter c ∆ as where r ∆ is the spherical radius within which the mean interior density equals ∆ times the critical density ρ c of the Universe at the cluster redshift. Instead of working with r ∆ , it is more common to use M ∆ , i.e., the total mass contained within the overdensity radius r ∆ , In the literature, the typical choice of the overdensity characterizing the halo mass is ∆ = 200, while higher overdensities, such as ∆ = 500 and 2500, are used to characterize the properties of halos in their inner regions. In our analysis, we set ∆ = 200. Thus, the free NFW parameters that we have used for our analysis are Once the choice for the mass density profile has been made, it is finally possible to compute analytically the integrals for the extended potentials from Eqs. (2.25) and (2.29), which we omit to write here explicitly just for the sake of clarity.
E. Gravitational lensing
All the previous machinery is fundamental to calculate the quantity which we will then compare with observational data which, as explained in next section, are based on gravitational lensing event analysis from the clusters of galaxies we have considered.
The general configuration for a gravitational lensing system [66,67] has a foreground object (the lens) between the observer and the background source of light. The angular diameter distances between the observer and the lens and between the observer and the source are denoted by D L and D S , respectively, while the angular diameter distance between the lens and the source is D LS . The angular diameter distance as a function of redshift is defined as: In a ΛCDM scenario, the Hubble function H(z) is given by the first Freedman equation, In our analysis, we assume as our fiducial background cosmology the one from the latest release of the Planck survey [1], with Ω m = 0.308, H 0 = 67.89 and Ω k = 0 (from which Ω Λ = 1 − Ω m ). It is important to note here that we are implicitly assuming that the non-local model we are analyzing behaves on cosmological scales as this chosen ΛCDM one, at least effectively. Any cosmological implication and analysis is out of the scopes of this paper, however it is worth noticing that, according to the Deser and Woodard model [28] which we are essentially adopting here, using non-local term is a natural way to address dark energy behaviour and recover the observed late universe (see also [22]. In this perspective, assuming ΛCDM is in agreement with this result. It is generally verified that the distances D L and D LS are much larger than the physical extension of the lens, so that the latter can be approximated as a two-dimensional system ("thin-lens" approximation). In such a configuration the relation among the angular position of the source ( θ s ) and the angular position of the image ( θ) is given by the lens equation: where α is the deflection angle, which, in GR, is defined as:ˆ with ∇ ⊥ being the two-dimensional gradient operator perpendicular to the light propagation and z the lineof-sight direction. The deflection angle is then directly related to the quantity which we will use to constrain our model, the convergence where: R is the two-dimensional projected radius in the lens plane 2 ; r = √ R 2 + z 2 is the three-dimensional radius; ∇ 2 r is the Laplacian operator in spherical coordinates; and c is the speed of light. If we make use of the Poisson equation we then obtain the final expression for the convergence where Σ(R) is the surface density of the lens, defined as and Σ c is the critical surface density for gravitational lensing, If we want to generalize all the results which we have obtained so far, valid in GR, we must express the convergence in its most general form as 2 It is clear from the context that this R is a radius which must not to be confused with the above curvature scalar.
where the potentials Φ and Ψ which we are going to use are those defined in Sec. II C.
III. THE DATA
The data sets we use for our analysis are obtained from the CLASH program [41]. One of the main goals of the CLASH program was to precisely determine the mass density profiles of 25 high-mass galaxy clusters using deep multi-band HST imaging, in combination with wide-field weak-lensing observations [68]. The CLASH sample contains 20 hot X-ray clusters (> 5 keV) with nearly concentric X-ray isophotes and a well-defined X-ray peak located close to the brightest cluster galaxy (BCG). Notice that no lensing preselection was used to avoid a biased sample towards intrinsically concentrated clusters and those systems whose major axis is preferentially aligned with the line of sight. Cosmological hydrodynamical simulations suggest that the CLASH X-ray-selected subsample is mostly composed of relaxed systems (∼ 70%) and largely free of such orientation bias [69]. Additionally, the CLASH sample has five clusters selected by their exceptional lensing strength so as to magnify galaxies at high redshift. These clusters often turn out to be dynamically disturbed systems [67].
The CLASH sample spans nearly an order of magnitude in mass (5 < ∼ M 200 /10 14 M < ∼ 30) and covers a wide redshift range (0.18 < z < 0.90 with a median redshift of z med = 0.40). For each of the 25 clusters, HST weak-and strong-lensing data products are available in the central regions [70]. For 20 of them (16 Xray-selected and 4 lensing-selected clusters), radial convergence profiles were reconstructed [65] from the combination of ground-based weak-lensing shear and magnification data and HST lensing data.
In our analysis, we focus on 15 X-ray-selected and 4 lensing-selected clusters taken from the CLASH subsample analyzed in [65]. Here, one of the X-ray-selected clusters (RXJ1532) has been discarded because no multiple image systems have been identified in the cluster [70] and thus the mass reconstruction is based only on the widefield weak-lensing data [65]. Our analysis sample spans a redshift range of 0.187 ≤ z ≤ 0.686, with a median redshift of z med = 0.352. The typical resolution limit of the mass reconstruction, set by the HST lensing data, is 10 arcseconds, which corresponds to ≈ 35h −1 h kpc at z med . Note that, according to [69], about half of the selected sample clusters are expected to be unrelaxed.
It was found in [65] that the ensemble-averaged surface mass density Σ(R) of the CLASH X-ray-selected subsample is best described by the NFW profile, when GR is considered. The NFW model describes well the DM distribution in clusters, which is the dominant component over the whole cluster scale. The cluster baryons, such as the X-ray-emitting hot gas and BCGs, are sensitive to non-gravitational and local astrophysical phenomena. Accordingly, hydrostatic total mass estimates, based on the X-ray probe, are highly influenced by the dynamical and physical conditions of the cluster. In contrast, gravitational lensing can provide a direct probe of the projected mass distribution in galaxy clusters.
A. Statistical analysis
The aim of this work is to constrain the parameters of the non-local model (2.1) and the parameters describing the NFW profile for each individual cluster. Thus, the vector of our free theoretical parameters is θ = {c 200 , M 200 , r η , r ξ }. The χ 2 function for each cluster used in the analysis is defined as where κ obs is the data vector containing the observed convergence values. The data vector consists of 15 data elements, each representing the value of κ measured in each radial bin. The vector κ theo (θ) contains theoretical predictions for the model convergence calculated from Eq. (2.43). Finally, C is the covariance error matrix constructed by [65].
The χ 2 function is then minimized using our own Monte Carlo Markov Chain (MCMC) code written in Wolfram Mathematica. The convergence of the chains has been checked according to the method proposed in [71]. Full convergence has been reached for 18 out of 19 sample clusters, while MACSJ0717 shows a pathological behaviour. Such behaviour is due to a peculiar shape of the χ 2 function, with two different minima, which is shared by all the samples, but is especially pronounced in MACSJ0717. This shape is directly related to the degeneracy of the geometrical and the matter effects, as will clearly emerge from the results of our analysis.
In order to assess the validity of our non-local model against the standard GR case, we calculated the Bayesian evidence E, so as to provide a statistical meaningful comparison tool between the two theories. We have calculated the Bayesian evidence using the algorithm proposed in [72]. As this algorithm is stochastic, in order to reduce the statistical noise we run it ∼ 100 times, obtaining a distribution of values from which we extract the best value of E, as the median of the distribution, and the corresponding error.
Since the Bayesian evidence depends on the choice of the priors [73], we have always used uninformative flat priors on the parameters. For each cluster, we have assumed flat positive priors on the NFW parameters, i.e., c 200 > 0 and M 200 > 0 (note that the choice of NFW priors is different from that of [65], who used flat logarithmic priors on M 200 and c 200 ), while for the non-local parameters we use flat logarithmic priors, −5 < log r η,ξ < 5.
Finally, the Bayes factors B are computed for each sample cluster. The Bayes factor is defined as the ratio of evidence factors of two models where M j is the reference model, which, in this case, is GR. The model selection is then performed by using the so-called Jeffreys scale [74], which states that: for ln B i j < 0 there is evidence against the model M i , i.e. the reference model is statistically favored; for 0 < ln B i j < 1 there is no significant evidence in favor of the model M i ; for 1 < ln B i j < 2.5 the evidence is substantial; for 2.5 < ln B i j < 5 the evidence is strong; for ln B i j > 5 the evidence is decisive.
IV. RESULTS AND DISCUSSION
First of all, we have performed the fits in the classical GR scenario (second column of Table I), which will be our reference model. We can thereby cross-check our modelling and statistical analysis algorithm with results from the literature for the same sample. In Fig. 1, we compare our results with [65], the original work were the lensing data we are using were first obtained and presented. Note that a direct comparison is possible because the same NFW parametrization, {c 200 , M 200 }, has been used, with the same mass modelling, i.e. no further components (gas, galaxies) have been used. The cross-check shows an excellent agreement, with all the nineteen estimates of both NFW parameters, c 200 and M 200 , which agree within the 1σ level.
Concerning the non-local model, results are shown in the third column of Table I. The NFW parameters are well constrained by the lensing data. From Fig. 2 and Figs. 4-7, one can see that the estimates of concentration parameter c 200 show no significant differences between GR and our non-local model, being all consistent with each other at the 1σ level, although the non-local model tends to show higher concentrations than GR. On the other hand, this trend is much clearer in the cluster mass M 200 , whose non-local estimates clearly deviate from the GR ones.
Such increased estimates of M 200 are very likely related to the form of the metric potentials and the role/weight of the correction terms. As explained above, if the nonlocal corrections are small and the Φ 0 and Ψ 0 terms are the dominant contributions, the theory does not reduce to GR, because the potential Ψ 0 only takes into account 1/3 of the contribution which would be expected. Thus, in the non-local model, the cluster mass (mostly, and slightly for c 200 ) must be increased to compensate the missing contribution from Ψ 0 to the convergence. From Figs. 4-7, it immediately appears that the 1σ-and 2σregions shift toward higher masses, except for two cases (A2261 and MACSJ0717) where the 1σ contours do not overlap.
As a further check, in Fig. 8 we compare the (c 200 , M 200 ) constraints obtained in our work for GR and for the non-local model with c-M relations from the literature. As expected, the points representing the c-M relation for each cluster scatter due to the different physical properties of the samples. However, for GR, the re- gion spanned by the clusters agrees with the bands representing the relation obtained in the literature. Instead, for the non-local model, the same region shifts towards higher concentrations and masses, hence it does not coincide with expected results, especially with the green band derived in [75] using the same sample of our work. The gap is around 2σ, thus the non-local model is just slightly statistically disfavoured respect to GR and can-not be discarded.
When we consider the non-local length scales r η and r ξ , the statistics does not appear as much regular as in the case of the NFW parameters. The MCMC sampling does not identify a clear minimum in the χ 2 function; instead, the χ 2 exhibits a shallow valley in the parameter space. This is due to the fact that the non-local corrections are too small to be effectively detected given the observa-tional uncertainties. We find that the MCMC samples are mostly concentrated in the region −1 < log r η , ξ < 5, and only lower limits can be extracted (see column 3 of Table I).
Lower limits on the typical non-local scales can be set with the present data. They are r η > 4 × 10 −5 − 7 × 10 −2 kpc and r ξ > 2 × 10 −5 − 3 × 10 −2 kpc, so that the magnitudes of the non-local corrections φ 1 and ψ 1 in Eq. (2.20 -2.21) are φ 1 ∼ 10 −28 − 10 −25 kpc 2 s −2 and ψ 1 ∼ 10 −27 − 10 −24 kpc 2 s −2 . Thus, such terms might be dominant or of comparable magnitude with respect to the zeroth-order terms, φ 0 and ψ 0 , when the non-local parameters approach their lower bounds. This result would appear to conflict with the increased estimates of c 200 and M 200 that we obtained for the non-local model.
However, a deeper insight of the MCMC results shows that it naturally emerges from the degeneracy of the geometrical and mass effects. In fact, given that the theory cannot be reduced to GR, and that Ψ N L can only account for Ψ GR /3, there exist only two possibilities to fit the observations: an increase of estimated cluster mass or a strong contribution of the non-local corrections, Φ 1 (r) and Ψ 1 (r), to the lensing potential. Both options are statistically viable, leading to an agreement with data at a level statistically equivalent to GR.
This degeneracy of geometrical and matter effects corresponds to a peculiar shape of the χ 2 function, which presents two minima. Such behaviour is extremely noticeable in MACSJ0717, whose Markov chain does not remain in a specific region and consequently does not converge to particular values of the parameters. In particular, for MACSJ0717, the minimum corresponding to low values of the non-local length scales (i.e. strong nonlocal correction to the gravitational potential) is remarkably deep and the associated estimates of M 200 are extremely low. It follows that the non-local model seems to be able to fit the observations thanks to its non-local geometrical contributions to the lensing potential, with a very good statistical viability. Moreover, the fact that the corresponding M 200 estimates are very low means that little matter contribution is necessary to fit data, so that it would open to the possibility to fit the gravitational lensing observations without dark matter. Further studies will be necessary to investigate in detail this possibility.
On the other hand, the χ 2 function of our non-local model shows a low sensibility with respect to the nonlocal parameters, r η and r ξ , so that the χ 2 minimum corresponding to their lower limits results in an unstable equilibrium point. In contrast, the χ 2 minimum corresponding to increased values of the NFW parameters turns out to be a stable equilibrium point and, as a result, the MCMC sampling is concentrated in this specific area.
This behaviour is dominant in all the sample clusters except for MACSJ0717. Such an example is illustrated in Figure 3. The upper panel shows an overlap of the nonlocal lensing potential with that of GR, demonstrating that the two theories are able to fit the data at similar levels of significance. In the lower panels, the two contributions to the non-local lensing potential, Φ(r) and Ψ(r), are presented separately and each of them is decomposed into its zeroth order and first order terms. One can immediately see that Φ 1 (r) is completely subdominant with respect to the zeroth order term, which is greater (more negative) than the GR potential due to the increased mass estimate. Thus, the resulting effective potential is dominated by the contribution that corresponds to the "2/3 of GR" minimum. It follows the ostensibly contradictory results: the posterior constraints on the NFW parameters are dominated by regions of high posterior probability, while the lower bounds of the non-local length scales are related to the minimum corresponding to the fully non-local regime. Both solutions can fit data at similar levels of statistical significance, as a result of the matter-geometry degeneracy.
We may now compare our results with those of [42], which are obtained by numerically simulating the S2 star orbits around our Galactic centre. It immediately appears that the two results for r η are not consistent: in [42] the authors obtain a constraint of 10 7 km < r η < 10 10 km, while our lower bound is r η > 10 14 km. Instead, the two estimates for the parameter r ξ are consistent with each other, because our lower bound r ξ > 10 12 km is within that found in [42], r ξ > 10 6 km. These results are well expected. Our analysis is performed at galaxy cluster scales, while [42] is at galactic scales. Even though the theoretical parameters should be independent of the test scale, it is difficult to reach a constraint of the AU order if the resolution limit of the galaxy clusters data is of the order of ∼ 10 kpc. Notice that the results for r ξ are consistent, probably due to the fact that this parameter is associated with the scalar field which is not dynamical, but only plays an auxiliary role to localize the original Lagrangian in Eq. (2.1).
Finally, the computed Bayes factors are presented in the fourth column of Table I. Using the Jeffreys scale, we can see that there is no evidence in favour of the nonlocal model with respect to GR. For ten samples we have 0 < ln B i j < 1, for eight samples ln B i j is slightly negative and for one sample ln B i j > 1. However, in both negative and "substantial" cases the logarithm of the Bayes factor is consistent with [0, 1] within few σ.
V. SUMMARY AND CONCLUSIONS
Since the non-local theory provides a viable mechanism to explain the late time cosmic acceleration with no need to introduce any form of dark energy, it is of great interest to perform further tests of this model also to address dark matter issues. In fact, its features and the physical consequences of non-locality have to be further analysed both on astrophysical and cosmological scales.
In this work, we have performed a completely new test of the non-local model, using gravitational lensing data at galaxy cluster scales. The theory provides two effective ways to fit the observations at the same level of statistical significance as GR. On the one hand, when the highvalue limit of the non-local parameters is reached, the non-local model reduces to a GR-like theory, being able to fit the data at the cost of increased cluster mass. In this scenario, the non-local theory mimics GR at galaxy cluster scales, affecting only the estimated cluster mass. We cross-checked our results by comparing them with c 200 − M 200 relations from the literature, finding that the non-local model is slightly disfavoured with respect to GR. However, further comparisons with the constraints from different probes are necessary.
On the other hand, when the low-value limit of the non-local length scales is reached, the non-local corrections to the lensing potential become larger and comparable to, or even dominant over, the standard zeroth-order terms. In such a scenario, the non-local scenario may be able to mimic GR, neither affecting the mass estimates nor the statistical viability of the model. Moreover, when the non-local contributions becomes completely dominant, the non-local theory seems to be able to fit the lensing observations with extremely low cluster mass. Consequently, it emerges an intriguing possibility to fit data with no dark matter. In order to investigate such a scenario, further studies should be performed, taking into account the baryonic contributions from the hot gas and stellar components in galaxy clusters. [76]; orange band: c-M relation from [77]; green band: c-M relation for CLASH clusters derived by [75]. The upper and lower limits of the colored bands correspond to the minimum and maximum redshift values of CLASH clusters. | 10,235.4 | 2022-05-05T00:00:00.000 | [
"Physics"
] |
Extended DBI and its generalizations from graded soft theorems
We analyze a theory known as extended DBI, which interpolates between DBI and the $U(N)\times U(N)/U(N)$ non-linear sigma model and represents a nontrivial example of theories with mixed power counting. We discuss symmetries of the action and their geometrical origin; the special case of SU(2) extended DBI theory is treated in great detail. The revealed symmetries lead to a new type of graded soft theorem that allows us to prove on-shell constructibility of the tree-level S-matrix. It turns out that the on-shell constructibility of the full extended DBI remains valid, even if its DBI sub-theory is modified in such a way to preserve its own on-shell constructibility. We thus propose a slight generalization of the DBI sub-theory, which we call 2-scale DBI theory. Gluing it back to the rest of the extended DBI theory gives a new set of on-shell reconstructible theories -- the 2-scale extended DBI theory and its descendants. The uniqueness of the parent theory is confirmed by the bottom-up approach that uses on-shell amplitude methods exclusively.
Introduction
In past few decades, the calculational techniques for perturbative on-shell scattering amplitudes in weakly coupled quantum field theories experienced rapid development. The textbook approach based on Feynman diagrams has been supplemented by new methods which either allow to calculate the amplitudes more effectively or bring about completely new insight in the very structure of the perturbative quantum field theory. The former are based on the most general properties such as locality, unitarity and analytical structure of the amplitudes and represent a modern reincarnation of the bootstrap methods originally developed in the sixties of past century -typical examples are those based on generalized unitarity [1,2] and various sorts of recursion relations [3][4][5][6][7][8][9][10]. The latter methods have the ambition to completely reformulate the very paradigm of quantum field theory and reveal new mathematical structures behind it -let us mention e.g. the color-kinematics duality [11][12][13] and the geometrical approach based on positive geometry, namely the amplituhedron for planar N = 4 SYM [14][15][16][17][18][19][20][21] or the associahedron [22][23][24]. Another interesting representation of the scattering amplitudes of a particular set of theories is provided by the CHY formula [25,26] which calculates them as an integral over a punctured sphere which can be transformed into a sum over solutions of the scattering equations. The CHY representation reveals among others deep interrelations between amplitudes of different theories which belong to the set known as the web of theories [27], and also manifestly incorporates various sorts of soft theorems [28][29][30].
Remarkably, this progress is not limited to the case of well-behaved renormalizable theories. Many of the above new methods are applicable also to the power-counting nonrenormalizable low-energy effective ones. This usually happens provided they posses some special properties, namely particular symmetries, which are strong enough to define the theory uniquely. Such symmetries are in close relation to the properties of the scattering amplitudes. Typically they are responsible for some sort of soft theorems and in many cases just these soft theorems can be used to define the theory [8,[31][32][33][34][35][36][37]. This applies e.g. to the case of exceptional scalar field theories (the nonlinear sigma model (NLSM), the DBI scalar, the Special Galileon), vector theories (Born-Infeld electrodynamics) or scalar-vector theories (the Special scalar-vector Galileon [38]), all of which can be uniquely reconstructed from the corresponding soft limits [33].
Some of these theories were discovered first just by constructing their tree-level amplitudes and only then identified with a particular Lagrangian. And even when the Lagrangian was known, the symmetry responsible for the soft behavior of the amplitudes was far from being manifest. In this paper we discuss in more detail one of these cases, namely the theory proposed by Cachazo et al. [27] which is referred to as extended Dirac-Born-Infeld theory. The CHY representation of this theory was also mentioned in [39], where the double copy structure was established, and in [40], where the soft behavior was discussed.
Originally, the amplitudes of the extended Dirac-Born-Infeld theory were constructed using a particular procedure of squeezing and dimensional reduction applied to the CHY representation of the General relativity amplitudes and subsequently, its Lagrangian was conjectured in a closed form. The latter has been recognized as a theory interpolating between NLSM and DBI theory. In this context, a natural question arises, whether this Lagrangian is unique, what are the symmetries and what is their geometrical origin, and which properties of the amplitudes are the key ones for the possible amplitude bootstrap. Note also that this theory differs from the above mentioned exceptional theories: its amplitudes are not homogeneous functions of the momenta, while almost all the theories discussed in the context of amplitude methods were limited to cases with unmixed powercounting 1 . Also, it was so far not completely clear how to study soft limits of amplitudes without unique powercounting. Note that the two "boundary theories" of the extended DBI theory, namely NLSM and DBI, have different soft behavior and their on shell reconstruction is based on different soft theorems. This indicates that provided the extended DBI theory is in some sense uniquely reconstructible from its soft limits, some generalization of the usual soft bootstrap is needed. In this paper we address all these issues in detail.
Let us briefly summarize the main outcomes of this paper. First, we introduce the framework of effective field theories (EFTs) whose Lagrangian consists of operators with mixed power counting (so called multi-ρ theories). Section 3 then generalizes the concept of soft theorems, which were so far mostly applied to theories built of operators with a fixed power counting (single ρ theories), to the more general arena of multi-ρ theories. In particular, formulas (3.4)-(3.7) build towards a criterion for a multi-ρ EFT, that would decide whether it has an on-shell constructible tree-level S-matrix. This criterion is formulated in (3.8) as the graded soft theorem. Section 4 introduces a simple multi-ρ EFT consisting of scalars only, which allows us to illustrate the application of graded soft theorems to a not overly complicated model. It also sets the stage for the introduction of the main character of this paper -the extended DBI theory -in Section 5. There we analyze its symmetries and various subtheories resulting as limits in couplings of the Lagrangian. The discussion of implications of the symmetries for soft theorems is touched upon in this section, but is mostly deferred to Section 7. Section 6 treats the special case of SU(2) extended DBI theory in detail. Its main purpose is to clarify the more abstract constructions from previous sections and provide the reader with completely explicit expressions. In Section 7 we extract the potential of symmetries previously established for the extended DBI theory and reformulate them in terms of soft theorems. Those are then used in the proof of on-shell constructibility of the tree-level S-matrix of the extended DBI theory. Section 8 serves two purposes. First, based on the bottom-up approach of recursive amplitude construction, it verifies that conclusions made before are consistent. On top of that, it also provides a strong hint that there might exist more general on-shell reconstructible theories (parametrized by more couplings) than the DBI theory or extended DBI theory, respectively. The hunt for these generalized theories is organized in Section 9. Their existence is indeed confirmed and the Lagrangian of the 2-scale DBI theory is presented in (9.9) while the one for the 2-scale extended DBI theory in (9.13). We briefly summarize and draw our conclusions in Section 10. Technical results are collected in three appendices.
Multi-ρ effective field theories
The Lagrangian of low-energy effective field theory contains usually a (possibly infinite) tower of elementary vertices V . These correspond to monomials L V in fields decorated with increasing number of derivatives and accompanied by couplings g V with decreasing mass dimension, (2.1) Each vertex V represented by L V gives rise to a unique tree-level contact term g V A ct V contributing to some scattering amplitude. It is useful to characterize the individual vertices V using the power-counting parameters ρ V which are defined as follows Here D V is the mass dimension of the contact term 2 A ct V and N V is the number of its external legs (i.e. the number of fields of the corresponding term L V in the Lagrangian).
Assume now a contribution to some scattering amplitude given by a Feynman graph Γ with V Γ vertices, I Γ internal lines, N Γ external lines and L Γ loops. The mass dimension D Γ of such contribution (with the coupling constants stripped) is then and the number of external legs N Γ can be expressed as Using the topological relation L Γ = I Γ − V Γ + 1, (2.5) we get the generalization of the Weinberg formula For a given graph Γ we can then define the power-counting parameter (2.7) The relations (2.6) have a nice graphical interpretation in the two-dimensional plane. Each graph can be represented in such a plane by a point P Γ with coordinates (N Γ − 2, D Γ − 2), while the elementary vertices correspond to the vectors v V with components (N V − 2, D V − 2). To get the point P Γ representing the graph, we have to shift the starting point (−2L Γ , 2L Γ ) by the sum of the vectors v V corresponding to all the vertices of Γ, (2.8) Of course, the same point can represent several different graphs (see Section 4 and Fig.1 for a particular example). Note that the power-counting parameter ρ V has the meaning of the slope of the vector v V . Provided ρ V is the same for all the elementary vertices of the theory, than all the vectors v V are parallel. Therefore the points corresponding to the contributions of all the L−loop graphs sit on a single line in the (N Γ − 2, D Γ − 2) −plane. For tree level graphs such a line goes through the origin. We refer to such cases as single-ρ theories. Typical examples are the non-linear sigma model (ρ V = 0), the DBI scalar (ρ V = 1), the Born-Infeld electrodynamics (ρ V = 1) and the Galileon (ρ V = 2).
The opposite cases, which we denote as multi-ρ theories, contain elementary vertices with at least two different ρ V 's. In such a multi-ρ theory, let us define two distinguished ρ's, namely ρ min = min V ρ V and ρ max = max V ρ V . Clearly, the points P Γ representing tree-level contributions of individual graphs to the scattering amplitudes are situated inside a wedge whose vertex is at the origin of the (N Γ − 2, D Γ − 2) −plane, and which is bounded by lines with slopes ρ min and ρ max . The points on the border of this wedge correspond to graphs built solely using vertices either with ρ V = ρ min or ρ V = ρ max . They correspond therefore to scattering amplitudes of two single-ρ theories with Lagrangians which can be treated as "subtheories" of the multi-ρ theory. The complete theory then "interpolates" between these two. Typical example of such a multi-ρ theory is the DBI Galileon [41], which interpolates between the DBI scalar with ρ = ρ min = 1 and the general Galileon with ρ = ρ max = 2.
The points P Γ in the interior of the above mentioned wedge correspond to the graphs with vertices with different ρ V 's. For a general tree-level amplitude (with a fixed number of external legs N Γ ) we can then write where the single-ρ components A (ρ) are sums of contributions of all graphs with the same ρ Γ = ρ (cf. (2.7)). In our graphical language all the graphs which contribute to A (ρ) sit at the same point in the (N Γ − 2, D Γ − 2) −plane.
As mentioned above, the only graphs which contribute to A (ρ min ) and to A (ρmax) are those with vertices from L ρ min and L ρmax respectively. Therefore the components A (ρ min ) and A (ρmax) correspond to the amplitudes of the single-ρ subtheories L ρ min and L ρmax with smallest and largest ρ. On the other hand, the components A (ρ) with ρ min < ρ < ρ max cannot be treated independently and attributed to amplitudes of some single-ρ theory since in general the graphs with vertices with different ρ V contribute to them.
The general properties of the single-ρ components A (ρ) can differ. Nevertheless, given some property based on cancellation between different Feynman graphs which is valid for the complete amplitude A, the same property has to be shared also by the individual components A (ρ) , since graphs with different ρ Γ cannot communicate with each other.
Graded soft theorems
The Lagrangians of the low-energy effective field theories (2.1) can have in principle an infinite number of elementary vertices L V and an infinite number of corresponding coupling constants g V . This general picture can be substantially changed in the cases, when the theory is subject to some symmetry. Provided the symmetry requirements are strong enough, the number of independent parameters can be reduced to a finite set or even to just one independent coupling constant (representing then the so-called exceptional theory [33]). Such symmetric theories have usually many interesting properties which manifest themselves at the level of the tree on-shell scattering amplitudes. The most prominent such properties are related with soft limits of the amplitudes and can be expressed in terms of soft theorems. For instance, provided the low energy theory describes dynamics of Goldstone bosons of some spontaneously broken symmetry, the amplitudes possess in many cases a so called Adler zero [42], i.e. they vanish in the limit when one external Goldstone particle becomes soft. Provided the broken symmetry manifests itself at the Lagrangian level as a generalized polynomial shift symmetry, the Adler zero can be even enhanced [43], that means the amplitudes behave in the soft Goldstone boson limit p → 0 as where the soft exponent σ > 1. The enhanced Adler zero condition can be often used to define the theory uniquely in terms of the soft BCFW recursion [8]. We call them the on-shell reconstructible theories and they can be characterized by the power counting parameter ρ (provided they are single-ρ theories) and by the soft exponent σ. The criterion of reconstructibility for scalar theories can be expressed as (cf. [8,33]) for (ρ, σ) = (1, 1). The well known examples of the pure scalar reconstructible theories are the nonlinear sigma model (ρ = 0, σ = 1), the DBI scalar (ρ = 1, σ = 2), the general Galileon (ρ = 2, σ = 2) and the Special Galileon (ρ = 2, σ = 3). All these theories allow to reconstruct all their tree-level amplitudes recursively, using the seed amplitudes (four-point and/or five-point) as the only free input. The reconstructibility is not limited to theories of Goldstone bosons only. Recently it has been shown [34], that Born-Infeld electrodynamics is reconstructible using the soft behavior of its amplitudes with respect to the multi-chiral soft limit as its defining property. The latter is defined as a special limit when all the photons with the same helicity simultaneously become soft. Provided such a limit is applied to helicity plus photons and writing their momenta in terms of the helicity spinors, p i = [i|σ|i /2, then it is taken so that the corresponding holomorphic spinors |i are sent to zero (similarly for helicity minus photons we send instead the antiholomorphic spinors [i| to zero). In both cases of the multi-chiral soft limit, the tree-level amplitudes of the Born-Infeld electrodynamics vanish. Let us note that Born-Infeld theory is a single-ρ theory with ρ = 1.
Also the theories which couple photons (or massless vector particles) to Goldstone bosons can be reconstructible from their soft limits. This is the case for the Special scalarvector Galileon and its generalizations discussed recently in [38]. In this theory, which is a single-ρ theory with ρ = 2, the enhanced Adler zero condition for the soft scalars is combined with the generalized soft theorem for the soft photons. In the latter case, the amplitude does not vanish in the soft photon limit but it is rather related to the lower point amplitudes, which enables the recursion.
All the above mentioned examples are single-ρ theories. The problem of reconstructibility of multi-ρ theories has been addressed in [37], however, the systematical classification is still missing. As discussed in [37], the criterion of reconstructibility for a scalar multi-ρ theory with enhanced soft limit with soft exponent σ is similar to the case of single-ρ theories, namely for (ρ max , σ) = (1, 1) we require The example of such a reconstructible theory is the DBI Galileon mentioned above where the soft behavior with σ = 2 is a consequence of the non-linearly realized Lorentz symmetry in dimension D = 5.
The most interesting case is the multi-ρ theory which interpolates between L ρ min and L ρmax , where both these two subtheories are reconstructible using the soft BCFW recursion based on different sorts of soft theorems. For instance, the soft exponent σ of the enhanced Adler zeros can be different, i.e. for the subamplitudes A (ρ min ) and A (ρmax) we can have with σ min < σ max . Clearly, the complete amplitude cannot then behave better than Provided this is the case, only the amplitude components A (ρ) with ρ ≤ σ min satisfy the reconstructibility conditions. The reconstructibility of the complete amplitude depends then on the value of the power-counting parameter ρ max . Assuming the hierarchy: then there is a gap σ min < ρ < ρ max for which the amplitude components A (ρ) cannot be reconstructed using the recursion based on the soft theorem (3.5). However, for σ min = ρ max such a gap shrinks to an empty set and in fact the complete amplitude is reconstructible, since the A (ρmax) component can be reconstructed using the recursion based on its own soft behavior A (ρmax) = O (p σmax ). In summary, provided we can construct the soft BCFW recursion leaning on the graded soft theorem For a pure scalar theory, it is based on the analytical properties of the function where A n (z) and A (ρmax) n (z) are the deformed n−point amplitudes depending on the complex parameter z through all-line soft shift of the original kinematic configuration (cf. [8,33]) (3.10) Such a deformation is possible in D dimensions provided n > D + 1. Note that as a consequence of (3.7) lim z→∞ f n (z) = 0 (3.11) and the soft behavior of the amplitudes cancels the apparent poles of f n (z) at z = 1/a i . Therefore, the only singularities of f n (z) are the unitarity poles z ± F related to the factorization channels F . The latter are determined by vanishing of the corresponding propagator denominator and z ± F are the two roots of this quadratic equation. Applying now the residue theorem to the meromorphic function f n (z)/z, i.e. the fact that the sum of the residues at all its poles (including infinity) vanishes, we can write The residue at the unitarity poles factorizes into products of lower-point amplitudes, and thus the formula (3.13) gives the desired recursion.
Simple example
Let us give a simple example of the above considerations. Assume a theory in D = 4 dimensions given by the Lagrangian 3 Here and in what follows we use the mostly minus signature ηµν = diag(1, −1, −1, −1).
containing two dimensionful parameters Λ and λ, with mass dimensions [Λ] = 1, [λ] = −1. The Lagrangian describes the dynamics of a U (N ) multiplet of scalars in the adjoint representation φ a , a = 1, . . . , N 2 , arranged into a U (N ) matrix Here φ = φ a T a and the U (N ) generators T a satisfy and we use the shorthand notation for the traces · ≡ Tr (·). The Lagrangian is manifestly invariant with respect to the U (N ) L × U (N ) R (V L , V R ) symmetry acting on U as while the axial transformations of the form V, V † are spontaneously broken and their action on the fields φ a is nonlinear. Explicitly for V = exp (λα), we get in the first order This second symmetry is of the form of a generalized shift symmetry and therefore the amplitudes of the theory are guaranteed to have Adler zero with soft index σ = 1. The theory is an example of a multi-ρ theory with 0 ≤ ρ ≤ 1 (see Fig. 1). We easily identify the subtheory with ρ = ρ min = 0, which is nothing else but the nonlinear sigma model and corresponds to the Λ → ∞ limit of (4.1) The latter shares the symmetries of the original Lagrangian (4.1) and the corresponding amplitudes A (0) have the soft exponent σ = σ min = 1.
The subtheory with ρ = ρ max = 1 can be identified with (multi) DBI theory with the Lagrangian, which can be obtained as the λ → 0 limit of (4.1) This subtheory shares the U (N ) V symmetry of the original theory and a linearized form of the shift symmetry (4.6) obtained formally as its limit for λ → 0 and two vertices which can contribute to it via one-propagator graph Γ.
On top of these two it possesses also the higher polynomial shift symmetry 4 (4.10) This symmetry is responsible for the enhanced Adler zero of the amplitudes A (1) with soft exponent σ = σ max = 2. Therefore the multi-ρ theory (4.1) satisfies (3.7) and can be then reconstructed by means of recursion based on the graded soft theorem (3.8).
Extended DBI theory
In this section we introduce the main subject of our further studies, which represents a nontrivial generalization of the simple example from the previous section and which we will use as a theoretical laboratory illustrating the above general considerations. We will start with the Lagrangian of the theory and rewrite it in a more formal mathematical language, which will be well suited for the investigation of its symmetries and their geometrical origin. We will also discuss various limiting cases.
Lagrangian formulation
In [27], Cachazo et al. derived a theory that interpolates between Dirac-Born-Infeld (DBI) theory (see [44] for a review) and the non-linear sigma model [45][46][47] with U(N ) target space. They constructed the model via the scattering equations approach to the S-matrix (the CHY formalism). The latter allows to express on-shell n-point amplitudes as integrals of CHY integrands over moduli spaces of n-punctured Riemann surfaces (genus zero at tree level). The authors started with the known integrand corresponding to tree-level amplitudes for Einstein gravity and applied on it a set of non-trivial operations (dimensional reduction and squeezing) that resulted in a new CHY integrand that defined a new theory. This construction allowed the authors to compute on-shell tree-level amplitudes up to 10points and consequently partially reconstruct the action of the newly proposed effective field theory. Quite remarkably, they were able to extrapolate and conjectured a complete action (to all orders in fields). It takes the form 5 and depends on three real couplings Λ, λ and c of mass dimensions Note that compared to [27] we introduced one extra coupling c. The original action corresponds to c = (Λλ) −2 . Now let us define the various building blocks appearing in the above expression. As in the previous section, the term represents the building block for the NLSM Lagrangian (at leading order in derivative expansion, L NLSM = 1 2 η µν g µν , cf. (4.7)), where U ∈ U(N ) is defined as with φ = φ a T a ∈ u(N ) anti-hermitian (and additionally traceless for SU(N )). Normalization of the generators is chosen according to (4.3). The next piece F µν =∂ µ A ν − ∂ ν A µ is the field strength of an abelian gauge field A µ . Finally, W µν is an anti-symmetric tensor field constructed from the scalars φ in the form of a weak field expansion as At first sight it looks rather daunting, but we will argue later on that it is a unique and very elegant expression originating from topology of (special) unitary groups. 5 Note that the sign in front of the 1 Λ 2 term is irrelevant since det(S + A) = det((S + A) T ) = det(S − A) for S symmetric and A anti-symmetric matrices. The other signs are on the other hand very important to have canonically normalized kinetic terms.
At least classically, the theory can be written down in a space-time of arbitrary dimension (as the nice feature of CHY formalism is that it holds in a general dimension). However, then the mass dimension of λ would be [λ] = 1 − d 2 and powers of the mass scale Λ in front of various terms would be different, which effects the important interpolating properties of the action. In any case, in this paper we will study this model in four dimensional Minkowski space-time.
Following the terminology of [27], we will call this model the extended DBI theory. The action in (5.1) is the starting point for our analysis of the extended DBI model. In (9.13) we will give a further generalization of this theory.
Note on inclusion of the extra coupling c
When we introduced the extended DBI theory in (5.1), we included one extra dimensionless coupling c and stated that the original theory in [27] corresponds to the choice c = (Λλ) −2 . Let us explain our motivation for enlarging the theory in this way and comment on the (im)possibility of generalizing the CHY formalism to encompass this additional coupling. The approach of the authors of [27] was to invent a CHY integrand that interpolates between NLSM and DBI models. On the level of the original Lagrangian it was achieved by the limiting procedure according to the scheme 6 In other words, this interpolation property was encoded at the heart of their construction. Our point of view is slightly different. We relax the particular interpolation assumption (5.6) and instead search for the most general theory of this type (i.e. a multi-ρ theory including NLSM and DBI as boundary subtheories corresponding to ρ min = 0 and ρ max = 1 respectively) that has sufficiently constraining soft theorems. By this we mean that the soft theorems are powerful enough to yield the tree-level S-matrix on-shell constructible by soft BCFW recursion. This reasoning led us to enlarge the extended DBI theory of [27] by the extra coupling c in (5.1). Analysis of soft theorems associated with this action and study of their implications for on-shell reconstructibility of the tree-level S-matrix will be the main subject for the rest of this paper.
Imposing the NLSM/DBI interpolation property of [27] in (5.1) leads to c = c num (Λλ) −a with a ∈ (0, 2) and c num purely numerical, i.e. independent of the dimensionless combination Λλ. The authors of [27] presented the theory with the choice c num = 1 and a = 2. From a simple Feynman diagram analysis, we will show that a can indeed be fixed to the particular value a = 2. However, fixing c num is more difficult. It is not known a priori which property makes the choice c num = 1 special. Now, let us take an opposite approach and investigate the possibility of generalizing the CHY formalism in order to include a general c. This appears to be much harder, in 6 Strictly speaking, the NLSM comes with a decoupled free photon.
fact we do not know if such a modification can be consistently made. Let us remind, that the CHY integrands are classified according to the number of external legs, their division to scalars and photons and additionally according to the algebraic structure of traces (over the group associated with NLSM). So each scattering amplitude specified by these data has a uniquely associated CHY integrand. In order to include a generic c, these unique integrands would have to be further subdivided based on additional criteria that are not obvious.
We now turn to a simple example illustrating the above issue. Let us consider a 6-pt amplitude with four scalars and two photons (see Fig. 2). There are four graphs contributing to this process. Those in the first line, Fig. 2(a,b), are pure DBI and are irrelevant for our discussion (they have a different structure of traces). So let us concentrate on the second row of graphs (c) and (d) in Fig. 2. The important property to observe is that they both have the same structure of traces Tr(T T T T ), but different dependence on couplings (the amplitude in (c) is proportional to c 2 λ 6 while the one in (d) to λ 2 Λ −4 ). However, both of them must arise from a unique CHY integrand as they have the same trace structure (and clearly the same number of scalars/ photons in external legs). Since this unique CHY integrand comes with a given normalization (dependence on couplings), it implies that normalizations of these amplitudes have to be proportional c 2 λ 6 ∼ λ 2 Λ −4 . This condition results in c = c num (Λλ) −2 and therefore fixes a = 2 as we anticipated. It does not impose any condition on c num though. Thus to keep c generic, away from this special value, we would have to split the unique CHY integrand into two independent ones. Of course this subdivision would have to be performed on all CHY integrands containing the c-vertex in a consistent way. It is not clear to us whether this is possible.
Geometrical formulation of the action
The coset manifold M of the U(N ) NLSM is and in parallel we can consider also the SU(N ) version. Let U ∈ U(N ) be a coset representative. In what follows, we will use the local coordinates on U (N ) or SU (N ) which correspond to the Cayley parameterization (5.4). The left(right) invariant Maurer-Cartan and the bi-invariant metric on the coset manifold is then given as Next, let us define a local 2-form B on the coset manifold, which is expressed in coordinates corresponding to the Cayley parametrization (5.4) as A map from Minkowski spacetime to the coset manifold induces a pull-back X * of the metric h and the 2-form B to spacetime. Finally, we denote by η the Minkowski metric and by F a 2-form field strength of an abelian U(1) gauge field on spacetime, which conveniently combines with the pull-back of With these definitions at our disposal the action of the extended DBI theory (5.1) can be written in a more compact form with all the matrices entering the determinant manifestly dimensionless.
Symmetries of the action
The isometry group of the coset space M = G H in (5.7) is G = U(N ) × U(N ). By definition, the metric h is invariant with respect to these isometries. The first U(N ) corresponds to the left action on a point U ∈ M : U → g L U , while the second U(N ) corresponds to the right action U → U g R . It is useful to take linear combinations of these two groups of generators in u L,R , such that they form the Lie algebra of H = U diag (N ) and the rest will form the tangent space to M The new generators on the right hand side are formed in terms of the old ones In the sigma model community it is customary to denote the generators v as vector symmetries while a as axial symmetries, hence the notation. In this language, the isometry group becomes We already stated that the metric is bi-invariant, i.e. its Lie derivative vanishes for both v and a On the other hand the 2-form B is only invariant with respect to H However, we could restore a full U(N ) L × U(N ) R invariance of the action (5.16) if L a B would be a closed and hence exact 2-form (since H 2 dR (U(N )) = 0 and the same holds for SU(N )). For the 2-form L a B we would have L a B = dβ for some 1-form β (we denote its pull-back to spacetime X * β as b). In that case, under an infinitesimal transformation in the direction of the Killing vector field a, the terms of the Lagrangian density (5.16) inside the determinant would transform as It is clear that we can arrange a full U(N ) L × U(N ) R invariance if the term in square brackets stays invariant, which we can easily achieve by imposing a shift symmetry for the gauge field A under an infinitesimal transformation in the direction a The proof that L a B = dβ is carried out by an explicit computation for U(N ) in appendix A. In section 6 it is shown for the special case of SU(2) S 3 using just standard differential geometry on the 3-sphere. Here we wish to give an argument based on group cohomology. Suppose that we are looking for a local two-form B defined on the coordinate chart (5.4) which is invariant under v-transformations and such, that its Lie derivative in direction of a is closed, i.e.
Using the fact that the external differential and Lie derivative commute, we get immediately Therefore dB has to be invariant under a-transformations. However, we required that B and hence dB is invariant under v-transformations. This implies that dB is a local biinvariant 3-form defined on the coordinate chart (5.4) of a compact group U(N ) or SU(N ), i.e.
On the other hand, it is a mathematical fact that a bi-invariant form on a compact connected group is harmonic (in a bi-invariant metric which always exists under these assumptions).
The bi-invariant 3-form dB is thus a representative of third cohomology of either U(N ) or SU(N ). On each compact connected group there is at least one 3-form satisfying these properties, which is the Cartan 3-form where σ L is the left invariant Maurer-Cartan form defined in (5.8). But in our case the third Betti number for either of the relevant groups is equal to one therefore there is precisely one bi-invariant 3-form -the Cartan 3-form Ω. Note that this form coincides for U(N ) and SU(N ). Every unitary matrix U can be written as U = e iαÛ , U ∈ SU(N ). The left invariant Maurer-Cartan form of U(N ) then splits as however the dα piece completely drops out in the wedge product, leaving us with Since the unique bi-invariant 3-form Ω is closed, locally in every coordinate patch {V α } of U(N ) or SU(N ) there exists a unique (up to an exact form) 2-form C α such that where κ is an appropriate normalization. Then dB is bi-invariant and as a consequence, L a B is closed as desired. This finishes the proof of existence of B. In the coordinates (5.4) it coincides with (5.11). For an explicit confirmation of this fact and fixing of the normalization κ, see appendix A, in particular (A.13). To summarize, we have shown that there is a unique way how to ensure the shift symmetry of the gauge field A in (5.24) and thus a full U(N ) L × U(N ) R symmetry of the action (5.16) 8 . In particular we have proved, that the basic building blocks g µν and F µν are separately invariant. This means that any sensible Lagrangian built of these basic building blocks will be invariant too. In the next subsection we will give an explicit example of such Lagrangian. The full U(N ) L × U(N ) R invariance of the action implies soft theorems for scalar particles described by the field φ(x) with values in u(N ). Those will be discussed and exploited in section 7 to prove on-shell constructibility of the tree-level S-matrix of the extended DBI theory.
Significant limits in coupling constants
The extended DBI theory was engineered by the authors of [27] to interpolate between NLSM and DBI theories. However, modification of the action that we introduced in (5.1) consisting in the introduction of one extra coupling c for W µν and altering the power of the mass scale Λ of this term slightly modifies these interpolating properties. Now we have more freedom and thus the web of Lagrangians emerging from various limits in the three couplings Λ, λ and c will be richer. In particular, we will obtain the NLSM Lagrangian in a two step procedure with the intermediate Lagrangian of interest in its own right. It is of the form L[g µν , F µν ] and as discussed in the previous subsection and explicitly shown in appendix A all such theories enjoy the full chiral symmetry U(N ) L × U(N ) R which subsequently implies soft theorems for the scalars. It will be discussed in section 7 that such theories have an on-shell constructible tree-level S-matrix.
In order to present the flow in the space of couplings (Λ, λ, c) in a more elegant way, it is beneficial to assign to the coupling λ a geometrical meaning as it is proportional to the square root of the scalar curvature R S of the compact coset manifold Then it becomes clear that for λ → 0 the coset manifold expands to a flat space R N 2 and thus the theory flows to a DBI model. Let us remark that for the original theory in [27] 7 We could add to B an arbitrary exact 2-form dγ, which could be however absorbed in a redefinition of the gauge field A → A + γ. 8 Let us remark that the 3-form Ω might have on top of its topological meaning also a more physical corresponding to the choice c = (Λλ) −2 there is one further limit which appears beyond the weak field expansion and which reduces (5.16) to the BI theory. Note that according to the above geometric interpretation of the parameter λ, for λ → ∞ the coset manifold shrinks to a point. For the SU(2) extended DBI theory, we can show that both the metric h and the 2-form B vanish in this latter point-like limit and thus the theory flows to a BI theory when λ → ∞. We however defer the discussion of this BI limit to the next section, since it requires a closed form expression for the 2-form B, which will be given in (6.21).
The various limits of the Lagrangian L eDBI in (5.1) are presented in Fig. 3 Not to get caught in the web of limits presented in Fig. 3, it is useful to have the following geometrical picture in mind. The extended DBI can be alternatively interpreted as a theory living on a worldvolume of a flat 3-brane R 1,3 embedded in an ambient space R 1,3 × U(N ) equipped with the metric where η µν and h ab are metrics on R 1,3 and U(N ), respectively. The pull-back of the U(N ) metric to the 3-brane is denoted g µν as above, and finally H µν stands for the induced metric on the 3-brane worldvolume R 1,3 . These are natural objects from which actions of individual theories in the diagram are constructed. The last needed building block is provided by the generalized field strength Based on this view of a 3-brane living in a curved ambient space, the action of the extended DBI theory (5.1) can be rewritten as and all limits following from this action have a natural interpretation: • λ → 0 : the curvature of the U(N ) manifold goes to zero and thus the ambient space becomes flat R 1,3 × R N 2 , and at the same time the 2-form B vanishes, so to obtain an action resulting from this limit, it is enough to replace the curved metric h ab by a flat one δ ab (for the induced metric • c → 0 : this limit turns off the 2-form B on U(N ) and so the generalized field strength simply reduces to an ordinary one, thus we just make a replacement F → F in the starting Lagrangian • Λ → ∞ : this is the "decoupling limit", one is instructed to extract the linear and quadratic leading order terms from the square root DBI-like Lagrangians in order to obtain the action resulting from these limits this is the "reduced" λ → 0 limit. As before, the ambient space becomes flat which results in the replacement H µν → ∆ µν , but the form B survives in this limit being Let us now describe various branches of Fig. 3 in more detail.
Λ → ∞: path towards NLSM via a minimal model with shift symmetry To perform this limit one needs to expand the square root to order O(Λ −4 ) (order O(Λ −2 ) vanishes due to anti-symmetry of F while order O(1) is cancelled by the Λ 4 term in the action). This immediately yields the result of the limit Λ → ∞ which is the minimal invariant Lagrangian of the form L[g µν , F]. It non-trivially couples scalars to massless vectors. The first term is the Lagrangian of NLSM and the second term is a minimal Lagrangian for the generalized field strength F. Thanks to the shift symmetry (5.24), this theory is invariant with respect to the full chiral symmetry. As discussed in section 7, this property is sufficient for showing that its tree-level S-matrix is on-shell constructible. One can further reduce it by taking either c → 0 or λ → 0. This results in the following chain of theories where the last Lagrangians are decoupled theories of either NLSM or free scalars together with a free U(1) photon.
λ → 0: DBI theory As discussed above, in this limit the metric H goes to a flat metric ∆ on flat ambient space R 1,3 × R N 2 and the 2-form W vanishes, thus F → F . Therefore we get the ordinary (multi-)DBI theory Sending the strength of the W µν interaction c → 0 trivially leads to DBI theory, describing a 3-brane in R 1,3 × U(N ) The above theory still depends on two couplings Λ, λ that can be sent to infinity and zero, respectively. The theories one obtains are either NLSM with a decoupled free photon or DBI, which we have already seen c → c * = (λµ) −3 , λ → 0: reduced extended DBI theory In order to define this limit we introduce an additional mass scale µ and then send c to the special value c * = (λµ) −3 . The effect of this operation is that only the first term in the expansion of W µν survives, while all higher order terms vanish for λ → 0 Defining F * µν = F µν + W * µν , we can write the resulting reduced extended DBI theory as As before, by sending µ → ∞ or Λ → ∞, we complete the full chain of flows where the Lagrangians of the reduced minimal theory and of free scalars take the form Note that by the limiting procedure we got single-ρ theories as well as multi-ρ theories. The list of ρ values for the former ones is: ρ NLSM⊕free(γ) = 0, ρ rmin = 1 2 and ρ DBI = 1. The range of ρ values for the second class of multi-ρ theories is: 0 ≤ ρ eDBI ≤ 1, 0 ≤ ρ U(N )DBI ≤ 1, 0 ≤ ρ min ≤ 1/2 and 1 2 ≤ ρ reDBI ≤ 1. Their graphical representation in the (N − 2, D − 2) plane is depicted in Fig. 4.
Geometry of SU(2) extended DBI theory
In this section we present a detailed example of the constructions discussed so far for the case of SU(2) theory. We specialize therefore to the coset space of the NLSM. The advantage of doing so is that we will be able to carry out all computations explicitly. In particular we will derive a closed form expression for the 2-form B on S 3 SU(2). So let us start with basic differential geometry of S 3 . We will work in the Cartan formalism and express all objects in terms of the vielbein (triad in this case) and its dual. Computing the metric defined in (5.10), we get We see that the φ-coordinates are those that yield S 3 as conformally flat, i.e. they are the coordinates of a stereographic projection of S 3 to R 3 from the north, respectively south pole (we need two coordinate patches V N and V S to cover S 3 ). We will be interested almost exclusively in local considerations, so we will work in the north patch V N . It will turn out to be very useful to introduce spherical coordinates on the R 3 image of the stereographic projection The reason is that these coordinates are well adapted to the 2-form B as we will see in a moment. A standard computation then gives the fundamental objects of differential geometry -the triad e a , its dual E a , the spin connection 1-form ω a b and the curvature 2-form R a b . The triad defined in (5.8) reads (we work with the left invariant version from now on, unless otherwise stated) (1 + λ 2 R 2 ) 2 dR 2 + R 2 dθ 2 + sin 2 θdϕ 2 . (6.5) The dual triad takes the form Cartan's first structure equation yields the unique spin connection (remind that it is torsionless and hence anti-symmetric) Cartan's second structure equation gives the curvature 2-form with the result From the above one obtains the Ricci tensor which leads to a scalar curvature R S = 6λ 2 . Thus we see that in this case the coupling λ is equal to the inverse radius of the 3-sphere a concrete incarnation of the general formula (5.35).
Next, in order to perform explicit calculations, we need the Killing vectors v and a given in (5.18) in terms of left(right) invariant vector fields X L,R on SU(2). They have the following form (6.14) Finally, we derive a closed form expression for the 2-form B. Then we will have all the ingredients to check the U(N ) L × U(N ) R invariance of the action.
We start with the definition of B in (5.11) and as a first step realize that for φ ∈ su(2) The double summation (see Fig. 5) ranges over the lower wedge which divides the first quadrant of the Z 2 lattice in two equal parts (with m on the x-axis and k on the y-axes). The sum is originally arranged in such a way that we first sum over points in the vertical direction k (blue lines) and then add up the results in the horizontal direction m. We wish to change variables such that we first sum across diagonals (orange lines) and then add up those. In other words, we define which transforms the expression for B into The inner sum [. . .] evaluates to and luckily the hypergeometric function is of special type and can be further simplified.
If we express it in a standard way as a sum of Pochhammer symbols, there are telescopic cancellations among them, leaving us with Collecting partial results, they fortunately combine into a very simple expression that admits a closed form presentation 2L + 2 2L + 2n + 3 −λ 2 R 2 L+n Tr (dφ ∧ dφφ) .
with f (R) given as The expression for the 2-form B justifies the choice of spherical coordinates for the stereographic projection as was anticipated. We see that B is supported and constant on 2-spheres corresponding to a fixed radius R in the R 3 plane of the stereographic projection.
Hodge decomposition for an arbitrary 2-form, in particular B takes the form where the codifferential is expressed in terms of the Hodge star as δ = d . Note, however, that second cohomology of S 3 is trivial and thus the harmonic 2-form h is missing. We already commented that the shift by an exact form dγ is trivial as it can be absorbed by a redefinition of the gauge field A. Thus we get (now already for our particular form B) for a yet to be determined function F (R). Taking the Hodge star of (6.21) results in a differential equation for F (R) which can be easily solved leading to (a trivial additive integration constant has been dropped) It is now straightforward to compute both sides of (5.33) and fix the normalization κ. It is derived for the more general U(N ) or SU(N ) case in (A.13) with the result κ = 1/12. Here, we just give an expression for dB, as it will be useful for further analysis Since dB is essentially the volume form, it is evident that L a dB = dL a B = 0 as the volume form and equally the metric are invariant under the full isometry group. Thus L a B is a closed and hence exact 2-form, L a B = dβ, and we are all set to compute the 1-form β. We do not display the results in full generality for all three Killing vectors {a 1 , a 2 , a 3 }. Rather, for the sake of brevity, we pick the simplest case of a 3 , and illustrate the shift in the gauge field A generated by the flow in this direction. So β corresponding to a 3 is Using this expression, we conclude by writing down the shift symmetry in the abelian gauge field A defined in (5.24) under the flow generated by the Killing vector a 3 Similar, just more complicated, results hold also for the other two directions a 1 and a 2 . Provided this shift symmetry is postulated, the action is invariant under both L v (trivially) and L a , i.e. under the full isometry group U(N ) L × U(N ) R . So we managed to prove what we set out to do, and in due course computed all quantities explicitly as an illustration (at least in the simplest case of SU(2)).
We conclude this section by exploring one extra limit of the extended DBI Lagrangian that was briefly anticipated in Section 5.5. We postponed its discussion until this point, since we have proven it just for the SU(2) extended DBI theory. In fact, it is different in nature compared to the web of limits presented in Section 5.5. Those were "weakly coupled limits", valid without resummation of the W µν interactions. On the other hand, this limit demands a closed form expression for the 2-form B (or equivalently its pull-back to spacetime W µν ), in order to have its λ → ∞ behavior fully under control.
λ → ∞: BI theory
For the original theory [27] corresponding to c = (Λλ) −2 it can be verified that the metric h and the 2-form B on the coset go smoothly to zero as the coset manifold shrinks to a point in the λ → ∞ limit. Indeed, looking at the explicit formulae (6.5) and (6.21), we readily compute This fact then trivially implies that the Lagrangian reduces to a BI theory
Soft theorems and reconstructibility
According to our classification discussed in Section 2, the theory with Lagrangian (5.1) is a multi-ρ theory with ρ min = 0 and ρ max = 1. The subtheories which correspond to these boundary values of ρ are the nonlinear sigma model and the multi DBI theory coupled to a U (1) gauge field In the previous sections we have demonstrated that the Lagrangian (5.1) is invariant with respect to the generalized shifts defined as (cf. (4.6) and (5.23), (5.24)) where α is a generator of U (N ) and λ an infinitesimal parameter. Here b µ is at least quadratic in φ and its derivatives and it is determined by the condition According to the general theorem [33], this symmetry of the action is responsible for the Adler zero of the scattering amplitudes when one of the scalar particles becomes soft A p φ , 1 φ , . . . , k φ , (k + 1) h , . . . , n h p→0 = O(p).
(7.5)
Here we use condensed notation for the momenta p i ≡ i and the superscript denotes either the type of the particle or its helicity. The above symmetry is valid also for the lowest ρ subtheory L 0 . On the other hand, the highest ρ subtheory L 1 obeys instead the following linearized shift symmetry and also a higher polynomial shift symmetry which corresponds to the nonlinear realization of the higher dimensional Lorentz symmetry extended to the U (1) gauge field living on the brane [48] δ The latter implies enhanced Adler zero for soft scalars, namely Note that the tree amplitudes A (ρmax) without scalars are determined by the Lagrangian of the Born-Infeld electrodynamics and therefore they vanish under the multichiral soft limit [34] when all the particles with the same helicity are simultaneously soft. This type of soft limit is formulated within the spinor-helicity formalism. It is taken in such a way that for helicity plus particles, the holomorphic spinors are sent to zero (in the case of helicity minus particles we use instead the antiholomorphic spinors). This choice ensures that no artificial soft suppression stemming from the polarizations of the soft particles appears. We get then lim |1 ,...|n →0 A (ρmax) 1 + , . . . , n + , (n + 1) − , . . . , 2n − = 0 (7.10) and similarly for the helicity minus multichiral soft limit. The extended DBI theory with Lagrangian (5.1) obeys therefore graded soft theorems (7.5) and (7.8) and for the pure vector highest ρ amplitudes we have also the multichiral soft limit (7.10).
Let us write the scattering amplitudes with n φ scalars and n γ vectors in the form (2.10) and define the all-line shift (which is guaranteed to exist for n φ + n γ ≥ 6) for scalars, helicity plus and minus vectors respectively. Then the various components A (ρ) with ρ fixed behave under such a shift as Note that the improvement with respect to the naive scaling O z ρ(n φ +nγ −2)+2 (based on the power-counting parameter ρ) is due to our choice of the shift for the vector particles, since to each external vector, an undeformed pair of spinors is attached according to the little group scaling. Therefore provided ρ < 1, the function (cf. (3.9)) vanishes for z → ∞ and has only the unitarity poles due to the validity of the soft theorem (7.5). Similarly, for ρ = 1 and n φ = 0, the function has the same properties as a consequence of the soft theorem (7.8). Therefore, we can reconstruct all the amplitudes A n φ nγ with n φ = 0 from their residues at the unitarity poles, i.e. from the amplitudes A m φ mγ with m φ + m γ < n φ + n γ , using the soft BCFW recursion based on the graded soft scalar theorem precisely as in Section 3. What remains are the amplitudes A 0,nγ . These coincide with the amplitudes of the Born-Infeld electrodynamics and according to [34] they can be recursively reconstructed using the soft theorem (7.10). Here we can use e.g. the all but two shift: for all helicity plus particles 9 i = 1 + , . . . , (n γ /2) + we take | i(z) = (1 − bz) |i , (7.16) and for two helicity minus particles j − and k − we compensate the violation of the momentum conservation as Then the function vanishes for z → ∞ and has only the unitarity poles and thus the amplitude A (1) 0,nγ can be reconstructed recursively.
To summarize, the scattering amplitudes of the theory with the Lagrangian (5.1) are fully reconstructible either using the graded soft theorem (in the case when n φ = 0) or using the multichiral soft limit (for amplitudes with n φ = 0). The corresponding seed amplitudes are the 4pt ones. They can be easily calculated using the Feynman rules derived from the Lagrangian (5.1) (see Appendix B for details). The explicit form for the only nonzero seed amplitude reads (momenta are implicit, they are labelled by numbers corresponding to external particles) 10
Bottom-up reconstruction of the three-scalar and photon case
The results of the previous section suggest that we have several complementary possibilities how to define the extended DBI theory. The original one is based on the explicit form of the CHY integrand [27] and this definition was conjectured to be equivalent to the theory described by the Lagrangian (5.1) with particular value of the coupling c. The second possible definition is just to start with the Lagrangian (5.1). The latter was found to posses strong symmetries leading to a remarkable set of soft theorems which determine uniquely all the tree-level amplitudes of the theory provided the seed amplitudes are given. This therefore suggests the third possibility how to fix the theory, namely postulating just the soft theorems and power-counting as its defining property. This possibility naturally raises a question whether such an amplitude-based definition leads uniquely to the theory with Lagrangian (5.1) or whether there is some space for possible generalizations.
Since the soft BCFW recursion described in the previous section is based solely on the power-counting and the soft theorems, the only possibility for generalization is connected with the freedom to choose more general seed amplitudes which serve as the initial conditions for the recursion. As we have seen, the five nonzero seeds (7.19) are parametrized by three parameters, i.e. there exist nontrivial constraints on the seed provided we wish to reproduce the amplitudes generated by the Lagrangian (5.1). On the other hand, completely arbitrary choice of the seeds might be inconsistent, since the soft BCFW recursion could lead to objects which cannot be identified with amplitudes of any sensible theory.
Note that the recursive construction depends on a set of free parameters a i and b i which parametrize the soft shift (cf. (7.12)), while the resulting amplitudes have to be independent of them. The consistency check based on this a i and b i independence typically requires some constraints on the seeds. We can also proceed differently and try to construct the higherpoint amplitudes using a generic ansatz with appropriate pole structure and including a full set of generic contact terms. Then we demand both the right factorization on the poles and the appropriate soft behavior corresponding to the soft theorems. This procedure can be treated as a recursion starting with the seed amplitudes. At each n−th step, we construct full basis of n-point contact terms with free coefficients which parametrize the ansatz and the soft theorems are used to fix them. In general we obtain a set of linear equations for these free coefficients and the conditions of existence of a solution for this set can put constraints on the seeds. Both these strategies were used for classification of theories based on soft theorems and are known as the soft bootstrap [33,34,36,49]. In this section we apply this approach to the problem of possible generalizations of the extended DBI.
Instead of discussing the most general U (N ) case, we will assume a theory with only three scalars φ ± , φ 0 in the spectrum. Here we are anticipating the SU (2) extended DBI, but we relax the full SU (2) symmetry and suppose only global U (1), with respect to which the particles φ ± are charged.
• graded soft theorem of the form i.e. we suppose Adler zero for any ρ and enhanced soft limit for ρ = 1.
Note that some of the assumptions might be superfluous, however, their inclusion from the beginning simplifies considerably the study. According to the above discussion, we will suppose the existence of a theory with amplitudes satisfying the above requirements and try to reconstruct it recursively. We expect that consistency of this procedure will put nontrivial constraints on the free parameters of the seed amplitudes. As there are amplitudes with only even number of legs, the seed amplitudes are the contact 4pt vertices. We can create a basis of all allowed monomials; the number of individual terms is summarized in Table 1. There are all together seven independent constants c (ρ) i andc (ρ) i which parametrize the seed amplitudes, explicitly 3 (s 13 + s 14 )s 12 +c where s ij = (p i + p j ) 2 are the Mandelstam variables. One possible strategy of the soft bootstrap continues then with a general ansatz for the 6pt amplitudes. To get it, we glue the on-shell seed amplitudes together with corresponding propagators as if they were vertices corresponding to Feynman rules and then add a linear combination of a complete basis of the 6pt contact terms with free coefficients. The number of independent terms for various values of ρ is given in Table 2. Such a construction guarantees the right factorization properties of the resulting amplitude. The free parameters of the ansatz should be then fixed applying the graded soft theorem. As discussed above, this procedure might create constraints on the parameters c (ρ) i andc (ρ) i of the seed amplitudes as the necessary condition for the existence of the solution for the 6pt couplings.
However, we can proceed more economically, without the necessity of classifying the 6pt contact terms. Using the all-line shift for the 6pt amplitude we can construct the meromorphic function f 6 (z) of the shift parameter z according to the prescription (3.9) and (3.10). Following the discussions in Sections 3 and 7 it is easy to verify that Employing the residue theorem on f 6 (z)/z we can try to reconstruct the amplitude A 6 (0) using (3.13) and check the consistency of such reconstruction investigating the independence on the parameters a i of the shift. However, we can use the residue theorem directly on f 6 (z).
Provided the 6pt amplitude exists and is consistent, the sum of the residues still vanishes: reducing originally seven 4pt constants down to two, one standing for ρ = 0 and one for ρ = 1 vertices. Of course, the next recursion step can in principle bring further constraints on the inputs, but we can prove that this is not the case. Note that we know one particular example of a theory which satisfies the above requirements. It is nothing else but the SU (2) variant of the theory discussed in Section 4 and described by Lagrangian (4.1). Its seed amplitudes correspond to the choice and the very existence of this theory with two independent constants proves that no new constraints can occur in the higher recursion steps. We can interpret this result also the other way round: the SU (2) variant of the theory with Lagrangian (4.1) is uniquely defined by the requirements of power counting, the graded soft theorem and global U (1) symmetry as formulated above. Note that these requirements are strong enough to ensure even stronger SU (2) global symmetry, which is in this case emergent. Now we will put also a massless vector particle (photon) into the game under the same assumptions on the amplitudes as before supplemented by the multichiral soft limit (7.10) for the pure vector amplitudes. Note this additional condition is equivalent to demanding that the ρ = 1 theory in the pure photon sector is Born-Infeld. Allowing interaction of 4pt vertex degree constant Table 3. List of possible 4pt vertices of a scalar triplet and a photon.
the massless vector with the scalar particles φ ± and φ 0 and limiting the power counting by 0 ≤ ρ ≤ 1, we have five additional 4pt seed amplitudes parametrized by the constants d
[14][24]
Note that there is always only one possible monomial for the given combination of photon helicities and/or scalar flavours. It is not possible to construct e.g. the vertices Though it is possible to write down a candidate for the A(1 φ 0 , 2 φ 0 , 3 + , 4 + ) or A(1 + , 2 − , 3 + , 4 + ) vertex, such terms violate the anticipated enhanced soft limit already by itself, i.e. already at the 4pt order. As in the previous pure scalar case, we can summarize also the types of independent 6pt vertices (see Appendix C). However, this is again only for reference purposes because as before we can use soft BCFW recursion to reconstruct the six-and higher-point amplitudes without explicit knowledge of the corresponding basis. Repeating the same reasonings as in the pure scalar case, we can use the bonus relations connected with 6pt amplitudes to obtain the constraints on the 4pt seeds. The bonus relations will provide us with the following conditions on top of (8.5) and (8.6) The above mentioned multichiral soft photon limit applied directly to the seed amplitude A(1 + , 2 + , 3 − , 4 − ) leads to an additional constraint We end up therefore with four independent constants which parametrize the sought theory, two in the scalar sector, c 1 , c 2 , one in the photon sector, namely d (1) 4γ and the mixed one d (1/2) γ . As in the pure scalar case we can ask whether the higher recursion steps will give rise to some additional constraints. Let us note that a particular solution of our amplitude reconstruction problem, namely the SU (2) variant of the extended DBI with Lagrangian (5.1) corresponds to the choice (cf. (7.19)) i.e. in this theory there is an additional constraint The original CHY [27] variant of the same theory is even more restrictive, since it demands on top of it c = (Λλ) −2 , i.e.
but this theory is a special case of the previous one. Provided the SU (2) variant of the extended DBI (5.1) is the unique solution, the answer to our question should be positive, i.e. the higher recursion steps would demand the constraint (8.12) as a consistency condition of the amplitude bootstrap. However, similarly to the pure scalar case, the final decision whether the above four parameters are really free would be given provided we found a theory which fulfills all the above requirements on its amplitudes and which is parametrized just by four unconstrained parameters c 4γ and d . Search for such a theory is described in the next section.
Generalization of extended DBI
From the consistency of on-shell recursion discussed in the previous section, we learned that there might be space for generalizing the SU (2) variant of extended DBI theory. Let us concentrate on its ρ = 1 subtheory. Within the bottom-up approach, it can be obtained from the general case by sending all the input constants c (ρ) i and d
(ρ)
A for ρ < 1 to zero and by fixing the remaining two as However, as was noted, the first recursive step does not require the 4pt coupling d (1) 4γ to be fixed to this value, which indicates that it can be kept free. Even in that case all the consistency conditions dictated by the first step of the recursive amplitude construction are still satisfied. This indicates that a 2-parametric ρ = 1 theory satisfying all the requirements dictated by the soft theorems might exist. We will show that it indeed exists and its Lagrangian which will be given in (9.9) corresponds to the following choice of 4pt seed couplings parametrized by two mass scales Λ and M . As discussed in Section 7, the ρ max = 1 theory can be regarded as independent from the point of view of the soft bootstrap. Reconstruction of its tree-level amplitudes relies on its own soft theorems that are valid just for the special ρ max = 1 subtheory of the given multi-ρ theory (extended DBI in this case). Therefore, once the existence of the 2-scale ρ = 1 theory is established, we can just replace the ρ = 1 DBI subtheory of extended DBI by this newly constructed theory. Since soft reconstructibility of ρ < 1 branches of the extended DBI theory is unaffected by modification of its ρ max = 1 subtheory, this procedure is expected to output a consistent multi-ρ theory -a generalization of extended DBI parametrized by four 4pt seed couplings Lagrangian of this generalized extended DBI theory will be presented in (9.13).
2-scale single-scalar DBI theory
In the previous section we have seen that amplitudes A n φ nγ with n φ ≥ 1 of the singleρ = 1 multi-DBI theory (7.2) can be reconstructed by the soft bootstrap based on the enhanced O p 2 Adler zero. In the same theory, the pure photon amplitudes A (1) 0,nγ can be reconstructed using the multichiral soft limit. It is then a natural question whether these two soft theorems define a unique theory or whether there is a wider class of theories obeying the same soft behavior. Of course, once the 4pt seed amplitudes are fixed, the soft BCFW recursion determines the whole tree-level S−matrix. Apparently then, such a class of theories could be uniquely parametrized by the set of all possible seed amplitudes. However, as we have seen, the consistency of the recursion might in general require some additional constraints on the input and the couplings of the 4pt seeds might be correlated. Of course, this is the case of the theory with Lagrangian (7.2), where all the 4pt couplings are expressed in terms of just one dimensionful coupling Λ. But, as we will demonstrate now, this is not the most general solution.
Let us try to construct a ρ = 1 theory of massless scalars and a U (1) gauge field (photon in what follows), whose amplitudes A (1) n φ nγ satisfy the following requirements • for n φ ≥ 1 the amplitudes A (1) n φ nγ obey the enhanced O p 2 Adler zero for soft scalars • the amplitudes A (1) 0,nγ obey the multichiral soft limit for soft vectors Assume just a single scalar case for simplicity. It is natural to suppose that the action we are looking for is invariant with respect to the polynomial shift symmetry (7.7), i.e. that the scalar is the DBI one, since such symmetry automatically guarantees the required enhanced Adler zero. The most general Lagrangian, which couples a photon to a single DBI scalar in a way invariant with respect to this symmetry reads 11 The induced metric is defined as where g µν is its inverse, g = | det g µν | = − det g µν and we have denoted for simplicity g −1 F µ ν = g µα F αν . In this theory, the tree-level pure photon amplitudes are generated by the Lagrangian of the BI type Tr which can be obtained form (9.4) setting φ → 0. As it is known [34], the multichiral soft limit together with helicity conservation applied to this pure photon theory fixes uniquely the constants c α in such a way that L γ appears to be the BI Lagrangian with some scale M . With these c α we can therefore sum up the above Lagrangian (9.4) to the form which can be finally rewritten as The resulting Lagrangian is two-scale. The pure scalar amplitudes are governed by the Lagrangian with the scale Λ which sets the strength of the pure scalar interaction while the pure photon amplitudes by the Lagrangian (9.11) with the parameter M which sets the scale of the nonlinearities in the photon sector.
Since the complete Lagrangian satisfies the same soft theorems as the one scale M = Λ classical DBI Lagrangian, the amplitudes of this two-parametric theory are reconstructible in the same way as in the M = Λ case. The seed amplitudes are the 4pt ones, but now depending on two independent parameters Λ and M .
On the other hand, the most general helicity conserving 4pt amplitudes in the single scalar case, which are compatible with the enhanced O p 2 Adler zero, read (here s ij = (p i + p j ) 2 ) Note that they apparently depend on three free parameters. However, in the same way as in the previous section we can prove that the consistency of the soft BCFW recursion in fact reduces this freedom and only two free parameters c 40 and c 04 remain 12 . This means, that the two-scale DBI Lagrangian is the most general solution in the single scalar case. Generalization to the U (N ) case is then straightforwardly obtained by replacing ∂ µ φ∂ ν φ → δ ab ∂ µ φ a ∂ ν φ b in the Lagrangian (9.9).
2-scale extended DBI theory
In previous sections we learned that: (i) the branch 0 ≤ ρ < 1 of extended DBI theory has an on-shell reconstructible treelevel S-matrix from soft theorems for the scalars φ (7.5), which follow from shift invariance (7.3) and a resulting full chiral symmetry U(N ) L × U(N ) R of the action (ii) the most general ρ = 1 theory (that we know of) with an on-shell reconstructible treelevel S-matrix is the two-scale DBI theory introduced in (9.9), whose constructibility is based on the O(p 2 ) enhanced Adler zero for soft scalars as well as the multichiral soft limit for amplitudes with photons exclusively These two branches of the S-matrix can be merged into a multi-ρ theory with 0 ≤ ρ ≤ 1. It will be called 2-scale extended DBI theory. Its relation to extended DBI is the same as that 12 Note also that identifying φ with the neutral particle φ 0 of the SU (2) case discussed in the previous section, and taking into account the U (1) symmetry within the latter theory, we can identify also the tree amplitudes with only neutral scalars and photons with those of the single scalar theory. The reason is that the recursive reconstruction of these amplitudes does not depend on the amplitudes with the external charged scalars as a result of charge conservation. of 2-scale DBI to DBI. The fusion is simple, it merely consists of replacing the flat metric δ on the scalar coset manifold with the metric h on the group manifold U(N ) together with the replacement of the photon field strength with the generalized field strength F µν → F µν in the action of the 2-scale DBI theory (9.9). This readily yields the Lagrangian of the 2-scale (Λ, M ) extended DBI theory (9.13) which interpolates between NLSM (ρ = 0) and two-scale DBI (ρ = 1). By construction this theory clearly enjoys all the symmetries (namely the generalized shift symmetry (7.3) and the polynomial shift symmetry (7.7) for its ρ = 1 branch) and soft theorems that guarantee on-shell constructibility of its tree-level S-matrix. An explicit expansion of this Lagrangian and calculation of the corresponding 4pt vertices is done in Appendix B. Here we only quote the resulting 4pt seed amplitudes (9.14) Comparing with the outcome of the bottom-up approach in Sec. 8 we can conclude that it is a unique Lagrangian (up to a reparametrization) fulfilling the mentioned symmetries and soft theorems.
Significant limits of 2-scale extended DBI theory
In Fig. 6, we present a web of theories (with on-shell constructible tree-level S-matrices by soft bootstrap) emerging from particular limits of the single 2-scale extended DBI theory. The Lagrangians as well as the seed amplitudes for these theories can be obtained taking the corresponding limits of (9.13) and (9.14) respectively. The list of various types of possible limits was introduced already in Section 5.5. There is, however, one more decoupling limit on top of Λ → ∞, namely M → ∞, which has an analogous effect as the former and which has not been mentioned yet. The limit M → Λ is not included in Fig. 6, since it reduces the 2-scale extended DBI theory to the extended DBI theory, whose limits were already analyzed in Sec. 5.5 and visualized in Fig. 3,4. Using the same notation as in Section 5.5 we can rewrite the Lagrangian (9.13) in the form As in Section 5.5, H µν and ∆ µν is the induced metric in curved and flat ambient space respectively and H µν and ∆ µν denote the matrix inverse to H µν and ∆ µν . We also define H = − det(H µν ) and similarly ∆ = − det(∆ µν ).
Let us list all the non-trivial Lagrangians appearing in Fig. 6. Our naming conventions are partially inspired by the brane interpretation introduced in Section 5.5, however it was not easy to make them completely coherent. For instance the letter "e" in front of a theory name means extended (i.e. the generalized field strength F µν appears in the Lagrangian instead of the ordinary one), while U(N ) in front of a theory name means that the ambient space is curved (i.e. the U(N ) metric h ab enters the action instead of the flat δ ab ). Let us first explore theories in the left column of Fig. 6, which have not appeared so far We named these theories after the second hallmark term (supplemented by a cosmological term on the 3-brane), which is a Maxwell kinetic term. One just uses the induced metrics H µν , ∆ µν on the 3-brane instead of the Minkowski metric (and in the first Lagrangian replaces the field strength by a generalized one). All theories in this sequence have 0 ≤ ρ ≤ 1, except for the last one, which is a ρ = 1 theory. Next, we proceed with the middle column of Fig. 6 L 2eDBI The first two theories in this chain have 0 ≤ ρ ≤ 1, while the last 2-scale extended DBI theory has ρ = 1 by construction. Finally, we list theories in the rightmost column of Fig. 6 L 2eDBI The first NLSM ⊕ BI theory has 0 ≤ ρ ≤ 1, while the second one [free φ] ⊕ BI is a ρ = 1 theory. The minimal theory L min = 1 2 η µν g µν − 1 4 F µν F µν as well as the remaining two theories NLSM ⊕ [free γ], [free φ] ⊕ [free γ] already appeared while analyzing the limits of extended DBI in Sec. 5.5.
There is one special series of limits of the 2eDBI theory which has not been depicted in Fig. 6, namely c = (λµ) −3 , λ → 0. This limit can replace all the λ → 0 arrows in Fig. 6 and leads to nontrivial new theories provided it is not preceded by a c → 0 limit. In this way we obtain the reduced 2eDBI theory with 1/2 ≤ ρ ≤ 1 where 20) and its descendants which correspond either to the M → ∞ limit, which can be identified with the reduced 3-brane extended Maxwell theory (1/2 ≤ ρ ≤ 1) (9.21) or to the Λ → ∞ limit, which gives reduced NLSM⊕eBI theory (1/2 ≤ ρ ≤ 1) Finally, taking both M, Λ → ∞ we get the reduced minimal theory (ρ = 1/2) All these reduced theories are invariant with respect to the reduced shift symmetry which is the c → (λµ) −3 , λ → 0 limit of the symmetry (7.3).
Conclusions and outlook
The purpose of this work was to explore soft bootstrap methods for multi-ρ effective field theories (i.e. theories whose Lagrangian consists of operators with mixed power counting). The condition deciding whether a given multi-ρ EFT has an on-shell constructible tree-level S-matrix was formulated as the graded soft theorem in (3.8). The takeaway message of this analysis is that multi-ρ EFTs have two distinguished branches: • a branch consisting of terms with the minimal number of derivatives per field in the Lagrangian (ρ min branch) • a branch consisting of terms with the maximal number of derivatives per field in the Lagrangian (ρ max branch) Each of these two branches represents by itself an independent subtheory which can have its own soft behavior O(p σ ), with σ = σ min or σ = σ max , respectively. We can assume the following hierarchy which guarantees that both subtheories are reconstructible. Provided the amplitudes of the full theory behave as O(p σ min ), it follows that a given multi-ρ EFT has an on-shell constructible tree-level S-matrix by soft BCFW recursion if there is no gap between σ min and ρ max , i.e. σ min ≥ ρ max (cf. (3.7)). The full theory can be then reconstructed by soft BCFW recursion based on the graded soft theorem (3.8).
The goal was to apply this formalism to a particular theory of this class -the extended DBI theory -proposed by the authors of [27]. We discussed in detail the symmetries of this theory and their geometrical origin and managed to show that its tree-level S-matrix is indeed reconstructible from soft theorems. Along the route we introduced other interesting reconstructible models corresponding to particular limits of the original theory. The soft bootstrap method allowed us to construct generalizations of some theories belonging to the web of theories associated to extended DBI. In particular, we found a 2-parametric generalization of the DBI theory, presented as the 2-scale DBI theory in (9.9) as well as the 2-scale extended DBI theory (see (9.13)) that generalizes the extended DBI theory. Various limits of this theory provided us with additional interesting examples of on-shell reconstructible theories.
Let us mention some open questions connected with other approaches to construction of the (tree-level) S-matrix. We wish to highlight the following two: • the Cachazo-He-Yuan (CHY) formalism introduced in [25,50] and further developed in other works including [27] • the color-kinematics duality (BCJ duality) and the associated double-copy structure [11] Since the tree-level S-matrix of the original extended DBI theory (i.e. with the extra coupling c fixed to the special value c = (Λλ) −2 ) has a CHY formulation, it is logical to ask whether also the generalized 2-scale extended DBI theory in (9.13) might have such a formulation. The existence of a CHY representation for a given theory is closely connected with its double-copy structure. The latter was worked out for the (original) extended DBI theory from its CHY representation in [39]. Thus a natural question arises, whether also the 2-scale extended DBI theory admits a double-copy structure. Its existence seems plausible, as many theories derived from the 2-scale extended DBI theory (e.g. (extended) DBI, NLSM) already have a known double-copy structure.
A Explicit derivation of U(N ) L × U(N ) R invariance of the action Let us assume the Lagrangian The symbol · · · is used for trace over U(N ) in this appendix. The group element U ∈ U(N ) is given in (5.4), F µν is the abelian field strength and finally W µν is defined in (5.5).
The purpose of this appendix is to prove by explicit computation that the Lagrangian (A.1) is invariant with respect to the full chiral symmetry U(N ) L ×U(N ) R U(N ) V × U(N ) A . As usual, the vector subgroup U(N ) V will be realized linearly, while the axial one non-linearly.
We begin by computing the exterior derivative of the 2-form B on U(N ) (the pull-back of B to space-time is W ) Using total anti-symmetry of dφ a ∧ dφ b ∧ dφ c this can be further simplified as a sum over cyclic permutations σ of the indices (a, b, c) Note that for a cyclic permutation σ and matrices A i , i = 1, 2, 3, the following identity holds Since φ is anti-hermitian, we can find a unitary matrix V such that φ = V ϕV † , where ϕ is diagonal with eigenvalues f k ϕ = diag (f 1 , f 2 , . . . , f N ) . (A.7) Let us denoteT a = V † T a V , then e.g. This allows us to sum up over l and express the exterior derivative dB as The sum can be calculated explicitly with the result (A.11) Computing the left invariant Maurer-Cartan form U † dU = 2 1 1 + λφ λdφ 1 1 − λφ (A. 12) and plugging it into the expression for dB finally gives the final elegant formula dB = 1 12 The right hand side is nothing else than the Cartan 3-form (5.32) and thus the normalization introduced in (5.33) is fixed as κ = 1/12. From the formula above also easily follows that the 3-form dB is manifestly invariant with respect to the chiral (V R , V L ) ∈ U(N ) R × U(N ) L transformation For an infinitesimal transformation of φ with respect to a vector transformations V L = V R = exp (λα), we get On the other hand, one can express the variation as and therefore where L δ A φ is the Lie derivative with respect to the vector δ A φ. Due to the Cartan formula where i δ A φ is the inner product we get The first term is already exact, let us calculate the second one. As a first step it is useful to compute and thus i δ A φ U † dU = λα + λU † αU. (A.25) Using d U † U = 0, the second not manifestly exact term in the Cartan formula for the Lie derivative can be expressed as is invariant with respect to the chiral symmetry U(N ) R × U (N ) L as we wanted to prove in this appendix. The minimal one can be written as which is a multi-ρ theory with 0 ≤ ρ ≤ 1/2. Finally, let us comment that the reduced extended DBI Lagrangian L reDBI , as well as the reduced minimal Lagrangian L rmin (see section 5.5 for definitions and notation) are invariant with respect to the reduced shift symmetry δφ = α, δA µ = − 2 3 µ −3 αφ∂ µ φ . (A.33)
B Seed amplitudes for two-scale extended DBI
The Lagrangian of the for two-scale extended DBI reads where F µν = F µν + cW µν and where Expanding L 2eDBI up to the terms quartic in the fields we get For further convenience it is useful to use the spinor notation writing where in our convention σ µ = 1, −σ i and ε 12 = ε · 1 · 2 = 1 . For individual terms in the Lagrangian we get then This leads to the following 4pt seed amplitudes (here we use the Feynman rules which assign √ 2|p]|p] and √ 2|p |p to helicity plus and minus vector external lines respectively) (B.9) | 20,574.4 | 2021-07-09T00:00:00.000 | [
"Mathematics"
] |
High Incidence of Active Tuberculosis in Asylum Seekers from Eritrea and Somalia in the First 5 Years after Arrival in the Netherlands
Three quarters of tuberculosis (TB) patients in the Netherlands are foreign-born; 26% are from Eritrea or Somalia. We analyzed TB incidence rates in asylum seekers from Eritrea and Somalia in the first 5 years after arrival in the Netherlands (2013–2017) and performed survival analysis with Cox proportional hazards regression to analyze the effect of age and sex on the risk for TB. TB incidence remained high 5 years after arrival in asylum seekers from Eritrea (309 cases/100,000 person-years) and Somalia (81 cases/100,000 person-years). Age >18 years was associated with a higher risk for TB in asylum seekers from Eritrea (3.4 times higher) and Somalia (3.7 times higher), and male sex was associated with a 1.6 times higher risk for TB in asylum seekers from Eritrea. Screening and treating asylum seekers from high-incidence areas for latent TB infection upon arrival would further reduce TB incidence in the Netherlands.
TB elimination in low-incidence countries, the Netherlands is aiming to reduce TB incidence by 25% in the next 5 years (2)(3)(4)(5). The ultimate aim is to reach the preelimination phase for TB (<1 TB patient/100,000 population/year) and subsequently elimination (<1 TB patient/1 million population/year). One of the priority actions for low-incidence countries to proceed toward this goal is to have screening programs in place for active TB and latent TB infection (LTBI) in selected high-risk groups, such as asylum seekers from high-incidence countries (4).
Nearly one fourth of the world population has LTBI, which is especially prevalent among those living in countries with high incidence of active TB (6). LTBI refers to a persistent host immune response to Mycobacterium tuberculosis antigens without evidence of clinically manifest active TB. Persons with LTBI generally have no symptoms of TB but are at risk for active TB. This risk is highest in the first 2 years after infection. Unlike active TB, which can usually be diagnosed on the basis of a combination of signs and symptoms, imaging (e.g., chest radiograph), and bacteriologic examination, LTBI is diagnosed by tuberculin skin test and interferon-γ release assays. Therefore, screening programs for active TB differ from those for LTBI. Treatment of LTBI, which typically requires fewer antibiotic drugs over a shorter period compared with active TB, can prevent future onset of active TB and transmission of the disease (7).
In the Netherlands, asylum seekers and immigrants from countries with a WHO-estimated TB incidence of >50 cases/100,000 population and who have an intended stay in the Netherlands of >3 months undergo mandatory screening for active TB. Asylum seekers are screened within the
High Incidence of Active Tuberculosis in Asylum Seekers from Eritrea and Somalia in the First 5 Years after Arrival in the Netherlands
Three quarters of tuberculosis (TB) patients in the Netherlands are foreign-born; 26% are from Eritrea or Somalia. We analyzed TB incidence rates in asylum seekers from Eritrea and Somalia in the first 5 years after arrival in the Netherlands (2013-2017) and performed survival analysis with Cox proportional hazards regression to analyze the effect of age and sex on the risk for TB. TB incidence remained high 5 years after arrival in asylum seekers from Eritrea (309 cases/100,000 person-years) and Somalia (81 cases/100,000 person-years). Age >18 years was associated with a higher risk for TB in asylum seekers from Eritrea (3.4 times higher) and Somalia (3.7 times higher), and male sex was associated with a 1.6 times higher risk for TB in asylum seekers from Eritrea. Screening and treating asylum seekers from highincidence areas for latent TB infection upon arrival would further reduce TB incidence in the Netherlands.
first 3 days after reporting to a reception center; immigrants are screened usually within the first 3 months of arrival in the country. Furthermore, asylum seekers and immigrants from countries with a WHO-estimated TB incidence of >200 cases/100,000 population (e.g., Somalia, which has an incidence of 270 cases/100,000 population) (8) or from countries with a high TB prevalence at entry screening in the Netherlands (e.g., Eritrea, which has a WHO-estimated incidence of 74 cases/100,000 population but a prevalence of >280 cases/100,000 population at entry screening in the Netherlands) (8, 9) are offered biannual follow-up screening by chest radiograph during the first 2 years after arrival (5,9). The coverage of entry screening of asylum seekers is nearly 100%. However, the coverage of follow-up screening drops to 14% at 6 months after entry and 6% at 2 years after entry. A recent 5-year evaluation of the Netherlands' TB screening program for asylum seekers concluded that radiologic follow-up screening is not effective because of its low coverage. Only 36% of TB patients who were eligible for follow-up screening and did not have TB diagnosed at entry screening were found through follow-up screening (10).
Replacing radiologic follow-up screening with an LTBI screening and treatment program for asylum seekers from high-incidence countries upon arrival in the Netherlands is likely to be more effective in reaching the targets set by the Netherlands' TB Control Strategy. Such screening would identify persons at risk for active TB in the future and provide opportunities to prevent the disease. The Netherlands' Committee for Practical TB Control already recommended replacing radiologic screening with LTBI screening for immigrants and asylum seekers <18 years of age. As of the publication date of this article, this approach was being implemented for immigrants <18 years of age but not yet for asylum seekers (5,9). To inform policy makers and professionals on the potential benefit of an LTBI screening program for asylum seekers from high-incidence countries, we analyzed trends in TB incidence rates in asylum seekers from Eritrea and Somalia in the first 5 years after their arrival in the Netherlands.
Methods
We performed a retrospective cohort study in asylum seekers from Eritrea and Somalia who arrived in the Netherlands from January 1, 2013, through December 31, 2017. Because Eritrea was not yet an independent country before 1991, persons from Eritrea who were born before 1991 were actually born in Ethiopia. Because our data sources reported on country of birth (instead of nationality), we combined the groups of asylum seekers from Eritrea whose country of birth was listed as Eritrea or Ethiopia (3.4% persons in this combined group were born in Ethiopia).
We obtained data from the Netherlands' Immigration and Naturalization Service (IND) on asylum seekers from Eritrea and Somalia arriving in the Netherlands during the study period. IND provided data on numbers of asylum seekers and reason of request (e.g., first applications, repeated applications, family reunifications, and invited asylum seekers) by country of birth, month and year of arrival, sex, and age group. We excluded repeated applications because these are usually from asylum seekers who reapply after a failed first application without leaving the country in between applications. The IND does not provide information on duration of stay in the Netherlands of asylum seekers after registration (i.e., no linked data of asylum seekers who left the country or died are available). Because asylum seekers from Eritrea and Somalia are usually granted asylum in the Netherlands and therefore stay in the country (11), we assumed that the follow-up period of each person in the study population lasted either until the end of the study period (December 31, 2017) or until the event (TB diagnosis) occurred.
We obtained data from the Netherlands' National TB Register (NTR) on TB patients from Eritrea and Somalia who arrived in the Netherlands during the study period (i.e., persons diagnosed with active TB through December 31, 2017). NTR contains detailed information on patient demographics (including date of arrival in the Netherlands, age, sex, and country of birth), diagnostic and disease characteristics, and treatment outcome. NTR also has information on whether patients belong to specific risk groups, such as asylum seekers or immigrants. Because asylum seekers who have onset of TB after obtaining asylum are registered as immigrants in NTR, we included asylum seekers and immigrants from NTR as long as they had arrived on or after January 1, 2013. We excluded TB patients with unknown date of arrival in the Netherlands (n = 41).
We defined cases of prevalent TB as active TB in patients who were registered in NTR as being found through entry screening, independent of the time that had passed since arrival. We defined cases of incident TB as active TB in patients who were not found through entry screening, including patients who self-reported symptoms and patients found through follow-up screening or contact tracing. Patients with pulmonary and extrapulmonary TB were included. Because entry screening is conducted by using chest radiograph, mainly pulmonary and some forms of intrathoracic TB (e.g., pleural TB) are detected by screening. TB diagnosis follows the criteria set by European Union member states (i.e., cases are confirmed if M. tuberculosis is found in patient specimens; cases are deemed probable or possible if bacteriologic or clinical criteria are met) (12).
We merged both datasets (the cohort of asylum seekers from Eritrea and Somalia who arrived during the study period and the TB patients registered in NTR) by month and year of arrival, country of birth, sex, and age. We calculated the total follow-up time (in person-months) for cases by subtracting the date of arrival from the date of diagnosis, and for noncases by subtracting the estimated date of arrival (set at the 15th day of the registered month of arrival) from December 31, 2017.
We analyzed data by using the statistics software package Stata/SE 15.1 (https://www.stata.com). We described and compared characteristics of (prevalent and incident) cases and noncases and calculated incidence rates by number of years after arrival. Because we were interested in the risk for TB over time in persons with different follow-up periods, we performed survival analysis with Cox proportional hazards regression. We calculated cumulative incidences and analyzed the effect of country of birth, calendar year of entry, age, and sex on the risk for active TB.
Characteristics of the Study Population
The study population consisted of 26,057 persons (21,182 [81%] asylum seekers from Eritrea and 4,875 [19%] from Somalia ( Table 1). The number of asylum seekers from Eritrea and Somalia arriving per calendar year varied. Whereas the peak of asylum seekers from Eritrea arriving in the Netherlands occurred in 2015, the arrival of asylum seekers from Somalia peaked in 2013 (and the years before), resulting in different median follow-up periods of the study population: 27 months (interquartile range 13-32 months) for those from Eritrea and 49 months (interquartile range 39-53 months) for those from Somalia. Asylum seekers from Eritrea were more often >18 years of age (65%) than those from Somalia (30%) (p<0.001). The proportion of men and boys in the study population from Eritrea was higher than that in the study population from Somalia (61% vs. 48%; p < 0.001).
A total of 546 TB patients were identified. Seventy-eight patients (61 from Eritrea and 17 from Somalia) had prevalent TB found through entry screening, indicating a TB prevalence at entry of 288 (95% CI 224-370) cases/100,000 population for asylum seekers from Eritrea and 349 (95% CI 217-560) cases/100,000 population for those from Somalia. The other 468 patients had incident TB (338 were from Eritrea and 130 from Somalia), corresponding to overall incidence rates of 747 (95% 672-831) cases/100,000 population for asylum seekers from Eritrea and 712 (95% CI 600-846) cases/100,000 population for those from Somalia. Sixteen percent of incident cases were identified through follow-up screening. The proportion of pulmonary TB was higher among patients identified through entry screening than those identified after arrival (76% vs. 51%; p<0.001).
Incidence Rates over Time and Survival Analysis
We determined the trend in TB incidence rate over the first 5 years after arrival in the Netherlands, stratified by country of birth ( Figure 1). Among asylum seekers from Eritrea, the incidence rate dropped from 925 (95% CI 796-1,073) cases/100,000 person-years in the first year after arrival to 150 (95% CI 62-360) cases/100,000 person-years in the fourth year after arrival and to 309 (95% CI 44-2,195) cases/100,000 person-years in the fifth year after arrival. For asylum seekers from Somalia, the incidence rate dropped from 1,086 (95% CI 828-1,425) cases/100,000 personyears in the first year after arrival to 260 (95% 135-500) cases/100,000 person-years in the fourth year after arrival and to 81 (95% CI 11-575) cases/100,000 person-years in the fifth year after arrival. The large 95% CI around the fifth year incidence rate in asylum seekers from Eritrea reflects the small number of this population that had been followed up in this study for 5 years. Figure 2 depicts the Kaplan-Meier curve for onset of TB over time. The cumulative risk for TB was ≈3% over the first 5 years after arrival in both groups.
Effect of Age and Sex
When stratified by country of birth, age >18 years was associated with a higher risk for TB in the study population (hazard ratio 3.4 [95% CI 2.4-4.9] in asylum seekers from Eritrea and 3.7 [95% CI 2.6-5.3] in those from Somalia) ( Table 2). In asylum seekers from Eritrea, male sex was also associated with a higher risk for TB (hazard ratio 1.6 [1.3-2.1]); in those from Somalia, no association with sex was found. Because of strong (graphic) evidence against the proportional hazards assumption for the variable calendar year of arrival, we further stratified by this variable (data not shown). The effect of age and sex in a model with stratification by country of birth and calendar year of arrival appeared similar to the model with stratification by country of birth only but was not statistically significant because of small numbers in each stratum.
Discussion
Our study showed that asylum seekers in the Netherlands from Eritrea and Somalia have a high risk for TB: 0.3% had TB upon arrival, and ≈3% had onset of TB in the first 5 years after arrival. Although incidence rates gradually declined, they were still 10-50 times higher than the overall TB incidence in the Netherlands. Furthermore, our study provides additional insight in specific risk groups for active TB: adult (mainly those 18-35 years old) asylum seekers from Eritrea and Somalia were at higher risk for TB compared with those <18 years of age, as were men and boys from Eritrea compared with women and girls from Eritrea.
These results are consistent with a study conducted in the Netherlands in 2004, which showed that the incidence of pulmonary TB remained high in immigrants from high-incidence countries at least a decade after arrival in the Netherlands (13). A study in Denmark showed that in the 1990s, the annual incidence of TB in immigrants from Somalia decreased only gradually during the first 7 years of residence, from 2,000 to 700 cases/100,000 population (14). Although these studies provide data on changes in incidence over time, we used survival analysis methods to analyze and depict the risks of a cohort of newly arrived asylum seekers, which enabled us to take into account the different follow-up periods for each person in the study. The TB prevalence and incidence rates in asylum seekers from Eritrea and Somalia in our study were much higher than the WHO-estimated TB incidence in Eritrea (74 cases/100,000 population) and in Somalia (270 cases/100,000 population) (8). A plausible explanation for this finding is the additional risk for infection while traveling to Europe, where overcrowding and unsanitary conditions are common along travel routes, on top of the baseline infection risk in the country of birth (15,16). Walker et al. (17) found molecular and epidemiologic evidence for this in their study of a cluster of multidrug-resistant M. tuberculosis infections among patients arriving in Europe from the Horn of Africa. A second explanation could be an increased risk for TB because of vitamin D deficiency, malnutrition, and stress (15). These conditions are common in asylum seekers during the often stressful asylum application procedures and during the first years of settlement in the new country. Third, transmission within ethnic groups in the new country of residence can also contribute to the higher TB rates found in asylum seekers. Occasional outbreaks have been reported in ethnic groups, including recently arrived asylum seekers (18). Finally, the WHO figures could be an underestimation of actual TB rates (18)(19)(20).
Our findings support the recommendations for LTBI screening of asylum seekers from high TB-incidence countries (4). In our study, most TB cases in asylum seekers from Eritrea and Somalia occurred after initial radiologic screening for active TB, and only a few cases were identified by radiologic follow-up screening (partly because of the low coverage of follow-up screening). LTBI screening and treatment can prevent active TB, including extrapulmonary forms. Furthermore, because LTBI might reactivate to active disease many years after infection, LTBI screening also has the potential to prevent TB in asylum seekers many years and even decades after arrival in the new country. Implementing an LTBI screening program in asylum seekers is not easy. A survey conducted by the WHO Regional Office for Europe and the European Respiratory Society showed that 53% of countries in Europe performed systematic LTBI screening in refugee populations (21). A study conducted in 11 selected countries of Europe indicated that these countries had very different methods and policies for migrant TB or LTBI screening (22). Systematic reviews have demonstrated that limited information is available on the yield and effectiveness of migrant LTBI screening (22,23). Furthermore, cost-effectiveness of LTBI screening as predicted in mathematical models is highly setting-specific, with best results achieved if restricted to migrants from high-incidence countries (24). Our study had several strengths. We were able to combine national comprehensive data on immigration and TB notification; thus, we could calculate incidence rates for specific groups of asylum seekers and show trends over time after arrival. Moreover, by using a Cox proportional hazards regression model, we were able to assess the effect of risk factors such as sex and age on the risk for TB.
Our study also had some limitations. First, no data were available on the actual follow-up period of persons in the study population who did not have TB diagnosed. Although most asylum applicants from Eritrea and Somalia are granted asylum and will therefore stay in the Netherlands (11), some might have moved to another country (or died) before the end of our study period, meaning that we possibly underestimated the TB incidence rates in asylum seekers from Eritrea and Somalia. On the other hand, whereas we included only asylum seekers (not immigrants) from the IND database, we did not differentiate between asylum seekers and immigrants among the TB patients included in our study. The reason for this was that asylum seekers who obtained a residence permit before having their TB diagnosed are registered in NTR as immigrants, even though most arrived in the Netherlands as asylum seekers. Very few asylum seekers from Eritrea and Somalia come to the Netherlands as immigrants (11,25), so we expect that this limitation has not led to a substantial overestimation of TB incidences in our study. Second, no information on travel routes was available for our study population, and no distinction could be made between asylum seekers who had undertaken the often long and stressful journey by land and water and those who came directly by airplane, for example, for the purpose of family reunification. Future studies should take these differences into account. Moreover, we only analyzed data on asylum seekers from 2 countries with high TB incidence countries (Eritrea and Somalia), so the results might not reflect trends in onset of active TB in asylum seekers from other high-incidence countries. However, because asylum seekers from other countries in Africa often share the same hazardous journey, their risk for TB is probably similarly elevated. An investigation into whether the risks for active TB after arrival in the Netherlands differ between asylum seekers and other migrants from high-incidence countries (e.g., persons migrating to the Netherlands because of work or study) would be warranted. We recommend additional studies of longer follow-up periods to enable a more extensive analysis of trends in TB incidence rates, molecular studies differentiating disease caused by in-country transmission or reactivation of premigration acquired infection, and studies evaluating the effectiveness and impact of LTBI screening programs in asylum seekers.
In conclusion, our study results clearly show that asylum seekers from Eritrea and Somalia remain at high risk for active TB for at least the first 5 years after arrival in the Netherlands. This finding underscores the need for an LTBI screening and treatment program for high-risk groups. LTBI screening and preventive treatment will also accelerate TB control and contribute toward the elimination of TB. | 4,799.2 | 2020-04-01T00:00:00.000 | [
"Medicine",
"Biology"
] |
Mathematical Theory of Compressible Magnetohydrodynamics Driven by Non-conservative Boundary Conditions
We propose a new concept of weak solution to the equations of compressible magnetohydrodynamics driven by ihomogeneous boundary data. The system of the underlying field equations is solvable globally in time in the out of equilibrium regime characteristic for turbulence. The weak solutions comply with the weak–strong uniqueness principle; they coincide with the classical solution of the problem as long as the latter exists. The choice of constitutive relations is motivated by applications in stellar magnetoconvection.
Introduction
The large scale dynamics arising in stellar magnetoconvection is driven in an essential way by the boundary conditions, see Gough [11].The flux separation and pattern formation arise in the turbulent regime when the fluid flow is far from equilibrium.As the underlying field equations are non-linear, the existence of global in time smooth solutions in such a regime is not known.Indeed the vast majority of global existence results in the class of classical solutions is restricted to the initial state close to a stable equilibrium, see a.g.Matsumura and Nishida [13], Valli [18], among others.What is more, the recent results of Merle et al. [14], [15] indicate that classical solutions may develop singularities in a finite time.
In view of the above arguments, the concept of weak solution represents a suitable alternative to restore global-in-time existence even for problems with large data and solutions remaining out of equilibrium in the long run.We consider a mathematical model of fully compressible three dimensional fluid convection driven by an externally imposed magnetic field.The fluid occupies a bounded domain Ω ⊂ R 3 with regular boundary.The time evolution of the density ̺ = ̺(t, x), the (absolute) temperature ϑ = ϑ(t, x), the velocity field u = u(t, x), and the magnetic field B = B(t, x) is governed by the compressible MHD system of field equations (cf.[6]):
The right-hand side of equation (1.4) represents the entropy production rate, which, in accordance with the Second law of thermodynamics, must be non-negative.Accordingly, we consider Newtonian fluid, with the viscous stress tensor where the viscosity coefficients µ > 0 and η ≥ 0 are continuously differentiable functions of the temperature.Similarly, the heat flux obeys Fourier's law, where the heat conductivity coefficient κ > 0 is a continuously differentiable function of the temperature.
The existence of global-in-time weak solutions for the compressible MHD system (1.1)-(1.8)was shown in [6] under certain physically relevant restrictions imposed on constitutive equations and transport coefficients.The boundary conditions considered in [6] are conservative, (1.9) characteristic for closed systems.If the driving force g in the momentum equation is conservative, meaning g = ∇ x G, G = G(x), the total energy of the system is conserved and the dynamics obeys the rather "boring" scenario formulated by the celebrated statement of Clausius: The energy of the world is constant; its entropy tends to a maximum.
A rigorous mathematical proof of this statement for the Navier-Stokes-Fourier system was given in [10].
As pointed out by Gough [11], a rich fluid behaviour is conditioned by a proper choice of boundary conditions.Motivated by models in astrophysics, we suppose the boundary ∂Ω is impermeable and the tangential component of the normal viscous stress vanishes on it, (1.10) However, the theory presented in this paper can accommodate more general boundary conditions for the velocity field discussed in Section 6.
Similarly to the well known Rayleigh-Bénard problem, see e.g.Davidson [5], we impose the inhomogeneous Dirichlet boundary conditions for the temperature, To incorporate the effect of an exterior magnetic field, we suppose that B is (not necessarily small) perturbation of a background magnetic field B B , div x B B = 0, In the context of astrophysics, we may think of B B as being the magnetic field imposed by a massive star.As for b, we suppose either The boundary condition (1.12) is of Dirichlet type, compatible with the requirement of solenoidality of B. The condition (1.13) is of flux type, similar to the first condition (1.10) and must be accompanied by another flux condition related to the electric field, namely The flux in (1.14) may be inhomogeneous as well.The borderline case B B = 0 in (1.12) and (1.13) corresponds to a perfectly isolating and perfectly conducting boundary, respectively (see e.g.Alekseev [1]).
For possibly technical but so far unsurmountable reasons, a mathematically tractable weak formulation of compresible MHD system cannot be based on merely rewriting the system (1.1)- (1.4) in the sense of distributions.The available a priori bounds are not strong enough to render certain terms, notably p(̺, ϑ)div x u in the internal energy balance (1.4), integrable.A remedy proposed in [6] is replacing (1.4) by the entropy equation (1.6).Unfortunately, the entropy production rate is a priori bounded only in the non-reflexive space L 1 of integrable functions.As a result, any approximation scheme provides merely an inequality satisfied in the sense of distributions.
Replacing entropy equation by inequality definitely enlarges the class of possible solutions and gives rise to an underdetermined problem.To save well posedness, at least formally, the integrated total energy balance/inequality is appended to the system (1.1)-(1.3),(1.15) in [6].The total energy balance reads (1.16) If the system is conservative, the total energy flux vanishes on the boundary and (1.16) integrated over Ω yields d dt It turns out that the equations (1.1)-(1.3), the inequality (1.15), together with the integral identity (1.17) represent a suitable weak formulation for the conservative system.Indeed the existence of global-in-time weak solutions for any finite energy (initial) data was proved in [6].The weak solutions comply with a natural compatibility principle.Any sufficiently smooth weak solution is a classical solution of the problem.In addition, the weak solutions satisfy the weak-strong uniqueness principle: A weak solution coincides with the strong solution on the life span of the latter, see [7].
The situation becomes more delicate for open (non-conservative) systems, with inhomogeneous Dirichlet boundary conditions.The heat flux q • n as well as the induction flux (the normal component of the electric field) [B × u × B + ζcurl x B × B] • n do not necessarily vanish on ∂Ω and give rise to additional uncontrollable sources of energy in (1.17).In [4] (see also the monograph [9]), a new approach has been developed to handle the inhomogeneous Dirichlet boundary conditions for the temperature.The total energy balance (1.17) is replaced by a similar inequality for the ballistic energy 1 2 where θ is an arbitrary extension of the boundary temperature ϑ B inside Ω. Pursuing the same strategy, we introduce a "magnetic" variant of the ballistic energy After a straightforward manipulation, we deduce equality The mathematical theory we propose is based on imposing the weak form of the equations (1.1)-(1.3),together with the entropy inequality (1.15), and the ballistic energy balance (1.19) as a weak formulation of the compressible MHD system.The basic hypotheses concerning the state equation and the transport coefficients as well as the exact definition of weak solution are given in Section 2. In Section 3 we introduce the basic tool to investigate stability properties in the class of weak solutions -the relative energy inequality.In Section 4, we show that the weak solutions enjoy the weak-strong uniqueness property.In Section 5, the existence of global-in-time weak solutions is established by means of a multilevel approximation scheme.The paper is concluded in Section 6 by a brief discussion on possible extensions of the theory to a larger class of boundary conditions.
Weak formulation
We start by a list of structural hypotheses imposed on the equation of state and the transport coefficients.
Equation of state
Our choice of the equation of state is motivated by [9,Chapter 4].In particular, we consider the radiation contribution to the pressure/internal energy relevant to problems in astrophysics, cf.Battaner [3].In accordance with Gibbs' relation (1.5) we suppose that where the function P ∈ C 1 [0, ∞) satisfies This implies, in particular, that Z → P (Z)/Z In accordance with (1.5), the entropy takes the form where (2.6)
Transport coefficients
We suppose the viscosity coefficients in the Newtonian stress S(ϑ, ∇ x u) are continuously differentiable functions of the temperature satisfying Note that α = 1 2 corresponds to Sutherland's law relevant in astrophysics, see Yang et al. [21].Similarly, the heat conductivity coefficient in the Fourier heat flux q(ϑ, ∇ x ϑ) is a continuously differentiable function of the temperature satisfying (2.8) Here, the case β = 3 reflects the effect of radiation.Finally, we suppose the magnetic diffusivity coefficient (2.9)
Boundary data
We suppose the background magnetic field Similarly, we suppose the boundary temperature ϑ B can be extended inside Ω,
Weak solutions
Before discussing the concept of weak solution, it is useful to introduce the function spaces Both H 0,τ and H 0,n are endowed with the Hilbert norm , see e.g.Alexander and Auchmuty [2].
and the integral identity
In addition if the boundary condition (1.12) is imposed or for the boundary conditions (1.13), (1.14).The integral identity in the case of boundary conditions (1.12), for the boundary conditions (1.13), (1.14).
, and the integral inequality • Ballistic energy inequality.The inequality Remark and write On the one hand, as Ψ vanishes on ∂Ω and B is solenoidal, we have whence the integral identity (2.19) holds for ∇ x Ψ.On the other hand, the function (ϕ − ∇ x Ψ) is solenoidal, and, as ∇ x Ψ × n| ∂Ω = 0, a legal test function in (2.19).
If ϕ satisfies (2.21), we simply consider -the standard potential in the Helmholtz decomposition.
Remark 2.3.Unlike ̺, ̺u, and B, the total entropy ̺s(̺, ϑ) is not weakly continuous in time.However, it can be deduced from the entropy inequality that the one sided limits Remark 2.4.As we shall see below, the "magnetic" ballistic energy E BM introduced in (1.18) is in fact a strictly convex l.s.c function of the variables (̺, S = ̺s(̺, ϑ), m = ̺u, B).In particular, its integral is a weakly lower semi-continuous function; whence (2.23) holds for any time τ with the convention for entropy discussed Remark 2.3.Alternatively, we may impose a stronger integrated version of (2.23) in the form The existence of global-in-time weak solutions in the sense of Definition 2.1 will be shown in Section 5 below.
Relative energy
A suitable form of the relative energy for the compressible MHD system reads In applications, the quantity (̺, ϑ, u, B) stands for a weak solution of the compressible MHD system while (r, Θ, U, H) are arbitrary sufficiently smooth functions satisfying the compatibility conditions As a consequence of hypothesis of thermodynamic stability stated in (2.4), the energy is a strictly convex l.s.c.function if expressed in the variables (̺, S = ̺s(̺, ϑ), m = ̺u, B), see [9, Chapter 3, Section 3.1] for details.Moreover, we have where e(̺, ϑ) − ϑs(̺, ϑ) + p(̺,ϑ) ̺ is Gibbs' free energy.Consequently, the relative energy can be seen as Bregman divergence associate to the convex function E. In particular, E ̺, ϑ, u, B r, Θ, U, H ≥ 0, and E ̺, ϑ, u, B r, Θ, U, H = 0 ⇔ (̺, ϑ, u, B) = (r, Θ, U, H) as long as r > 0.
Relative energy inequality
In the remaining part of this section, we derive a relative energy inequality provided (̺, ϑ, u, B) is a weak solution of the compressible MHD system specified in Definition 2.1 and (r, Θ, U, H) arbitrary smooth functions satisfying (3.2).Our starting point is the ballistic energy inequality (2.24).As noted in Remark 2.5, we may flip B B for H, and, of course, θ for Θ obtaining
Momentum perturbation
Our first goal is to replace |u| 2 by |u−U| 2 .This can be achieved by considering U as a test function in the momentum balance equation (2.15).After a straightforward manipulation explained in detail in [9, Chapter 3, Section 3.2.1],we obtain for any (Θ, U, H) as in (3.2).
Magnetic field perturbation and the final form of relative energy inequality
Since we may rewrite (3.5) in the final form for any "test" functions (r, Θ, U, H) specified in (3.2).
Weak-strong uniqueness principle
The first important property of the weak solutions introduced in Definition 2.1 is the weak-strong uniqueness principle.We suppose that (r, Θ, U, H) is a smooth solution of the problem, specifically, together with the relevant initial and boundary conditions.
Remark 4.2.As we assume existence of a classical solution in Theorem 4.1, the initial data are also regular, in particular, inf Remark 4.3.Remarkably, the result holds in the full range of exponents α, β specified in (4.2).
In particular, we remove the gap between the weak-strong uniqueness principle stated in [4], [9] for β = 3 and the existence result requiring β > 6.The main novelty is formulated in Lemma 4.4 below.
The rest of this section is devoted to the proof of Theorem 4.1.Note that existence of local in time strong solutions to the compressible MHD system can be established by the nowadays well understood technique proposed by Valli [18], Valli and Zajaczkowski [19], or by a more recent approach via maximal regularity in the spirit of Kotschote [12].As noted in Remark 3.1, the conclusion of Theorem 4.1 remains valid for the strong solutions in the maximal regularity class used in [12].
The idea of the proof of Theorem 4.1 is simple: We consider the strong solution (r, Θ, U, H) as test functions in the relative energy inequality (3.7) and use Gronwall's type argument.We proceed in several steps specified below.
Magnetic field
As U solves the momentum equation, we get Similarly, H being the exact solution of the magnetic field equation, Regrouping the terms in (3.7), (4.4), (4.5) that do not contain magnetic dissipation, we get the expression Indeed the integrals on the right-hand side can be treated as follows: Summing up the previous discussion, we may rewrite inequality (3.7) in the form In addition, we have We claim Indeed either B, H satisfy the boundary condition (1.12) and then (B − H) × n = 0 or H satisfies the flux condition (1.14).In both cases the surface integral in (4.9) vanishes.Thus relation (4.7) takes the form
Pressure and entropy
After a simple manipulation, we can rewrite (4.10) in the form with a quadratic remainder Using the identity ∂s(r, Θ) Consequently, inequality (4.11) can be written as with a remainder
Diffusive terms
First, as ϑ, Θ coincide on ∂Ω, we can integrate by parts: Putting all diffusive terms on the left-hand side of the relative energy inequality (4.13), we get Finally, Thus (4.13) can be rewritten in the final form with R 2 given in (4.14).
Refined estimates
Similarly to [9, Chapter 4, Section 4.2.1],we introduce the "essential" and "residual" component of a measurable function.We set The remaining part of the proof of weak-strong uniqueness principle follows essentially the arguments of [9, Chapter 4, Section 4], with the necessary modifications to accommodate the terms containing the magnetic field as well as the complete slip/Dirichlet boundary conditions.First, we recall the coercivity property of the relative energy: where the constant depend on inf r, sup r, inf Θ, sup Θ.
Temperature gradient
The following crucial estimate was proved in [9, Chapter 4, Section 4.2.2] for β = 3.Here, we extend its validity to general β ≥ 3.
Proof.We consider first the essential part.Rewrite Applying Hölder's inequality we deduce from (4.21) where ξ depends on Θ.As a matter of fact, the only hypotheses to be imposed on κ is that κ(ϑ) > 0 whenever ϑ > 0.
As for the residual part, we first rewrite Consequently, as inf Θ > 0, it remains to handle a quantity where C is a positive constant depending on Θ, inf Θ.Note that this step requires ϑ 2 < ∼ κ(ϑ).To proceed we consider ϑ > 0 to be fixed below.We write Thus it remains to handle the integral Finally, it remains to handle the integral ϑ≥ϑ On the one hand, using Sobolev-Poincaré inequality we get
Next, by Jensen's inequality, where q = 8 5 − α .(4.29) Next, repeating the same arguments, we get The previous estimates, together with (4.32), allow us to rewrite the inequality (4.18) in the form where the remainder R 2 is specified in (4.14).
Completing the proof of weak-strong uniqueness
The rest of the proof of weak-strong uniqueness consists in absorbing all integrals appearing in the remainder R 2 by the left-hand side of (4.33) and applying Gronwall's argument.We omit the details as the whole procedure is described in [9, Chapter 4].
We have proved Theorem 4.1.
Remark 4.6.The Lipschitz regularity of the domain Ω required in Theorem 4.1 may not be sufficient for the existence of the strong solution to the MHD system.
Existence of weak solutions
The proof of existence of weak solutions can be carried out by means of the approximate scheme, a priori estimates, and compactness arguments specified in Chapter 5 and Chapter 12 of the monograph [9].
The magnetic field equations can be incorporated exactly as in [6] without any additional difficulties.Similarly to [9,Chapter 12], two additional assumptions must be imposed on the constitutive relations, specifically, lim Z→∞ S(Z) = 0, ( where S is the function defining the entropy s M .Moreover, we require where β is the exponent in (2.8).While (5.1) corresponds to the Third Law of Thermodynamics, hypothesis (5.2) is purely technical to ensure the necessary a priori bounds.
Approximation scheme
The existence of weak solutions can be shown by solving the following multi-level approximation scheme.The equation of continuity (1.1) is replaced by its parabolic regularization: supplemented by the Neumann boundary conditions and the initial condition ̺(0, •) = ̺ 0,δ , ( where ̺ 0,δ > 0 is a smooth regularization of the initial density ̺ 0 .Here and hereafter, ε and δ are small parameters to be sent to zero successively in the limit passage.The momentum equation (1. as long as u B •n = 0.This enables to include problems of Taylor-Coutte type.The extension to general in/out flow boundary conditions for the velocity would require a more elaborated treatment in view of the presence of the magnetic field.For the in/out flow boundary conditions for the Navier-Stokes-Fourier system in the absence of magnetic field see [9].
• The Dirichlet boundary conditions for the temperature can be replaced by a flux type condition on a part of the boundary: Note that this type of condition is particularly relevant in the modelling of stellar magnetoconvection, see Thompson and Christensen-Dalsgaard [17].
• The induction flux (electric field) can be prescribed in (1.14): • Mixed type boundary conditions imposed on different components of ∂Ω can be accommodated without essential difficulties.
5. Note carefully that the ballistic energy inequality (2.23) remains valid if we replace B B by any other extension B such that div x B = 0, and B × n| ∂Ω = B B × n| ∂Ω , or B • n| ∂Ω = B B • n| ∂Ω , respectively.Indeed the difference B B − B becomes an eligible test function for for the weak form of the induction equation (2.19), endowed with the boundary conditions (2.20), (2.21), respectively. | 4,438 | 2023-04-02T00:00:00.000 | [
"Mathematics"
] |
Two-flavor lattice QCD with a finite density of heavy quarks: heavy-dense limit and “particle-hole” symmetry
We investigate the properties of the half-filling point in lattice QCD (LQCD), in particular the disappearance of the sign problem and the emergence of an apparent particle-hole symmetry, and try to understand where these properties come from by studying the heavy-dense fermion determinant and the corresponding strong-coupling partition function (which can be integrated analytically). We then add in a first step an effective Polyakov loop gauge action (which reproduces the leading terms in the character expansion of the Wilson gauge action) to the heavy-dense partition function and try to analyze how some of the properties of the half-filling point change when leaving the strong coupling limit. In a second step, we take also the leading nearest-neighbor fermion hopping terms into account (including gauge interactions in the fundamental representation) and mention how the method could be improved further to incorporate the full set of nearest-neighbor fermion hoppings. Using our mean-field method, we also obtain an approximate (μ, T) phase diagram for heavy-dense LQCD at finite inverse gauge coupling β. Finally, we propose a simple criterion to identify the chemical potential beyond which lattice artifacts become dominant.
Introduction
Lattice QCD at non-zero baryon density suffers from the so-called "sign problem" [1]. It also displays a new type of lattice artifact: because of the Pauli exclusion principle, the lattice cannot support more than one quark per site (and per spin, color and flavor). The main goal of this paper is to characterize the effects of this new discretization error, so as to better disentangle genuine physics from lattice artifacts.
We first briefly recall the foundations of lattice QCD in the presence of a chemical potential µ and some well-known features of the sign problem which appears when µ = 0.
JHEP02(2016)051
We then focus on the half-filling point (section 2) and the associated fermion saturation. Using the heavy-dense limit (section 3), we elucidate the properties of the half-filling regime and analyze, using a mean-field calculation which takes leading nearest-neighbor fermion hoppings and gauge interactions into account (appendix B), how far some of these findings generalize to full QCD. Finally, using our mean-field method, we obtain an approximate (µ, T ) phase diagram for heavy-dense LQCD, which can be compared with current state of the art complex Langevin investigations [3].
QCD at finite density
In this paper, we adopt the Wilson discretization of the Dirac operator. For a single flavor at chemical potential µ it reads: where (x, y) are multi-indices labeling different lattice sites, (I, J), (a, b) are color and Dirac indices respectively and U ν,IJ (x) is the (I, J) component of a link variable that points from site x to (x + ν). The hopping parameter κ is related to the bare lattice quark mass m by κ = (2 m + 8) −1 , and the boundary conditions are assumed to be periodic in spatial directions and anti-periodic in the time direction.
Using matrix notation, we write (1.1) simply as D(µ), keeping its dependency on the gauge field implicit. From the definition (1.1), it follows that where µ * is the complex conjugate of µ, which shows that which can be used, together with Wilson's lattice gauge action, (1.7) to sample gauge configurations by Monte Carlo. This generalizes to the case of N f flavors as long as the degeneracy factor for each quark mass is even, i.e. as long as there is always an even number of flavors that have the same quark mass.
The sign problem
For Re(µ) = 0, the fermion determinant (1.3) becomes in general complex and loses its probabilistic interpretation. In order to continue sampling the gauge field by Monte Carlo, one is then forced to invoke reweighting techniques. For example, if the theory contains an even number N f of mass degenerate flavors, one can use |Det(D(µ))| N f = Det(D(µ)) N f /2 Det(D(−µ)) N f /2 instead of Det(D(µ)) N f to sample the gauge field and treat the complex phase, . (1.10) Although the reweighting procedure (1.9) is in principle exact, its applicability is limited by the statistical fluctuations of the phase R[U ]. To see this, consider the expectation value of the phase, where ∆f = f − f q is the difference in the free energy densities of the unquenched and the quenched theory and L and N t are respectively the spatial and temporal system sizes.
JHEP02(2016)051
For sufficiently large systems, ∆f becomes approximately independent of the system size and (1.11) shows that R q then decays exponentially with increasing system size. As per definition the modulus of R[U ] remains equal to 1, this shows that the fluctuations in the reweighted observable, O[U ] R[U ] / R q , grow exponentially with the system size and so does the statistical error. The dependency of the latter on the number of measurements is known to be proportional to 1 / √ # meas.. This means that the statistics required to obtain equally accurate results for different system sizes must scale like required statistics ∝ e 2 L 3 Nt ∆f . (1.12) The exponential growth of the required statistics as a function of the system size in (1.12) is a manifestation of the so-called sign problem which is generic in the numerical treatment of strongly correlated fermion systems at finite density.
Half-filling and saturation
As mentioned above, the sign problem is generic in the numerical study of strongly correlated fermion systems at finite density and appears therefore also in solid state physics when working with e.g. the fermionic Hubbard model. There, finite density simulations are often carried out at the so-called half-filling point, i.e. at the value of the chemical potential where the fermion density assumes half its maximum value. Due to the particle -hole symmetry that exists at this point, the sign problem disappears and it is possible to simulate much larger systems than at generic non-zero values of the chemical potential. The half-filling point also exists in lattice QCD (LQCD). The reason for this is of course that the quarks, as they are fermions, are subject to the Pauli exclusion principle, which implies that on each site, each of the 2 × N f × N c fermionic states can be occupied only once. For two flavor QCD (N f = 2, N c = 3), the maximal number of fermions per site is 12 and the half-filling point should therefore correspond to a fermion number density of 6. Figure 1 illustrates this for the case of a tho flavor system with an isospin chemical potential (i.e. a phase quenched two flavor system): it shows the isospin number density as a function of the chemical potential µ for different system sizes. The figure also illustrates that the location of the half-filling point is independent of the system size as the different curves (corresponding to different system sizes) all cross in precisely the same point at n I = 6, µ ≈ 1.3. In figure 2 we also show the condensates ψ ψ and ψγ 4 τ 3 ψ as a function of isospin-µ for the same set of system sizes. Also here we see volume independency at half-filling as the different curves cross in a single point at µ ≈ 1.3, but in contrast to the situation with the isospin density, the values of the condensates at half-filling are not half-way between their corresponding values at µ = 0 and at saturation µ → ∞. To see where the volume independency comes from, we define the local isospin density, Figure 2. Quark (left) and "isospin" (right) condensate as a function of isospin µ for different system sizes, recorded at κ = 0.15 and β = 5.0. All curves cross in a single point, the half-filling point at µ ≈ 1.3, but in contrast to the situation with the isospin density in figure 1, the values of the condensates at half-filling are not in the middle between their values at µ = 0 and µ → ∞.
where tr c,d is the trace with respect to color and Dirac indices, such that and consider its average space-time variance, given by This quantity is shown on the left-hand side of figure 3 for the same ensembles that were used in figure 1. As can be seen, (2.4) is essentially zero at the half-filling point, which means that the half-filling is realized very homogeneously. As, according to the right-hand Figure 3. Average isospin density space-time variance eq. (2.4) (left) and isospin density ensemble variance (right) as functions of µ for different system sizes, recorded at κ = 0.15 and β = 5.0. The figures show that at the half-filling point at µ ≈ 1.3, both the space-time variance and also the ensemble variance of the isospin density are essentially zero, which suggests that the isospin density becomes independent of the gauge fields for this particular value of µ. side of figure 3, also the ensemble variance of the total isospin density (2.3) is approximately zero at the half-filling point, we can conclude that the homogeneity of the local isospin density (2.2) at this point is due to the fact that its dependency on the gauge field is highly suppressed at half-filling, which explains the volume independency.
In figure 4 we also show the average sign (or average phase) (1.11) for a two-flavor system as a function of the chemical potential (left) and as a function of the isospin number density (right), for two different sets of simulation parameters: once for a system with L 3 N t = 4 4 , inverse coupling β = 5.0 and hopping parameter κ = 0.15 and once for one with L 3 N t = 5 4 , β = 5.3 and κ = 0.175. As can be seen, for both systems the average sign has a local maximum at the half-filling point, where it almost reaches a value of one again. However, for the larger system a clear deviation from one is visible. The right-hand part of figure 4 also shows an approximate symmetry about the half-filling point.
Although the average sign is not exactly one at half-filling, the fact that it has a local maximum, implies that isospin number density and quark number density must be the same at this point, as we have , (2.6) which vanishes at an extremum of R q (µ). This is of course also true at the minima of R q (µ), which means, that although the sign problem is worst at these points, the quark number density could there be obtained with high accuracy. The problem is, however, to determine the location of these points, as they will not be volume independent as is the case for the half-filling point. In figure 5 Figure 4. Average sign as a function of µ (left) and as a function of the isospin number density (right) for two different sets of hopping parameter κ, inverse coupling β and system size. The figures show that the average sign has a maximum at half-filling where its value is close to one. For the larger system there is however a clearly visible deviation from unity. . Difference between average quark number density and average isospin number density as a function of µ for the same ensembles used in figure 4. The quark number density was obtained by reweighting. The dotted lines correspond to fits of the form n I,sat − n I (µ) = a e Nt Q (µ) to the data for µ > 1.5μ, whereμ = − log(2κ) is the half-filling value of µ in each ensemble. As can be seen, both fits yield Q ≈ −2, although the simulation parameters are quite different. figure 4. The density difference was obtained by reweighting the quark number density from the quenched to the un-quenched system and then subtracting the isospin number density.
We mentioned that, in the Hubbard model, the sign problem disappears at half-filling due to a particle-hole symmetry. We could now ask if also in LQCD such a particle-hole symmetry is the origin of the (almost) disappearing sign problem at half-filling. A first indication that the answer to this question could be yes, comes from figure 6, which shows, again for a two-flavor system, coupled to an isospin chemical potential µ, the quantity n I,sat − n I (µ) for two different ensembles, where n I,sat = lim µ→∞ n I (µ) is the saturation value of the average isospin density n I (µ) at large µ. We could think of n I,sat − n I (µ) as being the density of "holes in the saturated state".
JHEP02(2016)051
For the isospin density itself we would expect n I (µ) ∝ e Nt Q µ for µ μ, wherẽ µ = − log(2κ) is the half-filling value of the chemical potential and Q = 2 is the charge of an elementary excitation (charged meson). The fits in figure 6 now show that n I,sat − n I (µ) behaves in precisely the same way for µ μ, but with Q = −2, which means that the "hole-excitations" from the saturating state at large chemical potential behave just like the anti-particles of the elementary excitations of the theory at small chemical potential. The strong interaction treats therefore fermion holes in the saturated state in a similar way as the fermions themselves in the vacuum, such that the holes also have to form gauge invariant combinations of the form of mesons and baryons.
Having this symmetry between particles at zero density and holes at saturation, makes it plausible that at half-filling, where particles and holes appear with equal densities, they indeed behave symmetrically. The same should be true for the non-phase-quenched system where the elementary excitations would be baryons with Q = 3 at zero density and holes of the form of anti-baryons with Q = −3 at saturation. Again this suggests that at half-filling, where baryons and baryon-holes have equal density, we should have particle-hole symmetry.
Dominance of lattice artifacts: a simple criterion
In contrast to the systems studied in solid state physics, where the lattice is physical and half-filling describes a physical state as in the fermionic Hubbard model, the lattice in LQCD is jut a regulator which has to be removed (e.g. in numerical works, by doing continuum extrapolation) in order to extract real physics. The half-filling state of a LQCD system is therefore just an unphysical lattice artifact and should be of no relevance for the continuum physics.
As long as we are running simulations sufficiently far away from the continuum limit (such that the maximal fermion density on the lattice (in physical units) is far below the density where the Pauli exclusion principle would become important in the continuum), the first appearance of a minimum in the average sign as a function of increasing chemical potential (or as a function of increasing isospin number density) as shown in figure 4, indicates the point where lattice artifacts start to become dominant. This becomes clear by noting that the average sign is a measure for the overlap between a system with a quark chemical potential and the corresponding phase-quenched system (with an isospin instead of a quark chemical potential). As the right-hand side of figure 4 shows, the average sign drops dramatically as soon as the isospin density becomes non-zero, reflecting the fact that a pion condensate develops in the isospin system, leading to a ground state which is rather different from that of the corresponding system with a quark chemical potential. The fact that the overlap between the two systems starts to increase again with increasing µ (i.e. that the average sign starts to increase again) indicates, that the influence of the Pauli exclusion principle starts to become dominant on the lattice: the fact that the quark chemical potential favors the u and d quarks, while the isospin chemical potential favors u and d, starts to become less important as for example the "d-hole" in the system with the quark chemical potential starts to play the role of the d in the isospin system and vice versa. This happens at densities significantly below half-filling, and measurements of observables taken at larger densities should be considered with caution.
JHEP02(2016)051 3 Heavy-dense analysis
In the following section we will analyze the half-filling point of LQCD in the heavy-dense limit and at strong coupling. These simplifications will allow us to understand the origin of the properties of the half-filling point.
The heavy-dense approximation
The goal of this section is to obtain an expression for the Partition function in the so-called heavy-dense approximation at strong coupling, which can be integrated analytically. The heavy-dense approximation usually consists of taking the limit κ → 0, µ → ∞, keeping κ e µ finite while terms proportional to just κ or κ e −µ vanish. In our case, it would be more appropriate to call it the static quark limit, as we will just drop the spatial hopping terms from the Dirac operator (1.1), but not the one corresponding to backward hopping in time, which is proportional to κ e −µ . The resulting fermion determinant is well-known as the leading term in the spatial hopping expansion that was already used in [6] to derive an effective model for QCD or in [2] to obtain a holomorphic action for complex Langevin simulations of LQCD.
Let us start by expanding the determinant of the Dirac operator (1.1) in terms of closed fermion loops C l 0 of length l 0 [4]: with M C l 0 = H x 1 x 2 · · · H x l 0 x 1 being the matrix product of hopping terms H xy = (S + T ) xy along the contour C l 0 of length l 0 , where S and T are the spatial and temporal hopping matrices defined in (1.1). The subscripts "c" and "d" of "det" and "tr" indicate that the operators act on color and Dirac space only. To get from the second to the third line in (3.1), we have used that k can be written as k = l 0 n, where l 0 is the length of the contour C l 0 , and n the number of windings around C l 0 . The change in the denominator (k → n instead of k → l 0 n) comes from the fact that Tr H l 0 n contains tr c,d M C l 0 n exactly l 0 times, once for every possible base point (or starting point) of a loop on C l 0 , which cancels the l 0 in the denominator. As already mentioned, the static quark approximation now consists of dropping the spatial hopping matrix S from (1.1) and (3.1), which ultimately means that M C l 0 is nonzero only if C l 0 wraps around the temporal direction, i.e. l 0 = n t (we use from now on JHEP02(2016)051 a lower-case n t to represent the temporal system size) and M Cn t has to be one of the n x · n y · n z matrices − e µ nt P x ⊗ (1 − γ 4 ) nt = T x,x+ 4 · · · T x+(nt−1) 4,x (3.2) or their time-reversed versions where P x is the Polyakov loop at spatial position x. The minus signs on the left-hand sides of (3.2) and (3.3) come from the anti-periodic boundary conditions in temporal direction. With this approximation, the determinant (3.1) reduces to a product of single site determinants: More precisely, the last line of (3.4) shows that for each site, we get four factors, each in the form of a determinant in color space: the first two correspond to the two distinct states of a spin-1/2 particle while the second two are due to its anti-particle. These color-determinants can be re-written in terms of traces of powers of the Polyakov loop: By using that the characteristic equation for a matrix X ∈ SU(3) reads and, according to the Cayley-Hamilton theorem, X satisfies its own characteristic equation, χ X (X) = 0 (in the spectral sense), it follows that (3.7) and therefore tr c X 3 = 3 + tr c (X) tr c X 2 − tr c X † tr c (X) , (3.9) tr c X † = tr 2 c (X) − tr c X 2 /2, (3.10) which can be used to simplify (3.5) further: Finally, expressing the traces in (3.11) in terms of the eigenvalues of the Polyakov loop P x , we arrive at det 2 and similarly, 14) The single site fermion determinants in (3.4) reduce therefore to the simple form: Using the Haar measure for the trace of the Polyakov loop, (3.17) and neglecting the plaquette action (i.e. considering the strong coupling limit β = 0), we can write down a heavy-dense partition function for QCD with two flavors, u, d:
JHEP02(2016)051
where κ u/d and µ u/d are the hopping parameter and the chemical potential corresponding to the u/d flavor, Λ is the spatial lattice with |Λ| sites, and Z s (µ u , µ d , κ u , κ d , n t ) is the single site partition function.
The integral (3.18) can be evaluated explicitly but results in a rather lengthy expression. For the purpose of illustration its explicit form is shown in appendix A for the case of degenerate quark masses, κ u = κ d = κ, once with an isospin (µ = µ u = −µ d ) and once with a quark (µ = µ u = µ d ) chemical potential.
Heavy-dense staggered fermions
The Staggered fermion operator is given by with the Staggered phase η µ (x) = (−1) 3 x 1 +2 x 2 +x 3 and the bare lattice fermion mass m.
The full static quark fermion determinant for (3.19) is more difficult to obtain than the Wilson fermion analogue (3.4). The reason is that Staggered fermions allow for retracting fermion loops, such that even without spatial hoppings, several distinct temporal loops are possible. However, if we are just interested in the heavy-dense limit, where µ and m are assumed to be large while e µ−log(2 m) is of order one, the leading term reads (3.20) Comparing (3.20) with (3.4) reveals that the Staggered heavy-dense determinant (3.20) can be obtained from the heavy-dense limit of (3.4) by replacing 2 κ by 1/(2 m) and dropping the square of the color-determinant.
Analytic expressions for some observables
In this section we derive some observables with respect to the system described by (3.18).
Average sign
In terms of (3.18), with κ u = κ d = κ, the average sign is computed as where φ is the complex phase of the single flavor determinant (3.4), and n x n y n z is the spatial system size.
Isospin and quark number density
The isospin density is obtained from (3.18) by
Heavy-dense quark propagator
The heavy-dense quark propagator is most easily obtained by using that [6] and We then obtain: where P y (y 4 ) is the Polyakov loop with base point y and P y (x 4 , y 4 ) is a Polyakov line at spatial position y that, for x 4 = y 4 , starts and ends at euclidean times x 4 , y 4 respectively (by going in positive time direction), while P y (x 4 , x 4 ) = 1. The inverse of the matrix 1 + (2 κ e µ ) nt P y (y 4 ) can easily be carried out (e.g. with Cayley-Hamilton and Leverrier-Faddeev), provided the matrix is not singular: where the determinant in the denominator is given by (3.11). Similarly we get: and therefore with (3.25): The heavy-dense quark propagator (3.32) could be used to get analytic expressions for average meson and baryon propagators from which one could determine the corresponding masses. But due to the projection properties of (3.32) in Dirac space, the mass spectrum will be highly degenerate. We will therefore use (3.32) in the following just to facilitate the derivation of some other observables.
Local isospin number density
The local isospin number density in the heavy-dense case can be obtained, by starting from equation (2.2) and replacing the full Dirac operators and propagators by their corresponding heavy-dense counterparts, i.e. just dropping the spatial hopping terms from (1.1) and using (3.32) as the corresponding propagator. We then obtain: where after the second equality sign it was used that (1 ± γ 4 ) are orthogonal projectors and that for example i.e. the link variable U 4 (x) coming from the term in the Dirac operator that is not projected out by the (1 − γ 4 ) of the propagator, closes the Polyakov line P x (x 4 + 1, x 4 ) to a Polyakov loop P x (x 4 ), starting and ending at x. Analogously:
Condensates
The quark condensate for a two-flavor system, is in the static-quark limit obtained by taking the expectation value of x is the static-quark propagator (3.32) for y = x and κ u , κ d and µ u , µ d are the hopping parameters and chemical potentials for the two flavors.
Analogously the isospin condensate, is obtained as the expectation value of where in the first line 1 c,t is the identity with respect to color and time indices.
Half-filling point
Having obtained the heavy-dense partition function for two-flavor LQCD in the strong coupling limit, and defined some basic observables, we now use these results to study the origin of the properties of the half-filling point in the heavy-dense/strong coupling limit, and check, how far our findings could also apply to full LQCD.
Location of the half-filling point
To find the location of the half-filling point, we consider the isospin density (3.22) in its integral form: For sufficiently large values of µ, the second term within the curly brackets in (3.40) can be neglected; setting µ = − log(2κ), this term is of order O (2κ) 2nt while the first term is of order 1 and becomes completely independent of P , as and we obtain for the isospin density (3.40): which means that µ =μ ≡ − log(2κ) corresponds to the half-filling point, independently of n t (up to O (2κ) nt corrections), as is visualized in figure 7, where the isospin number density (3.22) is shown as a function of µ for different system sizes and it can be seen that the curves, corresponding to different system sizes, all cross at the half-filling point, just as in the case of full LQCD shown above in figure 1. From (3.40) and (3.41) it also follows that the dependency of the local isospin density (3.33) on the gauge field is highly suppressed at half-filling: gauge field dependent terms are suppressed by a factor of O (2κ) 2 nt such that the space time variance of (3.33) nearly vanishes at half-filling, again just as in the case of full LQCD shown above in figure 3. Nevertheless, in full LQCD, the half-filling point is shifted towards a slightly larger value of µ: while in the heavy-dense case, we haveμ = − log(2 κ) ≈ 1.2 for κ = 0.15, we find in full LQCD, for the same value of κ and with β = 5.0, that the half-filling point is located at µ ≈ 1.3. This shift is due to spatial fermion hopping which causes corrections to the quark mass. Corrections coming from spatial hoppings and a finite value of β will of course also appear in the expressions for observables and give rise to deviations that could be much larger than O (2 κ) 2 nt . These corrections are considered in sections 3.5 and 3.6.
Particle-hole symmetry and average sign
Consider the single flavor fermion determinant (3.15) under the transformation µ → 2μ−µ that corresponds to reflection about the half-filling point: where the last line of (3.43) is true for µ ∈ [0, 2μ]. Comparing (3.43) with Det(D(µ, κ, n t )) * = Det(D(−µ, κ, n t )) = det 2 we see that they agree up to an irrelevant gauge field independent pre-factor (which is unity at the half-filling point) and terms which are suppressed by at least a factor of (2κ) nt . As the complex conjugate of the fermion determinant can be interpreted as resulting from a charge conjugation of the original fermion fields, this shows that the half-filling state possesses an exact T = 0 particle-hole symmetry also in the heavy-dense/strong coupling limit of LQCD. We can also check the behavior of the heavy-dense quark propagator (3.32), under the transformation µ → 2μ − µ. For y 4 = x 4 and µ ∈ [0, 2μ] we find: which by noting that and remembering that shows that: i.e. up to a minus sign and terms of higher order in (2κ), we find that for y 4 = x 4 , reflecting µ aboutμ turns the quark propagator into its Hermitian conjugate. For the equal time part, y 4 = x 4 we find in a similar way: For the two condensates introduced in section 3.2.5, we then find for the phase quenched case: and at half-filling exactly in the middle between their corresponding values at µ = 0 and for µ → ∞.
In the un-quenched case, the relations would be: and Returning to the single flavor fermion determinant (3.15), we can see from (3.43) and (3.44) that it is essentially real at µ =μ and the average sign (3.21) should therefore be 1 + O (2κ) nt . This can also be verified more directly by using (3.15) to show that for µ =μ, we have: det c 1 + (2κ eμ) nt P = 1 + (2κ eμ) nt tr c P + (2κ eμ) 2 nt tr c P † + (2κ eμ) 3 nt = 2 + tr c (P ) + tr c (P † ) = 2 (1 + Re(tr c (P ))) , (3.58) i.e. we find again that the dominant part of the single flavor fermion determinant (3.5) at half-filling, det 2 is real and positive up to terms of order O (2κ) 2 nt . The average sign (3.21) in the heavy-dense limit is shown in figure 10 as a function of the chemical potential (left) and as a function of the isospin number density (right) for the same system sizes and values of the hopping parameter κ that were used to generate the corresponding plots in full LQCD shown above in figure 4. By comparing the two figures, it can be seen, that in the heavy-dense case, the average sign is much more symmetric about the half-filling point and at the half-filling point itself, it deviates much less from being unity than in full LQCD, which is again due to the absence of spatial fermion hoppings, such that the deviation is really just of order O (2κ) 2 nt . 3.4 Mean-field method for heavy-dense QCD at finite gauge coupling β So far we have only considered heavy dense LQCD in the strong coupling limit, β = 0.
In this section, we would now like to get a glimpse of finite β effects by introducing an effective nearest-neighbor Polyakov loop action, which is motivated by the leading terms of the character expanded gauge field Boltzmann factor, as derived for example in [6], and then using a mean-field approximation. Our mean-field treatment is similar to one of the approaches considered in [8] but differs from the mean-field calculation in [7] as we are considering the Polyakov loops as our effective degrees of freedom while in [7], this role was taken by spatial links. The nearest-neighbor Polyakov loop action is obtained as follows: we start with a character expansion of the SU(3) Yang-Mills Boltzmann factor (cf. [5], chapter 3.4), where the product is over all plaquettes p, χ r (U p ) is the character of the SU(3) group element U p (corresponding to the plaquette p) in the representation r, and a r (β) = c r (β)/c 0 (β) with c 0 (β) being the expansion coefficient of the trivial character χ 0 (U p ) = 1.
We now drop the summation over r and keep just the terms corresponding to the fundamental representation. After integrating out the spatial links, we are then left with [6]: where the products run over all pairs of nearest-neighboring sites, i, j . If we now require that the Boltzmann factor corresponding to the desired effective nearest-neighbor Polyakov loop action should, to lowest order, be proportional to (3.61), we find that the effective JHEP02(2016)051 action should be given by: where L i = tr c (P i ). At this point it should be mentioned that in contrast to the situation with the U(1) or SU(2) Yang-Mills action, where the coefficients of the character expansion can be written in closed form in terms of Bessel functions, no closed form is known for these coefficients in the case of SU (3). To compute a f (β), we made use of the power series representations for c 0 (β) and c f (β), given in [5] We now proceed by applying the mean-field approximation to (3.62), i.e. we write L i = L + δL i , keep only terms of order O δL , and then write again δL i = L i − L (and proceed analogously for L * i ), which, after dropping constant terms, leads to the following single site mean-field action: which we use to define an additional probability weight, w L, L * , L, β, n t = e 6 a n t f (β) (L * L + L * L) , (3.66) that has to be included in the single site partition function defined in (3.18), i.e.: For general values of µ u , µ d , κ u and κ d , the product of the two fermion determinants in (3.67) is usually complex. As a consequence L and L * differ and it is a subtle issue how to proceed in a mean-field treatment [8]. To bypass the subtleties associated with L * = L when setting L = L and L * = L * , we define L to be the mean-field value of L with respect to the phase quenched system, where L * q = L q holds and the identification L = L q , L * = L * q therefore leads to L * = L. The mean-field L is therefore determined by solving the following self-consistency equation: |Det(D(θ 1 , θ 2 ; µ u , κ u , n t )) Det(D(θ 1 , θ 2 ; µ d , κ d , n t ))| w L, L(θ 1 , θ 2 ), β, n t , (3.68) where w L, L(θ 1 , θ 2 ), β, n t ≡ w L, L, L(θ 1 , θ 2 ), β, n t and where is the phase-quenched partition function. After one has determined the stationary L with respect to (3.68) for a particular set (µ u , µ d , κ u , κ d , n t ) of parameters, one can reweight to the non-phase-quenched system by using L µ u , µ d , κ u , κ d , n t in (3.67) when computing expectation values of observables.
This difference between L * µ u , µ d , κ u , κ d , n t and L µ u , µ d , κ u , κ d , n t can clearly be seen in figure 11 where we show the two quantities for the mass degenerate case (i.e. κ u = κ d ) as a function of a quark chemical potential µ = µ u = µ d .
It has been mentioned in [8] that in a mean-field treatment, the reweighting method can be no more than an approximation scheme: while in a full Monte Carlo simulation, reweighting is exact in the limit of infinitely many sampled configurations, a mean-field treatment relies only on the most dominant configuration. In our opinion this argument does not hold as in a mean-field treatment, the expectation value of an observable is determined on the active site, usually by integrating exactly over all possible values of its configuration variables, and reweighting should therefore work perfectly well! Setting L * = L, the integrals in (3.67) and (3.69) can be carried out exactly, leading to solutions in terms of infinite sums of modified Bessel functions of the first kind: respectively, where the coefficients C l 1 ,l 2 µ u , µ d , κ u , κ d , n t are given by Unfortunately, the evaluation of (3.72) and (3.73) to the required accuracy is numerically rather expensive and it turned out to be more efficient to use direct numerical integration to solve for L in (3.68) and for computing observables. Expressions (3.72) and (3.73) were therefore merely used for cross-check purposes. An expression for (3.72) in the more general case of L * = L could be found along the lines of [9] where the mean-field action (including correction terms) is derived for the case of a pure SU(N ) Polyakov line model with a chemical potential.
Mean-field heavy-dense phase diagram and finite β effects
In figure 12 we show the average Polyakov loop for the mass degenerate two-flavor case as a function of isospin chemical potential µ = µ u = −µ d and inverse coupling β for five different temperatures, n −1 t , as obtained with our mean-field method described in the previous section. As can be seen, for sufficiently large β a deconfinement transition occurs and the value of β at which this transition happens becomes smaller with increasing temperature (decreasing n t ).
A finite value of the inverse gauge coupling β has also an effect on the average sign, which is illustrated in figure 13. There we show mean-field results for the average sign as a function of µ = µ u = µ d for a mass degenerate (κ = 0.15) heavy-dense two-flavor system of spatial size V = L 3 = 4 3 and temporal extent N t = 2, 3, 4, 8. The left-hand part shows the strong-coupling limit, β = 0, while the right-hand part shows the β = 5.0 case. For static quarks, the location of the half-filling point is not affected by the finite β value, but the overall temperature dependency of the average sign clearly changes: at finite β the sign-problem becomes weaker with increasing temperature and almost disappears after the deconfinement transition.
Note that the computation of the average sign with our mean-field method comes with a slight complication: the active site couples to its six nearest neighbors and there are therefore 6 interaction terms entering the mean-field action. But the ratio of links to sites should be 3 : 1 on a periodic 3-dimensional lattice, which means that by using simply a formula of the form of (3.21) to compute the average sign with our mean-field partition functions (3.67) and (3.69), i.e. e 2i φ (µ, κ, β, n t , n x n y n z ) = Z s µ, κ, n t , L(µ, κ, n t ) Z s,q µ, κ, n t , L(µ, κ, n t ) smallest representative subset of a larger system, in which for example even sites are active and odd sites are passive or vice versa, and the computed sign will correspond to such a system). This factor is obtained by taking the ratio of the average fermion determinants in the non-phase-quenched and phase-quenched case. The average sign then becomes: e 2i φ (µ, κ, β, n t , n x n y n z ) = Z s µ, κ, n t , L(µ, κ, n t ) Z s,q µ, κ, n t , L(µ, κ, n t ) Det(D) Det(D) µ, κ, n t , L(µ, κ, n t ) |Det(D) Det(D)| q µ, κ, n t , L(µ, κ, n t ) nx ny nz /2 , (3.76) where Det(D) is the static quark determinant (3.4) and the factor of 1/2 in the exponent in (3.76) is there because the term inside the bracket is now the reweighting factor for two sites. Figure 14 finally shows the average Polyakov loop as a function of temperature and isospin (left) or quark (right) chemical potential i.e. it essentially shows the (T, µ) phase diagram of our simplified model in the phase-quenched and un-quenched case: one can read off how the pseudo-critical temperature for the deconfinement transition changes as a function of the chemical potential. The right-hand part of figure 14, corresponding to the un-quenched case, can be compared, e.g. to the phase diagram in [3, figure 2], obtained by complex Langevin. In order to simplify the comparison, figure 15 shows the data from figure 14 using the same scales used in [3, figure 2], assuming that the lattice spacing of a = 0.15 fm, determined in [3], should apply equally well to our system, as we used the same simulation parameters κ = 0.04, β = 5.8. In our effective model, we take the gauge field only in the fundamental representation into account. But at high temperature, effects coming from higher representations are much less suppressed than at low temperature (the coefficients a r (β), if included in the effective Polyakov loop action, would appear only with small exponents, leading to a weaker suppression of the higher order terms), which explains why in our figure the deconfinement transition is generally shifted towards larger temperatures compared to [3, figure 2].
From the heavy-dense to the full fermion determinant
The heavy-dense fermion determinant is the leading term in the so-called spatial hopping expansion of the full fermion determinant which, for one flavor, can be obtained as follows: where S and T are the spatial and temporal hopping terms as defined in (1.1) and we have added a subscript s to the spatial hopping parameter, just for book-keeping purposes. The matrix (1 − κ T ) −1 is the heavy dense quark propagator given by (3.32). We can now proceed in a similar way as in (3.1) to write (3.77) in terms of a product of smaller JHEP02(2016)051 determinants of "loop matrices", but this time, the loops are purely spatial and the matrices carry also a time-index, i.e.
where the subscripts in tr c,d,t , det c,d,t indicate that these operators act on color, Dirac and time indices. C s 0 describes a closed spatial path of length s 0 (where, in contrast to (3.1), backtracking is now allowed) and the matrixM Cs 0 is given by the (ordered) product of the matrices S(1 − κ T ) −1 along that spatial path (see figure 16), x i+1 is understood to be a matrix with color, Dirac and time indices.
The final form of (3.78), which could be called a spatial loop expansion, is particularly useful if one is aiming towards including spatial fermion hoppings into the mean-field treatment. In this case one can just restrict the product over s 0 in (3.78) to the factors with s 0 = 0, 2 but still get the full interaction between nearest-neighboring sites. In contrast, in the original spatial hopping expansion (3.77), a nearest-neighbor truncation would limit the accuracy to O κ 2 s . In order to see how the presence of spatial hoppings changes the properties of the static-quark system, it is sufficient to take just the lowest order terms in κ s of (3.78) into account. These terms lead, after integrating out the spatial links, to corrections up to order O κ 2 s a nt f (β) (see appendix B). Using this improved effective nearest-neighbor Polyakov loop action within the mean-field framework described above in section 3.4, we can for example compute the average Polyakov loop for a mass degenerate two-flavor system. 3. and the one from section 3.4, which neglects fermion hopping completely (dotted red curve).
As can be seen, allowing for spatial fermion hopping in the effective theory shifts the value of µ where the average Polyakov loop is maximal closer to the corresponding value found in full LQCD. With increasing approximation order also the magnitude of the average Polyakov loop gets closer to the LQCD result. In the right-hand part of figure 17 we tried to compensate for the truncated spatial nearest-neighbor interaction in the effective theory by increasing the value of the inverse gauge coupling β. Setting β = 6.035 in the effective theory, the average Polyakov loop obtained by mean-field with the O κ 2 s a nt f (β) effective action from appendix B then almost coincides with the corresponding LQCD result for β = 5.0.
Finally, figure 19 shows the average sign (3.21) as a function of µ, again for a massdegenerate (κ = 5.0) two-flavor system of spatial size V = L 3 = 4 3 , computed by meanfield, using our improved effective action and However, the value of the hopping parameter κ = 0.15 used in figures 17 and 18 is already almost too large to be used in a calculation based on a O κ 2 s a nt f (β) truncated nearest-neighbor interaction. For larger values of κ or lower temperatures (i.e. larger N t ), the deviation of the mean-field result from the Monte Carlo data becomes larger and it is no longer possible to match the data by adjusting the inverse gauge coupling in the effective model as was done in the right-hand part of figure 17. This is not surprising as, concerning the physics, the O κ 2 s a nt f (β) truncation of the nearest-neighbor interaction term, det c,d,t 1 − κ 2 sM C 2 , implies that mesons and baryons (the low energy degrees of freedom of the theory) remain essentially static and cannot undergo spatial hoppings. But when lowering the temperature and/or the quark mass, it is precisely the hopping of these low energy degrees of freedom that becomes more important. From a more technical point of view, looking at the expansion of the fermionic nearest-neighbor interaction term,
JHEP02(2016)051
where the c k (A) for a rank-n matrix A are defined by the characteristic polynomial of A, it becomes clear that the κ 2 s term does not necessarily give the dominant contribution to (3.80) as the c k M C 2 can become rather big (especially if n t is large) and to guarantee that the κ 2 s -term dominates the expansion, one would have to choose κ s much smaller than we did.
To incorporate spatial meson and baryon hopping into the mean-field calculation, one should include at least the κ 6 s -terms in the expansion of (3.80). Although this is probably feasible, already at order κ 4 s the computation by hand of the corresponding terms in the effective action becomes a delicate issue and it would be desirable to automate the combinatorics required to get the correct dependency on a f (β).
In order to demonstrate that the deviation of the mean-field result from the Monte Carlo data in figures 17 and 18 is merely due to the truncation of the nearest-neighbor interactions and not caused by our mean-field method itself, we try to reproduce figure 6 of [6], which shows L and L * for a single flavor system with κ = 0.01, N t = 200 and β = 5.7, obtained once by a Monte Carlo and once by a Complex Langevin simulation of the effective model derived in [6]. Our mean-field action is obtained by applying (B.43) to the partition function (B.40), which is of order κ 2 s in κ s , while for [6, figure 6] also terms proportional to κ 4 s have been taken into account. However, as κ is rather small, we should nevertheless get a result comparable to [6, figure 6] if our mean-field method works correctly. In figure 20, left, we show [6, figure 6] superimposed with the corresponding result from our mean-field calculation, where also for this single flavor system, we determined the mean-field value L within the phase-quenched system and then used reweighting to obtain L and L * in the phase-unquenched case. As the figure shows, our mean-field results (dotted lines) match remarkably well the data obtained by full Monte Carlo and complex Langevin simulations. On the right hand side of figure 20, we also compare the mean-field result obtained with the O κ 2 s truncated effective fermion action with the corresponding result obtained with the "full" (O κ 2 s a Nt f (β) truncated) effective fermion action (B.33). As can be seen, even for the small value of κ = 0.01 and large N t = 200, the higher order terms in the effective fermion action lead to a clearly observable difference in the result.
Summary
After a short introduction to the sign problem, we have shown that the half-filling point, i.e. the value of the chemical potential where the fermion density assumes half its maximal value, has similar properties in LQCD as in e.g. the fermionic Hubbard model used in solid states physics: the sign problem almost disappears at half-filling and the system possesses an apparent particle-hole symmetry. We traced the origin of these properties by analyzing the heavy-dense fermion determinant and the corresponding strong coupling partition function. However, in contrast to the Hubbard model, where the lattice and the half-filling state are physical, in LQCD the lattice is just a regulator that has to be removed in order to extract continuum physics and the state corresponding to half-filling of that lattice is therefore of no physical relevance.
As the half-filling state in LQCD and the corresponding maximum in the average sign are just lattice artifacts, it seems sensible that the first appearance of a minimum in the average sign (as a function of increasing chemical potential) indicates the point where lattice artifacts start to become dominant and measurements of observables taken at larger values of the chemical potential should therefore be considered with caution.
B Higher order corrections to the effective Polyakov loop action
In this section we derive an effective nearest-neighbor Polyakov loop action that includes not just the nearest-neighbor effects coming from the gauge field action, but also those coming from the fermion determinant. We start with the single flavor partition function which, using the spatial loop expansion (3.78) for the fermion determinant and the character expansion (3.61) for the gauge field Boltzmann factor, can be written as: where x, y are nearest-neighboring sites spanning a path C 2 . Equation (B.3) would capture the full spectrum of nearest-neighbor interactions but is unfortunately still rather complicated. We simplify the expression further by expanding the determinants det c,d,t 1 − κ 2 sMx,y to order κ 2 s and by considering the gauge field only in the fundamental representation and only along temporal plaquettes. With these simplifications, the two products in (B.3) turn into the following expression: The Boltzmann factor for the desired effective action should then coincide with (B.4) up to order O κ 2 s a nt f (β) (the single site/non-interaction terms coming from the factor Det(1 − κT ) in (B.2) are not considered as part of the effective action).
To find such an action, we start by writing out tr c,d,t M x,y with y = x + i and i ∈ {1, 2, 3}: · tr c ( U i (x, x 4 ) P y (x 4 , y 4 ) 1 + (2 κ e µ ) nt P y (y 4 ) −1 Integrating over the spatial links in (B.6) at order O a 0 f (β) leads to the constraint y 4 = x 4 (see figure 21) as for SU(3) integrals, we have: According to the definition of P x (x 4 , y y ) given below eq. (3.29), we then have P x (x 4 , x 4 ) = 1 and find therefore: which is the same as eq. (2.28) of [6], as can be seen by noting that: and tr c 2 κ e −µ nt P † To obtain non-zero contributions from terms in (B.6) for which y 4 = x 4 , we have to take plaquette terms into account. To see in more detail how this works, let us as an example consider the top left diagram in figure 22. It shows a contributing diagram to the first term inside the large bracket in the sum over x 4 , y 4 in eq. (B.6) for the case where y 4 − x 4 = 2. If we would integrate out the spatial links in the corresponding term in (B.6) without taking into account plaquette terms, the result would just vanish due to the left-hand identity in (B.7). But allowing for plaquette terms coming from the non-trivial gauge-field part JHEP02(2016)051 in (B.4), we can form the two left-most diagrams on the second and third row of figure 22, and get for example for the one on the second row, a term like and Integrating over the three spatial links U i (x, x 4 ), U i (x, x 4 + 1) and U i (x, x 4 + 2) then yields where, as per definition (see section 3.2.3), and P x (x 4 + 2, x 4 ) = U 4 (y, x 4 + 2) . . . U 4 (y, n t − 1) U 4 (y, 0) U 4 (y, x 4 − 1) , (B.16) we can simplify U † 4 (y, x 4 + 1) U † 4 (y, x 4 ) P y (x 4 , x 4 + 2) = 1 , and to get either the identity or a closed Polyakov loop. With this, we finally obtain for eq. (B.14): In a similar way we can proceed with the other terms in (B.6) and find, after grouping them according to the power of their factors of a f (β): 2 mod(y4−x4,nt) tr c 1 + (2 κ e µ ) nt P y −1 tr c 1 + 2 κ e −µ nt P † + (a f (β)) mod(x4−y4,nt) tr c (2 κ e µ ) nt P y 1 + (2 κ e µ ) nt P y −1 tr c 1 + (2 κ e µ ) nt P x −1 Note that all the traces in (B.20) are time-independent. The time-dependency of the individual terms in the sum is only in the different exponents of a f (β), (2 κ) 2 and (2 κ) −2 which form essentially simple geometric sequences. The (finite) sum can therefore easily be carried out and yields: (B.21) For x 4 = y 4 , there is a third class of diagrams, which are always of order κ 2 s a nt f (β),
JHEP02(2016)051
depicted in the last row of figure 22. If we take as an example again the left-most diagram on that row, we obtain by integrating out the spatial links, using the identity a term of the following form: we can simplify: , if x 4 = y 4 , (B.25) and (B.23) becomes for x 4 > y 4 : − a nt f (β) 2 (2κ e µ ) nt tr c P y tr c P y 1 + (2κ e µ ) nt P y −1 − tr c P 2 y 1 + (2κ e µ ) nt P y and for x 4 < y 4 : − a nt f (β) 2 (2κ e µ ) nt tr c P † y tr c 1 + (2κ e µ ) nt P y −1 − tr c P † y 1 + (2κ e µ ) nt P y −1 tr c P x tr c P x 1 + (2κ e µ ) nt P x −1 − tr c P 2 x 1 + (2κ e µ ) nt P x (2κ e µ ) nt tr c P y tr c P y 1 + (2κ e µ ) nt P y −1 − tr c P 2 y 1 + (2κ e µ ) nt P y −1 tr c P x tr c P x 1 + (2κ e µ ) nt P x −1 − tr c P 2 x 1 + (2κ e µ ) nt P x
Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. | 13,347.6 | 2016-02-01T00:00:00.000 | [
"Physics"
] |
Implementation of Simple Additive Weighting and Profile Matching Methods to Determine Outstanding Students at Universitas Malikussaleh
Decision support system (DSS) is a computer-based system used to support data analysis and decision modeling, with the aim of increasing the effectiveness of decisions taken. In this research, SPK is needed to determine Outstanding Students. Through this research, it is hoped that the selection process for outstanding students can be optimized by choosing the evaluation method that best suits the student's characteristics and institutional goals. The results of this research also have the potential to improve the quality of graduates by providing fairer and more objective awards to those who excel. The aim of this research is to design and implement the concept of the Simple Additive Weighting (SAW) and Profile Matching methods in a system for determining outstanding students at Universitas Malikussaleh and to find out the ranking results of the two methods (SAW and Profile Matching) in selecting outstanding students at Universitas Malikussaleh. The research methodology used was literature study, data collection, Simple Additive Weighting and Profile Matching calculations, application design, testing and evaluation. The results obtained from this research are the application of the SAW and Profile Matching methods to determine outstanding students resulting in preferences with the highest score of 1 for the SAW method and the highest score of 5 for the Profile Matching method. These two methods can be applied in selecting outstanding students to help decision making because both this method produces the same best alternative.
Introduction
Higher education is an important aspect in the formation of quality human resources [1].In the tertiary environment, one way to prove that who can be an outstanding student is by measuring the extent of their level of success through student honors.Therefore, in every tertiary institution it is necessary to look for students who can do both and are given awards as students.who excel [2].The process of selecting outstanding students which is carried out on the Universitas Malikussaleh campus still has obstacles such as the data processing process for selecting outstanding students which takes a long time, apart from that, the phenomenon where there are many outstanding students in the tertiary environment is an additional factor which makes it difficult to determine the most successful students.achievement.The significant number of outstanding students can create challenges in assessment and selection, especially when the evaluation methods used are not able to provide a clear and objective picture of their achievements [3].In other words, the abundance of outstanding students can create obstacles in formulating fair and adequate criteria for determining who deserves to be awarded as an outstanding student.
To solve this problem, a decision support system for selecting outstanding students is needed.There are many methods used in implementing decision support systems [4], so it is necessary to apply two methods, including the Simple Additive Weighting (SAW) method with Profile Matching which aims to determine the differences in process results between the two.Apart from that, the application of these two methods aims to determine the level of accuracy of the information provided.
Simple Additive Weighting is a method that gives weight to each criterion and adds up the scores obtained by students [5].In SAW, decisions are taken based on the highest value after a normalization process and criteria weighting.This method offers clarity in determining outstanding students through measurable mathematical calculations.
Profile Matching method is a method that evaluates the suitability of student profiles with predetermined achievement criteria [6].A student profile involves various aspects, including academic achievements, extracurricular activities, and participation in research projects.This method focuses on the level of conformity between the student profile and the predetermined achievement standard.
This research aims to design and implement the concept of the Simple Additive Weighting and Profile Matching methods in a system for determining outstanding students at Universitas Malikussaleh and to find out the ranking results of the two methods (SAW and Profile Matching) in selecting outstanding students at Universitas Malikussaleh.
Literature Review
Previous related research became one of the author's references in conducting this research to get an overview or comparison that had been carried out by previous researchers, so that differences will be seen with this research.There are several studies that have become literature reviews, including those related to research conducted by [5].The criteria used in this research are price, location, KPR, house type, facilities and initial payment.The results of the comparison of the SAW and Profile matching methods produce the same ranking as the 4th alternative, namely Sawangan Permai being the main choice in the calculation, for the SAW method with a value of 0.74 and profile matching 11.48.So that assessments using the SAW and Profile Matching methods can be used in decision making in selecting a house in the Depok city area using existing criteria.
The latest research was conducted by [7].The criteria used in this research are information about incapacity, parents' income, number of parents' dependents, and average report card score.The sensitivity test results of this research show that the sensitivity percentage result of the SAW method is 5.9166% while the Profile Matching method is 27% which can be concluded that the superior method in this case is the Profile Matching method.
The latest research was conducted by [8].The criteria used in this research are parental income, home ownership status, condition of the parents' house, number of dependents, and parental status.The results obtained are that the Profile Matching method can select scholarship recipients better than the Simple Additive Weighting method.The assessment criteria used consist of parents' income, homeowner status, condition of the parents' house, number of dependents and parental status.Comparison of the Profile Matching method produces the highest accuracy of 100% compared to the Simple Additive Weighing method which only produces 96% accuracy.
Apart from these studies, the author also takes references from other research with the aim of providing more references on related research including a decision support system for suitable soil types for food crops using SMARTER and SAW [9], a decision support system for determining disease in eggplant plants using the Simple Additive Weighting method [10], a decision support system for determining lecture recipients using the SMART method [11], and application of the Profile Matching Analysis method in a decision support system for study program recommendations [12].
From previous related research, there are differences with this research.This research focuses on designing and implementing the concept of the Simple Additive Weighting (SAW) and Profile Matching methods in a system for determining outstanding students and knowing the ranking results of both methods (SAW and Profile Matching) in selecting outstanding students and there are differences in the criteria used in selecting students achievement.Apart from this research, there are several studies that have been carried out by researchers regarding the application of methods in decision support systems and the creation of application systems, including the decision support system for selection of outstanding students using the fuzzy TOPSIS method [13], implementation of the moora method in selection of achievement students during the covid-19 pandemic [14], utilization of the laravel framework and bootstrap framework in developing a web-based hijab sales application [15], java application based decision support system in the production process of freshwater fish seed breeding in talang kemulun village [16], design and development of a data processing system for the toraja church, situru rante damai congregation based on client server [17].Apart from this research, there are several studies that have been carried out by researchers regarding the application of methods in decision support systems and the creation of application systems, including research on the decision support system for determining PKH acceptance using the naïve bayes method [18], classification of student scientific work using the Naive Bayes Classifier method [19], the implementation of fuzzy c-means to determine the level of student satisfaction in online learning [20].
Research method
The method or stages carried out in this study are shown in Figure 1.
Figure 1. Research methods or stages
The following is an explanation of This step involves the design and development of a decision support system based on an analysis of user needs and predetermined specifications.This includes creating system architecture, programming, and functional testing.e. System Testing After the decision support system is built, the next step is to carry out testing to ensure that the system functions well and meets user needs.This testing includes white-box testing and black-box testing.f. Conclusions and Recommendations After the decision support system has been developed and tested, the final step is to draw conclusions based on the results of development and testing.These conclusions include an evaluation of system performance, suitability to user needs, and impact on the decision-making process.
Data Collection Results
The data obtained in this research is student data containing the student's name, student registration number, study program, GPA, english course grades, superior course grades, previous achievements, and organizational activity.These data can be seen in Table 1.
Table 1 The data obtained in this research amounted to 251 data, all of this data was obtained from questionnaires obtained by the author directly from students
System Flowchart Design Results
The system scheme for implementing the Profile Matching and Simple Addtive Weighting methods can be seen in Figure 2.
Application of Simple Additive Weighting Methods
The manual calculation of the Simple Additive Weighting method is as follows.
Determine criteria and criteria weights
The criteria and criteria weights that will be used in this calculation are can be seen in Table 2.The graph of the calculation results from the SAW method can be seen in Figure 3.
Figure 3. Graph of SAW calculation results
The conclusion from the results of manual score calculations using the SAW method is that it can be determined that the student with the highest score is X65 (Muharram Muhammad Arif) with a final score of 1.
Application of Profile Matching Methods
The manual calculation of the Profile Matching method is as follows.1.
Determine criteria and standard weight values
The criteria and standard weight values used can be seen in Table 6.Gap Mapping Process The mapping process that occurs actually has one general formula that applies to calculating the weight of each criterion, namely as follows: The results of the criteria mapping process can be seen in Table 7 below. 3.
GAP Mapping
The gap mapping can be seen in Table 8 below.
GAP value conversion
The results of the GAP value conversion can be seen in Table 9.
CF and SCF grouping
After the process of determining the weight of the gap value for each criterion, the criteria are then grouped again into two groups, namely core factors and secondary factors.The core factor calculation can be seen in equation 2. The results of the core factor and secondary factor calculation process can be seen in Table 9 below.
Calculation of Total Value and Ranking
From the results of each aspect above, the total value is then calculated based on the presentation of the core factor and secondary factor values which are estimated to influence the performance of each profile.
To calculate the total, a formula is used: N = (X)% NCF + (X)% NSF (4) Where : N = Total value for each aspect NCF = Average core factor value NSF = Average secondary factor value (X)% = The percentage value entered The final results and ranking of each alternative can be seen in Table 10 below.
161
The graph of the calculation results of the Profile Matching method can be seen in Figure 4.
Figure 4. Graph of profile matching calculation results
The conclusion from the results of manual score calculations using the profile matching method is that it can be determined that the student with the highest score is X65 (Muharam Muhammad Arif) with a final score of 5.
System Implementation (System Output)
From the implementation of the system that the author has created, the output produced from the system is in the form of the final value of each alternative and the ranking of each alternative.
1.
Criteria Data Page The add data, CF and SF weights, search, edit and delete buttons can be found on the criteria data page, admins can add criteria data by pressing the add data button, the data that can be added are criteria names, attributes, types, weights, standard weights and methods.assessment, admins can also edit and delete the data using the edit and delete features can be seen in Figure 5 Alternative Data Page On the alternative data page, the admin can add student data by pressing the add data button, then the user is asked to fill in the Employee id Number, name and study program, the admin can also change and delete data by using the edit and delete features can be seen in Figure 6.Assessment Data Page The Assessment Data Page is a page where the admin can add scores from students that have been added previously.The assessment is based on predetermined sub-criteria data can be seen in Figure 7.The final results data page is the page that the admin uses to see the results of calculations that have been carried out on this system.On this page the system will display the final ranking results from the Profile Matching and Simple Additive Weighting methods, the data displayed is in the form of alternative names, total scores and rankings, the admin can also print the final result data using the print data feature can be seen in Figure 8. From the results of the research carried out in the research implementation of Simple Additive Weighting and Profile Matching Methods to determine outstanding students at Universitas Malikussaleh, the results obtained are that the decision support system can help streamline the time of Universitas Malikussaleh in making decisions to determine students achievement.By applying the SAW and Profile Matching methods to determine outstanding students, from the 251student data entered into the system it produces preferences with the highest score of 1 in the SAW method and the highest score of 5 in the Profile Matching method with the same best alternative, namely X65 (Muharam Muhammad Arif).So, these two methods can be applied in selecting outstanding students to help decision making, because these two methods produce the same best alternative.
Figure 1 .
The methods or stages carried out in decision support system research using the Profile Matching and Simple Additive Weighting (SAW) methods are as follows: a. Study of Literatture This stage involves research and analysis of relevant literature related to the topic or problem that the decision support system wants to solve.It helps in understanding the theoretical basis, methodology, and technology used in the development of such systems.b.Data Collection In this research, the author collects data directly from the original source or location where this research was conducted.The basic data in this research is in the form of a questionnaire.c.Calculation of Profile Matching and Simple Additive Weighting The next step is to carry out calculations using the Profile Matching and Simple Additive Weighting (SAW) methods to evaluate the predetermined criteria and to calculate the total value of a series of existing alternatives.d.Design and Manufacture of Decision Support Systems
5 Figure 2 .
Figure 2. System scheme of core factor values IC = Number of core factor sub-criteria And for secondary factor calculations, you can see equation 3. secondary factor value NS = Total number of secondary factor values Sistemal si: Jurnal l Sistem Informal si ISSN:2302-8149 Volume ?, Nomor ?,bulal n ?: hal lal mal n ?diisi editor e-ISSN:2540-9719 IS = Number of secondary factor sub-criteria
Figure 5 .
Figure 5. Criteria data page
Figure 6 .
Figure 6.Alternative data page
Figure 7 .
Figure 7. Assessment data page
13 Figure 8 .
Figure 8. Final results data page
Table 2 . Criteria and criteria weights
In order to form a student assessment decision matrix, it can be done by taking 10 samples of student data which are shown in Table3below.
Table 4 . Final result normalized
The final results of the final score calculation can be seen in Table5below.
Table 10 . Alternative final results and ranking
. | 3,729.6 | 2024-07-29T00:00:00.000 | [
"Education",
"Computer Science"
] |
Elevated Circulating and Placental SPINT2 Is Associated with Placental Dysfunction
Biomarkers for placental dysfunction are currently lacking. We recently identified SPINT1 as a novel biomarker; SPINT2 is a functionally related placental protease inhibitor. This study aimed to characterise SPINT2 expression in placental insufficiency. Circulating SPINT2 was assessed in three prospective cohorts, collected at the following: (1) term delivery (n = 227), (2) 36 weeks (n = 364), and (3) 24–34 weeks’ (n = 294) gestation. SPINT2 was also measured in the plasma and placentas of women with established placental disease at preterm (<34 weeks) delivery. Using first-trimester human trophoblast stem cells, SPINT2 expression was assessed in hypoxia/normoxia (1% vs. 8% O2), and following inflammatory cytokine treatment (TNFα, IL-6). Placental SPINT2 mRNA was measured in a rat model of late-gestational foetal growth restriction. At 36 weeks, circulating SPINT2 was elevated in patients who later developed preeclampsia (p = 0.028; median = 2233 pg/mL vs. controls, median = 1644 pg/mL), or delivered a small-for-gestational-age infant (p = 0.002; median = 2109 pg/mL vs. controls, median = 1614 pg/mL). SPINT2 was elevated in the placentas of patients who required delivery for preterm preeclampsia (p = 0.025). Though inflammatory cytokines had no effect, hypoxia increased SPINT2 in cytotrophoblast stem cells, and its expression was elevated in the placental labyrinth of growth-restricted rats. These findings suggest elevated SPINT2 is associated with placental insufficiency.
Introduction
Aberrations in placentation, particularly those amounting to restricted vascular remodelling, are associated with a constellation of obstetric complications, with significant implications for mothers and babies. This includes foetal growth restriction (FGR), in which affected foetuses fail to achieve their unique growth potential in utero, owing to inadequate uteroplacental perfusion. This confers an increased risk of perinatal morbidity and mortality upon the foetus [1]; in fact, FGR is recognised as the single largest risk factor for stillbirth [2]. Alternatively or simultaneously, placental insufficiency may manifest maternally as preeclampsia, which is characterised by persistent maternal hypertension and end organ dysfunction, arising from vascular endothelial injury [3].
Currently, there is an absence of effective and targeted treatments for both preeclampsia and FGR, and the latter, in particular, eludes precise diagnosis. Consequently, there are no interventions to rescue a poorly functioning placenta; except for iatrogenic preterm delivery, which has its own associated risks.
In the search for circulating biomarkers of placental insufficiency, SPINT1, a serine protease inhibitor, also called HGF activator inhibitor 1 (HAI-1), has been identified as a promising candidate [4]. SPINT1 is highly expressed in the placenta, where it is localised to the cell surface of villous cytotrophoblasts, and secreted in a proteolytically truncated form [5] through ectodomain shedding [6] into the maternal circulation. By virtue of its dual Kunitz domains, SPINT1 inhibits the activity of proteolytic substrates that are critical for normal placentation. Therefore, SPINT1 mediates the trophoblast secretion of degradative enzymes (serine proteinases, metalloproteinases, and collagenases), which regulate the invasion and remodelling of endometrial spiral arteries [7,8]. Inadequate or superficial remodelling may result in a suboptimal placenta, through oxidative stressinduced placental growth suppression [9], and intermittent placental perfusion, which leads to ischaemia-reperfusion injury [10]. We have recently demonstrated that SPINT1 is reduced in FGR placentas and is modulated by hypoxia; both in human placental cells and in a mouse model of FGR [4].
The validation of this serine peptidase inhibitor as an indicator of placental dysfunction justifies the investigation of its analogue SPINT2/HAI-2. To date, SPINT2 has not been thoroughly assessed in the human placenta; thus, its application in FGR diagnosis is yet to be explored. SPINT2 has a comparable tissue distribution to SPINT1 [11], and contains two extracellular inhibitory Kunitz domains, making it structurally similar to SPINT1. As with SPINT1, SPINT2 regulates matriptase [12], a transmembrane serine protease that is responsible for the degradation of the extracellular matrix components fibronectin and laminin [13]. The involvement of SPINT2 with matriptase in the placenta suggests its importance in placental development [12,14]. Indeed, in mouse placentas, SPINT2 is expressed for the duration of development in the placental labyrinth layer (the site of murine foetomaternal exchange) [12,15]. As reported in Spint1 knockout mouse models, Spint2-deficient mice suffer from placental defects. However, the effects of the loss of Spint2 extend beyond the placenta, causing embryonic lethality, unless matriptase is simultaneously ablated, in which case there are impairments to the neural tube closure [12].
Given the previous findings of dysregulated SPINT1 in FGR, it was hypothesised that the expression of SPINT2 would be similarly deranged in the placenta and maternal circulation of pregnancies that are complicated by FGR, even prior to diagnosis. Further, the expression of SPINT2 in placental trophoblasts was expected to be regulated by hypoxia and inflammation, which are signature contributors underlying placental insufficiency. Therefore, the aim of this study was to characterise the expression of SPINT2 at the mRNA and protein level in placental and plasma samples from pregnancies that have been affected by preeclampsia and/or FGR, as well as in a rodent model of placental insufficiency, and to observe any hypoxic-or inflammation-mediated changes in expression in vitro.
SPINT2 Expression Is Deranged in Placental Dysfunction
Given that SPINT2 has not previously been analysed in the human placenta, this study first characterised its expression in pregnancies that were known to be compromised by FGR and/or preeclampsia.
In preterm FGR placentas (n = 14), SPINT2 mRNA expression (Figure 1a) was highly variable and did not significantly differ from the controls (n = 19). In contrast, the placentas from pregnancies that were complicated by both preeclampsia and FGR (n = 20) had significantly decreased SPINT2 mRNA expression (68% of control, p = 0.002), whereas those affected by preeclampsia only (n = 60) had significantly increased SPINT2 mRNA levels (119% of control, p = 0.03). Figure 1. SPINT2 expression in placentas of patients with established placental disease. Compared to preterm controls, SPINT2 mRNA expression (a) was not altered in placentas from normotensive pregnancies affected by foetal growth restriction (FGR), but it was significantly decreased in those from pregnancies compromised by concurrent preeclampsia (PE) and FGR, and increased in preeclamptic placentas of AGA infants. SPINT2 protein expression (b) in these same placentas was also not changed in FGR-affected normotensive pregnancies, but was significantly elevated in all PE cases (with and without FGR). Each data point represents an individual patient sample; data are expressed as median ± IQR; * p < 0.05, ** p < 0.01.
Circulating SPINT2 in FGR and/or Preeclampsia
We next sought to measure SPINT2 within the maternal circulation in prospective cohorts, prior to any diagnoses.
In maternal plasma (collected upon presentation to MHW for caesarean section at term; Figure 2a), SPINT2 was modestly elevated (p = 0.0507) in those women whose infant was born small for the gestational age (SGA, birthweight < 10th centile; n = 75, median = 4020 pg/mL), compared to appropriate for the gestational age (AGA, birthweight > 10th centile) controls (n = 152, median = 3407 pg/mL). Circulating SPINT2 was significantly elevated (p = 0.002) in the SGA (n = 128, median 2109 pg/mL, IQR 1355-3069 pg/mL) samples that were collected at 36 weeks' gestation ( Figure 2b), compared to the AGA controls (n = 182, median = 1614 pg/mL, IQR: 1139-2360 pg/mL). This association was lost, however, earlier in gestation, where 24-to 34-week plasma from women with underlying vascular disease (MAViS clinic samples, Figure 2c, Table S1) demonstrated no difference between the AGA control (n = 179) and SGA (n = 58) levels of SPINT2. In this cohort, SPINT2 did not vary across gestation (Figure 2c) in the controls, but there was a trend towards a modest increase (p = 0.054) in SPINT2 across gestation in those women who were destined to birth an SGA infant (R 2 = 0.0645). In the blood of women on the day of delivery (a), SPINT2 protein expression was increased (approaching statistical significance, p = 0.051) in those who delivered an SGA infant, compared to AGA controls. This association was stronger at 36 weeks' gestation, in which there was a significant elevation of SPINT2 levels among women who later delivered a small-for-gestational-age (SGA) infant (b) as well as in those women who subsequently developed PE (d), although the significance of the latter was lost when accounting for outliers. Earlier in the pregnancy, however, at 24-34 weeks, there was no association between circulating SPINT2 and SGA (c) nor PE (e) cases in samples from women with underlying vascular disease. In this cohort, SPINT2 did not fluctuate across gestation in controls nor PE; however, there was an apparent increase in SPINT2 across gestation in those women destined to birth an SGA infant. In the plasma collected on the day of delivery from women with diagnosed placental insufficiency (f), circulating SPINT2 was unchanged in cases, relative to controls. Each data point represents an individual patient sample; data are expressed as median ± IQR; linear regression showing 95% confidence intervals; * p < 0.05, ** p < 0.01.
At 36 weeks' gestation (Figure 2d), circulating SPINT2 was also elevated (p = 0.03) in women who were destined to develop term preeclampsia (n = 23, median = 2233 pg/mL, IQR: 1643-2661 pg/mL), relative to the controls (n = 182, median 1644 pg/mL, IQR: 1218-2480 pg/mL). In the 24-to 34-week plasma from women attending the MAViS clinic ( Figure 2e, Table S2), there was no difference in SPINT2 levels in those who were ultimately diagnosed with preeclampsia, relative to the controls, nor did the protein concentration change, relative to gestation, regardless of the disease status ( Figure 2e).
Interestingly, there were no significant differences in circulating SPINT2 in patients delivering preterm for preeclampsia or FGR, relative to the controls (Figure 2f).
Hypoxic Regulation of SPINT2 in Trophoblasts
Placental insufficiency is often associated with intermittent placental hypoxia; thus, we assessed the effect of hypoxia on SPINT2 expression.
In primary trophoblasts that were isolated from term placentas, SPINT2 mRNA transcripts were significantly increased in response to hypoxia (Figure 3a; mean = 193% of control, p = 0.002), while secreted SPINT2 was unchanged ( Figure 3b). In contrast, hypoxia had no effect on SPINT2 mRNA expression in first-trimester cytotrophoblast stem cells (Figure 3c), but SPINT2 protein secretion (Figure 3d) was significantly increased (mean = 412.8% of control, p = 0.008). Given SPINT2 is also likely expressed in syncytiotrophoblast, we measured expression and secretion in syncytialised first-trimester human trophoblast stem cells (hTSCs; Figure 3e), observing that oxygen tension had no effect on mRNA expression, but modestly decreased SPINT2 secretion (Figure 3f; mean = 85.6% of control, p = 0.008) in the syncytiotrophoblasts that were exposed to hypoxia. Figure 3. The effect of hypoxia on SPINT2 expression in placental cells. SPINT2 mRNA and protein secretion was measured in the following three types of trophoblast cultures: primary trophoblasts isolated from term placentas, and first-trimester cytotrophoblast and syncytiotrophoblast from a stem cell line. In the term primary trophoblasts (a), SPINT2 transcripts were significantly increased in response to hypoxia, while secreted protein levels (b) were not changed. Hypoxic conditions caused no alteration to the first-trimester cytotrophoblast stem cell SPINT2 mRNA (c), but did significantly increase the levels of SPINT2 secretion (d) compared to normoxic controls. The syncytialised firsttrimester stem cells had no change in mRNA (e), although they did demonstrate decreased SPINT2 secretion (f). Experiments were repeated n = 3-5 times; data are expressed as mean ± SEM. In placentas from a rat model of uteroplacental insufficiency, changes were identified in rat SPINT2 mRNA (rSpint2) expression in both the basalis (g) and labyrinth (h) zones, being depressed and elevated, respectively. Each data point represents an individual rat placenta; data are expressed as median ± IQR; * p < 0.05, ** p < 0.01.
The derangement of SPINT2 expression in response to hypoxia was also demonstrated in placentas from a rat model of uteroplacental insufficiency, induced by ligating the uterine vessels, thereby impeding placental perfusion. There are distinct morphological differences (see Furukawa et al., 2011 [15]) between the rat and human placenta, thus we separated the basalis and labyrinthine layers for analysis of SPINT2. In the basalis region of the restricted placentas (Figure 3g), SPINT2 mRNA expression was significantly depressed (median = 76.9% of control, p = 0.004), compared to that of dams who underwent sham surgery. Interestingly, the labyrinth layer-akin to the chorionic villi (including syncytiotrophoblasts, villous cytotrophoblast, stroma and blood vessels) of the human placenta-of restricted placentas had modestly upregulated SPINT2 mRNA expression (median = 108.4% of control, p = 0.04).
SPINT2 Is Not Regulated by Inflammation
Preeclampsia is associated with placental and systemic inflammation, and we therefore assessed whether SPINT2 is influenced by pro-inflammatory stimuli. In first-trimester cytotrophoblasts (Figure 4a,c) and syncytialised trophoblasts (Figure 4e,g), we observed no significant effect on SPINT2 mRNA expression. SPINT2 secretion was also unchanged in both the cell types (Figure 4b,d,f), with only low doses of IL-6 stimulating a modest decrease (p < 0.01) in syncytiotrophoblasts (Figure 4g). First-trimester cytotrophoblasts (a-d) and syncytiotrophoblasts (e-h) were treated with inflammatory cytokines, TNF or IL-6, at various doses. No significant changes were observed in SPINT2 mRNA (a,c,e,g) expression, nor in secreted SPINT2 (b,d,f); with the exception of IL-6-treated syncytiotrophoblasts (h), which stimulated a modest, but significant, decrease in SPINT2 secretion at lower doses. Experiments were repeated n = 5 times; data are expressed as mean ± SEM; ** p < 0.01.
Discussion
Throughout the first trimester of pregnancy, the intricate foetal-maternal interface is established through the process of placentation, which involves tightly regulated and complex pathways, the understanding of which is at present incomplete. The accumulation of anomalies in this process can lead to a dysfunctional placenta, which inadequately supplies the foetus, and can have serious consequences for the mother and baby, including preeclampsia and/or FGR. In this study, we sought to characterise the expression of SPINT2 in the placentas and maternal circulation of pregnancies that were complicated by preeclampsia and/or FGR, using three prospective cohorts, a rodent model, in trophoblasts isolated from human tissue at term, and in stem cells from the first trimester.
By measuring circulating SPINT2 levels in the cases of established disease (delivered at <34 weeks' gestation), it was apparent that SPINT2 expression is not dysregulated in FGR-like functionally related homologue SPINT1 [4]. While derangements in SPINT2 expression were apparent in the cases of placental insufficiency-mediated pregnancy complications, the measured fluctuations do not reliably reflect the disease status, making SPINT2 an overall poor biomarker candidate. Indeed, an association between circulating SPINT2 and placental insufficiency is apparent only at term (and near term, from 36 weeks onwards), with no distinction between the cases and controls in weeks 24-34, nor at preterm delivery (<34 weeks). As such, SPINT2 lacks the robust predictive potential of its relative, SPINT1 [4]. This is perhaps unsurprising, because, despite their similarities, SPINT2 is more ubiquitously expressed than SPINT1, and their encoding genes are located on different chromosomes (15 and 19, respectively). So, although they likely share a common ancestor gene, they have evolved distinctly [16]. Nevertheless, there is likely involvement of SPINT2 in placental function-given the changes in placental SPINT2 expression that have been observed.
The expression of SPINT2 mRNA in the preterm placentas was decreased in concurrent FGR and preeclampsia, but elevated where only preeclampsia is present (i.e., with AGA); whereas, SPINT2 protein expression was increased in all cases of preeclampsia (with and without FGR). It is interesting that SPINT2 mRNA and protein are both significantly elevated in preeclamptic (without FGR) placentas, whereas the placentas plagued by concurrent preeclampsia and FGR had decreased SPINT2 mRNA, but elevated protein. This is an unusual phenomenon, and the reason for this disparity has not been elucidated by the present study. It may suggest that there are post-transcriptional modifications in the preeclamptic/FGR placentas, to reduce SPINT2 protein turnover, as a compensatory mechanism for the low transcript levels; however, further study is needed to confirm this hypothesis.
In the cases of FGR, the circulating levels of SPINT2 were modestly elevated at term and at 36 weeks' gestation; however, at earlier gestations, there were no observed changes in expression. Similarly, there was elevated circulating SPINT2 at 36 weeks in those women who were destined to develop preeclampsia, while earlier gestation levels were unchanged, relative to the controls. Interestingly, SPINT2 was not altered in preterm disease, raising the possibility that derangements in circulating levels only arise in later-onset disease. Alternatively, the lack of statistical significance in the established disease plasma cohort may be attributable, in part, to having relatively few FGR samples (especially plasma; n = 6), and the high variability in expression for the samples that were available. A larger sample size would aid in verifying whether there are bona fide alterations in mRNA, and/or protein in the placentas and plasma of FGR-affected pregnancies.
Frequently, the dysfunctional placenta suffers from suboptimal perfusion and high levels of inflammatory factors, and, in previous research, SPINT2 has been shown to be regulated by hypoxia (in breast cancer cells) [17]. Having found SPINT2 levels to be elevated in placental insufficiency, we used in vitro methods to examine the effect of hypoxia and pro-inflammatory cytokines on the trophoblasts of the placenta, early in gestation and at term. SPINT2 expression did appear to be regulated by hypoxia in first-trimester human trophoblast stem cells (hTSCs), term primary trophoblasts, and in a rat model of restricted placental perfusion. Early in gestation (as modelled by hTSCs), SPINT2 secretion was elevated under hypoxia in cytotrophoblast stem cells, while being decreased in syncytiotrophoblasts. However, there were no changes in transcription at this early stage, with SPINT2 mRNA largely unchanged by oxygen tension. In contrast, in primary trophoblasts, isolated from placentas that were delivered at term, there was an increase in SPINT2 mRNA expression, but no change in protein secretion. This indicates that in response to hypoxic conditions early in gestation, trophoblasts alter the secretion of SPINT2; whereas, nearer to term, transcriptional changes dominate the response to hypoxia. The mechanism behind this difference is uncertain and requires further investigation. Importantly, fluctuations in SPINT2 expression, in relation to hypoxia, were also measured in rat placentas with induced uteroplacental insufficiency, with inverse changes in the basalis and labyrinth zones of the placenta. Notably, SPINT2 mRNA was upregulated in the labyrinthine region of restricted placentas, complementing the findings in term trophoblasts exposed to hypoxia.
Mouse models have previously established the importance of SPINT2 in placental development [15], and, consequently, embryonic survival. The findings presented here suggest that SPINT2 has a similar importance in human placentation, owing to its derangement in FGR and preeclamptic pregnancies.
Tissue and Blood Collection at Time of Preterm Delivery from Women with Established Placental Disease (Day of Delivery at <34 Weeks)
To characterise the expression of SPINT2 in the maternal circulation and placenta of FGR-and/or preeclampsia-complicated pregnancies, human specimens were obtained. All studies were approved by the Mercy Health Human Research ethics committee (R11/34).
Placental tissue samples were collected from consenting women, delivering by caesarean section at less than 34 weeks' gestation, with decision for delivery made independently by the treating obstetric team. The samples were classified as FGR (n = 14), PE (n = 60) or both (n = 20), according to preeclampsia guidelines from ACOG 2020 [18] and FGR defined as birthweight <10th centile on local birthweight charts [19]. The control samples (n = 19) were gestation-matched and obtained from women who were delivered preterm due to other complications not associated with placental insufficiency or hypertensive disorders of pregnancy, such as placenta praevia or spontaneous preterm rupture of membranes. Although the control sample comprises pregnancies with complications, gestation-matching is important when investigating proteins highly expressed in the placenta, as the pattern of expression commonly varies with advancing gestation. Samples in both the case and control group were excluded if there were congenital anomalies and/or histopathological evidence of congenital infection. Patient characteristics are detailed in Table S3.
Tissue was collected and processed within 30 min of delivery by caesarean section. Segments of tissue were dissected and washed in PBS, then samples of roughly equal size were immersed in RNAlater TM stabilisation solution (Thermo Fisher Scientific; Waltham, MA, USA) for 48 h, then snap frozen and stored at −80 • C. Subsequently, RNA or protein was extracted from tissue lysates.
Plasma samples were also collected on the day of delivery at less than 34 weeks' gestation from women delivering prematurely with FGR (n = 6), PE (n = 40) or both (n = 11). These were compared to gestation-matched blood specimens collected from control pregnancies delivered at term (n = 26). These samples were aliquoted and stored at −80 • C until future analysis. Patient characteristics of this cohort are detailed in Table S4.
Day of Delivery at Term-FLAG2
The Fetal Longitudinal Assessment of Growth 2 (FLAG2) study recruited 562 unselected women on the day of elective caesarean section at the Mercy Hospital for Women (MHW, Melbourne, Australia). Women who were aged over 18 years with a well-dated singleton pregnancy, at 36 +0 -42 +0 weeks' gestation, were eligible to participate. Exclusion criteria included any suspicion of major foetal anomaly or infection; ruptured membranes; labouring women; those who had undergone cervical ripening or steroid administration before the caesarean section; and those who were positive for hepatitis B, C or HIV. A study blood sample was taken at the time of intravenous cannula placement and birthweight centile was determined using the GROW Bulk centile calculator (v8.0.4, 2019). The FLAG2 study was approved by the Mercy Health Research ethics committee (ethics approval number R11/34) and written informed consent was obtained from all participants. The total number of remaining samples used for SPINT2 analysis was 227, comprising 152 controls (appropriate for gestational age, AGA) and 75 cases (SGA). Patient characteristics are shown in Table S5.
BUMPS-36 Weeks' Gestation
The Biomarker and Ultrasound Measures for Preventable Stillbirth (BUMPS) study is a large prospective cohort collection at MHW, with samples collected from an unselected population at 28 and 36 weeks' gestation. Women were screened for eligibility and invited to participate at their oral glucose test, universally offered to non-diabetic pregnant women around 28 weeks' gestation to test for gestational diabetes mellitus. Following written informed consent, women aged over 18 years, with a singleton pregnancy and normal mid-trimester foetal morphology examination were eligible to participate. The BUMPS study was approved by the Mercy Health Research ethics committee (ethics approval number 2019-012). For this study, a case-cohort of 364 samples was selected from the first 1000 BUMPS participants, including all cases delivering an infant <10th centile (SGA; n = 198) according to the GROW Bulk centile calculator (v8.0.4, 2019), all cases delivering with preeclampsia (defined according to ACOG guidelines; n = 23) and a cohort of controls (n = 182). Patient characteristics detailed in Table S6.
MAViS-24-34 Weeks' Gestation
SPINT2 was also measured in a high-risk cohort of patients at the Manchester Antenatal Vascular Service (the MAViS clinic; Manchester, UK). Women are referred to the clinic in early pregnancy for monitoring across gestation based on hypertensive disease, which predisposes to preeclampsia and/or FGR, allowing for longitudinal sampling between 24-and 34-weeks' gestation. The inclusion criteria for women in the MAViS study were as follows: 1. chronic hypertension (BP ≥ 140/90 at ≤20 weeks; 2. chronic hypertension requiring antihypertensive treatment from ≤ 20 weeks; 3. pre-gestational diabetes with evidence of vascular complications (hypertension, nephropathy); 4. history of ischaemic heart disease; and 5. previous early onset preeclampsia. A case-cohort of 294 participants was recruited between October 2011 and December 2016, with a plasma sample obtained between 24 and 34 weeks, and complete outcome data were included in the current study. These participants were selected from an overall cohort of 518 participants and included 179 control women and 115 who either delivered with preeclampsia, FGR or both. The study was granted ethics approval by the NRES Committee North West (11/NW/0426). Patient characteristics are listed in Table S7.
Placental Samples from a Rat Model of Placental Insufficiency
In order to assess the in vivo expression of SPINT2, samples were obtained from a previously established rodent model of FGR. The placental deficiency in this model was induced during late gestation (at day 18 of 22), providing an in vivo model of lateonset, placental-derived FGR [20]. Uteroplacental insufficiency was induced by means of bilateral uterine vessel ligation (of both the artery and vein), to restrict the blood and nutrient supply to the foetuses. The control group underwent sham surgery mimicking this procedure, without the ligation of uterine vessels. The details of this protocol can be found in Wlodek et al. (2005) [21].
The placentas were collected, weighed and the labyrinthine layer separated from the basalis layer before being immediately frozen in liquid nitrogen, then stored at −80 • C for later analysis. RNA was extracted from both regions. The development of this model of uteroplacental insufficiency in rats was approved by the La Trobe animal ethics committee (AEC: , in accordance with the National Health and Medical Research Council's (NHMRC) Australian code for the care and use of animals for scientific purposes.
Human Trophoblast Stem Cells (hTSCs)
To examine SPINT2 in response to hypoxia and inflammatory stressors, first-trimester human trophoblast stem cells (hTSCs) were obtained from the RIKEN BRC through the National BioResource Project of the MEXT/AMED (Japan), as previously detailed in the manuscript from Okae et al., 2018. This cell line was isolated from first-trimester placentas under ethical approval from Tohoku University School of Medicine [22]. The cells were then cultured in specialised media, according to the optimised conditions in Okae et al., 2018 [22]. Given the localisation of SPINT2 to both cytotrophoblast and syncytiotrophoblast in the placenta [23], some cells were propagated as multipotent cytotrophoblasts, while others were directed to differentiate into the syncytiotrophoblast lineage.
Term Primary Cytotrophoblast Isolation
Primary cytotrophoblast cells were isolated from term placentas according to the protocol optimised by Kaitu'u-Lino et al., 2014 [24]. In summary, a segment of placenta was resected, washed, mechanically dissociated, and enzymatically digested, allowing for the collection of the isolated cells in the supernatant [24]. Cells were then cultured in preparation for subsequent analysis.
Simulation of Trophoblast Hypoxia
Hypoxic conditions were simulated for first-trimester hTSCs and term trophoblasts to assess the effect of inadequate oxygen perfusion during placentation and approaching term, respectively. After a 24-h incubation in 8% oxygen at 37 • C, allowing cells to adhere to the basement membrane (iMatrix-511 for hTSCs, fibronectin for primary trophoblasts), cells were incubated in different oxygen concentrations. Given the physiologically relevant oxygen tension in utero is 8%, those cells designated normoxic were incubated at 37 • C in 8% oxygen for 48 h. Hypoxia involved exposure to 1% oxygen for the same duration. The media was collected for subsequent analysis and cells lysed for RNA extraction.
Simulation of Placental Inflammation
Two inflammatory cytokines, tumour necrosis factor alpha (TNFα; Life Technologies, Carlsbad, CA, USA) and interleukin-6 (IL-6; In Vitro Technologies, Noble Park, VIC, Australia), were added to the media of primary trophoblasts and first-trimester hTSCs (cytotrophoblasts and syncytialised stem cells) to simulate the inflammation common to the preeclamptic placenta. These cells were incubated at 37 • C for 24 h after plating, followed by treatment with 0 ng/mL, 0.1 ng/mL, 1 ng/mL or 10 ng/mL of the recombinant cytokine, diluted with fresh media. After being cultured for a further 24 h in the treatment media, cells and media were collected.
Protein Extraction
Protein was isolated from placental tissue and syncytiotrophoblast, using RIPA buffer containing protease inhibitor cocktail (Sigma-Aldrich; St. Louis, MO, USA) and Halt™ phosphatase inhibitor cocktail (Thermo Fisher Scientific; Waltham, MA, USA) to lyse cells and centrifugation to pellet debris. To quantify the protein content of each sample, a Pierce™ BCA assay (Thermo Fisher Scientific) was performed according to the manufacturer's protocol. Equal protein amounts were loaded for ELISA.
RNA Extraction
The Genelute™ mammalian total RNA miniprep kit (Sigma-Aldrich; St Louis, MO, USA) was used to extract RNA from cultured hTSCs, primary term trophoblasts and placental tissue, as per the manufacturer's protocol.
Reverse Transcription
RNA extracted from samples was converted to cDNA using the Applied Biosystems™ high-capacity cDNA reverse transcription kit (Thermo Fisher Scientific; Waltham, MA, USA), following the manufacturer's guidelines. The reaction comprised 150 ng RNA solution (appropriately diluted with DEPC-treated H 2 O). The iCycler iQ™5 (Bio-Rad, Hercules, CA, USA) protocol was run according to kit specifications, being held at 4 • C after completion until collection and storage at −20 • C for later PCR analysis.
Real-Time Polymerase Chain Reaction (RT-qPCR)
Quantitative PCR was carried out to ascertain the mRNA expression of Spint1 and Spint2, relative to reference housekeeper genes. TaqMan gene expression primers (Thermo Fisher Scientific; Waltham, MA, USA) specific to the genes of interest are detailed in Table S8, including the appropriate housekeeping genes for each sample set. All PCRs were performed on the CFX384 (Bio-Rad). The average C t of sample duplicates were normalised to appropriate reference genes before being calibrated to the average C t of experimental controls, allowing the results to be expressed as percentage relative to controls.
Enzyme Linked Immunosorbent Assays (ELISAs)
SPINT2 protein levels were measured in maternal plasma samples, hTSC media, and placental lysates via ELISA. The large cohort analyses were analysed using an ELISA kit for SPINT2 (Sigma-Aldrich, St. Louis, MO, USA), following manufacturer's specifications. The <34 week plasma was diluted 1:12 for SPINT2. Cellular SPINT2 in placental lysates was analysed using a SPINT2 DuoSet ® ELISA (R&D Systems; Minneapolis, MN, USA). Then, 5 µg of each sample was loaded, diluted in 1% BSA in PBS according to the concentration determined by the BCA assay. Cultured hTSC media was also analysed using the R&D Systems SPINT2 kit. Media samples were undiluted, with the exception of the hypoxia studies, which were diluted 1:2 with 1% BSA in PBS.
Statistical Analysis
In vitro experiments were carried out in technical triplicate and repeated 3-5 times. The results of in vitro experiments were normalised to controls so data could be expressed as % control. Using GraphPad Prism 8 (GraphPad Software, Inc., San Diego, CA, USA), statistical analyses were carried out, with data first assessed for Gaussian distribution, then analysed using appropriate statistical tests. Maternal characteristics and birth outcome data (Supplementary Tables S3-S7 were compared for all women who were preeclamptic and/or delivered an SGA baby against controls using Mann-Whitney U, unpaired t, Fisher's exact or Chi-square tests. For all other data, when two groups were compared, a Student's t-test or Mann-Whitney U test was used according to Gaussian distribution. For more than two groups, a one-way ANOVA or Kruskal-Wallis test was used, according to Gaussian distribution, and post hoc analyses ascertained by Dunn's multiple comparisons test. Outliers were identified and accounted for using a ROUT test.
Conclusions
Unlike SPINT1, circulating SPINT2 is not consistently dysregulated in diseases of placental insufficiency-in preeclampsia or foetal growth restriction. We have shown that SPINT2 is unlikely to be a clinically useful biomarker; however, we did identify changes in placental SPINT2, which suggest it may be functionally involved in human placentation; this is a role yet to be explored.
Informed Consent Statement:
All patients who participated in this study provided written informed consent.
Data Availability Statement: Raw data are available upon reasonable request from the corresponding author. | 7,240.8 | 2021-07-01T00:00:00.000 | [
"Medicine",
"Biology"
] |
Encoding Two-Qubit Logical States and Quantum Operations Using the Energy States of a Physical System
: In this paper, we introduce a novel coding scheme, which allows single quantum systems to encode multi-qubit registers. This allows for more efficient use of resources and the economy in designing quantum systems. The scheme is based on the notion of encoding logical quantum states using the charge degree of freedom of the discrete energy spectrum that is formed by introducing impurities in a semiconductor material. We propose a mechanism of performing single qubit operations and controlled two-qubit operations, providing a mechanism for achieving these operations using appropriate pulses generated by Rabi oscillations. The above architecture is simulated using the Armonk single qubit quantum computer of IBM to encode two logical quantum states into the energy states of Armonk’s qubit and using custom pulses to perform one and two-qubit quantum operations.
Introduction
Quantum algorithms are known to outperform their classical counterparts in a variety of computational tasks [1][2][3]; various proposals have also been suggested for the physical implementation of quantum computers, while multiple implementations have also taken place [4,5]. Most of the proposed implementation techniques rely on the representation of the quantum logical unit of information, the qubit, to a degree of freedom of the underlying physical system. There are thus qubits that have energy eigenstates as basis states, qubits that have spin eigenstates as basis states and so on. Although a typical quantum computing architecture may refer to fundamental configurations of qubits and their interaction, resulting implementations will normally involve error correcting mechanisms to accommodate for the various sources of quantum error such as measurement error, decoherence and depolarization. While classically, it is straightforward to copy the state of a bit to multiple bits and use redundancy for error correction, the no-cloning theorem prohibits this approach for qubits. Instead, the codes used for qubits involve entanglement; the bit flip code and the Shor Code [6] are typical examples of quantum error correction codes. The need for error correction imposes the necessity of implementing an extra number of qubits to any implementation of a quantum computing architecture. The totality of the qubits used to both store and perform quantum error correction is typically referred to as the physical qubits of the system. In contrast, the logical amount of information encoded in the system is referred to as the logical qubits. Therefore, a system implementing the bit flip code that uses two extra qubits to perform error correction to a single state will have three physical qubits and one logical.
In this paper, we investigate a way to reduce the amount of error, and thus the need to correct extra physical qubits, by investigating the principles of quantum error correction and performing them to the domain of the architecture, i.e., the domain of the logical computation itself. Instead of using the eigenstates of two-state physical systems to encode single qubits, we allow more eigenstates to be used, thus encoding multiple qubits to the Technologies 2022, 10, 1 2 of 10 eigenstates of a single system. This transforms quantum operations involving multiple qubits, such as the CNOT, to quantum operations that are performed using the eigenstates of a single physical system. In this sense, entangled states at the logical level can be created by involving a single system at the physical level. Since a main source of error is the interactions between qubits, this process is expected to reduce the overall amount of error.
The paper is structured as follows: In Section 2, we give a brief overview on how, in principle, multiple quantum logical states can be mapped to single physical states with an example of how a CNOT gate can be implemented using a harmonic oscillator. We then build upon the main idea of the harmonic oscillator to propose a more robust schema of encoding information using the charge degree of freedom of impurity atoms embedded in semiconductor materials. Section 3 provides the core idea by presenting how the mapping model is implemented in charge qubits defined by donor electrons of impurity atoms embedded in a semiconductor structure. The method by which single and two-qubit quantum gates are implemented in the model is also presented in Section 3. where, we also perform a simulation of the proposed architecture using the IBM Armonk single qubit computer [5]. Finally, Section 4 offers a discussion of the results of this work.
Materials and Methods
The idea of encoding multiple qubit states to a single physical state is not new. An example can be seen in the quantum oscillator case [7]. Though not a good candidate for the physical realization of quantum physical systems due to issues with scaling and equidistant energy separation, the quantum oscillator can be used to demonstrate the principle of mapping multiple qubit states to a single physical state.
Consider, for example, the following mapping: where subscript L corresponds to the logical quantum states. States on the right side, appearing without subscript, correspond to the energy levels of the quantum oscillator. The energy eigenstates of the quantum oscillator evolve with time as: Consequently, if we allow the system to evolve for time t equal to π/ ω then the state changes according to: so that odd labeled physical states (in this case, the |1 state) change sign. Applying for the logical states appearing in the Equation (1) state |10 , changes to |11 and vice versa, while the other two states remain unchanged, corresponds to the truth table of the quantum CNOT gate; considering the first qubit to be the control and the second one the target qubit. Although the quantum harmonic oscillator architecture presented above is more of a theoretical schema, architectures that divert from the typical mapping of a single physical degree of freedom to a single qubit state have been developed. A hybrid approach, for example, that uses different mechanisms to encode different parts of a quantum computation has been implemented in [8], where the control qubit of a C-SWAP Gate was implemented using a photon's polarization, whereas the SWAP part was implemented using four degrees of the photonic angular momentum. In general, the concept of hyperentanglement [9] allows the usage of multiple degrees of freedom of a single physical system to encode quantum information. The approach presented in this paper uses only one degree of freedom. The typical spin systems used for quantum computing consist of two eigenstates sufficient for encoding a single qubit. For the purpose of the current work, we needed to map multi-qubit registers to eigenstates of single physical systems; therefore, charge qubits are a better candidate that allow for such encodings. Charge qubits are implemented using the energy charge of freedom of a quantum system. Typical efforts to construct an architecture based on charge qubits include the encoding of a qubit based on the presence of Cooper pairs [10] or encoding to the charge degree of freedom of electrons in semiconductor devices [11,12]. More recently, architectures that are based on neutral atoms have been proposed [13]. These architectures make use of laser beams targeted at an atom ensemble to cool them to temperatures of the order of mK; they then use pulses to excite the atoms and use the energy states as the computational basis.
Similar to the two-spin system is the archetypal model for spin qubits, in which a two-level atom can be used for prototyping quantum logic operations on a single qubit. Scaling a physical system to allow for operations on an arbitrary number of qubits is one of the biggest challenges of quantum computing. In the case of the two-level atom, the straightforward method of scaling the system by adding more energy levels becomes quickly inefficient, as the gap between higher levels becomes very narrow and, after a certain point, practically continuous. This is also the case for the harmonic oscillator state presented above.
This difficulty can be overcome by various methods such as those mentioned in the first paragraph; for the purposes of the current work, a semiconductor material with a pentavalent donor impurity contributing one extra donor electron is considered ( Figure 1). Depending on the material and the doping substance, multiple energy eigenstates may be introduced in the semiconductor bandgap. For the purposes of the present treatment, it will be assumed that energy levels can be raised as desired by the appropriate placement of impurities in the semiconductor grid and that any degeneracies can be lifted by applying the appropriate external electric fields. It is further assumed that for the transitions of interest, the selection rules resulting from the symmetries of the material are always allowed and that energy levels may always be defined such that the energy differences between transition levels may always be matched by incoming electromagnetic pulses. All other energy levels are sufficiently detuned and thus not affected by the incoming pulse.
computation has been implemented in [8], where the control qubit of a C-SWAP Gate was implemented using a photon's polarization, whereas the SWAP part was implemented using four degrees of the photonic angular momentum. In general, the concept of hyperentanglement [9] allows the usage of multiple degrees of freedom of a single physical system to encode quantum information. The approach presented in this paper uses only one degree of freedom.
The typical spin systems used for quantum computing consist of two eigenstates sufficient for encoding a single qubit. For the purpose of the current work, we needed to map multi-qubit registers to eigenstates of single physical systems; therefore, charge qubits are a better candidate that allow for such encodings. Charge qubits are implemented using the energy charge of freedom of a quantum system. Typical efforts to construct an architecture based on charge qubits include the encoding of a qubit based on the presence of Cooper pairs [10] or encoding to the charge degree of freedom of electrons in semiconductor devices [11,12]. More recently, architectures that are based on neutral atoms have been proposed [13]. These architectures make use of laser beams targeted at an atom ensemble to cool them to temperatures of the order of mK; they then use pulses to excite the atoms and use the energy states as the computational basis.
Similar to the two-spin system is the archetypal model for spin qubits, in which a two-level atom can be used for prototyping quantum logic operations on a single qubit. Scaling a physical system to allow for operations on an arbitrary number of qubits is one of the biggest challenges of quantum computing. In the case of the two-level atom, the straightforward method of scaling the system by adding more energy levels becomes quickly inefficient, as the gap between higher levels becomes very narrow and, after a certain point, practically continuous. This is also the case for the harmonic oscillator state presented above.
This difficulty can be overcome by various methods such as those mentioned in the first paragraph; for the purposes of the current work, a semiconductor material with a pentavalent donor impurity contributing one extra donor electron is considered ( Figure 1). Depending on the material and the doping substance, multiple energy eigenstates may be introduced in the semiconductor bandgap. For the purposes of the present treatment, it will be assumed that energy levels can be raised as desired by the appropriate placement of impurities in the semiconductor grid and that any degeneracies can be lifted by applying the appropriate external electric fields. It is further assumed that for the transitions of interest, the selection rules resulting from the symmetries of the material are always allowed and that energy levels may always be defined such that the energy differences between transition levels may always be matched by incoming electromagnetic pulses. All other energy levels are sufficiently detuned and thus not affected by the incoming pulse. For the pair energy levels depicted in Figure 1, the following mapping between physical and quantum logical states is considered: Transitions between states will be analyzed for two cases, namely single qubit and two-qubit operations.
A typical method for a quantum state, to make transitions between energy eigenstates, is by making use of Rabi oscillations. The dynamics of Rabi oscillations have already been studied as candidates for encoding qubits and manipulating quantum information [14,15]; for the domain of semiconductors in particular, there are already results that demonstrate the feasibility of quantum control using spin qubits in GaAs quantum dots [16] and Si quantum dot systems [17]. Here we will give an overview on how the same approach can also be followed to manipulate the logical states, as these were defined in Equation (4).
Consider that an electric pulse is applied to the electron in Figure 1. It can be shown that under the rotating wave approximation [18], the state of the electron will evolve according to: c i is the amplitude of the ith state, Ω R the Rabi frequency determined by the energy of the incident pulse and the electric dipole matrix and ∆ = ν − ω the detuning, ν is the frequency of the incident pulse and ω = ω 2 − ω 1 is the frequency difference between the two states. An electric field that is near-resonant with the transition when applied for a finite time, can be used to perform an arbitrary rotation between the two states, the exact time being dependent on the detuning and Rabi frequency.
Consider the setup depicted in Figure 2, where ω 1→2 = ω 3→4 with ω 1→3 and ω 2→4 being sufficiently detuned that a pulse nearly resonant with ω 1→2 = ω 3→4 is applied. This pulse must be applied for sufficient time to perform any transition between states |1〉 and |2〉 if the electron is in one of these states, or between |3〉 and |4〉 if the electron is in one of those states. The mapping defined in Equation (4) corresponds to a single qubit operation on the second qubit. If a single qubit operation is required in the first qubit, the same argument may be followed for frequencies ω 1→2 = ω 3→4 , which will allow the first qubit to be arbitrarily controlled.
Transitions between states will be analyzed for two cases, namely single qubit and two-qubit operations.
A typical method for a quantum state, to make transitions between energy eigenstates, is by making use of Rabi oscillations. The dynamics of Rabi oscillations have already been studied as candidates for encoding qubits and manipulating quantum information [14,15]; for the domain of semiconductors in particular, there are already results that demonstrate the feasibility of quantum control using spin qubits in GaAs quantum dots [16] and Si quantum dot systems [17]. Here we will give an overview on how the same approach can also be followed to manipulate the logical states, as these were defined in Equation (4).
Consider that an electric pulse is applied to the electron in Figure 1. It can be shown that under the rotating wave approximation [18], the state of the electron will evolve according to: ci is the amplitude of the ith state, ΩR the Rabi frequency determined by the energy of the incident pulse and the electric dipole matrix and Δ = ν-ω the detuning, ν is the frequency of the incident pulse and ω = ω2 − ω1 is the frequency difference between the two states. An electric field that is near-resonant with the transition when applied for a finite time, can be used to perform an arbitrary rotation between the two states, the exact time being dependent on the detuning and Rabi frequency.
Consider the setup depicted in Figure 2, where ω1→2 = ω3→4 with ω1→3 and ω2→4 being sufficiently detuned that a pulse nearly resonant with ω1→2 = ω3→4 is applied. This pulse must be applied for sufficient time to perform any transition between states |1⟩ and |2⟩ if the electron is in one of these states, or between |3⟩ and |4⟩ if the electron is in one of those states. The mapping defined in Equation (4) corresponds to a single qubit operation on the second qubit. If a single qubit operation is required in the first qubit, the same argument may be followed for frequencies ω1→2 = ω3→4, which will allow the first qubit to be arbitrarily controlled. Though the above setup will only work for frequencies that are pairwise degenerate, the technique may be slightly modified to accompany non-degenerate states, providing those transitions are allowed by the selection rules and that all frequencies are sufficiently detuned. The modification is implemented to perform two pulses in succession; the detuned pulse will not affect the electron, while the resonant pulse will perform the desired rotation.
For the two-qubit case, based on Equation (4), and considering the rightmost logical qubit to be the controlled qubit, the required transitions for the CNOT gate at the physical representation are: Technologies 2022, 10, 1
of 10
If ω 3→4 is sufficiently detuned from any other transition frequency, a π Rabi pulse with this resonance will perform the desired transition.
Results
To establish the validity of the approach, we exhibited the dynamics of the system using the IBM Armonk, a single qubit quantum computer developed by IBM that can be accessed via the Qiskit SDK [5]. For the purpose of this work, encoded four quantum states into the physical states of Armonk's single qubit. Though Armonk provides its own set of single qubit gates, we drove it using custom-made pulses, making use of its higher energy states. The possibility of using higher energy levels of a transmon system has already been studied in [19], where the authors proved, by studying decoherence and decay times for π pulses used for consecutive excitation frequencies, that higher excited states could be used for computation.
In this work, for our proposed mapping, treated two separate cases: (a) Single qubit operations and (b) two-qubit operations
Single Qubit Operations
Single qubit operations involve the generation of pulses that, when applied to the system, alter only one of the qubits in the logical space. In a similar fashion, with the encoding of multiple qubit states in the charge degree of freedom of the electron of an impurity atom embedded in semiconductor material explained in Section 2, let us consider energy states |0 , |1 , |2 , |3 of Armonk's single qubit and follow a similar mapping, as in Equation (4): We investigated how we can create pulses that, when performed at the level of physical qubits, isolate qubits at the logical level. Taking the logical ground state |00 L for example, creating a superposition of equal probabilities for the first qubit will take the state to 1 √ 2 (|00 L + |01 L ), which, as can be seen by Equation (7), is equivalent to the physical state 1 √ 2 (|0 Armonk + |1 Armonk ). To drive this, we needed to create a pi/2 pulse between the ground and the first excited state of the physical qubit. This was achieved using IBM's Quantum Experience Aer library [5]. Briefly, the steps followed were:
1.
Calibration of the qubit to derive the transition frequency.
2.
Derivation of the characteristics of the pi Rabi pulse.
3.
Confirmation of the Rabi pulse by applying it to the ground state of Armonk's qubit.
4.
Clustering the samples of the measured results and an equivalent number of ground states to derive the mean values around the ground and first excited states.
5.
Based on the characteristics of the Rabi pulse derived in Step 3, define a pi/2 pulse with half the amplitude of the original Rabi pulse used to perform a full flip. 6.
Drive the Armonk's qubit originally set to the ground state, with the pulse derived at Section 3.1 and measure the results. Figures 3 and 4 show a scatter plot with the results obtained by performing the above steps in Armonk's qubit 1024 times. The two black dots correspond to the mean values of the ground and first excited states, as these were derived at Step 4 after calibrating the qubit. It can be seen that our results are roughly equally separated between the ground and first excited state, as was expected from the mappings discussed above. Drive the Armonk's qubit originally set to the ground state, with the pulse derived at Section 3.1 and measure the results. Figures 3 and 4 show a scatter plot with the results obtained by performing the above steps in Armonk's qubit 1024 times. The two black dots correspond to the mean values of the ground and first excited states, as these were derived at Step 4 after calibrating the qubit. It can be seen that our results are roughly equally separated between the ground and first excited state, as was expected from the mappings discussed above.
6.
Drive the Armonk's qubit originally set to the ground state, with the pulse derived at Section 3.1 and measure the results. Figures 3 and 4 show a scatter plot with the results obtained by performing the above steps in Armonk's qubit 1024 times. The two black dots correspond to the mean values of the ground and first excited states, as these were derived at Step 4 after calibrating the qubit. It can be seen that our results are roughly equally separated between the ground and first excited state, as was expected from the mappings discussed above. Although the above discussion depicts the feasibility of isolating qubits at the logical level, for a general single qubit gate, the full truth table should be taken into account when constructing pulses. The truth table of the Hadamard Gate, for example, when considering both states of the logical qubit that does not take part in the computation, can be summarized as: Therefore, it is necessary to also consider the higher energy states when constructing a full Hadamard Gate. Following the same approach as before, we constructed a pi/2 pulse between Armonk's higher energy states of |2 and |3 . Section 3.2 discusses how to construct such pulses, as these are needed for the two-qubit operations with the mappings used. Assuming that the pulses used to drive transitions between |0 and |1 , and between |2 and |3 are sufficiently detuned, as is the case for a correctly calibrated qubit, a combined pulse that consists of pi/2 pulses for each one of the transitions will be able to create superpositions of the first logical qubits, regardless of the state of the other qubit.
Two-Qubit Operations
Recalling the discussion in Section 3.1 and applying it to the Armonk qubit, the correspondence between logical and physical states for the CNOT Gate can be summarized as: It is thus sufficient to construct a pulse that performs a flip between states |2 and |3 of the Armonk's qubit. Unfortunately, there is no direct way of exciting higher energy states from the ground state of Armonk's qubit due to the limitations of maximum pulse power. To overcome this, we used the first excited state (which can be reached by applying a pi pulse to the ground state in a similar fashion as explained in Section 3.1) and then applied a sideband to this base pulse. We then gauged the qubit for a response and retrieved the candidate frequency for the 1→2 transition. After this, we can fully calibrated the other characteristics of the transition pulse (e.g., amplitude) following the same procedure as in Section 3.1. The definition of the 2→3 pulse followed the same rules; we excited the state from 0 to 1 and then to 2, after this, we applied another sideband to find the transition frequency of 2→3. Figure 5 depicts the definition of the sweeping pulse (main plus sideband) for the 1→2 transition. In contrast, Figure 6 depicts the measured signal for each of the test frequencies. For this particular experiment, the first two extrema, centered at around 2.63 GHz, were considered for constructing and testing the Rabi pulse for the transition. It is to be noted that, as the level of the excited state grows, experiments may become less reliable and dependent upon the calibration status of the system. However, they can be used to depict that, in principle, higher-level energy states can be used to perform encodings involving multiple logical quantum states.
Concerning the error propagation, we can estimate that each transition required induces an error that is of the order of the error for the Pauli X Gate of the architecture. For the Armonk quantum computer, this is equal to 3.27 × 10 -4 A single logical qubit operation requires two such pulses, whereas the controlled operation requires only one. Assuming It is to be noted that, as the level of the excited state grows, experiments may become less reliable and dependent upon the calibration status of the system. However, they can be used to depict that, in principle, higher-level energy states can be used to perform encodings involving multiple logical quantum states.
Concerning the error propagation, we can estimate that each transition required induces an error that is of the order of the error for the Pauli X Gate of the architecture. For the Armonk quantum computer, this is equal to 3.27 × 10 −4 A single logical qubit operation requires two such pulses, whereas the controlled operation requires only one. Assuming accumulative error and no extra error correction between the steps of computation, Table 1. depicts the total number of gates supported to achieve a computation with an accumulated error of less than 10%. It should be noted as the scaling factor increases (more logical qubit states are encoded into distinct energy levels), operations will involve more pulses, thereby further decreasing the circuit depth.
Discussion
In this paper, we investigated the possibility of using multiple energy states to densely encode logical qubit states. We pointed out a possible physical system where this architecture can be implemented; this consists of a semiconductor device embedded with impurities. These systems are generally robust enough to introduce multiple energy bands, as these can be controlled by the number and types of impurities. We finally demonstrated the physical possibility of manipulating such states by encoding a two-qubit register into the first four energy states of IBM's single qubit computer Armonk, and constructing specific pulses consistent with the logical truth tables of the quantum Hadamard and Controlled NOT gates. One interesting feature that was observed was the fact that for quantum gates that involve more than one qubit, the required physical manipulation was less complex than that required for the single qubit case. This behavior is to be expected, as altering the physical state of the underlying physical qubit may induce changes to multiple logical basis states. In principle, the more constraining the logical operation is (e.g., CNOT), the less manipulation of energy levels it will require.
Scaling the above schema to more dense coding is straightforward; however, the physical limitation may put an upper bound in the number of states encoded by a single physical system, with the exact bound being dependent on the underlying architecture. One limitation is the energy separation. Although we can, in theory, envisage introducing multiple controllable energy states for donor atoms, there is a limit where separating these states may become practically impossible. Another limitation is the number of pulses needed to perform quantum logical gates, which scales up as the number of logical quantum states that are encoded into the energy spectrum increases. For the case equal to two that was studied in the present work, we needed two pulses for single-qubit gates and one pulse for two-qubit gates; it is straightforward to see that for the mapping of a three logical state, we would need three pulses of a single-qubit gate, two pulses of a two-qubit case and we could perform a three-qubit case (e.g., Toffoli gate) with a single pulse. In general, the amount of single-system pulses grows linearly with the amount of qubits encoded. The extent to which our approach is efficient depends on the parameters of the underlying architecture. For example, for the transmon case, the Belem backend of IBM has an average error of an X gate equal to~2.5 × 10 −4 , while that of the CNOT is~1 × 10 −4 . The relaxation and dephasing times are equal to~75 us and~90 us respectively. Though these parameters are computed for the base case, where only the ground and first excited state are used and, therefore, need experimental re-evaluation for the case of higher excited states used in our work, it can be seen that in first-order, they hint that the number of single-qubit operations that can be performed before the error accumulated is comparable to that of the controlled case, is in the order of~100.
It should be noted that even with systems specifically designed to accommodate higher energy levels into the computation, it cannot realistically be expected that a complete circuit that is of a size sufficient to perform useful computation can be performed in its entirety in the energy spectrum of a physical system. By separating qubits into logical groups, within which only single system pulses are needed, we expect that the overall number of controlled pulses will be significantly reduced. Nevertheless, physical coupling operations will still be required to perform logical controlled operations between qubits that belong to different groups. Future work will focus on handling these issues by introducing couplings between neighboring physical systems; proof of the concept is being developed using Belem, a 5-qubit backend provided by IBM, with the aim of using the results to expand the semiconductor model. Funding: This research received no external funding. Data Availability Statement: All data are available to any researcher upon request.
Conflicts of Interest:
The authors declare no conflict of interest. | 6,930 | 2021-12-22T00:00:00.000 | [
"Physics",
"Computer Science"
] |
Chitosan Scaffolds as Microcarriers for Dynamic Culture of Human Neural Stem Cells
Human neural stem cells (hNSCs) possess remarkable potential for regenerative medicine in the treatment of presently incurable diseases. However, a key challenge lies in producing sufficient quantities of hNSCs, which is necessary for effective treatment. Dynamic culture systems are recognized as a powerful approach to producing large quantities of hNSCs required, where microcarriers play a critical role in supporting cell expansion. Nevertheless, the currently available microcarriers have limitations, including a lack of appropriate surface chemistry to promote cell adhesion, inadequate mechanical properties to protect cells from dynamic forces, and poor suitability for mass production. Here, we present the development of three-dimensional (3D) chitosan scaffolds as microcarriers for hNSC expansion under defined conditions in bioreactors. We demonstrate that chitosan scaffolds with a concentration of 4 wt% (4CS scaffolds) exhibit desirable microstructural characteristics and mechanical properties suited for hNSC expansion. Furthermore, they could also withstand degradation in dynamic conditions. The 4CS scaffold condition yields optimal metabolic activity, cell adhesion, and protein expression, enabling sustained hNSC expansion for up to three weeks in a dynamic culture. Our study introduces an effective microcarrier approach for prolonged expansion of hNSCs, which has the potential for mass production in a three-dimensional setting.
Introduction
The demand for human neural stem cells (hNSCs) is substantial in the fields of regenerative medicine and pharmacological development. These versatile cells play a crucial role in medical research and the treatment of challenging diseases such as Alzheimer's disease, Parkinson's disease, amyotrophic lateral sclerosis, Huntington's disease, and spinal cord injury [1,2]. These stem-cell based applications require the administration of tens of millions of purified cells for each patient. hNSCs are commonly grown on 2D plastic cultureware [3,4]. However, conventional 2D culture systems, commonly employed in hNSC growth, have limitations. These include restricted cell productivity due to limited growth area, the absence of microenvironmental cues resembling native tissues, and noncompliance with current good manufacturing practices (cGMP) guidelines, making mass production challenging and costly. As such, researchers have explored the utilization of three-dimensional (3D) culture systems for production of stem cells such as induced pluripotent stem cells (iPSCs), embryonic stem cells (ESCs), and mesenchymal stem cells to address these limitations and better mimic in vivo conditions [5,6].
Despite extensive investigations into 3D culture systems, [7,8], customized technologies specifically targeting the long-term, large-scale production of hNSCs in these settings are yet to be explored. One of the primary obstacles encountered in the 3D production of stem cells is necrosis, primarily caused by the formation of stagnant zones in the system and the presence of large cell clusters. To address these challenges, dynamic culture conditions, those commonly found in bioreactors, have been identified as an effective Unlike collagen, chitosan does not harbor zoonotic pathogens, and the purification process removes allergenic crustacean proteins, minimizing the risk of allergic reactions in humans [43]. The cationic nature of chitosan along with its structural similarity to glycosaminoglycans enables mammalian cells to adhere to it effectively [36]. Additionally, chitosan exhibits a balanced hydrophilic-hydrophobic nature and possesses antimicrobial properties. Compared to collagen, chitosan has a higher elastic modulus, making it more suitable for maintaining structural integrity in dynamic cultures [44]. Importantly, chitosan has been proven to be compatible with neural tissue regeneration [45], and it has been incorporated into numerous medical implants for nerve repair [46][47][48].
This study introduces porous chitosan scaffolds constructed and optimized as microcarriers for the expansion of hNSCs in dynamic cultures. The scaffolds were fabricated through lyophilization using solutions with varying concentrations of chitosan, with collagen serving as a control. Compression tests and atomic force microscopy (AFM) were conducted to assess the elastic modulus and overall mechanical strength of the scaffolds. The chitosan scaffolds demonstrated excellent stability in the culture medium for a duration of three weeks. By tailoring the pore structure of the scaffolds specific for hNSCs, optimal 3D distribution and infiltration of the cells were achieved while providing protection against shear stress inducted by the dynamic environment. Cell adhesion, proliferation, and multipotency were characterized to identify the most suitable type of scaffolds for culturing hNSCs in a dynamic setting. The study presents these chitosan scaffolds as viable microcarriers capable of scaling up hNSC production in dynamic and well-defined cultures.
Microcarrier Fabrication
All chemicals were purchased from MilliporeSigma (St. Louis, MO, USA) unless otherwise specified. To make chitosan porous scaffolds, chitosan (MW, 50-100 kDa; degree of deacetylation, 95-98%; MarkNature, Fullerton, CA, USA) was dissolved homogeneously in 1 N acetic acid at chitosan concentrations of 0.5 wt% (05CS), 2 wt% (2CS), and 4 wt% (4CS). To make collagen porous scaffolds, collagen was dissolved in 0.5 N acetic acid at 0.5 wt% (05COL). The solutions were cast into a 24-well plate and frozen at −20 • C for 8 h. Then, the frozen scaffolds were lyophilized in a VirTis Virtual Lyophilizer (SP Scientific, Gardiner, NY, USA) for 1-3 days. No crosslinking steps were performed on the scaffolds. The samples were sectioned into 15 mm in diameter and 0.8 mm thickness for cell culture or 3.0 mm thickness for mechanical testing and dried in a desiccator for 24 h. The dried samples were neutralized with a basic solution (NH 4 OH 33% 15 mL, deionized water (DI) 35 mL, ethanol 500 mL) for 30 min and rinsed with DI water to remove ammonia hydroxide and ethanol.
FTIR and 1 H NMR Spectroscopy
FTIR analysis of chitosan and collagen powders was performed using a Nicolet 5DXB spectrometer (Thermo Scientific, Boston, MA, USA). The polymer powders were analyzed by adding the polymer to a KBr powder. The polymer and KBr mixture were then pressed to form a thin film. The films were analyzed by averaging 32 scans at a resolution of 2 cm −1 over a range of 500-4000 cm −1 . 1 H NMR analysis was performed to verify the degree of deacetylation of the chitosan scaffold. Chitosan was first dissolved in 2.5% DCl D 2 O at 10 mg/mL. A 300 MHz spectrometer (Bruker Avance III 300, Billerica, MA, USA) was used to acquire the spectra in triplicates at 25 • C. The degree of deacetylation was determined by calculating the integrals of the protons on the H-Acetyl group and the protons on the H2/H6 group. The following equation was then used to determine the degree of deacetylation: where DD (%) is the degree of deacetylation in percent, I H-Acetyl is the integral of the protons on the acetylated group, and I H2/H6 is the integral of the protons on the monomer hexose rings.
Microstructure Characterization
The microstructure of dry scaffolds was examined using scanning electron microscopy (SEM). To prepare SEM samples, the scaffolds underwent a series of steps. First, they were neutralized with water and ammonia hydroxide. Then, the scaffolds were sterilized with ethanol. Subsequently, the scaffolds were dried under vacuum conditions. The dried scaffolds were mounted on a carbon-conductive adhesive tape (NEM Tape, Nisshin EM. Co., Ltd. Tokyo, Japan). These were imaged at 5 kV using a TM3000 tabletop SEM (Hitachi High-Tech Corporation, Tokyo, Japan). From SEM images, pore diameters were calculated with ImageJ software Version 1.53k (NIH, Bethesda, MD, USA).
The porosity of scaffolds was measured using a modified isopropanol displacement method. The dry scaffold volume (V, cm 3 ) and weight (W 1 , g) were measured as follows. The scaffolds were fully immersed in 5 mL of isopropanol (ρ s , 0.786 g/cm 3 ) under vacuum for 15 min to expel air from the pores. Saturated scaffolds were weighed (W 2 , g) immediately upon removal from isopropanol bath. The volume of the scaffolds did not change after isopropanol saturation. Porosity (%) was defined as the ratio of the volume of isopropanol absorbed by the scaffolds to the volume of the scaffold and calculated as follows (n = 10): where V is the volume of the dry scaffold, W 2 is the weight after removal from the isopropanol bath, W 1 is the initial weight of the scaffold, and ρ s is the density of isopropanol. The specific surface area of the scaffold was measured using the multipoint Brunauer-Emmett-Teller (BET) method in NOVA 4200e (Quantachrome Instruments, Boyton Beach, FL, USA). The scaffold was prepared and freeze dried again after the final wash. The dry scaffold was degassed at 50 • C for 12 h. Then, with nitrogen as the adsorbate, isotherms were acquired at 77 K. A multipoint BET was then performed on the isotherms to determine the specific surface area of each scaffold.
Mechanical Property
Uniaxial compression tests were carried out to understand the macromechanical properties of the scaffolds using an Autograph Table-TOP Precision Universal Tester AGS-X (SHIMADZU CORPORATION, Kyoto, Japan) at room temperature. Dry scaffolds were compressed at 0.4 mm/min until at least 40% strain. The compressive Young's moduli of the scaffolds were calculated as the slope of the linear regions of the stress-strain curves within the range of 0-15% strain.
AFM was performed with a Nanosurf FlexAFM (Nanosurf AG, Liestal, Switzerland). A contact AFM probe mode with a spring constant of 0.2 N/m and resonance frequency of 13 kHz was used to obtain the elastic moduli of the scaffolds immersed in PBS.
Degradation Test
The stability of the scaffolds was investigated by testing their degradation. Dry scaffolds were incubated in an Orbital Shaker PSU-10i (SIA Biosan, Riga, Latvia) with 37 • C Neurobasal medium at 100 rpm. After 7, 14, and 21 days of incubation, the samples were removed, rinsed with distilled water, and lyophilized. The remaining mass (%) of each scaffold after the incubation relative to the initial weight was calculated to assess the degradation. protocol, the cells were cultured as monolayers on Geltrex-coated tissue culture dishes, and fresh media were supplied every other day. Human recombinant basic fibroblast growth factor (bFGF, Gibco ® , Thermo Fisher Scientific, Waltham, MA, USA) and epidermal growth factor (EGF) were supplied daily at 20 ng/mL. The hNSC culture medium comprised a Neurobasal medium (Gibco ® ) supplemented with B 27, N2, MEM NEAA, heparin, and GlutaMAX. hNSCs were passaged every 3-5 days and dissociated with Accutase after reaching 90% confluency.
ReNcell VM was obtained from MillporeSigma (St. Louis, MO, USA). Following the manufacturer's protocol, the cells were cultured as monolayers on laminin (CC095-M, MillporeSigma)-coated culture dishes. Fresh medium (SCM005, MilliporeSigma), bFGF, and EGF at 20 ng/mL were supplied every other day. The cells were passaged every 3-5 days and dissociated with Accutase after reaching 80% confluency. All cells were incubated in a humidified incubator containing 5% CO 2 at 37 • C.
Cell Proliferation in a Rotational Bioreactor as a Dynamic Culture
One day after cell inoculation, scaffolds with hNSCs were transferred to a 15 mL flat-bottomed tube containing 1 mL of medium per two scaffolds. The samples were shaken at 65 rpm on an orbital shaker in the following culture period.
Cell proliferation was assessed by an alamarBlue assay (MilliporeSigma) after 3, 5, 7, 11, and 15 days of culture. The scaffolds were transferred to a 24-well plate and gently rinsed with PBS. The medium was replaced with alamarBlue reagent (11 µg/mL resazurin in culture medium). After incubation at 37 • C for 2 h, all solutions were transferred to 96-well black well plates to measure the fluorescence intensity at 590 nm with excitation at 560 nm using a SpectraMax M2 microplate reader (Molecular Devices LLC, San Jose, CA, USA).
Cell morphology and viability were monitored using a LIVE/DEAD TM Viability/Cytotoxicity Kit (Invitrogen Corporation, Waltham, MA, USA), following the manufacturer's protocol. Briefly, viable cells were stained with 1 µM calcein-AM, while dead cells were stained with 4 µM ethidium homodiemer-1 in a 1:1 mixture of culture medium and phosphate buffered solution for 15-30 min. The scaffolds were imaged using a Nikon TE300 inverted microscope (NIKON CORPORATION, Tokyo, Japan).
Flow Cytometry
Single cell suspensions were collected from the scaffolds. A fixable yellow dead stain kit (Invitrogen) was used to identify dead cells. The cells were fixed with 4% paraformaldehyde for 10 min on ice, permeabilized in 1% v/v Triton-X 100, washed with PhosFlow Perm/Wash Buffer I (BD Biosciences, San Jose, CA, USA), and resuspended in a buffer. Antibodies PE anti-nestin (BDB561230), PerCP-Cy5.5 anti-SOX1 (BDB561549), Alexa Fluor 647 anti-SOX2 (BDB560302), and Alexa Flour 488 anti-PAX6 (BD561664) were added, incubated on ice for 1 h, and washed with a buffer. The cells were resuspended in 200 µL of buffer and stained with DAPI. All samples were analyzed on a LSRII flow cytometer (BD Biosciences), and the data were plotted using FlowJo software Version 9.9.4 (Tree Star Inc., Ashland, OR, USA).
Immunocytochemistry for NSC Marker Proteins
Human neural stem cell ICC kits (Cat. A24354, Thermo Fisher Scientific) were used, following the manufacturer's instructions. Briefly, scaffolds bearing the cells were rinsed with PBS, fixed with cold 4% paraformaldehyde on ice for 10 min, permeabilized for 10 min, blocked for 1 h, and stained with SOX2 and nestin primary antibody overnight at 4 • C. Secondary antibodies, Alexa Fluor 488 and 555, were added to the scaffolds the next day and the scaffolds were incubated for 1-2 h on ice, washed thrice with PBS, stained with DAPI, and mounted in a ProLong Gold anti-fade reagent (Thermo Fisher Scientific). Fluorescence images were acquired using a Nikon TE 300 inverted microscope.
Statistical Analysis
All results are presented as the mean ± standard deviation (SD). Statistical significance was determined using one-way analysis of variance with Tukey's multiple comparison test. Significant differences were set at p-value < 0.05.
Development of Porous Microcarriers for hNSC Expansion in a Defined Environment Condition
Four main culture modes commonly employed in bioreactors are nonadherent (matrixfree) suspension, aggregate suspension, adherent nonporous microcarriers, and adherent porous microcarriers ( Figure 1). The utilization of microcarriers in adherent cultures allows for cell adhesion on controlled growth surfaces in dynamic culture conditions. The surface characteristics and microstructure of microcarriers play critical roles in cell quality and yield. In comparison to nonporous microcarriers, the porous design provides the largest growth surface area per volume and desirable interior porous structure to protect cells from shear stress. Therefore, we fabricated porous scaffolds made of chitosan to serve as microcarriers for the expansion of hNSCs in a rotational dynamic bioreactor platform. Chitosan scaffolds with varying weight percentages were utilized to investigate the influence of structural and mechanical properties on cell fate under dynamic conditions. Collagen was used as a control sample due to its well-established role as a scaffold material in tissue engineering [49][50][51]. Although both chitosan and collagen have been applied in various tissue culture substrates, including neural tissues, they possess distinct physical properties and bioactivities on hNSCs [51][52][53][54][55][56].
Scaffold Microstructure Analysis
The microstructure of the scaffolds plays a crucial role in facilitating nutrient cycling and metabolite exchange. To achieve the desired porous structure, the scaffolds were prepared through lyophilization, which involves phase separation during freezing and subsequent sublimation of the solvent. Precise control of nucleation and freezing solvent was employed to establish the desired porosity. Chitosan or collagen was mixed with KBr to form a pellet before FTIR analysis, while chitosan was dissolved in DCl/D2O for 1 H NMR analysis. The FTIR spectra of chitosan and collagen are shown in Figure 2a and Figure 2b, respectively, and exhibited good agreement with those reported previously [57,58]. The 1 H-NMR spectrum of chitosan, obtained at 300 MHz, 2.5% DCl/D2O, 25 °C, displayed the
Scaffold Microstructure Analysis
The microstructure of the scaffolds plays a crucial role in facilitating nutrient cycling and metabolite exchange. To achieve the desired porous structure, the scaffolds were prepared through lyophilization, which involves phase separation during freezing and subsequent sublimation of the solvent. Precise control of nucleation and freezing solvent was employed to establish the desired porosity. Chitosan or collagen was mixed with KBr to form a pellet before FTIR analysis, while chitosan was dissolved in DCl/D 2 O for 1 H Pharmaceutics 2023, 15,1957 7 of 17 NMR analysis. The FTIR spectra of chitosan and collagen are shown in Figures 2a and 2b, respectively, and exhibited good agreement with those reported previously [57,58]. The 1 H-NMR spectrum of chitosan, obtained at 300 MHz, 2.5% DCl/D 2 Figure 2c. The degree of deacetylation was calculated to be 97% using Equation (1), which falls within the range provided by the supplier [59,60]. Following lyophilization, the scaffolds were mounted on stubs using carbon adhesive tape for imaging purposes. ImageJ software was utilized for manual measurement of pore diameters. Figure 3a presents SEM images displaying the cross-sections of various scaffolds, including 0.5 wt% collagen (05COL), 0.5 wt% chitosan (05CS), 2 wt% chitosan (2CS), and 4 wt% chitosan (4CS). Lower polymer concentrations resulted in visibly larger interconnected pores. Pore size analysis was performed by measuring the pore diameters from SEM images (Figure 3b). The average pore diameter for 05COL scaffolds was 289 ± 67 µm, similar to commercially available collagen scaffolds [61]. The selected collagen concentration of 0.5 wt% aligns with that in previous studies [62][63][64]. On the other hand, 05CS scaffolds exhibited an average pore diameter of 214 ± 48 µm, significantly different from that of 05COL scaffolds. As chitosan concentration increased, pore diameter decreased, with average values of 85 ± 17 µm and 65 ± 13 µm for 2CS and 4CS scaffolds, respectively. All scaffolds possessed pore diameters suitable for stem cell growth [65], particularly hNSCs [36], providing ample internal surface area for cell proliferation. Moreover, the small pore sizes could limit the growth of hNSC clusters, mechanically preventing the formation of necrotic cores and aiding in the long-term culture and maintenance of hNSCs.
Scaffold porosity was determined using a modified isopropanol displacement method. Briefly, the scaffolds were immersed in isopropanol and subjected to a vacuum Following lyophilization, the scaffolds were mounted on stubs using carbon adhesive tape for imaging purposes. ImageJ software was utilized for manual measurement of pore diameters. Figure 3a presents SEM images displaying the cross-sections of various scaffolds, including 0.5 wt% collagen (05COL), 0.5 wt% chitosan (05CS), 2 wt% chitosan (2CS), and 4 wt% chitosan (4CS). Lower polymer concentrations resulted in visibly larger interconnected pores. Pore size analysis was performed by measuring the pore diameters from SEM images (Figure 3b). The average pore diameter for 05COL scaffolds was 289 ± 67 µm, similar to commercially available collagen scaffolds [61]. The selected collagen concentration of 0.5 wt% aligns with that in previous studies [62][63][64]. On the other hand, 05CS scaffolds exhibited an average pore diameter of 214 ± 48 µm, significantly different from that of 05COL scaffolds. As chitosan concentration increased, pore diameter decreased, with average values of 85 ± 17 µm and 65 ± 13 µm for 2CS and 4CS scaffolds, respectively. All scaffolds possessed pore diameters suitable for stem cell growth [65], par-Pharmaceutics 2023, 15, 1957 8 of 17 ticularly hNSCs [36], providing ample internal surface area for cell proliferation. Moreover, the small pore sizes could limit the growth of hNSC clusters, mechanically preventing the formation of necrotic cores and aiding in the long-term culture and maintenance of hNSCs.
concentrations promote inter-and intramolecular interactions, resulting in red noscale interaction of polymer chains, which leads to lower material specific a nanoscale level and lower porosity in 05CS scaffolds compared to those in 05C folds.
The microstructure analyses confirmed that the scaffolds met the structura ments of microcarriers, with highly interconnected pores possessing appropria ters to retain media, facilitate nutrient exchange, and provide a larger growth a pared to those of 2D flat surfaces. These characteristics make the scaffolds well-s their intended purpose of supporting hNSC expansion in a dynamic culture envi
Mechanical Properties of the Scaffolds
To understand the microenvironment provided by the scaffolds, their pot fluence on cell mechanosensing, and their ability to withstand agitation in dyn tures, a detailed analysis of their mechanical properties was conducted. This an compassed both dry scaffolds and those soaked in PBS. The compressive elasti (Figure 4a) of dry chitosan scaffolds exhibited an increasing trend from 4.1 ± 0 284.5 ± 22.9 kPa and 681.9 ± 43.0 kPa, corresponding to the increasing chitosan c tion of 05CS, 2CS, and 4CS, respectively. Dry collagen scaffolds possessed a com elastic modulus of 10.0 ± 0.008 kPa. Considering that the cell culture was condu medium while the scaffolds were hydrated, compression tests were also perfo "wet" scaffolds. In the hydrated state, the elastic moduli were 1.2 ± 0.4 kPa, 7.4 All data are presented as the mean ± SD. Statistical significance, indicated by *, was determined using Tukey's test (p < 0.05).
Scaffold porosity was determined using a modified isopropanol displacement method. Briefly, the scaffolds were immersed in isopropanol and subjected to a vacuum to remove air bubbles. Weight measurements were recorded before and after submersion. Porosity (Figure 3c) decreased from 92.0% ± 1.2% to 86.2% ± 2.6% as chitosan concentration increased from 0.5% to 4%. The porosity of 05COL scaffolds was comparable to that of 05CS scaffolds at 92.3% ± 1.4% (p > 0.05, not significant). Additionally, specific surface area analysis using BET (Figure 3d) revealed an increase in specific surface area with higher chitosan concentrations: 15.34 ± 2.66 m 2 /g, 12.2 ± 1.41 m 2 /g, and 5.4 ± 1.89 m 2 /g for 05CS, 2CS, and 4CS scaffolds, respectively. Porosity and surface area measurements account for the overall properties of the scaffold, encompassing both the internal intermolecular structures and the visible macropores (50-350 µm in diameter). Collagen and chitosan, being relatively hydrophilic materials, can form nanoscale crystals during freezing and leave voids after sublimation due to solvent (water) bonding in intermolecular spaces. The formation of intermolecular bonds via hydrophobic interactions and hydrogen bonding is more likely in chitosan than in collagen. Chitosan with a high uniform degree of deacetylation is known to exhibit higher crystallinity upon drying [66]. Higher polymer concentrations promote inter-and intramolecular interactions, resulting in reduced nanoscale interaction of polymer chains, which leads to lower material specific area at the nanoscale level and lower porosity in 05CS scaffolds compared to those in 05COL scaffolds.
The microstructure analyses confirmed that the scaffolds met the structural requirements of microcarriers, with highly interconnected pores possessing appropriate diameters to retain media, facilitate nutrient exchange, and provide a larger growth area compared to those of 2D flat surfaces. These characteristics make the scaffolds well-suited for their intended purpose of supporting hNSC expansion in a dynamic culture environment.
Mechanical Properties of the Scaffolds
To understand the microenvironment provided by the scaffolds, their potential influence on cell mechanosensing, and their ability to withstand agitation in dynamic cultures, a detailed analysis of their mechanical properties was conducted. This analysis encompassed both dry scaffolds and those soaked in PBS. The compressive elastic moduli (Figure 4a) of dry chitosan scaffolds exhibited an increasing trend from 4.1 ± 0.9 kPa to 284.5 ± 22.9 kPa and 681.9 ± 43.0 kPa, corresponding to the increasing chitosan concentration of 05CS, 2CS, and 4CS, respectively. Dry collagen scaffolds possessed a compressive elastic modulus of 10.0 ± 0.008 kPa. Considering that the cell culture was conducted in a medium while the scaffolds were hydrated, compression tests were also performed on "wet" scaffolds. In the hydrated state, the elastic moduli were 1.2 ± 0.4 kPa, 7.4 ± 0.7 kPa, and 71.2 ± 9.3 kPa for 05CS, 2CS, and 4CS scaffolds, respectively. However, wet 05COL scaffolds could not be evaluated through compression tests as they became excessively soft upon hydration. The elastic moduli of both dry and wet 2CS and 4CS scaffolds were higher than those of dry collagen scaffolds [36]. Representative stress-strain curves of compression tests are presented in Figure 4b, demonstrating an increase in ultimate compressive strength with a higher chitosan concentration. These results suggest that chitosan scaffolds may serve as superior protective structures for hNSCs compared to collagen scaffolds in dynamic cultures where microcarriers endure compression and shear forces. To evaluate the micro-to nanoscale elastic moduli of wet scaffolds, AFM analysis was employed (Figure 4c). This analysis allowed for the characterization of mechanical properties relevant to mechanosensing. While compression tests address macroscale structural integrity and the resistance of pore walls to buckling, AFM tips measure intermolecular attraction and the resistance of chitosan or collagen polymer chains on the interior surface of the pore walls. The 05COL scaffolds exhibited the lowest average elastic modulus (3.7 ± 17.9 kPa), whereas the values for chitosan scaffolds increased from 50.1 ± 123.9 kPa to 83.2 ± 62.3 kPa and 160.9 ± 121.5 kPa as the chitosan concentration increased from 05CS to 2CS and 4CS, respectively. The localized compression, tension, and nano-or microscale features of the substrate play a crucial role in regulating cell fate through cell transmembrane receptors, ultimately influencing cytoskeleton and cell morphology. In our previous study, we investigated the impact of different degrees of deacetylation on the mechanical properties of chitosan films [67]. We found that a higher degree of deacetylation led to a decrease in the elastic modulus of the films. However, we also observed that this higher degree of deacetylation resulted in enhanced cell attachment, proliferation, and multipotency. Furthermore, increasing the molecular weight of chitosan led to an increase in the scaffold's elastic modulus. This effect can be attributed to the entanglement of polymer chains [68].
In the subventricular zone and hippocampal dentate gyrus, where adult hNSC populations reside in humans and rodents, the reported elastic modulus is approximately 3 kPa [69,70]. However, there exists a considerable variation in measurement methods and results. Furthermore, the optimal elastic modulus for hNSC substrates remains uncertain, given the diverse outcomes observed in cell responses to softer substrates despite the success of conventional culture protocols on rigid plasticware. In this study, scaffolds with a wide range of mechanical properties were utilized to better assess the effect of these properties on cell fate. Mechanical properties, choice of materials, and resulting substrate surfaces collectively exert a coherent influence on cell responses.
Stability and Degradation in Culture Medium
Understanding the stability and degradation characteristics of scaffolds is crucial for designing effective tissue engineering strategies. To evaluate the stability of the scaffolds, their weights were monitored over a three-week period in a culture medium under rotation at 37 • C. Both chitosan and collagen have been shown to degrade in vitro and in vivo, with degradation rates depending on the specific conditions. Collagen, a widely used scaffold material, completely degrades after five weeks in a static culture medium [71]. Chitosan, on the other hand, can undergo partial depolymerization through hydrolysis within a few days when subjected to dynamic conditions in a medium [72]. It is worth mentioning that crosslinkers, such as genipin, can be added to the scaffolds to enhance mechanical properties and structural stability; however, they can also increase the autofluorescence of the scaffolds, making it difficult to image the cells [73].
In our study, all the scaffolds produced did not exhibit significant deterioration or degradation over the course of 21 days. Differences in the data may be due to scaffold-toscaffold variability. They maintained over 90% of their weight after this period (Figure 4d). However, the 05COL scaffolds showed more variability and experienced a greater decrease in weight compared to those of the chitosan scaffolds. We expect our scaffolds to perform similarly through prolonged durations; the cells may also leave behind proteins that could adhere to the scaffold walls. These findings indicate that chitosan scaffolds are more durable in dynamic cultures, suggesting their suitability for long-term culture applications.
Maintenance of hNSCs in Dynamic Cultures
We conducted dynamic culture experiments using porous scaffolds as microcarriers to support the growth of two different hNSC lines, namely hNSC-H14 and ReNcell VM. Initially, the cells were seeded onto the scaffolds in static well plates for one day and then transferred into dynamic culture vessels. The growth and proliferation of the cells were assessed using an alamarBlue viability/metabolic activity assay. The metabolic activity of hNSC-H14 and ReNcell in the scaffolds showed different trends (Figure 5a,b). For hNSC-H14, the metabolic activity in chitosan scaffolds showed a slight decrease on day 3 of the culture, followed by consistent increases until day 11. However, it decreased again on day 15, likely due to growth arrest caused by cell confluency. In contrast, cells in the 05COL scaffolds exhibited a modest increase on day 7 and overall limited growth after 15 days compared to those in chitosan scaffolds. As for ReNcell, the metabolic activity steadily increased in all scaffolds and reached its peak on day 11, followed by a decline on day 15, possibly due to confluency related factors. To accommodate longer culture periods, the initial cell seeding density could be decreased. Notably, the 4CS scaffolds demonstrated the highest overall metabolic activity for both hNSC-H14 and ReNcell. Consequently, the 05COL scaffolds exhibited restricted cell adhesion, which likely contributed to poorer activities compared to those in the 4CS scaffolds. Furthermore, the larger pore diameter of the 05COL and 05CS scaffolds might have failed to adequately protect or retain hNSC colonies. initial cell seeding density could be decreased. Notably, the 4CS scaffolds demonstrated the highest overall metabolic activity for both hNSC-H14 and ReNcell. Consequently, the 05COL scaffolds exhibited restricted cell adhesion, which likely contributed to poorer activities compared to those in the 4CS scaffolds. Furthermore, the larger pore diameter of the 05COL and 05CS scaffolds might have failed to adequately protect or retain hNSC colonies. To visualize cell adhesion and proliferation, the scaffolds were stained with calcein-AM and ethidium homodimer-1. Figure 5c illustrates the stained live and dead cells in the scaffolds, focusing on the hNSC-H14 cell line. As the culture progressed, the cells in the chitosan scaffolds exhibited more extensive expansion compared to that in collagen scaffolds. Moreover, the cells in the 4CS scaffolds displayed polarized morphology more frequently than those in the 05COL scaffolds did, suggesting a stronger adhesion to the 4CS scaffolds. Conversely, in the 05COL scaffolds, the cells formed larger clusters due to the To visualize cell adhesion and proliferation, the scaffolds were stained with calcein-AM and ethidium homodimer-1. Figure 5c illustrates the stained live and dead cells in the scaffolds, focusing on the hNSC-H14 cell line. As the culture progressed, the cells in the chitosan scaffolds exhibited more extensive expansion compared to that in collagen scaffolds. Moreover, the cells in the 4CS scaffolds displayed polarized morphology more frequently than those in the 05COL scaffolds did, suggesting a stronger adhesion to the 4CS scaffolds. Conversely, in the 05COL scaffolds, the cells formed larger clusters due to the preference for intercellular adhesion rather than cell-collagen interactions. Previous studies have reported that the increased surface positive charge resulting from the higher amino group content of chitosan promotes cell adhesion [74]. This favorable adhesion to chitosan scaffolds could further enhance cell proliferation [74].
Cells were harvested from the scaffolds over a period of 15 days, fixed, and then prepared for flow cytometry analysis. The multipotency of the cells collected from the microcarriers was assessed by staining for two crucial NSC protein markers, SOX2 and nestin. The time course of the populations positive for SOX2 + /nestin + in both cell lines is depicted in Figure 6a,b. Figure 6c illustrates the cell populations gated for SOX1 + /PAX6 + expression in ReNcells after seven days of culture, representing additional NSC protein markers. The 05COL scaffolds exhibited the highest populations of both SOX2 + /nestin + and SOX1 + /PAX6 + cells, while among the chitosan conditions, the 4CS scaffolds showed the most favorable results. Notably, hNSC-H14 demonstrated the highest percentage of SOX2 + /nestin + population on the 11th day of culture, which correlated with the metabolic activity data. Moreover, the porous scaffolds with large specific surface areas allowed hNSCs to proliferate for a longer duration compared to that with conventional 2D protocols while preserving their proliferative and multipotent state. Typically, in regular 2D culture protocols, hNSCs require passage every 3-5 days upon reaching 90-95% confluency to prevent growth arrest and spontaneous differentiation [75]. The growth kinetics and time course analysis of NSC proteins indicated that, in this study, the cells needed to be detached from the porous chitosan scaffolds before the 11th day of culture to ensure effective expansion of the entire population. However, despite having the narrowest specific surface area and porosity, the 4CS scaffolds achieved the highest yield of hNSCs, suggesting a potential protective effect against shear stress in a bioreactor. Stem cells possess mechanisms to sense mechanical stress, and the flow generated by agitation can induce cell death [75,76]. The higher compressive modulus of the 4CS scaffolds, compared to that of other chitosan scaffolds, may have shielded hNSCs from shear stress under dynamic conditions. Further investigation into longer culture periods, lasting up to three weeks, was conducted. Immunostaining for SOX2 and nestin (Figure 7) revealed that the cells were able to sustain expression of these crucial NSC marker proteins for an extended duration compared to that with regular 2D controls. Over the three-week culture period, hNSCs cultured on 4CS scaffolds formed adherent aggregates within the scaffold pores. SOX2 localization was predominantly observed in the nucleus, although some translocation into the cytoplasm was evident, indicating partial differentiation resulting from overcrowding within the pores. At this stage, some aggregates reached confluency, occupying the pores without exceeding the desired size range of 300-500 µm in diameter to prevent necrosis.
Chitosan has been reported to promote the proliferation and differentiation of neurons and astrocytes [76]. However, its impact on hNSC maintenance has shown inconsistent results. In this study, multipotent hNSC colonies were successfully maintained in chitosan porous scaffolds optimized for use as microcarriers in dynamic cultures for up to three weeks. The chitosan scaffolds demonstrated their feasibility for long-term expansion of hNSCs in bioreactors under xeno-free and chemically defined culture conditions.
Conclusions
In this study, we developed a 3D microcarrier designed to expand hNSCs in dynamic bioreactor culture systems. The microcarrier offers several advantages, such as providing additional growth space and shielding cells from the dynamic environment. Our investigation into the maintenance of hNSCs in dynamic cultures showed that the mechanical properties of the scaffolds, including their compressive elastic moduli and localized micro-to nanoscale elastic moduli, have a crucial impact on cell mechanosensing, structural integrity, and cell fate determination. By utilizing pure chitosan, we successfully achieved xeno-free cultivation of human stem cells suitable for clinical applications. Notably, this
Conclusions
In this study, we developed a 3D microcarrier designed to expand hNSCs in dynamic bioreactor culture systems. The microcarrier offers several advantages, such as providing additional growth space and shielding cells from the dynamic environment. Our investigation into the maintenance of hNSCs in dynamic cultures showed that the mechanical properties of the scaffolds, including their compressive elastic moduli and localized micro-to nanoscale elastic moduli, have a crucial impact on cell mechanosensing, structural integrity, and cell fate determination. By utilizing pure chitosan, we successfully achieved xeno-free cultivation of human stem cells suitable for clinical applications. Notably, this
Conclusions
In this study, we developed a 3D microcarrier designed to expand hNSCs in dynamic bioreactor culture systems. The microcarrier offers several advantages, such as providing additional growth space and shielding cells from the dynamic environment. Our investigation into the maintenance of hNSCs in dynamic cultures showed that the mechanical properties of the scaffolds, including their compressive elastic moduli and localized microto nanoscale elastic moduli, have a crucial impact on cell mechanosensing, structural in-tegrity, and cell fate determination. By utilizing pure chitosan, we successfully achieved xeno-free cultivation of human stem cells suitable for clinical applications. Notably, this is the first study to expand hNSCs using chitosan porous scaffolds in a dynamic culture system. The scaffolds maintained a stable microstructure and demonstrated long-term durability without degradation. The scaffold pores facilitated hNSC adhesion and distribution within a 3D space while possessing appropriate mechanical properties to support undifferentiated proliferation. When compared to collagen scaffolds, the optimized chitosan scaffolds outperformed them in maintaining the proliferation and multipotency of hNSCs. Moreover, the 4CS chitosan scaffolds were the best in supporting hNSCs in terms of proliferation and multipotency and were able to support hNSC expansion for up to three weeks. Overall, this study presents a dynamic bioreactor culture platform utilizing chitosan scaffolds as microcarriers capable of scaling up for hNSC production. | 8,383.2 | 2023-07-01T00:00:00.000 | [
"Biology",
"Engineering"
] |
KERNEL-COMPOSITION FOR CHANGE DETECTION IN MEDIUM RESOLUTION REMOTE SENSING DATA
A framework for multitemporal change detection based on kernel-composition is applied to a multispectral-multitemporal classification scenario, evaluated and compared to traditional change detection approaches. The framework makes use of the fact that images of different points in time can be used as input data sources for kernel-composition a data fusion approach typically used with kernel based classifiers like support vector machines (SVM). The framework is used to analyze the growth of a limestone pit in the Upper Rhine Graben (West Germany). Results indicate that the highest accuracy rates are produced by the kernel based framework. The approach produces the least number of false positives and gives the most convincing overall impression.
INTRODUCTION
Although the availability of modern remote sensing datasets increases -e.g.hyperspectral, high resolution optical satellite imagery, interferometric synthetic aperture radar -many change detection applications continue to require traditional datasets.The fact that e.g.Landsat data are available since 1972 makes them a valuable source of information for four entire decades.They can be seen as a way to recover information on past environmental conditions which are not observable any more by field campaigns.However, traditional methods like post-classification change detection based on overlaying classification maps raise accuracy issues (Serra et al., 2003).Therefore, more sophisticated change detection methods have been proposed in literature.Some approaches model the probability of transition from one class to another.Another approach is change detection based on kernel-composition (Camps-Valls et al., 2006b).These issues are exemplified on a change detection application from Upper Rhine Graben.Changes in the landuse are outlined with special focus on the construction of a limestone pit which continuously grows replacing near-natural ecosystems.Kernel based classifiers -like the well know support vector machine (SVM) (Boser et al., 1992), (Cortes and Vapnik, 1995) -work on kernel matrices.These kernel matrices represent the similarity between data points in high dimensional feature spaces (reproducing kernel Hilbert spaces, RKHS).The SVM chooses the most suitable points by optimizing a target function on the kernel choosing only a few training data points as SVs.These points are used to define a separating hyperplane which is usually non-linear in the input space.The conceptual advantage of kernel-composition is, that different kernel functions can by combined e.g. by addition, thus performing data fusion in the RKHS during classification.This circumstance is usually employed for data fusion (Tuia and Camps-Valls, 2009).However, it can also be employed for change detection.In (Camps-Valls et al., 2008), (Camps-Valls et al., 2006a) well know change detection techniques -like image differencing -are adapted for kernel-composition based approaches.An entire framework for change detection and multitemporal classification is presented.This framework is evalu-
MATHEMATICAL FOUNDATIONS
Within this section, the mathematical foundations of the main methods used will be given.A high number of profound introductions into the SVM problem (Burges, 1998), (Ivanciuc, 2007), (Zhang, 2001), (Schölkopf and Smola, 2002), (Camps-Valls and Bruzzone, 2009) and valuable reviews on the application of SVM in remote sensing (Mountrakis et al., 2010), (Plaza et al., 2009) have been published.For this reason, the foundations of SVM and state-of-the-art application examples will not be given exhaustively, but strictly focused on the kernel-composition problem.
Kernel matrices and the SVM problem
Given a data set X with n data points, kernel matrices are the result of kernel functions applied over all n 2 tupels of data (Shawe-Taylor and Cristianini, 2004).The outcome of a kernel function Kx i ,x j = f δ (xi, xj) is a similarity measure for the two training data xi and xj depending on some distance metric δ.Usually, δ is the Euclidean distance (Mercier and Lennon, 2003).However, kernel functions can be modified by e.g. by introducing different similarity measures (Amari and Wu, 1999).For instance, (Mercier and Lennon, 2003) and (Honeine and Richard, 2010) use the spectral angle as a similarity measure for hyperspectral SVM classification.To model complex distributions of the training data in the feature space, f δ is usually some nonlinear function.The most frequently applied family of non-linear functions are Gaussian radial basis functions (RBF) (Schölkopf et al., 1997).The closer two points are found in the feature space, the higher is their resulting kernel value.Given these facts, the kernel matrix simply represents the similarity between the points of the training data set.To understand how the kernel matrix is used in SVM classification, it is helpful not to look at the primal, but the dual formulation of the SVM problem (Ivanciuc, 2007).
The dual problem is given by Eq.1 The Lagrange multipliers λi are only greater than zero for the support vectors.These are usually identified by sequential minimal optimization (Platt, 1998).Hence, only training data which are both SVs contribute to the solution of Eq.1 (for all other cases, λiλj = 0 setting the second part of Eq.1 to zero).The class labels yi are in [−1, 1].Since the second part of Eq.1 is subtracted, only points with different class labels can maximize the term (their product yiyj = −1 renders the second part positive).
The problem is therefore maximized, if points are chosen as SVs which have different class labels but are found close to each other in the feature space (thus yielding a high value in the kernel matrix K(xi, xj)).Thus, the similarity values of the kernel matrix are used for finding the best suited training points as SVs.By setting the λi of all other points to zero, a sparse solution is found which only depends on the SVs.
Kernel-Composition
As can be seen in Eq.1, the training data xi do not enter directly into the SVM problem.In contrast, the data are represented by kernels K(xi, xj).According to Mercer's theorem (Mercer, 1909), valid kernel functions can be combined, e.g. through addition, to form new valid kernels.From there, different sources of information on the same training data can be fused through simple arithmetical operations (Camps-Valls et al., 2006b).For instance, KC ) fuses the information domains A and B on the training data xi, xj and forms a new kernel KC .Within the original framework on kernel-composition for data fusion (Camps-Valls et al., 2006b), the following fusion approaches are published.
Eq.2 is called direct summation kernel, the most simple form of kernel-composition.Eq.3 is called weighted summation kernel.Its main advantage is, that the weighting parameter µ ∈ (0, 1) allows to regulate the relevance of the two data sources A and B for the classification problem.Eq.4 is called the crossinformation kernel.It consist of four single kernels while the last two KAB and KBA allow incorporating the mutual information between the data sources A and B (e.g.differences between the value of both data sources yielded for a particular data point).
Based on these basic composition approaches (Camps-Valls et al., 2008), (Camps-Valls et al., 2006a) extend the kernel-composition framework to the field of multitemporal classification and change detection.The key idea is to use images from the same landscape but from different points in time as input data for kernelcomposition and SVM classification.Given two points in time t0 and t1 two kernels Kt0 and Kt1 are built.These kernels only incorporate the spectral information given at each point of time.
Then, a new kernel can be build using one of the Eqs.2 to 4. For instance, K Change (x C i , x C j ) = Kt0(x t0 i , x t0 j ) + Kt1(x t1 i , x t1 j ) represents a direct summation kernel which incorporates the information about the change of the spectral responses of pixels implicitly.Although the basic composite kernels can be used for multitemporal classification as well, the authors developed specialized kernels in order to combine traditional change detection techniques with kernel-composition.For instance, the image difference kernel is introduced in Eq.5.
Note that Eq.5 is a particular case of the cross-information kernel (Eq.4) that performs the change detection technique of image differencing in the RKHS.
RELATED WORK
Within this section, an overview on relevant contribution from the field of change detection and kernel-composition will be given.Since kernel-composition has been introduced only in 2006, it has been dedicated far less research than change detection in general.
Change detection and multitemporal classification
Herein, a short outline on important reviews and state-of-the-art papers in change detection is presented.A very comprehensive introduction into multitemporal classification is given by (Gillanders et al., 2008).(Singh, 1989) and (Coppin et al., 2004) present reviews with emphasis on signal processing.(Wang and Xu, 2010) give a comparison on change detection methods emphasising particular aspects of different applications.(Holmgreen and Thuresson, 1998) and (Wulder et al., 2006) (Kennedy et al., 2009).(Almutairi and Warner, 2010) present important considerations on accuracy assessment and the influence of accuracy to the final change detection result.(Van Oort, 2007) presents an insightful contribution on the importance of the error matrix of multitemporal classification.Some state-of-the-art papers are given e.g. by (Bruzzone and Serpico, 1997) and (Bruzzone et al., 2004) which present an iterative approach for change detection.(Coops et al., 2010) apply Landsat time series for assessing forest fragmentation.(Dianat and Kasaei, 2010) use a polynomial regression technique for change detection which considers neighborhoods.Application schemes based on SVMs are presented by (Nemmour and Chibani, 2006), (He and Laptev, 2009) and (Bovolo et al., 2008).(Mota et al., 2007) and (Feitosa et al., 2009) present fuzzy approaches based on modeling the class transitional probabilities.
RESULTS
Within this section, results for three change detection approaches will be presented.The main objective is to monitor the growth of a limestone pit close to the village Mauer (near Heidelberg) in the Upper Rhine Graben, Germany, Latitude: 49 • 19'50"N, Longitude: 8 • 48'1"E (cf.Fig. 1).Two 122 × 135 pixel (≈14.8km2 ) subsets of Landsat ETM+ images are used.The first is from 02-11-2001 (Fig. 2(a)), the second is from 17-4-2005 (Fig. 2(b)).Fortunately, the village is located in the very center of both images, so the failure of the Landsat ETM+ scan line corrector does not affect the work at all.Between the two points in time, the limestone pit has considerably grown.Although more landuse classes are assigned for classification in the first place (e.g.meadows, forests, settlements), only two classes of interest will be considered in the final result: LS-Pit present in 2001 (yellow) and LS-Pit new between 2001 and2005 (red).Complete groundtruth has been made available by a digitization in the field and is shown in Fig. 2(c).Except the limestone pit, all other landuse classes will not be considered and set to black.At first, change detection based on a post-classification approach will be employed.
Secondly, features will be stacked to represent the change of pixels intensities between the two points in time.Lastly, kernelcomposition approaches based on (Camps-Valls et al., 2008), (Camps-Valls et al., 2006a) and(Camps-Valls et al., 2006b) will be employed.These approaches also incorporate changes in pixels intensities.All change detection approaches are based on image classification.Each classification was done using an SVM with a Gaussian RBF kernel1 .Kernel parameters were tuned using a 5fold grid search in the ranges γ ∈ [2 −15 , 2 5 ] and C ∈ [2 −5 , 2 15 ].The LibSVM 3.11 library was utilized (Chang et al., 2001).
Post-classification approach
Two classifications are performed using the same landuse classes in each dataset.
Stacked-features approach
In order to provide implicit information on the changes of pixels intensities, a stacked-features approach was performed.The data matrices of both 8 channel Landsat datasets were concatenated to build a 16 channel data matrix.Within this feature space, the two
Kernel-composition approach
The last approach performed is similar to the stacked-features approach.In order to incorporate information on e.g.color changes, both datasets are combined to a new dataset.However, it is aimed to perform the fusion not in the feature space, but in the RKHS.Therefore, a composed kernel matrix was build, e.g. by The following kernelcomposition approaches were followed: direct summation (Eq.2), weighted summation (Eq.3), cross-information (Eq.4) and image differencing (Eq.5).The overall accuracy values for each approach can be seen in Tab.1.The best overall accuracy yielded by the direct summation approach on the two classes is 88.8%.
As can be seen, all kernel-composition approaches yield slightly higher accuracy values than the other approaches.Although specifically designed for this task, the image difference kernel does not yield the highest accuracy value.However, the performance difference to the direct summation kernel is only 0.2 percent points -a value which should not be over-interpreted.It should be noted that more simple kernels yield better results than more complex ones.A result which is in agreement with the findings of the inventors of the framework (Camps-Valls et al., 2006b), (Camps-Valls et al., 2008), (Tuia and Camps-Valls, 2009).A visual result after setting other classes to black is given in Fig. 2(f).There are much less false positives than in the other approaches.The only exception is a large barren field where open Loess soil mixed with limestone rocks is found (south-east corner of the image).
The spectral characteristics of this field are very similar to the limestone pit thus making the classifier susceptible for confusion with the limestone pit.
McNemar's Test
The advantages in overall accuracy of e.g.kernel-composition over post-classification may seem only a slight gain.Therefore, they were tested for significance using McNemar's test (Foody, 2004).McNemar's test is based on χ 2 statistics and can be employed to test the significance of differences between two nominal labellings.The advantage is considered as significant if the resulting test value |z| ≥ 1.96.Testing the advantage of kernelcomposition over post-classification yielded |z| ≈ 13.95 indicating a significant advantage.A test of kernel-composition against the stacked-features approach yielded |z| ≈ 6.50 which also is significant.The stacked-features approach yielded |z| ≈ 10.16 over post-classification.Thus, all advantages described are significant.
DISCUSSION
We present a comparison of change detection based on kernelcomposition with two traditional methods, post-classification change detection and a stacked-features approach.As Fig. 2 Approaches based on kernel-composition produce the most accurate results.However, there are slight differences when using kernel-composition that depend on the type of composition.
In agreement with other authors, more simple composition approaches tend to produce better results than more complex ones.In our case, the direct summation and the image difference kernel produced the best results.The highest overall accuracy yielded is 88.8% by a direct summation kernel.There are almost no false alerts and the change between 2001 and 2005 becomes most clearly visible.The advantages between the approaches may seem only moderate.However, in the major part of the pit, a separation between the two limestone pit classes seem to be quite simple and therefore, all approaches yield good results in a large part.Furthermore, it has to be kept in mind that a major source of error comes from confusion between the limestone pit and natural outcrops of limestone or open chalky soils.Confusion between these landcover types narrow the differences between the change detection approaches.It should be noted though, that false positives based on this source of error are much less for kernel-composition approaches and more concentrated to single spots.According to McNemar's test, the advantage in overall accuracy of the kernelcomposition approach over the other approaches are significant.
The reason for the advantage of the kernel-composition approach and the stacked-features approach over post-classification change detection is straightforward.While post-classification change detection does not include any information on the change in pixels intensities between the two points of time, both kernel-composition and stacked-features do incorporate this information implicitly.However, the advantage of kernel-composition over the stackedfeatures approach is remarkable.Both approaches include information on the change in pixels intensities.However, kernelcomposition appears to be a better suited technique to exploit this information.It is assumed that the main advantage lies in the fact, that the kernel-composition represents this information in the RKHS, while the stacked-features approach represents it in the original feature space.Since SVMs operate in the RKHS when finding their optimal solution, kernel-composition and SVM seem to be a more suitable combination for representing this implicit information.
CONCLUSIONS
Kernel based change detection is a conceptually elegant and useful method for change detection and multi temporal classification.
Standard techniques like image differencing can be executed in RKHS, thus benefiting from the advantages of kernel based SVM classification.Changes in landuse for the given dataset from Upper Rhine Graben can be visualized and furthermore quantified with high precision.In future work, the approach will be tested on more complex change detection problems.
Figure 1 :
Figure 1: Limestone pit near Heidelberg classes LS-Pit present in 2001 and LS-Pit new between 2001 and 2005 can be distinguished in a single classification step.While the class LS-Pit present in 2001 shows grey color in both images, LS-Pit new between 2001 and 2005 would change from e.g.green to grey.This indicates that a change from e.g.meadows to limestone pit has taken place between the two points in time.From there, only one classification needs to be performed.The overall accuracy on the two classes is 87.5%.A visual result after setting other classes to black is given in Fig.2(e).Note that the amount of false positive pixels is considerably reduced.False positives are now assigned to the class LS-Pit present in 2001.Much less pixels are found in LS-Pit new between 2001 and 2005.Since the latter class is characterized by a change in color from green to grey, it is less confused with bare soils which would stay grey in both points in time.
Figure 2 :
Figure 2: Landsat ETM+ image scenes, groundtruth and results present reviews International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012 XXII ISPRS Congress, 25 August -01 September 2012, Melbourne, Australia focused on applications of change detection of satellite images in forestry.A comparable contribution for landscape monitoring is given by The limestone pit is represented by a single class.Since classification of the two points in time is performed separately, it is not possible to assign the class LS-Pit new between 2001 and 2005 in the 2005 dataset.No features are available which indicate whether or not a pixel has belonged to the limestone pit in 2001 when classifying the 2005 image.From there, one class LS-Pit has been assigned in both datasets and the two classes of interest have been determined by overlaying the results afterwards.The overall accuracy on the two classes is 86.7%.A visual result after setting other classes (like meadows, forest, settlements) to black is given in Fig.2(d).Note the high amount of pixels falsely assigned to the class LS-Pit new between 2001 and 2005.Since the entire image scene is made up of limestone, many places of bare soils have been confused with the limestone pit.
Table 1 :
Approaches and overall accuracies | 4,251.8 | 2012-08-01T00:00:00.000 | [
"Environmental Science",
"Computer Science"
] |
FLOWERING LOCUS C -dependent and -independent regulation of the circadian clock by the autonomous and vernalization pathways
Background The circadian system drives pervasive biological rhythms in plants. Circadian clocks integrate endogenous timing information with environmental signals, in order to match rhythmic outputs to the local day/night cycle. Multiple signaling pathways affect the circadian system, in ways that are likely to be adaptively significant. Our previous studies of natural genetic variation in Arabidopsis thaliana accessions implicated FLOWERING LOCUS C (FLC) as a circadian-clock regulator. The MADS-box transcription factor FLC is best known as a regulator of flowering time. Its activity is regulated by many regulatory genes in the "autonomous" and vernalization-dependent flowering pathways. We tested whether these same pathways affect the circadian system. Results Genes in the autonomous flowering pathway, including FLC, were found to regulate circadian period in Arabidopsis. The mechanisms involved are similar, but not identical, to the control of flowering time. By mutant analyses, we demonstrate a graded effect of FLC expression upon circadian period. Related MADS-box genes had less effect on clock function. We also reveal an unexpected vernalization-dependent alteration of periodicity. Conclusion This study has aided in the understanding of FLC's role in the clock, as it reveals that the network affecting circadian timing is partially overlapping with the floral-regulatory network. We also show a link between vernalization and circadian period. This finding may be of ecological relevance for developmental programing in other plant species.
Background
Most eukaryotes and some prokaryotes have evolved a circadian clock to adapt to the 24 h day/night cycle. These clocks drive biological rhythms in many aspects of metabolism, physiology, and behavior, all with a period close to 24 h [1]. Circadian rhythms affect fundamental processes of plant life, such as photosynthesis and cell elongation [2]. Day-length measurement (photoperiodism) also depends on the circadian clock, which thereby controls seasonal rhythms such as the timing of flowering [3,4].
Described molecular-genetic models from various circadian organisms has each included a gene circuit with negative-feedback elements, involving 24 h rhythms in the levels of positively-and negatively-acting transcriptional regulators [5]. In Arabidopsis, there is emerging evidence that a set of about 20 genes create one, or more, feedback circuits (the 'circadian oscillator') to generate the 24 h period [2,6], and this rhythmically regulates the level of around 6% of transcripts [7].
Circadian clocks, including those of Arabidopsis, are reset by light and temperature signals in a characteristic fashion that entrains the clock to the local time in its environment [6]. However, circadian period is buffered against longterm changes in temperature, such that the period remains close to 24 h when assayed at various constant temperatures, over a physiologically relevant range. Such 'temperature compensation' is another distinguishing feature of circadian clocks, including those in Arabidopsis [8,9]. Whereas the mechanisms of photic entrainment are being elucidated [2,6], those governing temperature entrainment and temperature compensation remain to be determined.
A circadian clock maintains accurate timing because it is buffered against many environmental changes, yet several environmental-signaling pathways must affect the circadian oscillator for entrainment to occur. Limiting the input connections to the circadian clock from the rest of the plant-signaling network provides a potential mechanism to balance the opposing requirements of homeostasis and entrainment. In the gene network that regulates flowering time, for example, the circadian clock is an integral part of the photoperiodic sensor, receiving input from light signaling [3,4]. Current models indicate that output from the photoperiod pathway converges with several other pathways that control flowering time, but the photoperiod sensor is thought to receive no input from those pathways [3,4]. Genetic variation among Arabidopsis accessions prompted us to reexamine this notion.
Substantial natural variation has been detected in clockaffecting genes, based upon assays of rhythmic leaf movement under constant light [9][10][11]. This assay allowed us to map Quantitative Trait Loci (QTL) that affect circadian period in recombinant populations derived from crosses between accessions Cape Verde Islands (Cvi) × Landsberg erecta (Ler) and Columbia (Col) × Ler [10]. In each population, we located a major QTL towards the top of chromosome 5, close to the map location of FLOWERING LOCUS C (FLC). The Ler allele of FLC is weakly functional due to a transposon insertion within an intron of FLC [12,13]. The populations that we used included Ler as one parent, therefore FLC function segregates in these recombinant populations [14]. The Ler allele of the QTL short-ened the circadian period by 0.8 h, as did independent flc mutant alleles, leading us to conclude that the known allelic variation in FLC could account for the QTL [10].
FLC encodes a MADS-box transcription factor that had no known function in the circadian clock, but was well-characterized as a repressor of flowering. FLC expression is enhanced by FRIGIDA (FRI) and its paralogues, which are active in many late-flowering accessions [12,13]. FLC transcription is suppressed by genes of the autonomous floral-promotion pathways and by prolonged cold temperatures (vernalization, indicative of winter in nature; reviewed in [3,11,12]). As flc mutants harbor an altered circadian period, we hypothesized that other genetic and physiological regulators of FLC would have predictable effects on the circadian clock. We therefore tested whether the network of FLC regulators that was defined with respect to flowering time also functions in the control of circadian period. A substantial number of upstream regulators, a related gene, and a downstream target gene do have similar functions, but we also find clear distinctions between FLC-related pathways. The circadian period is also sensitive to vernalization, revealing a previouslyunrecognized connection between the gene circuits involved in responses to daily and to seasonal rhythms.
Dose-dependent effect of FLC on circadian period
FLC RNA abundance correlates with repression of flowering time and quantitatively mediates the vernalization response of flowering time [15]. We sought to determine whether FLC expression levels similarly regulated the circadian clock. To assay the plant's endogenous circadian period, rhythmic movement of the primary leaves of Arabidopsis seedlings were measured by video imaging under constant white light. Relatively large numbers of plants were tested in replicate experiments in order to increase the sensitivity of the assays, allowing us to detect small changes in circadian period (see experimental procedures). FLC RNA abundance was manipulated by two methods. Firstly, we tested a line expressing Table 1). Secondly, circadian experiments were carried out on lines harboring the four possible homozygous combinations of FLC alleles with alleles of the FLC activator, FRIGIDA (FRI), all uniformly in a Col background. These comprised the functional allelesFRI-Sf2 and FLC-Col (FRI and FLC) and recessive alleles fri-Col and flc-3 (fri and flc) [16]. Lines harboring functional FLC had a lengthened circadian period compared to flc lines ( Figure 1). Joint statistical analysis of 6 replicate experiments was used to reveal that FLC alone increased circa-dian period by an average of 0.6 hours, across both FRI genotypes (P = 0.004, Figure 1, Table 1). This is in agreement with the results of Swarup et al. (1999) [10], who showed that FLC lengthened circadian period in both FRI and fri backgrounds. Our findings are also consistent with the function of FLC in flowering time. fri;FLC plants flower slightly later than fri;flc mutants under non-inductive photoperiods, indicating FLC can function independently of FRI in the floral pathway [17]. Increasing the abundance of FLC transcript is therefore sufficient to increase the circadian period of the plant. The greater effect of 35S:FLC compared to endogenous FLC suggests that increasing FLC RNA levels increase circadian period in a graded manner, similar to FLC's dose-dependent delay of flowering [16,18]. It might be possible that a broader spatial domain of FLC expression in 35S:FLC plants contributed to this result, though such effects on the location of FLC expression have not previously been implicated in flowering-time control.
We suggest that functional FRI caused an additional increase in period in the presence of functional FLC (Figure 1; see also Figure 3). Although FRI;FLC had the longest mean period in each experiment, the interaction between FRI and FLC was not significant in the joint analysis (data not shown). This indicates that FRI can increase circadian period weakly and less consistently than FLC. In contrast, functional FRI strongly enhances FLC RNA levels and severely delays flowering [16,18], highlighting an obvious difference between circadian and flowering time control.
Effects of null flc and 35S: FLC on circadian period Again, it is possible that FRI does not enhance FLC expression in the cells that regulate leaf movement as much as 35S:FLC.
Effects of FLC regulators on circadian period
The above results lead us to the hypothesis that any factor that modulates FLC expression levels, including the genes of the autonomous pathway, would affect circadian period. In order to compare the network of circadian regulators to the pathways that regulates flowering time, we analyzed the circadian period of plants carrying mutations in several genes of the autonomous flowering-time pathway ( Figure 2), all of which contribute to regulate FLC RNA abundance (reviewed in Henderson et al., 2003 [19]).
FCA FCA is one of the genes that defines the autonomous flowering-time pathway. FCA encodes a nuclear-localized protein with RNA recognition motifs. It is involved in 3' RNA processing of FCA transcripts through physical interaction with the FY protein [20][21][22]. FCA promotes flowering by repression of FLC RNA levels [17,23]: plants with an fca lesion have high levels of FLC RNA and flower late. Assays on fca mutants revealed an increase in circadian period of nearly 1 hour compared to the Col-0 wild-type (τ = 25.28 ± 0.28 h vs. 24.44 ± 0.17 h, P = 0.002), in line with the hypothesis that elevated FLC levels increase circadian period ( Figure 2 and 5, Table 2).
LUMINIDEPENDENS (LD)
LD represses FLC expression and encodes a predicted nuclear protein with a glutamine rich Carboxy terminus, suggesting a role as a transcriptional regulator [16,24,25].
Of the autonomous pathway genes tested, LD had the most striking effect on circadian period. A period increase of approximately (Figure 2 and 5, Table 2), which in turn had a longer period than the flc mutants ( Figure 1). Thus the ld;flc double mutant has an intermediate phenotype, with a significantly longer period than the flc single mutant but shorter than the ld single mutant. We conclude that the effect of LD on period is at most partly dependent on FLC, andLD function must also influence the circadian clock independently of FLC. This contrasts with the FLC-dependence of the effects of LD on flowering [17].
FVE
FVE encodes a component of a histone-acetylation complex, which functions to strongly suppresses FLC RNA abundance, to thus function in the flowering-time pathway [23,26,27]. Additionally, FVE affects morphological traits such as leaf shape and inflorescence patterns [28]. Figure 2 and 5, Table 2).
These results indicate to us that FVE regulates circadian timing in a manner that is largely independent of FLC, again in contrast to its effect on flowering [17].
FPA
FPA is predicted to encode a protein that contains RNA recognition motifs and also represses FLC RNA and function in the flowering-time pathway [29]. The fpa mutant showed only a small increase in period (0.47 h) compared to the wild type, and this modest effect was not statistically significant (τ = 24.91 ± 0.27 h vs 24.44 ± 0.17 h, P = 0.08) (Figure 2 and 5, Table 2). Therefore, FPA seems to have less effect on the circadian clock of Arabidopsis than the other mutants tested. Though FPA has been functionally linked with FVE in the flowering time network, it differs from FVE in that FPA is less sensitive to FLC gene dosage [23], FPA interacts with genes of the photoperiodic-response pathway [30], and has been implicated in the gibberellin response [31]. These differences may reflect a range of molecular functions that limits the effect of FPA on circadian timing.
Effects of other MADS-box genes on circadian period SUPPRESSOR OF OVEREXPRESSION OF CONSTANS 1 (SOC1)
SOC1 (also referred to as AGL20) is a MADS-box gene that activates flowering, in response to signals from the autonomous and photoperiodic flowering-time pathways [32,33]. Unlike the genes tested above, SOC1 is described as a target of FLC-mediated transcriptional repression in the flowering-time pathway [17]. The soc1 mutant has a small increase in circadian period relative to wild type (τ = 24.98 h ± 0.22 h vs. 24.44 ± 0.17 h, P = 0.008), indicating that SOC1 normally shortens circadian period ( Figure 2 and 5, Table 2). If FLC represses SOC1 expression, this result is consistent with the idea that flc mutants shorten circadian period at least in part via increased expression of . We assayed the soc1; flc double mutant in order to test this notion, which would predict a long period in the soc1; flc double mutant, similar to the soc1 single mutant. The period of the double mutant was however intermediate between the single mutants, being slightly reduced compared to the soc1 single mutant (τ = 24.49 ± 0.24 h vs. 24.98 ± 0.22 h, P= 0.048). The resulting period of soc1; flc was identical to that of Col (Figure 2 and 5, Table 2), but longer than that of the flc null mutant (Figure 1). This result suggests that FLC may increase circadian period in part by repressing SOC1, but its effect also occurs by other means, consistent with the function of FLC in the floralrepression pathway [17]. Table 2), in contrast to the significantly shortened circadian period of the flc mutant. These results indicate that FLC may have a unique function in shortening the circadian period of Arabidopsis, which is not shared by other MADS box transcription factors that function in the flowering-time pathways.
Seasonal regulation of the circadian clock by vernalization
FLC expression represses flowering in biennial and winter-annual plants, causing overwintering in the vegetative state. Vernalization relieves the floral repression in part by stably suppressing FLC expression, so flowering can proceed in the Spring [37]. flc mutants retain some vernalization response [17], which may be mediated by other MADS-box genes [38]. Based on the prediction that any effect on FLC-expression levels, whether genetic or physiological, should alter circadian period, we sought to test the effect of vernalization on circadian period and the effect of flc mutations on the clock after vernalization. We assayed circadian period in seedlings harboring the FRI and FLC alleles, as described above, comparing seedlings that had been vernalized to controls grown without vernalization. Flowering-time analysis of these plants, following the leaf movement assays, confirmed the effectiveness of the vernalization treatments in accelerating flowering (data not shown). We found in duplicate experiments that vernalization consistently decreased circadian period (P < 0.001) but that none of the single-gene or gene interaction effects was significant (Figure 3, Tables 3 and 4). Therefore, vernalization consistently shortened circadian period, regardless of FLC. There is a possibility that development during the vernalization period may have caused the change in circadian period. However, prior to these experiments, we identified growth conditions for the vernalized and non-vernalized plants such that in these experiments, seedlings of both groups were phenotypically indistinguishable from one another. Furthermore, as the same primary leaf pair was assayed in both treatment groups, a directly comparable developmental trait comparison was made (see Materials and Methods).
Discussion
We report here that the genes of the autonomous floralpromotion pathway, and FLC itself, modulate the period of a circadian clock in Arabidopsis. The effects on period are modest, but our data measurements are accurate, as detected in plots of relative amplitude error (RAE) versus period length for individual cotyledon traces of a genotype in an experiment (see Additional file 1). Additionally, there is no noticeable increase in arrhythmic mutant plants relative to wild-type (data not shown). Data for all vernalized non-vernalized genotypes tested in this study were collected from multiple experiments and in each case the period effects relative to the wild type were consistent. The only exception to this was the fpa mutant, which had first a long period and then a short period, relative to wild-type, in two independent experiments. As expected from this result, statistical analysis of these data was unable to assign a function for FPA in the circadian clock. It should also be mentioned that in each of the multiple FRI;FLC mutant combination studies ( Figure 1A, Table 1), fri-flc double mutant period was always reduced compared to FRI-FLC period. Direct comparison with other genotypes between replicate experiments was not reasonable without the statistical analysis we performed using REML.
Effects of vernalization on the Arabidopsis clock
The mechanisms by which the floral-promotion genes affect circadian period are similar, but not identical, to their control of flowering time. Regulators other than FLC must be involved because, for example, LD and FVE affect the clock significantly in the flc mutant background. We also reveal a vernalization-dependent shortening of the circadian period. Recent studies in chestnut seedlings have shown that during the chilling period, circadian expression of genes homologous to Arabidopsis coreclock genes are suppressed, with cyclic expression of these genes resumes post-chilling [39]. Our studies however identify alterations in the Arabidopsis clock after the coldexposure period. FLC would be an obvious candidate gene to mediate this response, however, our studies did not fully support this possibility. Circadian analysis of mutants in other vernalization-responsive MADS-box genes, such as MAF2 [34,40] may shed light on the how the clock is altered by vernalization. It is unclear which components of the circadian-clock mechanism are the targets that mediate these period changes. Rhythmic, tran-scriptional-translational feedback loops are important in circadian timing and the genes tested here are regulators of gene expression, though FLC is not thought to be rhythmically regulated [41]. It is possible that the expression level of one of the clock genes is FLC-dependent, for example. Given the modest effects we observed upon circadian period, the FLC-dependent change in expression level might be very slight.
From an ecological perspective, the stable effects of vernalization allow plants to distinguish between Spring and Autumn, even though both seasons have an equal day length. Our work suggests that an additional mechanism may contribute to this distinction, namely that the circadian clocks of plants run "faster" in Spring than in Autumn.
Environmental changes can thus have "after-effects" on the circadian clock, in Arabidopsis, as in other organisms. These are typically observed as an alteration in the circadian period immediately after exposure to exotic lightdark or warm-cold cycles [11,42]. The period-shortening effect of vernalization is expected to be much longer-lasting. The physiological consequences of the period shortening will depend on which rhythms are affected, and how the change in period under constant conditions affects the rhythms under day-night cycles. Short-period mutations can reduce the critical photoperiod in Arabidopsis, leading to earlier flowering under shorter photoperiods [43]. If the shortened circadian periods due to FLC repression affected rhythmic CO expression, this would reinforce the acceleration of flowering in Spring days compared to Autumn days, by induction through the photoperiod pathway, in addition to the removal of autonomous-pathway flowering repression. Such cross- Mean circadian periods of Arabidopsis mutant and wild-type seedlings, tested as in Figure 1.
talk between the autonomous pathway and the circadian system emphasizes the networked structure of plant-signaling circuits. These include the circuits adapted to mediate plastic responses to rhythmic, daily, and seasonal environmental signals.
Conclusion
We demonstrated that several genes in the Arabidopsis autonomous-flowering pathway are also involved in regulation of the circadian clock. We identify FLC as a dosedependant regulator of circadian period and identify autonomous-pathway genes regulating the clock in both an FLC dependant and independent manner. As FLC expression levels are reduced by vernalization, we tested the hypothesis that circadian period was altered in vernalized FLC wild-type plants. Though we could not firmly establish FLC as the mediator of vernalization's effect on circadian period, we showed conclusively that vernalization alters circadian period in Arabidopsis. Figure 4 is an illustrated schematic of how vernalization and the genes we tested may be regulating circadian period in Arabidopsis.
Growth and imaging conditions
Seedlings were grown and followed by assays of rhythmic leaf movements by video imaging, as described by Dowson-Day and Millar et al. 1995 [48,49]. Briefly, surface-sterilized seeds were plated on 1.5% Murashige-Skoog agar medium plates [50] low-intensity white light (0.5-1.0 μmol m -2 sec -1 ). After the vernalization treatment, seedlings were transferred to continuous light for 4 days, then entrained and imaged as above. In order to confirm the effectiveness of vernalization, imaged seedlings were transferred from agar to soil immediately after the leaf-movement assay. Flowering time of these lines was measured as the number of rosette leaves when the floral bolt was 1 cm high. These studies confirmed the expected effects of FLC and FRI upon vernalization-responsiveness (data not shown).
Data analysis
Leaf movement data were analyzed by Fast Fourier Transform non-linear least squares program FFT-NLLS [51], essentially as described in Dowson-Day and Millar, 1999 [48]. The circadian period of each genotype was estimated as the variance-weighted mean of the most significant period within the circadian range (15-35 h) for each leaf. In order to make the most efficient use of data gathered in separate experiments, the data from all the experiments were analyzed jointly using REML [52] in the statistical package GENSTAT 5 [53]. REML is a generalization of analysis of variance and is appropriate for the analysis of unbalanced data. Genotypes to be compared directly were included in the same experiments. In the analyses, experiment, camera within experiment, plant within camera, and cotyledon within plant were taken as random factors, with mutant line as a fixed factor. The analysis was weighted to allow for the inherent variabilities of estima-tion of period from the different traces. The period estimate for each leaf recording was weighted for analysis by the reciprocal of the error associated with the period, as estimated by FFT-NLLS. Significance of FRI-FLC interactions and vernalization effects on period were assessed using the Wald test with variances derived from REML. The significance of the differences between the mean period of pairs of genotypes was assessed using the standard error of each difference, derived from REML. Figures 1, 2,3 report the conventional SE of each genotype mean.
Authors' contributions
NS, AJM, and SJD conceived the experiments and wrote the paper, with critical experimental and intellectual revisions from SDM and RMA. SDM and RMA generated reagents. NS carried out the experiments. JRL conducted statistical analysis. Mean circadian period of Arabidopsis mutant seedlings, tested as in Figure 1, with or without vernalization at 2°C for 8 weeks.
Additional file 1
Robustness of rhythmicity of all lines examined MS EXCEL file containing 3 worksheets. These include RAE plots for all genotypes examined (sorted with respect to Figure 1, 2 Statistical significance testing for circadian period effects of floral pathway mutant lines | 5,296.2 | 2006-05-31T00:00:00.000 | [
"Biology",
"Environmental Science"
] |
A Comparative Study for Speech Summarization Based on Machine Learning: A Survey
Abstract
INTRODUCTION
Humans use speech as the most natural and effective means of communication. In today's information technology era, spoken natural communication is of critical importance. The majority of IT researchers are working on developing highly effective spoken language understanding (SLU) systems using machine learning and artificial intelligence approaches applied to speech processing technology and natural language processing algorithms. Speech summarization is a hot issue in the SLU domain right now. Speech summarizing aids in the extraction of relevant information from a variety of spoken material sources, including meetings, broadcast news, talk shows, lectures, voice mails, and YouTube videos. Speech summarizing is an important method for dealing with the large quantity of data available in low-information-density audio recordings. By pointing to a short summary that will be listened to by an analyst at the end, speech summarizing is also particularly beneficial for commercial marketing analysts and government intelligence [1]. Abstractive and extractive summarization are the two categories into which text summarization is typically divided. For parsing, word reduction text summary generation, and abstractive summarization natural language processing (NLP) techniques are applied [2]. When compared to abstractive summarization, extractive summarization is stated to be flexible and time-efficient. In extractive summarization, the phrase is taken into account in matrix form, and the key sentences are then identified using some feature vectors. A feature vector is referred to as an ndimensional vector with numerical features that represent the object. A text summary is produced by speech summarizing using inputted speech data. In order to build a concise representation of the content, it must process extensive speech data (a series of
Al-Rafidain Journal of Computer Sciences and Mathematics (RJCM)
www.csmj.mosuljournals.com utterances) and extract crucial information. Additionally, speech involves fillers, disfluencies, redundancies (such as using the same sentences
MOTIVATION FOR SPEECH SUMMARIZATION
Speech summarizing has sparked a lot of interest in research due to the growing number of audio recordings because people are generally quite busy and locating adequate and appropriate knowledge base information has become extremely challenging [5]. Regarding broadcast news people find it difficult to identify news from vast news broadcast archives, and as a result, television program space is wasted. They may be preoccupied with other vital tasks and miss the news program that is carried out every day at a fixed time and they are rarely watch the entire news presentation; instead, they are interested in watching a specific news piece [6].
AUDIO SIGNAL PROCESSING USING DEEP LEARNING
To extract audio features, audio machine learning systems previously relied on classic digital signal processing techniques. However, since deep learning has become more widely used in recent years, it has had amazing success in handling audio. Traditional audio processing approaches are no longer required, and we can rely on standard data preparation rather than a lot of manual and customized feature development. Using deep learning, we don't work with audio data in its raw form. Instead, audio data are transformed to images and then process those images using deep learning methods such as conventional neural network(CNN) architecture. This is done by generating spectrograms from the audio signal [6].
CONTRIBUTION
Previous surveys till 2018 focused on researches, some of them include traditional methods for summarization and others, not includes recent methods for deep learning. So in this survey we explore the most techniques of deep learning were used recently. It also presents a speech summarization categorization based on a new different criterion. To the best of our knowledge this is the first survey that includes recent work on speech summarization using machine learning (beyond 2016) as well as recent studies for deep learning. It focuses on speech summarization models, Source of input corpus, number of stages in summarization process and evaluation metrics.
CATEGORIZATION OF SPEECH SUMMARIZATION PROCESS
This survey comprises fundamental studies based on speech summarizing processes. Speech summarization process can be classified based on a set of criterions as describes below.
A. Conventional Summarization Models
Techniques for converting speech audio files to text files, as well as text summarization on the text files are presented which are utilized for text summarization in the latter situation. words are allocated weights based on the number of times they appear in the text file. The recorded speech can be converted to text with the help of Google API [7]. To distinguish sentences, python string tokenization employs periods. The sentence is summarized once the index is identified and ranked according to the sentence's weight. We can deduce from the recognition time that sentences with a period and a question mark are recognized faster than those without [8]. To avoid having to read the entire text each time, a more efficient method of summarizing books into important keywords was developed. The suggested model summarizes the content using a weighted TF-IDF (Term Frequency Inverse Document Frequency), and then converts it to speech [9]. These models are considered out of our study.
B. Machine Learning and Deep Learning based Summarization Models
The basic studies which implemented machine and deep learning models were as follows: Chen, B., et al. presented an empirical study of the merits of two schools of training criteria for reducing the negative effects of imbalanced-data problem and improving summarization performance. One method is to train a summarizer's classification capabilities using pair-wise ordering information of phrases in a training document according to importance. The other method is to train the summarizer by directly optimizing the associated evaluation score or an objective that is tied to the final evaluation. Experiments on the summary of broadcast news show that these training criteria can provide significant gains over a few existing summarizing methods [10]. Liu, Z., Ng, A., Lee, S., Aw, A. T., & Chen, N. F. presented a neural architecture that works well and efficiently. It was shown that the hierarchical structure of dialogues is used to integrate topic-level attention mechanisms in pointergenerator networks. The suggested model outperforms competitive bust when it comes to long dialogue samples, and it also works well with limited training data [11]. Zhao, Z., et al. presented a hierarchical neural encoder based on adaptive recurrent networks to learn the semantic representation of meeting discussion. Then, for abstractive meeting summarizing, a reinforced decoder network was created to generate high-quality summaries constructing the HAS Hierarchical encoder-decoder network learning framework with adaptive dialogue segmentation [12]. Atsunori Ogawa., et al. suggested a compressive speech summarizing approach(performs both extraction and compression at the same time)based on integer linear programming (ILP), which maximizes the coverage of content words in the resulting summary. It was considered the first trial of compressive speech summarization at that time. A single step summary using the confidence, TF IDF and bigram LM scores, was conducted for each produced ASR hypothesis sequence that corresponds to a full lecture speech (12 min on average). The results showed that the compressive approach outperformed the extractive method, and compressive CN over compressive 1-best [13]. M Menacer, et al. designed a two-stage ASR and text summarization pipeline to provides an end-to-end dialog summarizing system. Users can first see a high-level summary of the information, then drill down into longer and more thorough summaries or listen to the raw audio itself using hierarchical summarization. PEGASUS the current state-of-the-art abstractive summarization model was used, which is capable of producing summaries of significantly higher human quality [14]. Kumar, B. D. (n.d.) used an Essence vector (EV) modeling which is an unsupervised paragraph embedding method aims to derive the most important information from a paragraph while also including general background information. First speech is transformed to text and fed into the Essence Vector (EV) model as a high-dimensional vector input, which summarizes the information in a low-dimensional space. The EV model's performance was improved by adding an Attention mechanism and employing LSTM to handle the speech to text module's faulty and erroneous speech conversions [15]. González-Gallardo, et al. offered a hybrid technique during the training phase, whereas summary creation was text-independent. It is based on employing textual information to learn an in formativeness representation based on probability distribution divergences, which is not taken into account by normal audio summarization with audio features. The length of the summary was set to equal 35% of the original audio length [16]. Weng, S.-Y., Lo, T.-H., Chen, B. extended the BERT-based method for supervised extractive speech summarization that is capable of performing robust summary on spoken documents containing erroneous ASR transcripts. To improve the summarization performance of a spoken material, many supplementary structural and linguistic features were applied to enrich the embeddings of the sentences. The results showed that in both the text document(TD) and spoken document(SD)cases, neural network-based methods (skip-gram(SG) and continuous bag of word (CBOW)) always outperform classic vector-based methods (vector space model(VSM) and latent semantic analysis (LSA)) when used unsupervised. In the TD scenario, supervised summarizers such as deep neural network (DNN), convolution neural network (CNN), and Refresh outperform SG and CBOW, as do most of them in the SD case. 10% was chosen as the summary ratio [17]. Sharma, R., Palaskar, S., Black, A. W., Metze, F. proposed three transformer-based modules: speech segmentation, speech recognition, and extractive text summarization. An extractive summarization module employs BERTSUM using the self-supervised learning model BERT for text summarization to select the most essential sentences from a text that contains recognized sentences. Each sentence is binary classified by the module, which then creates a summary that meets the desired repeatedly), and colloquial terminology in contrast to text input [3]. The automatic speech recognition (ASR) engine, which transcribes spoken documents into textual representation, is one of the most important parts of the speech summarizing technique. The ASR component is extremely dependent on spoken language, and academics all across the world have created language-specific ASR engines. Transcribing speech to text and then summarizing it, is the common two-stage process for speech summarization. Producing a summary directly from speech without having to transcribe it, is a different approach that could help to avoid some fundamental summarization issues [4].
summary rate [18]. Kano, T., Ogawa, A., Delcroix, M., & Watanabe, S. introduced a single model optimized end to end for speech summarization. The suggested model learns to directly summarize speech and it outperforms the earlier proposed cascaded model by three points. On ROUGE.ASR was used to pre train the sequence model, because training summarization models from start is difficult. Then, for speech summarization, the encoder-decoder model is finetuned.The effects of different window sizes and dilations on summarization were investigated, with the conclusion that larger window sizes are required for better models [19]. Dammak, N., &BenAyed, Y. presented the cascade connection of applying automatic speech recognition and text summarization that allows for the use of state-of-the-art modules which are optimized for each task separately, without the need for a large amount of paired data made up of speech data and associated summaries. Posterior probability fusion and Attention-based multi-hypothesis fusion approaches were used for speech summarization [20].Li, D., Chen, T., Tung, A., & Chilton, L. B. suggested a deep encoder-decoder model based on the attention mechanism (DEDA) for ASR transcripts. it takes advantage of the deep structure of RNNs based on a Long Short-Term Memory (LSTM) network. The key difference is to incorporate a powerful attention mechanism into the encoder-decoder structure to address the sequence problem in the summarization area. Experiments on the AMI Dataset show that the proposed strategy outperformed the state-ofthe-art on both extractive and abstractive models. The performance of summarized utterances and the reduction of occurrence repetition in summaries, were also highlighted in the experimental analyses [21]. Because these studies applied their methods on different corpus, it is not possible to compare them accurately and identify which machine or deep learning algorithm was the best.
Source of Corpus
A corpus is a group of authentic text or audio that has been arranged into datasets. 'Authentic' in this context refers to text produced by a native speaker of the language or dialect or audio produced by that speaker. Newspapers, books, recipes, radio broadcasts, television shows, motion pictures, and tweets can all be included in a corpus. A corpus of text and speech data used for natural language processing can be utilized to train AI and machine learning systems [22]. The characteristics of the speech domain corpora include: Corpus are (1) of different languages, (2) comprise one or two speakers, (3) range in size from small to moderate, and big [4]. Table 1 shows both Audio Speech and Multimodal Corpus for various studies which are publicly available.
A. Audio Speech Corpus
A Corpus of spontaneous Japanese (CSJ) was used which includes a training set with 3,212 spontaneous speeches from lectures and conferences, as well as three evaluation sets (eval1, eval2,and evel3). Every speech was recorded at a sampling rate of 16 kHz and a bit depth of 16 [3]. In [7] the pyaudio module is used to record and process audio. Continuously adding frames of audio is used to record audio. This phase's ultimate output is an audio file in the wave format. The MATBN corpus, (which contains roughly 200 hours of Mandarin Chinese TV broadcast news) collected by Academia Sinica and the Taiwan Public Television Service Foundation between November 2001 and April 2003, was used [10]. A training set of 100k dialogues was used, followed by a validation set of 1k dialogues. The test set was produced from 490 multi-turn talks between nurses and patients in a healthcare setting [11]. In [12] the AMI meeting corpus consists of 142 meeting records(which are 100 dialogs in the training set, 20 dialogs in the validation set, and 22 dialogs in the testing set) and associated abstractive summaries written by humans . The suggested approach is trained and tested using the CNN/Daily Mail summarization dataset. The documents and summaries from CNN news articles are included in this dataset [15]. A set of empirical experiments are done on a mandarin benchmark broadcast new (MATBN) corpus, while the training and validation sets were constructed using simulated data, the summarizing studies used a subset of 205 broadcast news documents collected between November 2001 and August 2002 [17]. Three corpora were used to train and evaluate speech summarization systems. CNN-Daily Mail (CNNDM), How2 and TED corpus [19].The AMI meeting corpus was used(100 hours of meetings recorded using multiple synchronized recording devices).The AMI corpus contains ASR transcripts for 137 meetings that were spoken by four participants who were assigned certain roles. Each meeting lasts an average of 35 minutes and includes about 800 unprocessed utterances, or nearly 6700 words [20] B
. Multimodal Corpus
The total video corpus consists of roughly 300 hours of video, with approximately 100 hours in each of the languages (French, English and Arabic) in [14]. How-2 dataset includes 2000 hours of instructional videos, as well as text transcripts, speech, video, translations, and summaries was employed [18]. A cascaded multimodal abstractive speech summarization model was described, which learned semantic concepts as an intermediary step.
The benefits of using multimodal inputs (How2 data set ) includes speech, video, human annotated transcription and a summary rather than unimodal inputs were tested for intermediate concepts, and consistent advantages were discovered [24].
The anchor person-based story identification and lexical chain algorithm were used to implement multimedia summarization of news broadcasts. This system allows users to create multimedia summaries of one or more input news broadcasts and search for and retrieve selected news stories using a keyword-based search and retrieval system [25].
SUMMARIZATION PROCESS:
Most researches focus on a two-stage process for extracting summary output from an audio file input. Speech to Text conversion is the first step, followed by text summarization. However, the output's efficiency is determined by the audio file's clarity [7].In [8] the proposed method uses automated speech recognition (ASR) to transcribe the audio, then summarize the transcript, and lastly returns the audio associated with thetext summary. Speech summarization is accomplished by integrating two primary sub-modules: an automated speech recognition (ASR) module and a text summarization system (TS) [13].
In [23] two stage summarization process was implemented. First, the speech is converted into text using Pocket Sphinx engine for transcribing spontaneous speech using three models. An acoustic model which contains phones acoustic properties, a phonetic model which involves word-to-phone mapping and a language model which limits the matching process by defining which words can come after previously recognized terms, then natural language processing preprocessing approaches were performed.
Speech transcripts, on the other hand, may be costly, unavailable, or of poor quality, which has an impact on summarizing performance. This leads to one stage summarization process. The complexity of the model structure with cascade topologies, and faults in the ASR which reduces summarization performance offers motivation for end-to-end(E2E) modeling for speech summarization [18]. Fig1. ONE AND TWO STAGE SUMMARIZATION PROCESS [2] 6. DEEP LEARNING APPROACHES FOR
SPEECH SUMMARIZATION
Deep learning approaches are now the most popular term in machine learning for extracting complicated data representations at a high level of abstraction, which is especially useful for exceedingly complex issues. It is a dataintensive method that produces better results than classic approaches (Naïve Bayes, HMM, SVM, and so on). A Long Short Term Memory (LSTM) network architecture is a special type of RNN network that can learn long term dependencies. In more than 1000 steps, an LSTM can learn to fill the gap between time intervals. To handle information in both directions, bidirectional LSTM has two hidden layers. The input sequences are processed forward by the first hidden layer, and backward by the second hidden layer. Both are then linked to the same output layer, which gives them access to the sequence's future and past context. As a result, BLSTM outperforms both traditional LSTMs and RNNs, as well as providing a substantially faster and more accurate model.
The gated recurrent unit (GRU) is a recurrent neural network extension that tries to handle memories of sequences of data by storing the network's prior input state and planning to target vectors depending on the prior input.
A recurrent neural network (RNN), on the other hand, is a type of artificial neural network model in which the connections between the processing units create cyclic paths.
It is recurrent because they take inputs, update the hidden layers based on previous calculations, and provide predictions for all sequence members.
In a traditional Recurrent Neural Network (RNN), data passes through only one layer on its way to the output layer before being processed. However, Deep Neural Networks (DNN) is a hybrid of deep neural networks (DNN) and RNNs [26].
EVALUATION METRICS
Since the early 2000s, there has been a set of measures for automatically evaluating summaries. The most extensively used metric for automatic evaluation is ROUGE.ROUGE comes in a variety of flavors, and the most popular ones are: ROUGE-n, ROUGE-L, ROUGE-SU+. Objective and subjective evaluation criteria were used in speech summarization. Objective evaluations includes ROUGE metric(ROUGE1, ROUGE2, ROUGE l) which are based on word and phrase overlaps in summary documents prepared automatically and manually, whereas subjective evaluations were used to assess the quality of the generated summaries based on interest, informativeness, abruptness, attractiveness, and overall quality. Users were particularly sensitive to the audio stream's linguistic coherence and continuity. The ROUGE measure, which includes ROUGE-1, ROUGE-2, and ROUGE-Lwas utilized as an evaluation metric in [10] [11][17] [19]. The suggested system's ROUGE value was 0.34343, which is likely comparable to other unsupervised summarization techniques like Lexrank and latent semantic analysis [15]. 1A subjective scaled opinion metric of 1-5 was used to assess the quality of the generated summaries and their components. Two objective metrics were also used: full score and average score metrics [16]. In order to obtain an overall score suitable for DEDA method, ROUGE scores for every meeting transcript in the test set were computed and then the macro-averaging method was used in [20]. ROUGE scores (ROUGE-1,ROUGE-2, ROUGE-SU) use n-gram overlap and skip-gram overlap to compare machine summaries to human gold-standard summaries were used in [12] [13]. A BERT Score is used to assess coherence, while the cosine similarity between sentence transformer embedding of a reference ASR segment and a model generated output summary is employed to determine what information is kept in [21].
SUMMARIZATION PROCESS
Regarding ASR, the basic difficulties and limitation are speech recognition errors, when tasks are well-defined single-speaker tasks, such as analyzing TED lectures, ASR error rates are reduced, but they remain difficult when tasks are less organized or involve multiple speakers, such as audio from meetings. To solve ASR output faults, machine learning, deep learning, and language models can be employed. Speaker turn identification is another problem for speech summarization. In accurate unit boundary detection can result in incorrect speaker identification across series of utterances. Although the number of speakers in BN is typically higher, speaker turns occur less frequently than in conference meeting data, resulting in a longer average speaker turn length in BN. Interruptions, overlapped speech, interleaved false starts, filler phrases (e.g. "of course", "ok", "you know"), non-lexical filled gaps (e.g. "umm", "uh"), and redundancies are all examples of speech disfluency. These disfluencies make identifying the semantic substance of speech more difficult, which can make summarization difficult. speech in broadcast news is the closest to organized text in terms of having the fewest disfluencies due to the presenters' professional training [4][27].
CONCLUSION AND FUTURE WORK
This survey paper emphasized various extractive and abstractive approaches for speech summarization. Most of the studies followed a two-step summarization process due to their commonly used and simplicity, while a few generates summary directly from speech. Deep learning and computer vision approaches can help in generating summary from speech without transcript it. In this survey, different studies which applied machine and deep learning models were analyzed. It is noticed an advance in the area of abstractive summarization with the presence of recent deep learning approaches. The source of materials in this survey were ranged from meeting, lectures, conferences and broadcast news with the focus on broadcast news because of their structural form in addition to ideal recording environment. No deterministic dataset was used and for the same dataset, different portions were employed for different studies, this leads to the difficulties in comparing these studies and evaluating them. It is recommended to employ existing datasets for latter studies and researches for accurate analysis and comparison. | 5,194 | 2022-12-27T00:00:00.000 | [
"Computer Science"
] |
Web-Based E-Teylor Sales Indormation System Design
. The design of the E-Tailor sales information system is a web-based application as a means for employees or business owners to make it easier to order clothes online. Websites with this system can provide solutions to owners or tailors and consumers or ordering goods for smooth orders, transactions and completion of ordered goods on time and this will also make it easier for users to be able to order sewing items online without having to come to a tailor shop. In the design here it is also explained how a system will be built and run according to the manufacturing method carried out, for the design of the E-Tailor Information System is presented using UML (Unified Modeling Language). The testing method on the design of the e-tailor information system using the black box method only focuses on input and output that informs the suitability of the application developed with the specified specifications. The test results show that the success rate of the application runs well in accordance with the tests that have been carried out.
Introduction
Clothing or clothing is one of the basic human needs.In the current era, the development of fashion is very fast and rapid.Many people choose to get clothes [1].One of them with sewing services.People are used to ordering sewing services at one of the tailors who have become customers [2].However, there are obstacles in ordering sewing services directly or manually, namely, having to come to the tailor directly, sometimes there are too many sewing orders for tailors, so the tailor refuses the service.Sometimes when a tailor has a lot of sewing orders, he can't be sure of the completion time of the sewing order [3] [4].
People prefer to buy ready-made clothes at malls or clothing stores rather than making clothes to tailors because of the factors mentioned above.Especially in today's increasingly advanced internet, people prefer to buy clothes online because it is more efficient and cheaper [5].However, sometimes problems arise again, the suitability of clothes seen in online media with clothes that have been purchased is very different, this is detrimental to consumers.Expectations to be expected on the clothes on display are very different [6].Many online merchants are concerned with quantity rather than the quality of the clothes they sew, because the demand for goods is very large and for the sake of price they are also offered to the market [7].From the various problems above, it provides an alternative to making online sewing orders that can characterize every consumer or customer.So that customers can choose their own fabric and enter their own size who wants to make costume size clothes or clothes that match the consumer's body size [8].
E-Tailor software is software used for online sewing orders.This system is related to several external entities, namely admin, buyer/customer/user.We named this sewing ordering web application E-TAILOR.This application can login as owner and customer.To log in as the owner, the owner can make orders to add new types of clothes needed, edit clothing details, delete clothing details, delete orders made by customers.To log in as a customer, the customer can place an order accordingly and the customer can see all the details of the clothes that are in the system, and can also edit the order data [9].
The large number of orders for tailors in the old way has made it difficult for a tailor in Bangkalan to handle the amount of work and time required for the transaction, and it is feared that the order cannot be completed within the allotted time because time is wasted just for negotiating the customer's goods [10].Therefore, we need a solution that can be a way out to maintain the quality of tailors in Bangkalan.E-Tailor as a means of online ordering system in the field of tailors focuses on completing orders for goods with a technological approach seeking to improve the performance of tailors, especially in the Bangkalan area.A website with this system can provide solutions to the owner / tailor and user / order of goods for smooth orders, transactions and completion of ordered goods on time and this will also make it easier for users to be able to order sewing goods online without having to come to a tailor shop.
The purpose of this project is to design an E-Tailor information system where this system is suitable for tailors, in making the system it will be built based on a website and with the PHP HTML programming language [11].Our target subject has sewing services for men's and women's clothes.This place has an owner who works alone in the sewing process and only accepts offline customers.So, this is very inefficient in doing a business because this owner can take orders for clothes online so that they can have many customers and also be able to develop their business.Therefore, a website was created that can be used to develop its business more broadly through the design of making a website-based E-Tailor information system [12].
System Development Method
For system development, this research uses the SDLC (Software Development Life Cycle) model [13].System Development Life Cycle (SDLC) is the process of creating and modifying systems and the models and methodologies used to develop a system.SDLC is also a pattern taken to develop a software system, which consists of the following stages: planning, analysis, design, implementation, testing and maintenance [14] [15].
The system development model is built using the spiral SDLC model in the development of this system.R. Eko Indrajit in his book "Management of Information Systems and Information Technology", states that the development of information systems can be categorized into three major groups.The first group is a project that is the construction of information technology infrastructure networks (starting from the procurement and installation of computers to the planning and development of LAN and WAN network infrastructure) [16] [17].
The second group is the implementation of application program packages purchased in the market and implemented in companies, ranging from small software such as Microsoft retail products to integrated applications based on high technology [18].The third group is the planning and development of specially made applications (customized software), both by internal organizations and in collaboration with external parties, such as consultants and software houses [19].
System Design Method
In designing this E-Tailor Information System, we use UML (Unified Modeling Language).UML is also a way to facilitate continuous application development.Undocumented applications or systems can usually hinder development because developers have to perform searches and study the program code.UML can also be a tool for transferring knowledge about the system or application that will be developed from one developer to another.Not only between developers to business people and anyone can understand a system with UML.Fig. 1.System design use case Figure 1 is an illustration of the use case for designing a web-based e-tailor information system to be built.There are several main Use Case names that represent the design of the system that was built starting from: Login, Account registration, viewing types and details of clothes, manage individual orders, manage clothes and manage all orders
Data Collection Method
To create this E-Tailor Information System, we collect data from clients in the form of interviews, analyze the desired needs and use direct observation so that what is needed can be in accordance with what the client or user wants.
Test Method
The black box testing method focuses on the functional requirements of the software.Therefore, black box testing allows software developers to create a set of input conditions that will exercise all the functional requirements of a program [20] [21].
The method used in this web test uses the black box method with boundary value analysis techniques.The boundary value analysis technique tests the quality of the web by showing that there are still some errors when entering data to be tested in the column to determine whether the input value is valid or not with a predetermined lower and upper limit.So that the problems that occur can cause the data stored in the database is not in accordance with the expected data.The test is carried out on an e-tailor web form that has input by testing the upper limit value and lower limit value through several predetermined stages for each column contained in the form.
Result and Discussion
In this test apply black box techniques for the testing process on a web-based e-tailor information system.Testing is done by following the description of the test.The results of these tests are then recorded in the test results column.Based on the test results, you can then determine by adjusting the results of the test and the expected results.If the results tested are in accordance with the expected results (there are still obstacles or errors) then the conclusion is successful.If the results tested are not in accordance with the expected results, then the conclusion is a failure.
The testing method taken using the black box technique includes the functionality testing, usibility testing, interface testing, compatibility testing, performance testing, and security testing methods.These methods are used to find out if the software is working properly.In these methods test data is generated, executed on the software and then the output of the software is checked whether it is as expected or not.
For example, the functionality testing method, where in this section there are things that are tested including database connection testing, form testing, especially on forms used for CRUD activities (create, read, update, and delete) on the order menu, login and register pages, Cookie testing, Testing syntax or source code.
Conclusion
Based on the tests that have been carried out using the black box method including functionality testing, usability testing, interface testing, compatibility testing, performance testing, and security testing methods.It can be concluded that testing on a web-based e-tailor information system which in the example tested the login page that informed the suitability of the developed application with predetermined specifications.The test results show that the success rate of the application runs well.
Fig. 2 .
Fig. 2. Testing the login page on a web-based e-tailor information system In Figure 2 there are 2 inputs.Username input in the form of username receives input in the form of numbers, based on boundary value analysis techniques, examples of valid input values are between a-z & A-Z while invalid ones are 0-9.Password input accepts input in the form of letters and numbers, based on boundary value analysis techniques, examples of valid input values between a-z, A-Z and numbers between 0-9.while the invalid ones are a-z & A-Z only or numbers 0-9 only
Table 1 .
Test Case Login Form | 2,466.8 | 2021-01-01T00:00:00.000 | [
"Computer Science",
"Business"
] |
Relative phase locking of a terahertz laser system configured with a frequency comb and a single-mode laser
Abstract. Stable operation is one of the most important requirements for a laser source for high-precision applications. Many efforts have been made to improve the stability of lasers by employing various techniques, e.g., electrical and/or optical injection and phase locking. However, these techniques normally involve complex experimental facilities. Therefore, an easy implementation of the stability evaluation of a laser is still challenging, especially for lasers emitting in the terahertz (THz) frequency range because the broadband photodetectors and mature locking techniques are limited. In this work, we propose a simple method, i.e., relative phase locking, to quickly evaluate the stability of THz lasers without a need of a THz local oscillator. The THz laser system consists of a THz quantum cascade laser (QCL) frequency comb and a single-mode QCL. Using the single-mode laser as a fast detector, heterodyne signals resulting from the beating between the single-mode laser and the comb laser are obtained. One of the heterodyne beating signals is selected and sent to a phase-locked loop (PLL) for implementing the relative phase locking. Two kinds of locks are performed by feeding the output error signal of the PLL, either to the comb laser or to the single-mode laser. By analyzing the current change and the corresponding frequency change of the PLL-controlled QCL in each phase-locking condition, we, in principle, are able to experimentally compare the stability of the emission frequency of the single-mode QCL (fs) and the carrier envelope offset frequency (fCEO) of the QCL comb. The experimental results reveal that the QCL comb with the repetition frequency injection locked demonstrates much higher stability than the single-mode laser. The work provides a simple heterodyne scheme for understanding the stability of THz lasers, which paves the way for the further locking of the lasers and their high-precision applications in the THz frequency range.
In the entire electromagnetic spectrum, the terahertz (THz) region (roughly defined between 0.1 and 10 THz) [11][12][13] shows great advantages in spectroscopy, imaging, metrology, and communications, on account of its unique characteristics, e.g., covering vibrational and rotational absorption lines (fingerprints) of plentiful molecules, transparency to some packaging materials, and broader potential communication bandwidth compared to microwave. [14][15][16][17][18] Highly stabilized THz radiation sources are of great importance for the various applications mentioned above. Among different THz radiation sources, the electrically pumped THz quantum cascade laser (QCL), showing high output power, 19 wide emission frequency range, 20,21 high operation temperature, [22][23][24] high-quality far-field beam, 25,26 and narrow intrinsic linewidth, 27 is an ideal candidate for high-precision frequency comb operation. 28,29 Although the intrinsic linewidth of THz QCLs is narrow, the practical devices normally show broad linewidths due to the disturbances such as temperature drift, current variation, optical feedback and other environmental noises. So far, many efforts have been devoted to improving the stability of THz QCLs. Danylov et al. employed an analog circuit to lock the beatnote signal between a 2.308-THz QCL and a local CO 2 optically pumped molecular THz laser to a microwave local oscillator (LO), increasing the long-term stability of the THz QCL. 30 Freeman et al. injection locked a QCL emitting around 2 THz to a difference frequency generated by a pair of comb lines of a fiber-based near-infrared comb, and the intermode beatnote of the comb is referenced to a microwave source. Thus, the linewidth of the locked QCL is reduced to the linewidth of the microwave reference, which is <100 Hz. 31 Similarly, many efforts have been put on locking a single-mode QCL to a reference standard. [32][33][34][35][36][37][38][39][40][41][42] In addition, a large amount of work has been done to stabilize THz QCL frequency combs by locking the repetition frequency f rep and/or carrier envelope offset frequency f CEO . [43][44][45][46][47][48][49][50] All the above-mentioned techniques require complex experimental facilities with a highly stable THz LO. Furthermore, the evaluation of the frequency stability of THz QCLs is still challenging. For instance, even though the frequency noise power spectral density (FNPSD) can provide precise evaluation of the laser stability, 27,51 the setup to achieve FNPSD is relatively complex and in need of a proper discriminator.
In this work, we propose a simple method, i.e., a relative phase-locking scheme, to evaluate the stability of THz QCLs without a need for a THz LO. The laser system is configured with a THz QCL frequency comb and a single-mode QCL. The emission of the comb laser is injected directly onto the front facet of the single-mode laser, and the single-mode laser is used as a photodetector (or mixer) to obtain the current signal resulting from multiheterodyne beatings of the two lasers. To implement the relative phase locking, the heterodyne signal is sent to a phase-locked loop (PLL) module to generate the error signal for phase locking. Two kinds of phase locks, by either controlling the drive currents of the single-mode QCL or the QCL comb, are implemented. By analyzing the current (or frequency) change of the locked QCL in each case, we are able to compare the stability of the two lasers.
Relative Phase-Locking Scheme
The relative phase-locking scheme is shown in Fig. 1. Two THz QCLs, i.e., comb QCL1 (red solid lines) and single-mode QCL2 (blue dashed line), are employed in this scheme. The leftmost gray line in Fig. 1(a) refers to f CEO of the comb QCL1 with a repetition frequency of f rep . Each frequency of the comb lines can be fully defined as f M ¼ f CEO þ Mf rep , where M is the line order of a comb line. f s represents the emission frequency of the single-mode QCL2. When f s beats with different comb lines, the corresponding heterodyne beating signals, f 1 ; f 2 ; …; f n , are generated, as shown in Fig. 1(a). It is worth noting that heterodyne signal f n is the frequency difference between f s and f M , and it is located in the microwave frequency range. Therefore, the traditional PLL can be employed to lock f n to a microwave LO. As shown in Fig. 1(b), one of the heterodyne signals, f 2 , is selected for the phase locking. To satisfy the bandwidth requirement of the PLL module, f 2 is further downconverted to f 0 2 . The error signal generated from the PLL is either sent to QCL1 (loop ①) or QCL2 (loop ②) for different locks. It is worth noting that the proposed scheme consists of locking one laser with respect to the other laser; no reference standard is used. Therefore, the locking is actually a relative phase locking rather than a complete locking of each laser. Although the relative phase locking is not able to firmly lock the THz lines of the two lasers, it is much easier to be implemented because a THz reference standard is not needed. Moreover, by employing the relative phase-locking scheme, one can retrieve and compare the instability of the two lasers.
It is worth noting that the experimental scheme shown in Fig. 1 is upgraded based on the laser beating scheme proposed in Ref. 52 for detecting the frequency tuning coefficient of a single-mode THz QCL. However, the two schemes are different in working principles and experimental implementations. First, in Ref. 52, both lasers are 6-mm long, while in this work, the cavity length of the single-mode laser is reduced to 2 mm for a better single-mode performance. Second, in this work, two QCLs are placed face to face on two arms of a Y-shape sample holder and the distance between the two laser facets is 20 mm, while in Ref. 52, the two lasers are fully separated and located in two different cryostats. Furthermore, the most important difference is that in the current work, we implement the relative phase locking onto the laser system, which allows the evaluation of the laser stability without the need for complex facilities and a stable THz LO.
By comparing the stability of f n or f 0 n in two locking conditions, we are able to compare the stability of the two lasers. To make the comparison easier, the repetition frequency of the comb laser (QCL1), f rep , is injection-locked. Therefore, we can directly evaluate the relative stability of the comb carrier frequency (f CEO ) and f s of the single-mode laser. The detailed process can be described as follows.
Following the representative scheme shown in Fig. 1(a), f n and f 0 n can be written as where f RF1 is the frequency of the LO used for the frequency downconversion RF1 in Fig. 2(a). Then, we introduce the frequency instability, which can be defined by Δf ¼ df∕dt. Δf shows the time-dependent frequency fluctuation and all frequency components shown in Eqs. (1) and (2) will contribute to the total frequency instability. Hence, the instability of f n and f 0 n can be expressed as It is worth noting that in this work the comb repetition frequency (f rep ) is injection locked and RF1 is the LO frequency. Both frequencies are highly stable, and their instabilities can be Guan et al.: Relative phase locking of a terahertz laser system configured with a frequency comb and a single-mode laser neglected in the ideal case. Therefore, Eqs. (3) and (4) can be rewritten as It can be seen that the total instability results from two causes, i.e, comb carrier instability and single-mode laser instability. Then, when the relative phase locking is implemented on f 0 n , in an ideal phase-locking condition, no matter the PLL error signal is sent to QCL1 or QCL2, f 0 n will be firmly locked to the LO signal of PLL [f RF2 , see RF2 in Fig. 2(a)]. Because f RF2 is generated from a highly stable RF source, for both phase locking of QCL1 and QCL2, we would not be able to see the difference in f 0 n . Although f 0 n in both PLL conditions are identical and demonstrate high stability as the LO signal (f RF2 ), the inner locking behaviors are different. For instance, when the error signal is fed back to QCL1 (loop ①), the working PLL forces the comb laser (QCL1) to follow the behavior of the singlemode laser (QCL2). In this case, Eq. (5) can be written as where f 0 CEO refers to the frequency change of QCL1 resulting from the feedback current control because of the PLL implementation. f RF2 is stable and its instability can be neglected, i.e., Δf RF2 ≈ 0. Therefore, from Eq. (6), we can conclude that when the PLL is implemented on QCL1, the instability of the single-mode laser (Δf s ) is equal to the measured frequency change of the comb laser (Δf 0 CEO ). And Δf 0 CEO can be experimentally obtained by measuring the current change ΔI 1 and tuning coefficient (r 1 ) of QCL1 during the phase-locking process. Finally, we can evaluate the single-mode laser instability by performing PLL on the comb laser (QCL1) and Δf s can be estimated as Similarly, when loop ② is activated (the PLL is implemented on QCL2), the instability of the comb laser (QCL1) with the repetition frequency being injection locked can be written as where Δf 0 s is the frequency change of QCL2 resulting from the feedback current control because of the PLL implementation, ΔI 2 and r 2 are the current change and frequency tuning coefficient, respectively, of QCL2 during the phase-locking process. Based on the above analysis, we can compare the instability of the single-mode laser and the comb laser by implementing relative phase-locking experiments.
Experimental Setup and Laser Performance
The experimental setup of the relative phase locking presented in Fig. 1 is shown in Fig. 2(a). The comb laser (QCL1) and the single-mode laser (QCL2) employed in this experiment are both based on a hybrid active region design that exploits the boundto-continuum transition for THz photon emission and resonant phonon scattering for achieving the population inversion. The entire active region of the QCL based on Al 0.25 Ga 0.75 As∕GaAs multiquantum-well structures 53,54 was grown on a semiinsulating GaAs substrate using the molecular beam epitaxy technique. Then the grown wafer was processed into a single plasmon waveguide configuration. Finally, the annealed laser bars with different cavity lengths were cleaved and mounted on copper heat sinks for characterizations. It is worth noting that for QCL1, an optimal ridge width of 150 μm and a cavity length of 6 mm are adopted because the two dimensions have been proved to be more favorable for frequency comb operation. 18,47,55 For QCL2, to obtain a stable single-mode operation, a cavity length of 2 mm is used. This is because a shorter cavity results in a larger free spectral range (FSR) or a larger mode spacing. Given an identical gain bandwidth, it is much easier for short cavity lasers to obtain single-mode operation around the laser threshold. According to the mode analysis of single-plasmon waveguide QCLs with a same active region structure, 55 the fundamental transverse mode can be maintained for a laser ridge width of 150 μm. Note that the lasing bandwidth of the QCL with a dimension of 150 μm × 6 mm is operated in the comb state and QCL2 with a dimension of 150 μm × 2 mm is operated in the single-mode state. The light of QCL1 (orange) and QCL2 (blue) is coupled to the facets of each other to enable the heterodyne beating between the two lasers. Herein the heterodyne beating signals in the microwave frequency range are detected by QCL2 utilizing the self-detection method. The detected signals are extracted using a bias-T and then amplified and split into two: one is sent to the spectrum analyzer for observation and analysis; the other is downconverted by mixing with RF1, filtered, amplified for phase locking. Simultaneously, the signal is sent to a frequency counter for the frequency stability evaluation. RF2 serves as the LO signal of the PLL module to generate the error signal. Loop ① and ② represent locks with the error feedback to QCL1 and QCL2, respectively. RF3 is employed for the injection locking of QCL1 to stabilize its repetition frequency. (b) and (c) are L−I−V curves of QCL1 and QCL2 measured in continuous-wave (CW) mode when the heat sink temperature is stabilized at 25 K. (d) Emission spectra of QCL1 and QCL2 measured using a Fourier transform infrared spectrometer. For the spectral measurements, QCL1 and QCL2 are, respectively, operated at drive currents of 1000 and 250 mA at 25 K.
active region was measured to be larger than 300 GHz centered at 4.2 THz. 54 For the heterodyne measurements, the two QCLs were screwed onto a Y-shape cold finger. 18 Even though the coupling between two lasers would affect the emission of the two lasers, the effect is quite limited because the coupling is weak and only hundreds of nW power from one laser are finally injected into the other one. There are several advantages for this geometry. First of all, no optics and alignment are needed. Second, when the two lasers sit on the same cold finger, they actually share the same temperature and vibration noises, and these common noises can be canceled in the heterodyne measurements. Furthermore, when we compare the stability of two lasers, it would be fair to put them in the same physical environment, which is the case in our experiment. Due to the fast carrier relaxation time (picosecond-level) of QCLs, in this work QCL2 is used as a fast THz detector (or mixer) to obtain the current signal resulting from the beatings between QCL1 and QCL2. Finally, the current spectrum is registered on a spectrum analyzer for real-time visualization. 18,56 As shown in Fig. 2(a), the microwave signal is first transmitted through a microstrip line mounted close to QCL2 and then extracted by a bias-T. After the bias-T, the signal is amplified and split into two: one is used for spectral measurements; the other is downconverted, filtered, and amplified for the relative phase locking. The error signal of the PLL is transferred to current, which is added to the direct current (DC) of the QCL, and the added up current is then applied to the QCL. All these are implemented using a power module of the PLL (ppqSense S.r.l, QubeCL). As we elaborated in Fig. 1, two kinds of locking are proposed to compare the stability of the two lasers. Loop ① and loop ② represent the feedback controls to QCL1 and QCL2, respectively. Note that in the experiment, the comb laser (QCL1) is injection-locked to stabilize its repetition frequency. Figures 2(b) and 2(c) show the measured light-currentvoltage (L−I−V) characteristics of QCL1 and QCL2, respectively, recorded in CW mode at a stabilized temperature of 25 K. The current oscillations around 6 V observed in the I−V curves correspond to the negative differential resistance of the lasers, which can be clearly seen when the power supply is operated in a constant voltage mode. The CW power is measured using a THz power meter (Ophir, 3A-p THz) from one single facet without any corrections for water absorption, window transmission, mirror reflections, etc. Although the two lasers have different dimensions, they both can output a maximum power of 1.5 mW. The typical emission spectra of the two lasers are shown in Fig. 2(d). To operate QCL1 as a comb and QCL2 as a single-mode emission, the drive currents of the lasers are set 1000 and 250 mA, respectively (see Fig. S1 in the Supplementary Material for the intermode beatnote mapping of QCL1). As expected, the single-frequency line of QCL2 is located in the comb spectral range of QCL1, which is essential for the heterodyne measurements proposed in this experiment.
Results and Discussion
To verify the heterodyne beating scheme shown in Fig. 1, we show the measured beatnote signals in Fig. 3. The intermode beatnote frequency of the comb laser is measured to be 6.064963 GHz, with a power of −48 dBm, as shown by the black spectrum in Fig. 3. Multiple beatnote signals, i.e., f 1 to f 8 , resulting from the beats between QCL1 and QCL2 can be clearly observed. The frequencies of the recorded beatnote signals can basically satisfy the mathematical relationships mentioned in Fig. 1(a), which proves that the signals are indeed generated from the multiheterodyne beatings between the different comb lines of QCL1 and the single-frequency line of QCL2. The results shown in Fig. 3 directly indicate that the detection bandwidth of the single-mode laser (QCL2) can reach ∼23 GHz (≈f 8 ). Compared to the experimental results shown in Ref. 52, where a 6-mm long QCL operated in single mode demonstrates a detection bandwidth of 15.3 GHz, the 2-mm long QCL in this work shows a far broader bandwidth. It can be explained as follows. As the laser cavity length is shortened, the response time of the laser as a detector becomes faster, and therefore, it demonstrates a much wider bandwidth than that of long cavity device.
In Fig. 3, the multiheterodyne beating scheme between QCL1 and QCL2 is experimentally proved. To implement the relative phase locking, one of the heterodyne beating signals, i.e., f 2 , is selected. To make the stability comparison simpler, in this work the repetition frequency of the comb laser (QCL1) is injection-locked by a stabilized microwave signal at 6.06365 GHz with a power of −25 dBm. A relatively low RF power is applied to maximally suppress the noise of the RF synthesizer, which normally presents large phase noise at a high RF power. 57 In Fig. 4(a), we show the "maxhold" traces of the intermode beatnote of QCL1 when the RF injection is on and off. Here, the maxhold function of the spectrum analyzer can store the spectra maxima for a given measurement duration, which can directly evaluate the long-term frequency stability of a signal. It can be seen that for a 10-s measurement time, the free-running intermode beatnote (without RF injection) shows a maxhold linewidth of 19 kHz, while, as the RF injection is applied, the linewidth is significantly reduced and locked to be identical as the RF synthesizer. It verifies that the term MΔf rep can be neglected when the intermode beatnote is RF injection-locked, as demonstrated in Sec. 2. It is worth noting that the signal that we measured with RF injection shown in Fig. 4(a) consists of two contributions: one is the intermode beatnote and the other is the signal directed from the RF source. However, this is not a problem in this experiment. If the intermode beatnote of the comb laser is not locked to the RF source, the superposition of the two signals will result in a broad pedestal at a power level of −53 dBm [see the dashed curve in Fig. 4(a)]. However, as shown in Fig. 4(a), the broad pedestal is not observed, which indicates that the intermode beatnote is injection-locked to the RF source. In Figs. 4(b) and 4(c), we further show maxhold traces of the heterodyne beatnote f 2 without RF injection and with RF injection, respectively, for a time duration of 30 s. From RF off to RF on, we can observe a maxhold linewidth reduction of f 2 from 4.4 to 3.6 MHz. From Fig. 4, we can see the RF injection can improve the stability of f 2 . However, the locking effect on f 2 is not as strong as that on the intermode beatnote signal. This shows that although the repetition frequency of QCL1 is locked, f CEO and f s are still moving and therefore we observe a relative large maxhold linewidth of f 2 , even as the RF injection locking is implemented.
In Fig. 5, we show the results of the proposed relative phase locking of f 0 2 , which is downconverted from f 2 to ∼100 MHz to satisfy the PLL requirement. In the phase-locking experiment, the RF injection locking is always applied onto the comb laser. Figure 5(a) shows the maxhold trace of f 0 2 for 30 s without PLL. The measured maxhold linewidth of 3 MHz shows a good agreement with the result measured for f 2 [see Fig. 4(c)]. It is worth noting that the 600 kHz difference between the two measurements is relatively small when the PLL is off. This is show the phaselocked spectra obtained by sending the error signal either to QCL1 or to QCL2, respectively. The LO signal of the PLL module is set as 98 MHz. We can clearly see that for a time duration of 30 s, the locked signal, f 0 2 , at 98 MHz for both cases demonstrates ultrahigh stability. The observed servo bumps next to the narrow peak at 98 MHz in each case can prove that the phase locking works well. Note that in Figs. 5(b) and 5(c), we can observe some side peaks. The side peaks are not equally spaced, and they randomly appear and disappear during measurements (see Videos 1 and 2 in the Supplementary Material). Therefore, we assume that the side peaks may result from mechanical vibrations or other environmental noises. Figure 6 shows the screenshots of Videos 1 and 2.
As we elaborated in Sec. 2, once the phase-locking circuit works ideally, no matter what PLL feedback is sent to QCL1 or QCL2, the locked signal, f 0 2 , will be firmly locked to the LO signal and the LO's linewidth is then transferred to f 0 2 [see Eq. (6)]. In Fig. 7, we show the phase noise spectra and high-resolution beatnote spectra of f 0 2 for the two different phase-locking configurations. It can be seen from Fig. 7(a) that the phase noise is almost identical for both PLL measurements. The two curves both begin at 10-Hz offset from the carrier with the phase noise around −50 dBc∕Hz and show the same tendency during the entire offset frequency range up to 10 MHz. The phase noise spectra are measured by employing the phase noise module (K40) of the spectrum analyzer. In this measurement, if the signal is stabler, the measurable starting offset frequency is lower. The low measurable starting frequency of 10 Hz refers to a high stability of the signals. Figure 7(a) experimentally shows that the locked f 0 2 possesses the same stability, no matter whether the error signal is fed back to QCL1 or QCL2. Furthermore, in Figs 7(b) and 7(c) we show the high-resolution beatnote spectra of f 0 2 for the PLL feedback to QCL1 and QCL2, respectively, using a resolution bandwidth (RBW) of 1 Hz. One can clearly see that the measured signal-tonoise ratio (SNR) for both signals is 35 dB, which further indicates that the both locks work well, and locked signals demonstrate identical frequency stability.
Based on the analysis in Sec. 2 and experimental results shown in Fig. 7 the two QCLs by evaluating the locked f 0 2 . Although the two locked f 0 2 demonstrate identical stabilities, the efforts taken to ideally lock the two signals are different. It can also be seen in Fig. S2 in the Supplementary Material that the fluctuations of the phase error in two conditions are different. Therefore, we can estimate the frequency instability of QCL1 and QCL2 by analyzing the dynamical locking processes of the two different phase locks. This can be explained in detail as follows. When the feedback control is applied onto QCL1, we actually change the current of QCL1 to change its frequency to follow the frequency shift of QCL2. In the dynamic process, the heterodyne beating signal between QCL1 and QCL2, i.e., f 2 , is unchanged (locked). Therefore, the measured current change of QCL1 can be transferred to the frequency change of QCL1, which actually characterizes the frequency instability of QCL2; see Eq. (7). On the other hand, when the PLL feedback works on QCL2, the frequency change of QCL2 that we measured during the locking process gives the frequency instability of QCL1; see Eq. (8).
To retrieve the frequency instability, i.e., Δf ceo and Δf s , for QCL1 and QCL2, respectively, we first measure the current tuning coefficients of the two lasers and the current changes during the two different phase-locking processes. Taking advantage of the method proposed in Ref. 52, we can measure the current tuning coefficient of QCL1 and QCL2 precisely. Figure 8(a) shows that f 2 decreases when the drive current of QCL1 increases from 960 to 961 mA with a step of 0.2 mA. We can then obtain the current tuning coefficient of QCL1 which is ∼4.9 MHz∕mA. In Fig. 8(b), we show the drive current change of QCL1 (green dots) in a time duration of 40 s under the phaselocked condition. It can be seen that during the locking process, the current change of QCL1 can vary from −1.6 to 1.6 mA with a span of 3.2 mA, which is far larger than the current change of 1 mA shown in Fig. 8(a). Considering the mismatch between the current changes shown in Figs. 8(a) and 8(b), we plot the frequency change of QCL1 (red dots) within the current change of 1 mA for the right y axis in Fig. 8(b). From the frequency tuning measurement in Fig. 8(a), we cannot obtain the tuning coefficient, as the current change is larger than 1 mA. However, the results shown in Fig. 8(b) can ensure that the frequency change is larger than 4.9 MHz. Therefore, we can conclude that the frequency instability of QCL2 is larger than 4.9 MHz, i.e., Δf s > 4.9 MHz, for a time duration of 40 s.
In Figs. 8(c) and 8(d), we show the measured frequency tuning and the current change of QCL2, respectively, when the error signal is fed back to QCL2. As the drive current of QCL2 is increased from 275 to 276 mA with a step of 0.2 mA, f 2 increases with a frequency change of 16.2 MHz. It can be seen from Fig. 8(c) that an opposite direction of frequency shift is observed compared to the result shown in Fig. 8(a). Actually, this can be clearly explained by analyzing the scheme shown in Fig. 1(a). When the current of QCL1 increases, the THz modes of the comb will shift to higher frequencies (blueshift), which then results in a decrease of f 2 . On the other hand, as the current of QCL2 increases, f s shifts to higher frequencies (blueshift) and then an increase of f 2 is observed. From Fig. 8(c), a current tuning coefficient of QCL2, i.e., 16.2 MHz∕mA, can be obtained. It is worth noting that the tuning coefficient of QCL2 is far larger (∼3 times larger) than that of QCL1, which is due to the difference in device dimensions. The single-mode laser (QCL2) with a cavity length of 2 mm is 3 times smaller than the comb laser (QCL1) with a cavity length of 6 mm. Therefore, the current in QCL2 is scaled down by 3 times, which makes QCL2 more sensitive to the current change. Figure 8(d) shows the recorded current change of QCL2 in a time duration of 40 s under the phase-locked condition. During the process, one can see the current change varies from −0.07 to 0.07 mA with largest span of 0.14 mA. Because the current change of 0.14 mA is within the range of current change of 1 mA employed for the tuning characterization [ Fig. 8(c)], we can safely conclude that the frequency change of QCL1 is ∼2.3 MHz under the phase-locked condition. The measurement also indicates that the frequency instability of the comb laser (QCL1) with the repetition frequency locked is ∼2.3 MHz, i.e., Δf ceo ≈ 2.3 MHz, for a time duration of 40 s. From the measured results shown in Fig. 8, one can clearly see that the comb laser (QCL1) with the repetition frequency locked is stabler than the single-mode laser (QCL2), and the frequency instability of the lasers for a time duration of 40 s is directly measured, i.e., Δf ceo ≈ 2.3 MHz and Δf s > 4.9 MHz. We have to emphasize that the optical LO working in the THz frequency range is rare, and in this work, no THz frequency standard is used. Although we perform the relative phase locking and the THz lines are not firmly locked, the presented locking scheme with two different configurations allows us to quantitatively evaluate the long-term stability of the injection-locked comb laser and single-mode laser by analyzing the current (or frequency) changes of two QCLs under different phase-locked conditions. Note that we, in principle, can also do the phase locking without the RF injection locking. As shown in Fig. 7 (a) Phase noise spectra of f 0 2 measured when the error signal is fed back to QCL1 (red curve) and QCL2 (black curve). (b) and (c) are high resolution phase locked spectra of f 0 2 obtained by sending the error signal to QCL1 or QCL2 recorded using an RBW of 1 Hz. (4), if the repetition frequency of the comb laser is not injection-locked, all three frequencies, i.e., f CEO , f rep , and f s , will contribute to the instability of f 2 or f 0 2 . Therefore, f 0 2 will be much noisier, which makes the implementation of the PLL more difficult or even results in a failure of the phase locking.
Eqs. (3) and
It is worth noting that from our experimental results, the comb laser with the repetition frequency-locked shows much higher stability than the single-mode laser. This can be understood as follows. First of all, for semiconductor lasers, the cavity FSR noise is the main noise source. In the current experiment, the FSR of the comb is locked using microwave injection locking. Therefore, the main noise of the comb laser is suppressed. However, for the single-mode laser, the cavity perturbation still exists. Therefore, we observed that the comb laser with f rep locked is stabler than the single-mode laser. On the other hand, the device geometry difference between the two lasers is the cavity length, i.e., 6 and 2 mm for QCL1 and QCL2, respectively. Generally speaking, for the longer cavity laser, the refractive index is more insensitive to environmental noises. Moreover, in this work, when the PLL is performed with feedback to the single-mode laser, the comb laser, in principle, can be regarded as an optical reference. Since the comb laser is stabler, the single-mode laser is forced to follow the comb laser and the frequency stability of the single mode is improved. Therefore, the relative locking technique is an effective method to stabilize a single-mode laser, which can be further used in some applications where a long-term frequency stability is required, e.g., low pressure gas sensing, linewidth measurements, etc.
Conclusion
In summary, we have experimentally demonstrated a simple method, i.e., a relative phase-locking scheme, to evaluate and compare the stability of a single-mode QCL and a comb QCL (with the repetition frequency-locked) emitting in the THz frequency range. The beatnote signals resulting from the multiheterodyne beatings between the single-mode QCL and comb laser were successfully obtained using the laser self-detection technique. The stability of the locked heterodyne beating signals with PLL feedback to the single-mode laser or the comb laser was investigated. The experimental results demonstrated that in terms of maxhold linewidth, phase noise, and SNR, the locked signal with feedback to either single-mode laser or comb laser showed the same stability. By analyzing the current (or frequency) changes under the two phase-locked conditions, the proposed relative phase-locking technique can quantitatively retrieve the long-term instability of the two lasers, i.e., Δf ceo ≈ 2.3 MHz and Δf s > 4.9 MHz. The relative phase locking provides an easy and effective method to improve the stability of single-mode THz QCLs under the present circumstance, where the THz frequency reference (LO) is rare, which can be further implemented for spectroscopic applications. | 7,954.8 | 2023-02-24T00:00:00.000 | [
"Physics"
] |
Separation of 44Sc from Natural Calcium Carbonate Targets for Synthesis of 44Sc-DOTATATE
The rapid increase in applications of scandium isotopes in nuclear medicine requires new efficient production routes for these radioisotopes. Recently, irradiations of calcium in cyclotrons by α, deuteron, and proton beams have been used. Therefore, effective post-irradiation separation and preconcentration of the radioactive scandium from the calcium matrix are important to obtain the pure final product in a relatively small volume. Nobias resin was used as a sorbent for effective separation of 44Sc from calcium targets. Separation was performed at pH 3 using a column containing 10 mg of resin. Scandium was eluted with 100 μL of 2 mol L−1 HCl. Particular attention was paid to the reduction of calcium concentration, presence of metallic impurities, robustness and simple automation. 44Sc was separated with 94.9 ± 2.8% yield, with results in the range of 91.7–99.0%. Purity of the eluate was confirmed with ICP-OES determination of metallic impurities and >99% chelation efficiency with DOTATATE, followed by >36 h radiochemical stability of the complex. A wide range of optimal conditions and robustness to target variability and suspended matter facilitates the proposed method in automatic systems for scandium isotope separation and synthesis of scandium-labeled radiopharmaceuticals.
Introduction
Due to their specific properties, interest in the positron-emitting scandium isotopes as supplementary PET isotopes has recently been observed. 43 Sc (t 1/2 = 3.89 h, branching ratio β + : 88%) and 44 Sc (t 1/2 = 3.97 h, branching ratio β + : 94.3%) are good alternatives to 68 Ga, as they use similar complexing mechanisms. However, their half-lives are almost four times longer, which promotes applications for imaging processes, having slower pharmacokinetcs profiles.
DOTA (1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid) is one of the most frequently used chelators acting as a conjugate between the radioisotope and a targeting molecule due to the quick and steady incorporation of the isotope and covalent bonds creation with biomolecules responsible for targeting. DOTA-octapeptides are a group of PET tracers that specifically bind to somatostatin receptors (SST) that are over-expressed on the neuroendocrine tumor (NET) cells. In particular, imaging of neuroendocrine tumors [1,2] exhibiting overexpression of somatostatin receptor type 2 (SSTR2) was promisingly demonstrated in some clinical and preclinical studies with somatostatine analogues [3][4][5].
The reason for the rapid increase in scandium applications is the development of new, efficient production routes for radioisotopes in cyclotrons by α, deuteron and proton irradiations. Methods where nat CaCO 3 was used as a target material have gained special attention due to the low cost of production. Effective production via the 40 Ca(α,p) 43 Sc reaction was presented in Ref. [6], but the number of cyclotrons providing regular and intensive α beams is limited. Thus, proton irradiation with standard medical cyclotrons of 44 Ca at its natural abundance (2.09%) in CaCO 3 or CaO can provide adequate activity and be cost-effective for research and preclinical studies. Introduction of target material enriched with 44 Ca allows to produce greater 44 Sc activity for clinical studies and further regular applications, but due to the relatively high cost of 44 CaCO 3 , the target material needs to be recovered [4]. For all cases, post-irradiation separation and preconcentration of the radioactive scandium from the calcium matrix is required to give the pure final product in a relatively small volume. Although calcium is non-toxic and is approved in radiopharmaceutical preparations, its excess could influence negatively the radiolabeling yield and, especially in the case of 44 Ca, should be recovered for further use. Therefore, methods that allow effective scandium capture for labeling with the simultaneous release of possibly uncontaminated calcium for further processing are most often used [7]. For this purpose, filtration and solid phase extraction methods have been employed. In the first approach the target is dissolved in acid and neutralized to neutral or slightly alkaline conditions and scandium is separated as Sc(OH) 3 precipitate on a 0.22 µm filter while calcium passes for further processing [8]. The chemical purity of the Sc product is important since the presence of other metals (Fe 3+ , Al 3+ , Zn 2+ ) which form strong complexes with DOTA reduces the labeling yield, thus solid phase extraction on selective chelating or extracting sorbents was used. Ion exchange resin Chelex 100 [9], N,N,N ,N -tetra-n-octyldiglicolamide (DGA) resin [4,10,11] or Uranium and Tetravalent Actinides (UTEVA) extraction resin [12] were used for minimizing metal impurities coming from processing the target or recovered material. Nobias PA-1 (iminobisacetic acid-ethylenediaminetriacetic acid chelate resin) was successfully applied in marine research, due to the fact that it has extremely low affinity for alkali metals and alkaline earth metals while on the other hand it shows high sorption of rare earth elements (REE) and was used for REE preconcentration and the elimination of alkali metals and alkaline earth metals in one step in seawater and salt water samples [13,14]. As trivalent scandium is comparable with trivalent REE with respect to chemical behavior, this work is focused on the experimental evaluation of Nobias as a sorbent for effective separation of 44 Sc from calcium targets. Particular attention was paid to the reduction of the calcium matrix, the presence of metallic impurities, robustness, and simple automation.
Results and Discussion
Natural calcium carbonate is an interesting target material for the production of diagnostic scandium isotopes for preclinical studies with Positron Emission Tomography (PET). Depending on the available infrastructure, reasonable activities of scandium-43 can be produced in the 40 Ca(α,p) 43 Sc and 40 Ca(α,n) 43 Ti→ 43 Sc reactions, using heavy ion cyclotrons, or scandium-44 in the 44 Ca(p,n) 44 Sc reaction by proton irradiation with medical cyclotrons of natural calcium containing 2.09% calcium-44.
In the experiments, 44 Sc was produced in reactions induced by 15 MeV protons. Twelve targets were irradiated resulting in 150-200 MBq at end of bombardment (EOB).
Targets were placed in 10 mL polypropylene tubes, and 1 mL of 2 mol L −1 HCl was added. During dissolution, some differences in solubility were observed. Targets produced by protons of low beam intensity up to 10 µA dissolved quickly with intensive release of carbon dioxide. When working with targets irradiated with proton beam intensities higher than 10 µA (up to 25 µA), slower dissolution of the target material was observed due to the conversion of calcium carbonate to oxide. Complete dissolution of these targets required additional vortexing of the tube.
To evaluate the effect of pH on the sorption of scandium on Nobias resin, a series of sample solutions containing radioactive scandium 44 Sc(III) at hundreds of kBq activities were adjusted to the pH range of 3.0-10.0 and processed according to the recommended procedure. During the separation process activity immobilized on column, activity of effluent and rinsing buffer, and eluted activity and residual activity on column after elution were measured with a wipe counter. The results obtained are given as sorption efficiency in Figure 1. For comparison, similar studies were performed for a 0.22 µm filter, which was recently applied to scandium separation by filtration [15]. The point at pH 12 was added to estimate the precipitate behavior at higher pH.
Molecules 2018, 23, x FOR PEER REVIEW 3 of 10 and residual activity on column after elution were measured with a wipe counter. The results obtained are given as sorption efficiency in Figure 1. For comparison, similar studies were performed for a 0.22 μm filter, which was recently applied to scandium separation by filtration [15]. The point at pH 12 was added to estimate the precipitate behavior at higher pH. In the pH range of 3-6, sorption on the resin is almost quantitative, above 95%, and is stable and reproducible over the whole range. From pH 6 it decreases gradually but still exceeds 65%. Separation by precipitation on the 0.22 μm filter is effective at higher pH, reaching 90% at pH 10, but the optimum pH range is relatively narrow, sharply limited from pH 9 and gently decreasing at pH above 10. The results obtained are presented as sorption efficiency in Figure 1.
To check the desorption efficiency and residual activity on the column or filter, the respective item was eluted with 0.5 mL of 2 mol L −1 hydrochloric acid and the ratio between initial column activity and eluate activity was calculated. The results obtained are presented as elution efficiency in Figure 2. In the pH range of 3-6, the elution was complete and instantaneous, while there was a slight decrease in effectivity in more alkaline solutions, probably caused by slower precipitate dissolution kinetics than desorption in an acidic environment. This favors application of Nobias resin, where all operations are carried out under conditions that preclude the formation of precipitate. Slow In the pH range of 3-6, sorption on the resin is almost quantitative, above 95%, and is stable and reproducible over the whole range. From pH 6 it decreases gradually but still exceeds 65%. Separation by precipitation on the 0.22 µm filter is effective at higher pH, reaching 90% at pH 10, but the optimum pH range is relatively narrow, sharply limited from pH 9 and gently decreasing at pH above 10. The results obtained are presented as sorption efficiency in Figure 1.
To check the desorption efficiency and residual activity on the column or filter, the respective item was eluted with 0.5 mL of 2 mol L −1 hydrochloric acid and the ratio between initial column activity and eluate activity was calculated. The results obtained are presented as elution efficiency in Figure 2. and residual activity on column after elution were measured with a wipe counter. The results obtained are given as sorption efficiency in Figure 1. For comparison, similar studies were performed for a 0.22 μm filter, which was recently applied to scandium separation by filtration [15]. The point at pH 12 was added to estimate the precipitate behavior at higher pH. In the pH range of 3-6, sorption on the resin is almost quantitative, above 95%, and is stable and reproducible over the whole range. From pH 6 it decreases gradually but still exceeds 65%. Separation by precipitation on the 0.22 μm filter is effective at higher pH, reaching 90% at pH 10, but the optimum pH range is relatively narrow, sharply limited from pH 9 and gently decreasing at pH above 10. The results obtained are presented as sorption efficiency in Figure 1.
To check the desorption efficiency and residual activity on the column or filter, the respective item was eluted with 0.5 mL of 2 mol L −1 hydrochloric acid and the ratio between initial column activity and eluate activity was calculated. The results obtained are presented as elution efficiency in Figure 2. In the pH range of 3-6, the elution was complete and instantaneous, while there was a slight decrease in effectivity in more alkaline solutions, probably caused by slower precipitate dissolution kinetics than desorption in an acidic environment. This favors application of Nobias resin, where all operations are carried out under conditions that preclude the formation of precipitate. Slow In the pH range of 3-6, the elution was complete and instantaneous, while there was a slight decrease in effectivity in more alkaline solutions, probably caused by slower precipitate dissolution kinetics than desorption in an acidic environment. This favors application of Nobias resin, where all operations are carried out under conditions that preclude the formation of precipitate. Slow desorption in alkaline media was also observed in [15], where stopped-flow elution from the filter was proposed for better recovery.
Both the narrow range of applicable pH and instability of elution conditions could explain the diversity in the efficiency of scandium separation procedures by filtration reported in the literature: 73% [8], 93.6% [16], and 96% Sc recovery [15]. These papers show some inconsistency in proposing optimal pH for precipitate formation from 6.5 to above 10 pH units. Our experience shows that the range is narrow and an optimal pH close to 10 is critical for effective separation. Experiments performed with a 0.22 µm Millex filter gave an efficiency of 73.3 ± 16.5%, with single results in the range 47.8-96.1%. The problems identified were pH fluctuations, time of eluent contact with the filter and clogging of the filter with precipitates and graphite particles from the target support, which significantly increased the back-pressure in the system and generated issues in automatic operation. Comparing with separation using Nobias resin, average separation efficiency was 94.9 ± 2.8%, with results in the range 91.7-99.0%. No backpressure effects were observed, and any graphite particles were immediately deposited on the top of the column without disturbing the flow. All the above results show that separation on Nobias could be more tolerant of any deviations in sample preparation or target variability.
Another important parameter is the final volume of eluate, as this affects the ability to obtain a solution with high specific activity. This parameter is critical for effective labeling, keeping control on the concentration of metallic impurities and for further preclinical application [10]. Scandium from the Nobias column was effectively and immediately eluted with 100 µL of 2 mol L −1 hydrochloric acid, giving a radioactivity concentration in the range 0.5-1.0 GBq/mL, depending on the initial activity, while for the 13 mm diameter Millex filter the minimum volume of eluent was 500 µL of 2 mol L −1 hydrochloric acid with 5 min stop-flow after rinsing the filter. In other filtration-based methods discussed above volumes of eluate start from 150 µL but representing only 55% of trapped activity [8], up to 3 mL of 6 mol L −1 HCl [16], where further removal of HCl excess was required.
In a situation where recovery is necessary for economic reasons (i.e., for 44 CaCO 3 targets), the fraction collected after passing the sample through the Nobias column contains 98.1 ± 0.3% of the total calcium mass in the dissolved target, while a similar experiment for filtration gives 91.8 ± 0.6%. Subsequent rinsing with water increased this ratio to 99.8% and 99.7% respectively.
Other separation methods used resins: UTEVA [12], DGA [4,10,11] or Chelex [9]. Comparison of the methods presented in Table 1 shows that separation using Nobias is comparable with the most effective methods proposed so far but consumes the smallest volume of eluent needed to wash the adsorbed isotope.
Chemical purity of the processed 44 Sc solution is important, since the presence of other metals may interact with the DOTA chelator, as it is a non-specific complexing agent. Therefore, careful control of the metallic impurities in the sample is important for further labeling efficiency. The competing metals in the final solution were examined with a number of non-irradiated targets to estimate the concentrations of metal impurities using the ICP-OES method. The results presented in Table 1 show the concentrations of potential interferents at sub-mg L −1 levels, differing favorably from their content in other procedures where this effect was studied. This can be explained both by the use of high-purity reagents that are available for the proposed procedure and by the specific properties of the resin used. Nobias shows extremely low affinity towards alkaline metals [17] combined with almost quantitative sorption of transition metals in pH 5-6 [18] while the affinity is decreased significantly in pH < 4 [19,20]. REE metals show quantitative sorption in a similar pH range to the transition metals [21] but extend this property to more acidic conditions: pH 4.2 was successfully reported [13] and even pH 2.5 is suitable for efficient sorption [22], which is consistent for scandium in the present results ( Figure 1). Thus, this pH value seems to be optimal, taking into consideration the sorption efficiency and simultaneous impurity removal. As the reactivity of radioisotope and ligand is an indirect method of quantifying the metallic impurities and the final quality of the separated scandium, to check the overall method performance, radiolabeling with DOTATATE was used to asses and confirm the chemical purity of eluates. The radiochemical yields exceed 99% for 30 min reaction at 95 • C. The 44 Sc-DOTATATE peak was observed at R f = 0-0.2 in citrate buffer, while 44 Sc 3+ migrated with the front of the solution and a signal was recorded at R f = 0.7-1.0. Reversed order was observed on the plates developed in ammonia acetate/methanol: unchelated Sc was deposited on the start line and 44 Sc-DOTATATE traveled with R f > 0.6. Maximum specific activity was 14 GBq/µmol but in routine experiments was set to 2.8 ± 0.3 GBq/µmol to standardize further steps. Both methods showed that labeling was effective and no deviations occurred due to poor quality of the Sc solution. Chromatograms and experimental results are available in Supplementary Materials.
Presence of metallic impurities in the labeling solution could cause the transmetallation and finally release of 44 Sc 3+ to the solution. Therefore, stability of labeled peptide could be thought as an indirect method of metallic contamination assessment. Proposed for DOTA-labeled peptides synthesis with 44 Sc from generator [24] was adopted for cyclotron produced Sc [4,15] and referred to main impurity (Ca 2+ ), metallic impurities behaving similarly to Sc 3+ (Fe 3+ ) or typical metallic impurities (Zn 2+ , Al 3+ , Ni 2+ , Cu 2+ ), showing no significant changes in stability. To assess the transmetallation, a stability test, where 44 Sc-DOTATATE was incubated for 36 h at room temperature with regular radiochemical purity determinations with HPLC was performed. To reduce the influence of the radiolytic decomposition of the peptide, mediated by γ-ray induced free radicals, 5% addition of ethanol as a scavenger was carried out. The results showed that transmetallation was negligible since the radiochemical purity did not drop below 99%, which confirmed the high stability of the 44 Sc-DOTATATE labeling. For comparison another approach, based on determination of the lowest chelator concentration, required for quantitative labeling [25] was tested. Seven DOTATATE solutions, containing 0.07-28 nmol of peptide, were labeled with 44 Sc under conditions previously successfully used, and the yield was then tested by TLC. All the samples gave satisfactory results, only for the lowest concentration yield decreased to 95.5%, showing the first signs of interferences in labeling, probably caused by cold metallic impurities competition. Comparable chelator amounts were used during DOTA labeling with 44 Sc produced in cyclotron and separated on DGA resin (0.07 nmol), while labeling with 44 Sc obtained from generator gave worse results and required at least 3 nmol [25] Molecules 2018, 23, 1787 6 of 10 of chelator. Similar values were presented in another study for DOTATOC labeled with generator produced 44 Sc, where more than 7 nmol of peptide was required for effective complexation [24], showing significant differences in labeling yields for 44 Sc obtained from generator and cyclotron.
ICP multi-element standard solution for MS (10 mg L −1 , EMD Millipore) was used for calibration standards in the determination of metallic impurities.
Apparatus
An ISMATEC peristaltic pump and 11 Elite (Harvard Apparatus, Holliston, MA, USA) syringe pump were used for liquid transfers, an Atomlab 500 dose calibrator and wipe tester (Biodex, Shirley, NY, USA) was used for activity determination, a Bioscan TLC reader Miniscan (Bioscan, Washington, DC, USA) with BioChrome software was used for thin layer chromatogram evaluations, a Thermo Scientific iCAP 6000ICP OES spectrometer was used for impurity determination. The instrumental settings of the manufacturers were as follows: RF generator power 1.15 kW, auxiliary gas flow 0.5 L min −1 , nebulizer gas flow 0.40 L min −1 , coolant gas flow 12 L min −1 . For stability assessment the Shimadzu AD20 HPLC system with UV-Vis (ultraviolet-visible) and radiometric detector GabiStar (Raytest, Straubenhardt, Germany) was used.
44 Sc Production from nat CaCO 3
The target uses the design presented in [26]. Briefly, 85-90 mg of calcium carbonate was compacted in the form of a pill of ca. 6 mm diameter. The pill was then pressed into a graphite target support and placed in an alumina holder, fitting a home-made station for solid target irradiation (RP patent no. 227402) with a standard GE Pettrace 830 medical cyclotron. Targets were irradiated for around 2 h with 10 µA 15 MeV proton beam, resulting in 150-200 MBq activities at EOB.
Preconcentration System
The preconcentration device (Figure 3) was equipped with a 3-valve module, common in many radiochemical devices i.e., Eckert-Ziegler. The target dissolution and reagent distribution were done in single sterile syringes screwed into the luer-lock connectors. Between the syringe and the column, a 0.45 µm filter was placed to remove any graphite particles, which could occur during target dissolution. The column was made in a 300 µL polypropylene pipette tip containing 10 mg of the resin placed between polyethylene frits. The sample and rinsing buffer were loaded with an ISM833 Ismatec peristaltic pump at 1 mL min −1 , while the column was eluted at 0.25 mL min −1 with a micro-syringe pump to reduce the eluate volume and manifold blank.
Molecules 2018, 23, x FOR PEER REVIEW 7 of 10 dissolution. The column was made in a 300 μL polypropylene pipette tip containing 10 mg of the resin placed between polyethylene frits. The sample and rinsing buffer were loaded with an ISM833 Ismatec peristaltic pump at 1 mL min −1 , while the column was eluted at 0.25 mL min −1 with a microsyringe pump to reduce the eluate volume and manifold blank.
Sorption Experiments
Targets were dissolved in 1 mL of hydrochloric acid and were aliquoted into volumes containing about 5% of target activity. To assess the sorption on Nobias, each portion was adjusted to a respective pH value from 3 to 10 with suitable buffers and sodium hydroxide, and then the solution was passed through the microcolumn. The column was rinsed with 3 mL of the buffer and activities of the column and eluate were measured with a dose calibrator. Elution of scandium was carried out using 0.5 mL of 2 mol L −1 HCl at a flow rate of 0.5 mL min −1 , and the activity of the eluate and residual activity on the column were measured.
Separation by Filtration
To check the efficiency of scandium separation by precipitation and filtration, the sample was pH adjusted to a respective value from 3 to 12 pH units with suitable buffers and sodium hydroxide and the solution was loaded into a 0.2 μm filter (Whatmann, Buckinghamshire, UK) to trap any possible precipitate. Subsequently, the filter was rinsed with 3 mL of the buffer and the activities on the filter and in the eluate were measured with a dose calibrator. The scandium from the filter was eluted by 0.5 mL of 2 mol L −1 HCl at a flow rate of 0.5 mL minL −1 with a 30 s stop-flow after wetting the filter. The activity of the eluate and the residual filter activity were measured. Each experiment was done in triplicate.
Target Processing Procedure
The irradiated target was disassembled with plastic tools and transferred to the syringe. 1 mL of 2 mol L −1 HCl was added and after complete dissolution of the calcium carbonate pellet 700 μL of 1 mol L −1 NaOH and 1 mL of 1 mol L −1 formic buffer pH 3.0 were added. Valve V1 was opened and the solution was pumped with a peristaltic pump through the column and the eluate was sent to wastes, where it could be collected separately for further recycling. Valve V1 was then closed and V2 was opened for rinsing the column with 2 mL of formic buffer pH 3.0. After evacuation of the solution V2
Sorption Experiments
Targets were dissolved in 1 mL of hydrochloric acid and were aliquoted into volumes containing about 5% of target activity. To assess the sorption on Nobias, each portion was adjusted to a respective pH value from 3 to 10 with suitable buffers and sodium hydroxide, and then the solution was passed through the microcolumn. The column was rinsed with 3 mL of the buffer and activities of the column and eluate were measured with a dose calibrator. Elution of scandium was carried out using 0.5 mL of 2 mol L −1 HCl at a flow rate of 0.5 mL min −1 , and the activity of the eluate and residual activity on the column were measured.
Separation by Filtration
To check the efficiency of scandium separation by precipitation and filtration, the sample was pH adjusted to a respective value from 3 to 12 pH units with suitable buffers and sodium hydroxide and the solution was loaded into a 0.2 µm filter (Whatmann, Buckinghamshire, UK) to trap any possible precipitate. Subsequently, the filter was rinsed with 3 mL of the buffer and the activities on the filter and in the eluate were measured with a dose calibrator. The scandium from the filter was eluted by 0.5 mL of 2 mol L −1 HCl at a flow rate of 0.5 mL minL −1 with a 30 s stop-flow after wetting the filter. The activity of the eluate and the residual filter activity were measured. Each experiment was done in triplicate.
Target Processing Procedure
The irradiated target was disassembled with plastic tools and transferred to the syringe. 1 mL of 2 mol L −1 HCl was added and after complete dissolution of the calcium carbonate pellet 700 µL of 1 mol L −1 NaOH and 1 mL of 1 mol L −1 formic buffer pH 3.0 were added. Valve V1 was opened and the solution was pumped with a peristaltic pump through the column and the eluate was sent to wastes, where it could be collected separately for further recycling. Valve V1 was then closed and V2 was opened for rinsing the column with 2 mL of formic buffer pH 3.0. After evacuation of the solution V2 was closed, V4 was switched to another position, V3 was opened and the syringe pump was started, pumping 100 µL of 2 mol L −1 HCl, which was collected in the 1.5 mL Eppendorf tube for manual operations or injected directly to the reaction vial of the Eckert-Ziegler module for automated synthesis. The sequence of operations is presented on the flowchart in Figure 4. was closed, V4 was switched to another position, V3 was opened and the syringe pump was started, pumping 100 μL of 2 mol L −1 HCl, which was collected in the 1.5 mL Eppendorf tube for manual operations or injected directly to the reaction vial of the Eckert-Ziegler module for automated synthesis. The sequence of operations is presented on the flowchart in Figure 4.
The entire process was performed with a number of non-irradiated targets to estimate the concentrations of metal impurities with ICP-OES.
Chelation Efficiency
Radiolabeling of DOTATATE with scandium was performed by mixing the eluted scandium with 40 μg (ca. 28 nmol, 20 μL of 2 μg μL −1 stock solution in water) DOTATATE in 200 μL 0.2 mol L −1 ammonium acetate buffer (pH 4.0) and equimolar vs. added HCl amount of NaOH then heating for 30 min at 95 °C. Radiochemical yield was determined by thin layer chromatography by developing of 2-5 μL spots on 10 cm silica gel strips in 0.1 mol L −1 citrate buffer pH 4.0 or 1 mol L −1 ammonia acetate:methanol (1:1, v/v). Radioactivity distribution was recorded on a Bioscan TLC reader Miniscan and quantitatively evaluated with BioChrome software. For stability assessment the Shimadzu AD20 HPLC system with UV-Vis and GabiStar radiometric detector was used. The separation was done on a Phenomenex Gemini C18 column (150 mm × 4.0 mm i.d., 5 μm), with 375:115:0.5 (v/v/v) water:acetonitrile:trifluoroacetic acid as a mobile phase and 1.5 mL/min flow rate.
Conclusions
A fast and simple method of scandium-44 separation from natural calcium carbonate on Nobias chelating resin was presented. Almost quantitative separation, followed by high chemical purity and low final volume, favors this method for routine processing of solid targets. A wide range of optimal conditions and robustness to target variability and suspended matter facilitates the application of the method in automatic systems for scandium isotope separation and synthesis of scandium labeled radiopharmaceuticals. The entire process was performed with a number of non-irradiated targets to estimate the concentrations of metal impurities with ICP-OES.
Chelation Efficiency
Radiolabeling of DOTATATE with scandium was performed by mixing the eluted scandium with 40 µg (ca. 28 nmol, 20 µL of 2 µg µL −1 stock solution in water) DOTATATE in 200 µL 0.2 mol L −1 ammonium acetate buffer (pH 4.0) and equimolar vs. added HCl amount of NaOH then heating for 30 min at 95 • C. Radiochemical yield was determined by thin layer chromatography by developing of 2-5 µL spots on 10 cm silica gel strips in 0.1 mol L −1 citrate buffer pH 4.0 or 1 mol L −1 ammonia acetate:methanol (1:1, v/v). Radioactivity distribution was recorded on a Bioscan TLC reader Miniscan and quantitatively evaluated with BioChrome software. For stability assessment the Shimadzu AD20 HPLC system with UV-Vis and GabiStar radiometric detector was used. The separation was done on a Phenomenex Gemini C18 column (150 mm × 4.0 mm i.d., 5 µm), with 375:115:0.5 (v/v/v) water:acetonitrile:trifluoroacetic acid as a mobile phase and 1.5 mL/min flow rate.
Conclusions
A fast and simple method of scandium-44 separation from natural calcium carbonate on Nobias chelating resin was presented. Almost quantitative separation, followed by high chemical purity and low final volume, favors this method for routine processing of solid targets. A wide range of optimal conditions and robustness to target variability and suspended matter facilitates the application of the method in automatic systems for scandium isotope separation and synthesis of scandium labeled radiopharmaceuticals.
Supplementary Materials:
The following are available online. Figure S1: pH dependence of Ca concentration in 44 Sc solution after separation, Figure S2: Elution profiles of Nobias column and 0.22 µm filter, Figure S3: Thin-layer chromatograms of 44 Sc-DOTATATE, 44 Sc and resolution test for the mixture of 44 Sc and 44 Sc-DOTATATE, Figure S4: HPLC Resolution test for 44 Sc and 44 Sc-DOTATATE, Figure S5: Stability test for 44 Sc-DOTATATE within 36 h after end of synthesis (EOS), Figure S6: γ-spectra of produced 44 Sc, Table S1: 44 Sc labeling yields for DOTATATE at different ligand concentrations.
Funding: This work and APC were financially supported by the National Centre for Research and Development, Poland, project PBS3/A9/28/2015. | 7,040.6 | 2018-07-01T00:00:00.000 | [
"Chemistry"
] |
Surface Chelation Enabled by Polymer-Doping for Self-Healable Perovskite Solar Cells
Polymer doping is an efficient approach to achieve self-healing perovskite solar cells. However, achieving high self-healing efficiency under moderate conditions remains challenging. Herein, an innovative self-healable polysiloxane (PAT) containing plenty of thiourea hydrogen bonds was designed and introduced into perovskite films. Abundant thiourea hydrogen bonds in PAT facilitated the self-healing of cracks at grain boundaries for damaged SPSCs. Importantly, the doped SPSCs demonstrated a champion efficiency of 19.58% with little hysteresis, almost rivalling those achieved in control atmosphere. Additionally, owing to the effective chelation by PAT and good level of thiourea hydrogen bonds, after 800 cycles of stretching, releasing and self-healing, the doped SPSCs retained 85% of their original IPCE. The self-healing characteristics were demonstrated in situ after stretching at 20% strain for 200 cycles. This strategy of pyridine-based supramolecular doping in SPSCs paves a promising way for achieving efficient and self-healable crystalline semiconductors.
Introduction
Stretchable hybrid organic-inorganic halide perovskite-based solar cells (SPSCs) are attractive photoelectric materials exhibiting the advantages of extraordinary powerconversion efficiencies (PCE over 18%), low cost, and easy manufacturing while exhibiting strong panchromatic sunlight absorption, long carrier diffusion lengths, and adjustable direct bandgaps [1][2][3]. SPSCs should attain high photovoltaic levels and properties fabricated by grid-connection PSCs, while synchronously sustaining remarkable stretchability and fatigue resistance [4][5][6]. However, poor crystallinity and fragility upon stretching would generate plenty of cracks at grain boundaries (GBs), consequently exacerbating the photovoltaic properties of SPSCs [7][8][9][10]. Nonradiative charge recombination, resulting from these defective GBs, would lead to the loss of photovoltaic efficiency and environmental stability in air [11,12]. Furthermore, cracks at GBs would rapidly spread to the whole device and the mechanical stability will become aggravated dramatically. Challengingly, the damaged areas struggle to heal themselves owing to the intrinsic brittleness of perovskite crystals [13,14]. In this context, various approaches on interface engineering and polymer doping have emerged to enhance the perovskite crystallinity of stretchable perovskite devices [14][15][16][17]. By doping organic molecules or metal oxide materials into films, the crystallinity could be enhanced prominently, and high stretchability (20% strain) can also be achieved [13,18,19]. On the other hand, PCE of SPSCs could also be improved with a satisfactory stretchability by doping into the polymer scaffolds interface of GBs [6]. However, self-healing is still the "Achilles' heel" of optoelectronic and mechanical stretchability [13,20].
In our previous work, pyridine-based polysiloxane was prepared and introduced into perovskite films to enhance the crystallinity. However, the self-healing time and efficiency still need to be improved, owing to the low transferability of urea-based hydrogen bonding units. Herein, an innovative self-healable PAT polymer containing plenty of thiourea hydrogen bonds was designed and introduced into FAPbI 3 perovskite films ( Figure 1). Significantly, abundant thiourea hydrogen bonds, endowing the PAT polymer with superior polymer transferability, afforded the improvement of the self-healing of cracks at GBs for damaged SPSCs. Accordingly, after 800 cycles of stretching, releasing and healing (at 100 • C for 15 min), the doped SPSCs retained 85% of their original IPCE. The healing characteristic were demonstrated in situ after stretching at 20% strain for 200 cycles. Moreover, pyridine units were also adapted to form strong intermolecular coordination interactions and passivate the grain boundary. The doped SPSCs prepared in 40% relative humidity (RH) demonstrated a champion efficiency of 19.58% with little hysteresis, almost rivalling those achieved in control atmosphere. This strategy of pyridinebased supramolecular doping in SPSCs paves a promising way for achieving efficient and self-healable crystalline semiconductors. improved with a satisfactory stretchability by doping into the polymer scaffolds interface of GBs [6]. However, self-healing is still the "Achilles' heel" of optoelectronic and mechanical stretchability [13,20]. In our previous work, pyridine-based polysiloxane was prepared and introduced into perovskite films to enhance the crystallinity. However, the self-healing time and efficiency still need to be improved, owing to the low transferability of urea-based hydrogen bonding units. Herein, an innovative self-healable PAT polymer containing plenty of thiourea hydrogen bonds was designed and introduced into FAPbI3 perovskite films ( Figure 1). Significantly, abundant thiourea hydrogen bonds, endowing the PAT polymer with superior polymer transferability, afforded the improvement of the self-healing of cracks at GBs for damaged SPSCs. Accordingly, after 800 cycles of stretching, releasing and healing (at 100 °C for 15 min), the doped SPSCs retained 85% of their original IPCE. The healing characteristic were demonstrated in situ after stretching at 20% strain for 200 cycles. Moreover, pyridine units were also adapted to form strong intermolecular coordination interactions and passivate the grain boundary. The doped SPSCs prepared in 40% relative humidity (RH) demonstrated a champion efficiency of 19.58% with little hysteresis, almost rivalling those achieved in control atmosphere. This strategy of pyridine-based supramolecular doping in SPSCs paves a promising way for achieving efficient and selfhealable crystalline semiconductors.
Fabrication of PSC Devices
Initially, both of the bottom and top transparent electrodes (hc-PEDOT:PSS) with a thickness of~0.15 mm were prepared, as in previous reports [21]. Briefly, PEDOT:PSS (Heraeus CLEVIOSTM PH1000, Shanghai, China) with 20 mg/mL Zn(TFSI) 2 (Sigma-Aldrich, Shanghai, China) were mixed together, then the ink were slot-die coated on the PDMS substrates via optimized shear stress. The conductivity is over 4000 S·cm −1 , which is comparable to that of the PET/ITO. As for matching the energy level alignment of device, a 30 nm hole-transport layer (HTL) PEDOT:PSS (Heraeus CLEVIOSTM Al4083, Shanghai, China) was then meniscus-coated the hc-PEDOT:PSS anode. Meanwhile, the PEI (Aldrich, Shanghai, China, 0.1 wt% diluted by isopropanol) was used to treat the PEDOT:PSS Al4083 layer for the top cathode. The 3M copper tape was applied to adhere to the electrode via silver glue.
Solar Cells Characterizations
The current density-voltage (J-V) curves are characterized using Keithley 2400 Source meter (Beijing, China,). The currents are measured under the solar simulator (EnliTech, Beijing, China, 100 mW cm −2 , AM 1.5 G irradiation) and the reference silicon solar cell is corrected from NREL. All the measurements are performed under nitrogen at room temperature. The reverse scan range is from 1.3 V to 0 V and the forward scan range is 0 V to 1.3 V, with 8.0 mV for each step, and the scan rate is 0.2 V s −1 , with a delay time of 30 ms. The incident photo-to-electron conversion efficiency spectra (IPCE) are detected under monochromatic illumination (Oriel Cornerstone 260 1/4 m monochromator equipped with Oriel 70613NS QTH lamp, Beijing, China,), and the calibration of the incident light is performed with a monocrystalline silicon diode. The area of PSCs was corrected by calibrated apertures (0.1 cm 2 ). The repeated stretching cycle tests are performed by a custom-made stretching machine which is actuated by a stepper motor (Beijing, China, Zhongke J&M). All the results of stretching test results are averaged from over 50 samples.
As for the self-healing J-V tests, all the samples were re-annealed on a hot plate at 100°C for 15 min.
General Characterizations
X-ray diffraction patterns (XRD) were recorded with a Bruker D8 Discover Diffractometer (Beijing, China) with Cu Kα radiation (1.5406 Å). The step size, testing temperature and weight of the samples were 0.02 • , 25 • C and 3 g, respectively. The testing angle (2θ), voltage and current were 5~80 • , 40 kV and 40 mA, respectively. Top-view, cross-sectional SEM images were obtained with a field-emission scanning electron microscope (JEOL, JSM-7500F, Tokyo, Japan) at an accelerating voltage of 15.0 kV. AFM were obtained by using Veeco IIIa Multimode scanning probe microscope. The ultraviolet-visible (UV-Vis) spectra are recorded by Ocean Optics spectrophotometer (Shanghai, China). Steady-state photoluminescence (PL) and time-resolved photoluminescence (TRPL) measurements at the peak emission of~770 nm (on the excitation at 470 nm) are carried out by the steady state and lifetime spectrometer (FLS920, Edinburgh Instruments Ltd. London, UK). The TRPL excitation fluence is~4 nJ·cm −2 from a 405 pulsed laser with a wavelength of 405 ± 8 nm and pulse width of 45 ps, at a repetition rate of 0.1 MHz. The PL decay data is recorded using time-correlated single photon counting technique. Fourier transform infrared spectra (FT-IR, Thermos Nicolet 6700 spectrometer, Berlin, Germany) were collected to characterize the surface chemical structure.
Results and Discussion
Various measurement techniques and theorical simulation were performed to verify the adequacy of PAT passivation crystallization upon the stretchable perovskite films. Initially, scanning electron microscope (SEM) of pristine and doped perovskite films were carried out to illustrate the enhancing of crystallinity (Figure 2a and Figure S5, Supporting Information). The grain size of perovskite crystals in SEM images were calculated by ImageJ software. ImageJ is a statistic analysis software based on Java designed by the National Institutes of Health (New York, NY, USA), which has been widely utilized to calculate and analyze the nanoparticle size in SEM images [13,20]. Obviously, with the incorporation of PAT, the grain-size enlarged remarkably from 0.650 µm to 1.25 µm (as shown in the inset graph). Furthermore, hydrophobic siloxane units were introduced into PAT molecular structure to increase the environmental stability. Contact angle (CA) measurements of pristine and doped perovskite films were carried out ( Figure S4, Supporting Information). The CA increased from 62.59 • to 78.32 • , demonstrating that the siloxane structures in PAT result in an excellent hydrophobic characteristic, and the moisture-resistance of perovskite films was dramatically enhanced [23]. Subsequently, steady-state photoluminescence and optical absorption performances were explored and showed an apparent increase. As the optical absorption spectra illustrated, the utilization ratio of light spectrum markedly improved with the introducing of PAT polymer (Figure 2c). Furthermore, it could be found from fitted the time-resolved photoluminescence curves (TRPL, Figure 2d) that the perovskite films doped with PAT polymer displayed fast and slow phase lifetimes of τ 1 = 8.6 and τ 2 = 39.7 ns, respectively, whereas the pristine perovskite films exhibited lifetimes of τ 1 = 5.3 ns and τ 2 = 24.2 ns, respectively. Attributed to this decay, the concentration of trap-states tended to be lower and the electronic quality of doped films were improved intensively [16,24]. Additionally, XRD spectra were also patterned to explore the enhanced crystallinity as shown in Figure S6. The weak peak located at 14.4 • and 28.2 • can be indexed to the (110) and (220) plane of α-FAPbI 3 , respectively. In theory, the compact coordination interactions between perovskite crystals and doped polymer could effectively passivate the GBs to withdraw various environmental stimuli. To profoundly demonstrate the mechanisms of improved crystallinity, first principle computational analysis based on density functional theory (DFT) was performed and the bichelation mechanisms were proposed. Briefly pyridine units in PAT, acted as Lewis bases and formed a chelation adduct with PbI2 (−1.601 eV) in the precursor, exhibiting strong intermolecular Pb 2+ -Namido, I − -Npyridyl, and Pb 2+ -Oamido coordination interactions ( Figure 3a). Consequently, the higher energy barrier generated by the plentiful PAT-Pb 2+ bichelation interactions would restrict the formation of FAPbI3 (formamidinium iodide as the organic cation). The higher energy barrier increased the critical concentration, contributing to the enlarged crystal grains. Moreover, the pyridine unit in PAT could be intensively adsorbed onto FAPbI3 surface with a higher adsorption-energy (−1.852 eV, Figure 3b) [25]. The original molecule and single-chelation passivation molecule showed an unstable state due to the lower adsorption energy, −0.183 eV and −0.231 eV, respectively. Additionally, iodine (I -) vacancy could also be passivated by pyridine units and compensated for the loss of electronic at GBs, preventing the photo-electrons being captured by these defects and thus reducing non-irradiative recombinations [26]. Therefore, attributed to these bichelation interactions of PAT as an inhibitor, intact crystallinity were achieved with oriented growth [27]. In theory, the compact coordination interactions between perovskite crystals and doped polymer could effectively passivate the GBs to withdraw various environmental stimuli. To profoundly demonstrate the mechanisms of improved crystallinity, first principle computational analysis based on density functional theory (DFT) was performed and the bichelation mechanisms were proposed. Briefly pyridine units in PAT, acted as Lewis bases and formed a chelation adduct with PbI 2 (−1.601 eV) in the precursor, exhibiting strong intermolecular Pb 2+ -Namido, I − -Npyridyl, and Pb 2+ -Oamido coordination interactions ( Figure 3a). Consequently, the higher energy barrier generated by the plentiful PAT-Pb 2+ bichelation interactions would restrict the formation of FAPbI 3 (formamidinium iodide as the organic cation). The higher energy barrier increased the critical concentration, contributing to the enlarged crystal grains. Moreover, the pyridine unit in PAT could be intensively adsorbed onto FAPbI 3 surface with a higher adsorption-energy (−1.852 eV, Figure 3b) [25]. The original molecule and single-chelation passivation molecule showed an unstable state due to the lower adsorption energy, −0.183 eV and −0.231 eV, respectively. Additionally, iodine (I − ) vacancy could also be passivated by pyridine units and compensated for the loss of electronic at GBs, preventing the photo-electrons being captured by these defects and thus reducing non-irradiative recombinations [26]. Therefore, attributed to these bichelation interactions of PAT as an inhibitor, intact crystallinity were achieved with oriented growth [27].
To verify the feasibility of PAT dopant and the self-healing of photovoltaic devices, SP-SCs with a structure of stretchable substrate (PDMS [28])/PEDOT:PSS/perovskites/PCBM/ PEDOT: PSS/PDMS were assembled. To explore the optimal doping concentration of PAT, PCE of different SPSCs were tested as shown in Figure S7. It could be found that, with the increase in PAT concentration from 0 (0.05 mg·mL −1 ) to 0.035 wt% (0.1 mg·mL −1 ), PCE increased gradually from 17.51% to 19.58%, which could be attributed to the enhanced crystallinity. However, when the concentration of PAT increased to 0.051 wt% (0.15 mg·mL −1 ), large amounts of pinholes formed in perovskite films, resulting in lower PCE. Based on these tests, 0.035 wt% (0.1 mg·mL −1 ) concentration were selected as the optimal concentration. Then, the photocurrent density versus photovoltage (J-V) curves were tested and drawn in Figure 4a. The doped device exhibited a short-circuit current density (J SC ) of 21.60 mA/cm 2 and an open-circuit voltage (V OC ) of 1.14 V under reverse-scan direction, a J SC of 21.66 mA/cm 2 , a V OC of 1.12 V under the forward-scan direction. Particularly, the champion PCE of 19.58% was firstly attained, which intrinsically verified the valid To verify the feasibility of PAT dopant and the self-healing of photovoltaic devices, SPSCs with a structure of stretchable substrate (PDMS [28])/PEDOT:PSS/perovskites/PCBM/PEDOT: PSS/PDMS were assembled. To explore the optimal doping concentration of PAT, PCE of different SPSCs were tested as shown in Figure S7. It could be found that, with the increase in PAT concentration from 0 (0.05 mg•mL −1 ) to 0.035 wt% (0.1 mg•mL −1 ), PCE increased gradually from 17.51% to 19.58%, which could be attributed to the enhanced crystallinity. However, when the concentration of PAT increased to 0.051 wt% (0.15 mg•mL −1 ), large amounts of pinholes formed in perovskite films, resulting in lower PCE. Based on these tests, 0.035 wt% (0.1 mg•mL −1 ) concentration were selected as the optimal concentration. Then, the photocurrent density versus photovoltage (J-V) curves were tested and drawn in Figure 4a. The doped device exhibited a short-circuit current density (JSC) of 21.60 mA/cm 2 and an open-circuit voltage (VOC) of 1.14 V under reverse-scan direction, a JSC of 21.66 mA/cm 2 , a VOC of 1.12 V under the forward-scan direction. Particularly, the champion PCE of 19.58% was firstly attained, which intrinsically verified the valid bichelation passivation by pyridine in PAT. Figure 4b-e display the detailed performance values of pristine and doped devices, demonstrating the excellent enhancing of SPSCs with PAT. The integration of the external quantum efficiency (EQE) spectra of the pristine and doped devices are shown in Figure 4f, being consistent with the data in Figure 4a. It is well known that the moisture-induced volatilization of organic cations has been restricting the development of PSCs [12]. Subsequently, environmental stability, as well as photovoltaic performances, is also one of the fundamental challenges to be settled for SPSCs. The un-encapsulation-doped and pristine devices were fabricated as expected and exposed in atmosphere whose relative humidity (RH) was kept at around 20%. It is worth noting that the devices still remain 83% of original PCE after storing for 2000 h ( Figure S8, Supporting Information). However, the PCE of pristine devices were only 65% of original devices. In addition to moisture, light stability was also verified under simulated solar light (AM1.5, 100 mW•cm −2 ). As shown in Figure S8, even after continuously irradiating for 300 h, the doped SPSCs still kept almost 94.5% of their initial PCEs. On the contrary, It is well known that the moisture-induced volatilization of organic cations has been restricting the development of PSCs [12]. Subsequently, environmental stability, as well as photovoltaic performances, is also one of the fundamental challenges to be settled for SPSCs. The un-encapsulation-doped and pristine devices were fabricated as expected and exposed in atmosphere whose relative humidity (RH) was kept at around 20%. It is worth noting that the devices still remain 83% of original PCE after storing for 2000 h ( Figure S8, Supporting Information). However, the PCE of pristine devices were only 65% of original devices. In addition to moisture, light stability was also verified under simulated solar light (AM1.5, 100 mW·cm −2 ). As shown in Figure S8, even after continuously irradiating for 300 h, the doped SPSCs still kept almost 94.5% of their initial PCEs. On the contrary, the PCE of pristine devices decreased rapidly to 60% under the same conditions. Remarkably, the stretchability and self-healing were deeply explored to enrich the contents of PSCs to wearable and stretchable electronic devices [29][30][31]. The changes of perovskite films under 20% strain were investigated in ambient conditions, as shown in Figure 5a,b. Apparently, upon stretching to 20% strain, PAT at GBs containing plenty of thiourea hydrogen bonds were damaged firstly and dissipated the strain energy. After healing for 15 min at 100 • C, the little cracks mostly self-healed, verified in situ by SEM and AFM images performed. In addition, the self-healing of photovoltaic performances under 20% strain were also explored ( Figure 5c) and verified for the doped SPSCs. Notably, even after 800 cycles of stretching and releasing, the doped SPSCs still retained 50% of their original IPCE, while the pristine ones retained 20%. However, after healing for 15 min, the IPCE of doped SPSCs dramatically increased to 85% due to the healing of cracks, demonstrating their excellent self-healing and stability. Compared with our previous work, the shorter healing time and higher healing efficiency may promote the practical applications of polymer-doped perovskite solar cells.
Conclusions
In summary, SPSCs with recoverable performances were successfully fabricated by introducing an innovative self-healable PAT with pyridine coordination units and plenty of thiourea hydrogen bonds. The doped SPSCs achieved a champion PCE of 19.58%, which is the best efficiency recorded to date for devices based on stretchable substrates. Moreover, moisture resistance and light irradiation resistance were also exhibited. Even after storing for 2000 h in 80% RH, the doped devices still retained 83% of their original PCE, attributed to the hydrophobic characteristic of siloxane in PAT polymer. Significantly, effective bichelation passivation and excellent self-healing properties were demonstrated by photovoltaic performances characterization and optical images performed in situ. After 800 cycles of stretching, releasing, and self-healing, the doped SPSCs retained 85% of their original IPCE. This strategy of bichelation passivation and thiourea hydrogen bonding healing offers a promising approach for crystalline semiconductors in wearable and stretchable electronic devices.
Supplementary Materials: The following supporting information can be downloaded at: www.mdpi.com/xxx/s1. Figure S1. Synthetic routes of the PAT polymers. Figure Figure S3. Typical stress-strain curves of the intact, 10 min, 30 min and 1 h healed PAT elastomers at 25 ℃. Figure S4. The contact angle measurements. (a) Contact
Conclusions
In summary, SPSCs with recoverable performances were successfully fabricated by introducing an innovative self-healable PAT with pyridine coordination units and plenty of thiourea hydrogen bonds. The doped SPSCs achieved a champion PCE of 19.58%, which is the best efficiency recorded to date for devices based on stretchable substrates. Moreover, moisture resistance and light irradiation resistance were also exhibited. Even after storing for 2000 h in 80% RH, the doped devices still retained 83% of their original PCE, attributed to the hydrophobic characteristic of siloxane in PAT polymer. Significantly, effective bichelation passivation and excellent self-healing properties were demonstrated by photovoltaic performances characterization and optical images performed in situ. After 800 cycles of stretching, releasing, and self-healing, the doped SPSCs retained 85% of their original IPCE. This strategy of bichelation passivation and thiourea hydrogen bonding healing offers a promising approach for crystalline semiconductors in wearable and stretchable electronic devices.
Supplementary Materials:
The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/nano12183125/s1. Figure S1. Synthetic routes of the PAT polymers. Figure Figure S3. Typical stress-strain curves of the intact, 10 min, 30 min and 1 h healed PAT elastomers at 25°C. Figure S4. The contact angle measurements. (a) Contact angle of Pristine perovskite films. (b) Contact angle of Doped perovskite films. Figure S5. Cross-section view of pristine and doped perovskite films. Figure S6. XRD spectrum of pristine and doped perovskite films. Figure S7. PCE tests of SPSCs with different PAT concentration. Figure
Data Availability Statement:
The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study. | 4,953.2 | 2022-09-01T00:00:00.000 | [
"Materials Science"
] |
A Method for Automatic Detection of Plasma Depletions by Using GNSS Measurements
Enhanced scintillation activities observed at transionospheric radio signals are often correlated with slant total electron content (STEC) depletions in the equatorial ionosphere. In this study, the data derived from high‐rate Global Navigation Satellite System (GNSS) receivers were used to analyze the observed STEC depletions, commonly associated with plasma bubbles causing radio scintillations in the equatorial ionosphere. We found that the observed STEC depletion can be described by a wedge‐shaped structure. To quantitatively describe the structure of STEC depletions, we developed an effective method to routinely characterize the depth and the width of equatorial plasma depletion in automatized data screening. The developed method has been validated by analyzing data obtained from mostly African GNSS stations in 2014 and 2015. The results confirm current knowledge regarding the seasonal occurrence of radio scintillations and related bubbles. The detection results are compared with those from other published plasma bubble detection techniques.
Introduction
The equatorial ionosphere with its complex dispersive features is of special interest in space weather research, which supports the operation of space-based radio systems such as the Global Navigation Satellite System (GNSS) and remote sensing radars. The equatorial ionosphere is commonly characterized by the occurrence of enhanced GNSS signal scintillations in the evening hours (e.g., Hlubek et al., 2014;Kriegel et al., 2017). As has already been described many years ago, for example, by DasGupta et al. (1983), the enhancement of amplitude scintillations is inherently associated with total electron content (TEC) depletions. Seemala and Valladares (2011) presented the results of a statistical study by applying an automatic detection algorithm to TEC depletions observed from the Low-Latitude Ionospheric Network, operated in South America during 2008. The method uses a band-pass filter technique applied to calibrated vertical TEC data to detect TEC depletions. To provide statistical information about plasma depletions at low latitudes, Magdaleno et al., (2012Magdaleno et al., ( , 2013 developed an ionospheric plasma bubbles seeker, including an automatized detection algorithm, in Java application. Nishioka et al. (2008) used the difference between the daytime rate of TEC index (ROTI) and the evening ROTI for each day at each GPS station to detect plasma depletions or bubbles during the years 2000. Recently, Blanch et al. (2018 improved the characterization and modeling of plasma depletion by modifying a previously developed technique for detecting medium-scale traveling ionospheric disturbances (Hernández-Pajares et al., 2006). Based on former scintillation studies by Hlubek et al. (2014) and Kriegel et al. (2017) at Bahir Dar, we present a new method of describing plasma depletions, which are often associated with GNSS signal scintillations. Here, we focus on describing a new plasma bubble detection algorithm and demonstrating its practical value for automatized bubble detection (and the corresponding statistical analysis). In future work, this method will be used for the automatic detection of plasma depletions and overall statistical analysis of related scintillation occurrences at GNSS measurements in the equatorial ionosphere. These stations are designed to receive and process multiple GNSS signals such as GPS (L1, L2, and L5), GLONASS (L1 and L2), Galileo (E1 and E5a), and BeiDou (B1, B2, and B3) at high data rates (e.g., Bahir Dar: 50 Hz and Tenerife: 20 Hz). The DLR GNSS receivers are connected to choke ring antennas to suppress multipath effects and allow tracking at low elevation scenarios. After removing cycle slips, key ionospheric parameters like amplitude scintillation (S 4 ), phase scintillation ( ), and slant total electron content (STEC) are calculated instantaneously and streamed together with the GNSS raw data to the central processing and controlling facility of the Experimentation and Verification network (Noack et al., 2005), operated at DLR, Neustrelitz, Germany. Sample skyplots in Figure 1 (bottom panel) show the calculated S 4 index (color coded by magnitude) for all satellites in view as a function of azimuth and elevation. As expected, enhancements of scintillation activities over the Tenerife Island GNSS station occur mostly to the south of Tenerife Island due to its position relative to the northern equatorial crest. Accordingly, the skyplots of Bahir Dar typically show enhanced S 4 values both in northward and southward direction since Bahir Dar is located in the middle of the maxima of the equatorial anomaly region (at approximately 15 • north and south of the geomagnetic equator). The occurrences of enhanced radio scintillations at both crests of the equatorial anomaly are rather typical (e.g., Hanson & Bamgboye, 1984). Nevertheless, it requires more studies to better understand the underlining physics.
Scintillations and Depletions
Strong electron density irregularities characterized by horizontal scales in the order of the first Fresnel zone may cause severe amplitude and phase fluctuations in GNSS signals. The top subpanels of Figure 2 show the observed scintillation indices (S 4 , ) at measurement station of Bahir Dar 02 (msbd02), on 16 March 2015. These observations were derived from GPS G21 and GLONASS R20 satellite signals. Near sunset, the strength of the prereversal enhancement causes equatorial spread F and plasma bubbles, in turn, are playing a dominate role in the occurrence of a strong amplitude and phase scintillations (e.g., Fejer et al., 1999;Woodman, 1970). In particular, the top and bottom subpanels of Figure 2 show a typical correlation of enhanced scintillation activities and STEC depletions observed by GPS G21 and GLONASS R20 satellite at Bahir Dar, on 16 March 2015. The depletions are believed to be caused by the Rayleigh-Taylor instability (e.g., Farley et al., 1970). It has to be noted that the used STEC measurements are not calibrated; that is, they are biased by a constant value. Thus, the analysis is not impacted by a simplifying of mapping function. Furthermore, link-related features like elevation and azimuth of considered signal paths can be used in subsequent studies to discuss the role of ray path geometry related to plasma depletion structures and associated scintillation activity. The slight time lag between enhanced scintillation and STEC depletion observed by the GLONASS R20 satellite around 21:52-22:52 LT may be derived from the interaction of GNSS link with limbs of plasma depletion, that is, attributed to the relative location and geometry of the receiver-satellite link with respect to plasma depletions in the crest of the equatorial anomaly. Generally speaking, a high correlation between the occurrence of equatorial plasma depletions and radio scintillations seems to be typical at low latitudes. Thus, more systematic and detailed studies on the relationship between equatorial plasma depletions and radio scintillations are required to interpret the occurrences and characteristics of equatorial plasma bubbles in a scientific way. The combined observations of Figures 1 and 2 indicate the concurrence characteristic of scintillations and plasma bubbles. Equatorial plasma bubbles often occur in the crest of the anomaly regions, and their monitoring can help us understand the generation and propagation of ionospheric irregularities in the low-latitude ionosphere (e.g., Valladares et al., 2001). To enable such studies by a broad database, a STEC depletion detection algorithm has been developed. This tool can be used to comprehensively demonstrate the relationship between plasma bubbles and scintillations by automatically analyzing a huge database of high-rate GNSS measurements.
Depletion Detection Method
As mentioned before, we focus on the detection of wedge-shaped structure of plasma depletions. The main descriptive parameters of such a structure are the depth and the width of the plasma depletion. The meaning of both parameters is shown in Figure 3. Hereafter, the width of the observed STEC depletion is defined as the time between the peak slopes of the wedge-shaped depletion, which means the time between the reduction phase (D) and the subsequent recovery phase (F). The STEC values marked at the well-defined position in (A), (B), and (C) are then used to define the depth of the STEC depletion, that is, the averaged STEC marked in (A) and (C) down to the minimum value marked in (B) (cf. equation (3)). Since using the observed data from a single GNSS station, a measured width of plasma bubble is characterized as a pseudowidth, which may move at an uncertain drift velocity and unknown direction. Moreover, there may be an unknown geometrical relationship between the GNSS link and the plasma bubble structure. These facts have to be considered when interpreting the results obtained by the detection algorithm proposed in this paper. To guarantee a representatively measured STEC, the observations are fitted by a polynomial function of fourth order. Its derivative can be represented by a polynomial function of third order, which will be useful to identify the three major phases (on, center, and off phases) of the plasma depletion structure. They can be expressed successively as follows: where P(t) stands for the wedged-shaped structure of plasma depletion and a 1 , a 2 , a 3 , a 4 , and a 5 , are the fitted coefficients. When computing the time derivative of the polynomial function described by equation (1), we get where P ′ (t) stands for the slope of the plasma depletion and b 1 , b 2 , b 3 , and b 4 are the coefficients of the smooth slope function. After fitting the polynomial function of fourth order to the measured STEC data, we compute the time derivative and can then define characteristic shape parameters of the plasma depletion, that is, the depth and width of the plasma depletion. These parameters can be easily deduced from STEC and time values at Points A, B, and C. In the right bottom subpanel of Figure 3, the slope values at Points D and F give a good indication about the steepness of the depletion walls. The deduced values P(t) and P ′ (t) are the key quantities for describing and characterizing the structure of equatorial plasma depletion and subsequently assist in the calculation of the depth and width of the STEC depletion. All specific positions shown in the right subpanels of Figure 3 (A, B, and C) and (D, E, and F) indicate the on, center, and off phases in the structure of plasma depletion as well as the minimum slope in the on phase, the inflection point in the center phase, and the maximum slope in the off phase in the STEC depletion structure. Referring to left subpanels of Figure 3, the peak scintillation is somewhat pronounced within edges of the STEC depletion, that is, using two points that would be located well inside the plasma depletion, rather than at "the outer lips" of the plasma depletion. This observation prompted us to develop our method for describing plasma depletions with only a few parameters that can easily be deduced from measurements obtained from an automatized data screening process within a maximum time frame of 1 hr. The amount of STEC in the on and off phases represents edges values in the STEC depletion structure. Hence, edges values can also be considered as a reference boundary between the plasma depletion and the background ionosphere. Considering the observed shape of equatorial plasma depletion, it is possible to define depth and pseudowidth of the equatorial plasma depletion accordingly. The depth (d) of the equatorial plasma depletion is the STEC difference between the edge phase and the center phase in the structure of the observed STEC depletion. It is written as follows: where STEC A , STEC B , and STEC C are the amount of STEC in the on, center, and off phases of the equatorial plasma depletion, respectively. The pseudowidth (pw) of the examined STEC depletion is defined by the time interval between Points A and C of the GNSS measurement: Taking into account the polynomial fitting procedure, it can be concretized as follows: Here, pw refers to the pseudowidth, commonly called the width of the plasma depletion, and t P ′ (t) min and t P ′ (t) max are the time of the minimum and maximum slope of the plasma depletion structure, respectively. The pseudowidth is measured in units of time indicating that it does not represent the real spatial structure of the depletion. This is due to the relative motion of the depletion and the location of the GNSS signal, which is scanning the plasma depletion depending on azimuth ( ) and elevation ( ) angle of the line of sight between the GNSS receiver and satellite. Thus, if a component of the depletion drifts vector (e.g., Kriegel et al., 2017) is in line with the velocity vector of the ionosphere piercing point, pw increases. In case, the depletion moves in the opposite direction as the piercing point moves, pw decreases. It is assumed that these motion related effects cancel out gradually by the better employment of the statistics. Analogously to scintillation and STEC depletion shown in the left subpanels of Figure 3, the top right subpanel of Figure 3 demonstrates the predominant structure of plasma depletion obtained from measurement (blue), Savitzky-Golay filter (yellow), and polynomial fitting technique (green). The bottom right subpanel of Figure 3 indicates the slopes of the STEC depletion (P ′ (t)), in particular marks the peak slopes as well as the inflection point (center) of the plasma depletion. From a technical point of view, the specific structure of plasma depletion is obtained by applying a sliding window computed every minute. The maximum length of the sliding window is around 1 hr to cover a full depletion. This method enables us to capture the required shape of STEC depletion from the overall observation (cf. right top subpanel of Figure 3). Edges and sharp slopes of the STEC depletion can be seen simultaneously at a given time axis. It is assumed that the sharp slopes of the STEC depletions can be attributed to enhanced scintillation activity in the defined time frame. In practice, the edges of the STEC depletions can be considered as a boundary between the plasma depletion and the background ionosphere. When considering the fitted polynomial function of fourth order in comparison with the observed data from the right top subpanel of Figure 3, it shows a good approximation and their root-mean-square deviation varies in the range from 1.5 to 4.4 TECU. These deviations indicate sometimes wave-like structures, which could be extracted as a by-product to characterize wave-like changes of plasma caused by other perturbation processes such as gravity waves. The simultaneous detection and analysis of traveling ionospheric disturbances (TIDs) may even help to study the relationship between gravity waves and the occurrence of plasma bubbles.
Application of the Method
The developed method has been applied to GNSS measurement data and has proven to be able to derive the structure parameters of plasma depletions. Basic requirements such as S 4 > 0.2, depth d ≥ 10 TECU, pseudowidth pw ≥ 15 min and slope P ′ (t) ≥ 10 mTECUs −1 are set up and applied on measurement data in the first study. So the influence of TIDs characterized by lower TEC amplitude can be avoided in the observation. The preliminary setting of these parameters will be proven in future studies and modified if required. The peak slopes of the STEC depletion are measured using a metric system [mTECUs −1 ], where 1 mTECU = 10 −3 TECU. To demonstrate the applicability of the developed tool for the detection of plasma depletion, we routinely analyzed additional data sets obtained from Lomé, Dakar, and Lima (see Figure 1). Based on the data availability, the percentage occurrence of plasma depletions with a depth level equal to or greater than 10 TECU amounted to 17% of days in 2015 at Bahir Dar, 7% of days in 2015 at Tenerife, 21.6% of days Figure 4 illustrate that the maximum occurrence of plasma depletions was observed at the equatorial ionosphere during equinox months. Unfortunately, frequent power outages caused data gaps at the Bahir Dar station, mostly happened between September and December in 2015. These outages might be responsible for an incomplete observation of peak plasma depletions between September and December in 2015. Taking the reduced data availability into account, the results are in line with other observations showing maxima of plasma bubble occurrence rate during equinox months (e.g., Blanch et al., 2018;Magdaleno et al., 2017). These plasma depletions, in turn, are associated with the maximum occurrence of scintillations in the African low-latitude ionosphere, as also indicated in the studies by Hlubek et al. (2014) and Akala et al. (2015). Our method for the automatic detection of plasma bubbles is comparable to a great extent with the detection techniques developed by Nishioka et al. (2008) and Blanch et al. (2018). As described by Nishioka et al. (2008), the differential value, |R ev − R da |, was used as index of plasma bubbles activity for one day at one station. Here, R da stands for the average value of ROTI during 3 hr from the noon, and R ev is the evening ROTI from sunset to midnight. When detecting plasma bubbles by the method of Nishioka et al. (2008), larger values of |R ev − R da | ≥ 0.1 have been taken to reduce the noise level of ROTI for each GPS receiver. According to Blanch et al. (2018), SIGMA (2DTEC) ≥ 0.714 TECU, disturbance duration ≥ 10 min and depth ≥5 TECUs, was considered as a threshold or requirement for the detection of plasma bubbles. Figure 4 indicates that the results of plasma bubble detection techniques convincingly show the seasonal occurrence of plasma bubbles by using our method (left subpanels), Blanch et al. (2018) method (middle subpanels), and Nishioka et al. (2008) method (right subpanels), respectively. As can be seen in Figure 4, the number of plasma bubbles detected by Blanch et al. (2018) is greater than the number detected by our method probably due to its lower thresholds and also due to TIDs, which commonly interfere with bubble signatures. The right subpanels of Figure 4 show the monthly occurrence rate of plasma bubbles and sunspot number. Generally speaking, the detection results observed from these three methods confirm that the occurrence of plasma bubbles peak near to equinox months in 2014 and 2015 (cf. Figure 4). The histogram of TEC depletion depths shown in Figure 5 agrees quite well with findings by Rama Rao et al. (2006); their study also indicated that mostly TEC depletions with durations ranging from 5 to 25 min and magnitudes from 5 to 15 TECUs are associated with L-band scintillations. It should be mentioned that in addition to the increased scintillation activity also the positioning accuracy of GNSS is affected by several meters. Compared with other methods referenced here, our detection method that describes depth and width of plasma depletions and has the advantage that it relies on smoothed STEC data, which are not impacted by mapping function errors. Our method can give the benefits for ionospheric scintillation studies when the derived TEC depletion parameters are available (see example in Figure 5). Furthermore, our method clearly indicates when the satellite-receiver links enter and leave a depletion zone by the derived slopes (Points A, C and D, F, respectively). This enables us to perform further studies on the relationship between ionospheric plasma bubbles and radio scintillations and their impacts on GNSS signals.
Conclusions
Simultaneous observations of enhanced scintillation activities and STEC depletions have shown their correlation across the GNSS links. Based on these preliminary observations, a new method has been developed that is able to describe the main features of the structure of equatorial plasma depletions, including a characterization of the depth and the width of the depletion structure. We found that depth, width, and peak slopes of the STEC depletions may range from 10 to 40 TECU, from 15 to 68 min, and from −10 to 40 mTECUs −1 , respectively. The presented results have been validated and compared with other GNSS plasma depletion detection techniques indicating a qualitative agreement. The deduced structure parameters such as depth, width, and slope of STEC depletions can help us to study the 3-D shape of plasma bubbles and the relationship between plasma depletions and scintillation activities. Having a better understanding of this relationship will be helpful in nowcasting and forecasting ionospheric scintillation activities of GNSS signals. The proposed method will be applied in more comprehensive studies for automatic detection of plasma depletions and related radio scintillation occurrences in the equatorial ionosphere. | 4,704 | 2020-03-01T00:00:00.000 | [
"Physics"
] |
An improved LC-MS/MS procedure for brain prostanoid analysis using brain fixation with head-focused microwave irradiation and liquid-liquid extraction.
High-performance liquid chromatography with tandem mass spectrometry detection (LC-MS/MS) allows a highly selective, sensitive, simultaneous analysis for prostanoids (PG) without derivatization. However, high chemical background noise reduces LC-MS/MS selectivity and sensitivity for brain PG analysis. Four common methods using different solvent systems for PG extraction were tested. Although these methods had the same recovery of PG, the modified acetone extraction followed by liquid/liquid purification had the greatest sensitivity. This method combined with hexane/2-propanol extraction permits the simultaneous analysis of other lipid molecules and PG in the same extract. We also determined that PG mass in brain powder stored at -80 degrees C was reduced 2- to 4- fold in 4 weeks; however, PG were stable for long periods (>3 months) in hexane/2-propanol extracts. PG mass was increased significantly when mice were euthanized by decapitation and the brains rapidly flash-frozen rather than euthanized using head-focused microwave irradiation. This reduction is not the result of PG trapping or destruction in microwave-irradiated brains, demonstrating its importance in limiting mass artifacts during brain PG analysis. Our improved procedure for brain PG analysis provides a reliable, rapid means to detect changes in brain PG mass under both basal and pathological conditions and demonstrates the importance of sample preparation in this process.
plication of LC-MS/MS requires special care for brain PG extraction and sample preparation before analysis, because of the complicated brain biological matrix that produces high chemical background noise, thereby reducing the selectivity and sensitivity of detection. Several different methods are used for brain PG extraction, including methanol extraction followed by solid-phase extraction (9,12,13), hexane/2-propanol extraction (14), ether extraction (15), and acetone/chloroform extraction (16). Although methanol extraction followed by solid-phase extraction (9) and ether extraction (15) have been used in different LC-MS/MS procedures, it is important to note that the simultaneous evaluation of these different extraction methods for use in brain PG analysis using LC-MS/MS has not been done.
Another important factor that must be considered during brain PG analysis is the method used to euthanize the animal and the subsequent handling of the brain sample. Brain PG mass in rodents euthanized by headfocused microwave irradiation is 10-to 40-fold lower than in animals euthanized by decapitation (17,18). Although it is assumed that this reduction in PG mass is the result of heat inactivation of the enzymes involved in postmortem PG formation (17)(18)(19), this reduction could also be the result of the trapping or destruction of PG in microwaved brain. Several lines of evidence support the assumption that PG are not trapped or destroyed during microwave treatment. Brain PG mass found in indomethacin-treated animals euthanized by decapitation does not differ from PG mass in brains from animals euthanized by microwave irradiation (18). Also, after intracerebral ventricular injection of radiolabeled PG before microwave irradiation, most of the recovered radioactivity was in the form of PG; however, the recovery of the radiolabeled PG from brains subjected to microwave irradiation was not examined in this study (19). Importantly, these studies do not provide direct evidence that PG are not trapped or destroyed in microwaved brains.
In the present study, we evaluated and modified existing methods for brain PG extraction and sample preparation for LC-MS/MS analysis. The modified method improved the limits of tissue PG detection by 4-to 20-fold in an individual PG-dependent manner and allowed the analysis of PG in ,10 mg of brain tissue with an extraction recovery that ranged from 85% to 95%. We also evaluated PG stability during storage and analysis and provide direct evidence that PG are not trapped or destroyed in microwaved brains.
Animals
This study was conducted in accordance with the National Institutes of Health Guidelines for the Care and Use of Laboratory Animals (Publication 80-23) and under an animal protocol approved by the Institutional Animal Care and Use Committee at the University of North Dakota (Protocol 0409-9). Male 129/SvEv strain mice (25-30 g) were maintained on standard laboratory chow diet and water ad libitum. The ages of the mice used in this study were between 9 and 11 months.
Brain PG extraction
Fasted male mice were anesthetized with halothane (1-3%) and euthanized using head-focused microwave irradiation (2.8 kW, 1.35 s; Cober Electronics, Inc., Norwalk, CT) to heatdenature enzymes in situ. The whole brain was removed, frozen in liquid nitrogen, and pulverized under liquid nitrogen temperatures to a fine, homogeneous powder.
The extraction protocol was a modification of a previously published procedure (16) that was adapted for tissue extraction. Pulverized tissue (10-20 mg) was homogenized in 3 ml of acetone-saline (2:1) containing PGE 2 -d4 and 6-oxo-PGF 1a -d4 (100 pg in 10 ml of acetonitrile) as internal standards and 0.005% butylated hydroxytoluene (BHT) to prevent PG oxidation using a Tenbroeck tissue grinder (Kontes Glass Co., Vineland, NJ). The homogenate was transferred to a screw-top tube, vortexed for 4 min, and subjected to 10 min of centrifugation (2,000 g) at 4jC. The supernatant was transferred to another screw-top tube and mixed with 2.0 ml of hexane by vortexing for 0.5 min. Then, the mixture was subjected to 10 min of centrifugation (2,000 g) at 4jC. The upper phase containing hexane with extracted lipids was discarded, the lower phase was acidified with formic acid to pH 3.5 (30 ml of 2 M formic acid), and 2 ml of chloroform containing 0.005% BHT was added. The mixture was vortexed for 0.5 min and again subjected to 10 min of centrifugation (2,000 g) at 4jC to aid in the separation of the two phases. The lower phase containing chloroform was transferred to a screw-top tube silanized with Sigmacote: (Sigma Chemical Co., St. Louis, MO), flushed with nitrogen, and cooled at 220jC for at least 2 h. This cooling allows the separation of any residual upper phase, which is then removed and discarded before analysis.
Sample preparation for LC-MS/MS
After the residual upper phase was discarded, 200 ml of methanol was added to the extract and it was dried down under a stream of nitrogen. The dried extract was transferred to 100 ml silanized microvial inserts (National Scientific, Rockwoods, TN; catalog No. C4010-S630) using 2 3 0.1 ml of chloroform containing 10% methanol and 0.005% BHT. The solvent in microvial inserts was dried down under a stream of nitrogen. The transfer procedure was repeated twice. Ten microliters of acetonitrile was added to the insert with dried extract, vortexed for 30 s, and mixed with 20 ml of water.
Reverse-phase HPLC electrospray ionization mass spectrometry
The separation was carried out using a Luna C-18(2) column (3 mm, 100 Å pore diameter, 150 3 2.0 mm; Phenomenex, Torrance, CA) with a stainless-steel frit filter (0.5 mm) and security guard cartridge system (C-18) (Phenomenex). The HPLC system consisted of an Agilent 1100 series LC pump equipped with a wellplate autosampler (Agilent Technologies, Santa Clara, CA). The autosampler was set at 4jC. Twenty-five microliters out of a 30 ml sample was injected onto a chromatographic column.
The solvent program for elution was modified from a previously described method (20). This modification was made to increase the sensitivity of detection by increasing peak sharpness and resolving PG from other chemical compounds coextracted from brain tissue. The solvent system was composed of 0.1% formic acid in water (solvent A) and 0.1% formic acid in acetonitrile (solvent B). The flow rate was 0.2 ml/min, and the initial solvent conditions started with 10% solvent B. At 2 min, the percentage of B was increased to 65% over 8 min; at 15 min, the percentage of B was increased to 90% over 5 min; and at 35 min, it was reduced to 10% over 2 min. Equilibration time between runs was 13 min.
MS analysis was performed using a quadrupole mass spectrometer (API3000; Applied Biosystems, Foster City, CA) equipped with a TurboIonSpray ionization source. Analyst software version 1.4.2 (Applied Biosystems) was used for instrument control, data acquisition, and data analysis. The mass spectrometer was optimized in the multiple reaction monitoring mode. The source was operated in negative ion electrospray mode at 450jC, electrospray voltage was 24,250 V, nebulizer gas was zero grade air at 8 l/min, and curtain gas was ultrapure nitrogen at 11 l/min. Declustering potential, focusing potential, and entrance potential were optimized individually for each analyte as presented in Table 1. Focusing potential was 2200 V, and entrance potential was 210 V for all analytes. The quadrupole mass spectrometer was operated at unit resolution. PGE 2 , PGD 2 , PGF 2a , and TXB 2 were quantified using PGE 2 -d4 as the internal standard, whereas 6-oxo-PGF 1a was quantified using 6-oxo-PGF 1a -d4 as the internal standard. Initially, we used PGD 2 -d4, PGF 2a -d4, and TXB 2 -d4 to normalize PGD 2 , PGF 2a , and TXB 2 , respectively; however, this approach did not improve variability or recovery results compared with quantification using only PGE 2 -d4. An example of brain PG LC-ESI-MS/MS analysis is presented in Fig. 1.
Statistical analysis
All statistical comparisons were calculated using a two-way, unpaired Student's t-test or a one-way ANOVA and a Tukey-Kramer posthoc test when appropriate, using Instat II (Graphpad, San Diego, CA). Statistical significance was defined as P , 0.05. All values are expressed as means 6 SD.
PG extraction
The brain has a complicated biological matrix that produces high chemical background noise, so that the use of LC-MS/MS to measure brain PG mass requires special care with regard to sample preparation before analysis. Although several methods for brain PG extraction and purification are currently used (9,12,(14)(15)(16)21), these methods have not been evaluated for use by LC-MS/MS analysis.
Here, we have evaluated the background chemical noise and limits of sensitivity for four different methods currently used for PG extraction and analysis. The efficiency of the extraction procedures was estimated by the recovery of the deuterium-labeled PG added to the samples before extraction and ranged from 85% to 95% for each of the methods tested; there were no significant differences between methods.
Brain extraction with hexane/2-propanol
We also tested hexane/2-propanol extraction (3:2, v/v), which allows for simultaneous extraction of brain phospholipids, neutral lipids, and PG (14). Briefly, ?20 mg of brain microwaved tissue was homogenized in 1 ml of hexane/2-propanol (3:2, v/v) containing PGE 2 -d4 and 6-oxo-PGF 1a -d4 (100 pg in 10 ml of acetonitrile) as internal standards using a 2 ml Tenbroeck tissue grinder. The homogenizer was rinsed three times with 1 ml of hexane/ 2-propanol. The homogenate was subjected to 10 min of centrifugation (2,000 g) at 4jC, and the supernatant was removed. The supernatant was then dried under a stream of nitrogen, redissolved in 15% methanol at pH 3, and purified on C 18 cartridges as described above (10). PG were prepared for LC-MS/MS analysis as described in Materials and Methods. The chemical background noise was similar to values for methanol extraction followed by solid-phase extraction on C 18 columns. Also, the sensitivity was 4-to 16-fold lower compared with the acetone liquid/ liquid extraction described in Materials and Methods (Table 2).
Because purification of hexane/2-propanol lipid extracts on C 18 cartridges did not increase the levels of sensitivity of LC-MS/MS analysis compared with other methods, we used acetone to reextract PG from hexane/2-propanol lipid extracts. To purify hexane/2-propanol lipid extracts with acetone, aliquots of extracts were transferred into silanized tubes, solvent was removed under a stream of nitrogen and redissolved in 2 ml of acetone containing 0.005% BHT, and then 1 ml of saline was added. This mixture was mixed by vortexing for 4 min. We then followed the procedures for PG analysis as described in Materials and Methods. Although the purification of lipid extract with acetone followed by liquid/liquid extraction did not significantly improve the levels of sensitivity compared with direct extraction with acetone (Table 2), this approach allows the simultaneous analysis of PG and other lipid molecules in the same sample.
Extraction recovery with acetone
We verified the recovery of PG extraction with acetone compared with extraction with hexane/2-propanol, because hexane/2-propanol affords a high recovery of PG from tissue (14). Because we found that hexane/2propanol extraction has reduced sensitivity as a result of high background, we induced brain PG formation by injecting mice with lipopolysaccharide (1 mg/kg ip) (22) at 3 h before head-focused microwave irradiation. We extracted the same brain samples using either acetone or hexane/2-propanol (3:2, v/v). There were no differences in PG mass found after hexane/2-propanol extraction compared with acetone extraction (Fig. 2), indicating that acetone yields a high extraction ratio of PG from the brain tissue. Because acetone extraction produced significantly less background chemical noise compared with hexane/2-propanol extraction, the standard deviations for the individual PG are smaller in samples analyzed from the acetone extract compared with the hexane/2propanol extract. Methanol followed by solid-phase extraction 3.9 6 1.0 (0. 5 In summary, tissue PG extraction with acetone followed by liquid/liquid extraction significantly increased the level of sensitivity in the LC-MS/MS analysis compared with other extraction methods tested in this study. This increased sensitivity was the result of a significant reduction of background chemical noise, probably attributable to better purification of PG extract from components that affect LC-MS/MS analysis. Also, dissolving the residue from a hexane/2-propanol lipid extract with acetone permits PG analysis in common lipid extracts that contain all major lipids, thereby extending the application of this method of extraction to other lipid parameters beyond PG, which is important when sample quantity is limited. Besides better sensitivity, PG extraction with acetone followed by liquid/liquid extraction is considerably less laborious when large sets of samples are analyzed and much less expensive compared with purification on C 18 cartridges. Therefore, we consider acetone extraction followed by liquid/liquid extraction to be the method of choice for PG analysis using LC-MS/MS.
Sample preparation for LC-MS/MS analysis
The solvent composition used to apply a sample onto an HPLC column may have a significant effect on analyte separation and peak sharpness, thereby affecting the limits of detection and the accuracy of analysis. Acetonitrile would be the best solvent to dissolve a sample before application on the column because it dissolves PG and is a component of the mobile phase. However, because of the small volume of the HPLC column used for PG separation and the low flow rate of solvents used in the LC separation program, a high acetonitrile concentration used to apply the sample reduces peak sharpness and increases peak leading (Fig. 3). We have found that the optimal acetonitrile-water ratio is 1:2 when 25 ml of sample is applied onto an HPLC column. Fig. 3. Effect of loading solvent composition of the separation of brain PG by HPLC. A sample of brain tissue (10 mg) from mice euthanized by decapitation was extracted and analyzed using a procedure described in Materials and Methods. The sample (25 ml) was loaded onto an HPLC column using either water-acetonitrile (1:2) (upper panel) or water-acetonitrile (2:1) (lower panel). cps, counts per second. (100, 100, 100, 100, 50, and 50 pg, respectively, in 10 ml of acetonitrile) was analyzed using a procedure described in Materials and Methods. cps, counts per second.
Antioxidants prevent PG degradation during analysis
BHT is often used to prevent PG oxidation during extraction and analysis. Different concentrations of BHT have been used in lipid analysis, ranging from 0.1% to 0.01% (3,30), although not all investigators use antioxidants during PG analysis. To evaluate the need for antioxidants, we analyzed three identical brain samples with 0.1% BHT, 0.005% BHT, or no BHT added to acetone and chloroform used in the extraction. We found that 0.1% BHT produced a precipitate that may clog the LC system. However, using 0.005% BHT in chloroform and acetone for PG extraction and sample preparation efficiently decreased the variability of analysis and prevented a 2.8-fold reduction in 6-oxo-PGF 1a mass without producing a precipitate in the loading mixture.
Use of head-focused microwave irradiation
Brain PG mass found in rodents euthanized by headfocused microwave irradiation is 10-to 40-fold lower than in animals euthanized by decapitation (17,18). Different processes may account for this difference in results, including postmortem PG formation (17)(18)(19), induction of Fig. 5. Induction of PG formation during brain tissue extraction. Two groups of animals were anesthetized with halothane (1-3%) and euthanized by decapitation, and their skulls were opened. The whole brains were removed at 1 min after animal death and either frozen in liquid nitrogen (A) or subjected to head-focused microwave irradiation (B) as described in Materials and Methods. A: Three identical nonmicrowaved brain samples were extracted either in ice-cold conditions or after sample incubation in extraction mixture for 1 or 5 min at room temperature. B: As a control for the completeness of extraction in ice-cold conditions, microwaved brains were extracted under the same conditions described for A. Values are expressed as means 6 SD (n 5 3). * P , 0.05 compared with samples extracted in ice-cold conditions. ww, wet weight. PG formation during extraction, or PG destruction or trapping in microwaved brains.
Because the induction of PG formation during extraction has not been tested in previous studies, we extracted identical nonmicrowaved brain samples either in ice-cold conditions or after sample incubation in extraction mixture for 1 or 5 min at room temperature. The mass of all PG analyzed was increased significantly at room temperature (Fig. 5A). As a control for the completeness of extraction in ice-cold conditions, microwaved brains with heat-inactivated enzymes were extracted under the same conditions described above. There were no differences between PG mass in microwaved tissue after extraction in ice-cold conditions compared with room temperature (Fig. 5B), indicating the same high extraction ratio in icecold conditions. These data indicate that induction of PG formation during extraction can occur, which is one factor contributing to the higher values and greater variability of PG mass found in nonmicrowaved brains.
Another reason for a reduction in PG mass in brains subjected to microwaved irradiation could be PG breakdown and/or trapping in irradiated tissue. Temperatures of 70jC to 100jC are reported a few seconds after expos-ing the animal to head-focused microwave irradiation (19), similar to our observations. Because PG are known for their instability and have a short half-life, PG breakdown in heat-denatured tissue should be considered as another factor accounting for the reduced PG mass observed in microwaved brains compared with nonmicrowaved brains. In addition, because PG are bound in vivo by a variety of carrier proteins (31,32), trapping of PG in heatdenatured proteins may also account for the reduction in PG mass observed after microwave irradiation. Although it is assumed that the observed reduction in PG mass in microwaved versus nonmicrowaved brain is the result of the heat inactivation of enzymes involved in postmortem PG formation (17)(18)(19), direct evidence that PG are not trapped or destroyed in microwaved brains has not been reported. What has been reported is that in indomethacintreated rats euthanized by decapitation, brain PG mass is not different from the levels in brains from rats euthanized by microwave irradiation (18). Additional evidence is that after injection (intracerebral ventricular) of radiolabeled PG into the brain before microwave irradiation, most of the recovered radioactivity was in the form of PG (19), suggesting heat stability in situ. However, the recovery of Fig. 6. PG are not destroyed or trapped in microwaved brain. Two groups of animals were anesthetized with halothane (1-3%) and euthanized by decapitation, and their skulls were opened. The whole brains were removed at 1 min after animal death and either frozen in liquid nitrogen or subjected to head-focused microwave irradiation as described in Materials and Methods. The temperature of microwaved brains ranged from 70jC to 85jC as measured using a thermocouple. As a control for enzyme inactivation in microwaved brains, a third group of animals was euthanized by microwave irradiation as described in Materials and Methods. Values are expressed as means 6 SD (n 5 3). * P , 0.05 compared with brains from mice euthanized by head-focused microwave irradiation without global ischemia; ** P , 0.05 compared with brains from nonmicrowaved brains of mice exposed to global ischemia. ww, wet weight. Fig. 7. Reduction in PG mass during tissue storage. Identical tissue samples were analyzed either the same day or 4 weeks after animals were euthanized by decapitation. Tissue powder was stored at 280jC. Values are expressed as means 6 SD (n 5 4). * P , 0.05 compared with brains analyzed the same day as the mice were euthanized. the radiolabeled PG from brains subjected to microwave irradiation was not examined in this study.
To address the possibility that microwave irradiation may affect the recovery of endogenous PG, we induced brain PG production by modeling global ischemia. Two groups of animals were anesthetized with halothane (1-3%) and euthanized by decapitation, and their skulls were opened. The whole brains were removed 1 min after death and either frozen in liquid nitrogen or subjected to microwave irradiation as described in Materials and Methods. The temperature of microwaved brains ranged from 70jC to 85jC as measured using a thermocouple. As a control for enzyme inactivation in microwaved brains, the third group of animals was euthanized immediately using headfocused microwave irradiation as described in Materials and Methods. The magnitude of increased PG mass found in nonmicrowaved brains was similar to the levels reported by others (17,18) (Fig. 6). For most PG analyzed, there were no differences between the two different fixation regimens subjected to induction of PG production via ischemia (Fig. 6), indicating that the recovery of brain PG was fixation-independent.
However, PGD 2 and TXB 2 mass were increased in nonmicrowaved brains compared with microwaved brains after induction of PG formation. There are several explanations for these data. First, PGD2 and TXB2 are formed during extraction because their mass was affected to a greater extent than the mass of other PG during the extraction of nonmicrowaved brains (Fig. 5A). Second, PGD 2 and TXB 2 are more heat-labile. To test this assumption, we incubated a PGE 2 , PGD 2 , PGF 2a , TXB 2 , and 6-oxo-PGF 1a mixture dissolved in acetonitrile-water (1:2, v/v) at 85jC for 10 min and analyzed PG mass as described in Materials and Methods. The mass of all PG tested was decreased to the same extent (10-15%; data not shown), indicating similar heat lability of the tested PG.
Together, these data support the need to microwave brain and provide direct evidence that PG are not trapped or destroyed in microwaved brains.
PG stability during tissue storage
Because of PG short shelf half-lives, we tested PG stability in brain tissue and extracts during storage. PG were analyzed in the same samples either the same day or 4 weeks after animals were euthanized by decapitation. Tissue powder was stored at 280jC. Four weeks of tissue powder storage at 280jC resulted in a 2-to 4-fold decrease in PG mass (Fig. 7); however, no decrease of PG was observed in lipid extracts stored in hexane/2-propanol (3:2) for several months at 280jC under nitrogen (data not shown). These data indicate the utility of rapid tissue extraction with hexane/2-propanol (3:2), which then can be stably stored in hexane/2-propanol for PG and other lipid analysis in the future.
Summary
In summary, tissue PG extraction with acetone followed by liquid/liquid extraction significantly increased the level of sensitivity of LC-MS/MS analysis compared with other extraction methods tested in this study. This increased sensitivity was the result of a significant reduction in background chemical noise. Dissolving residue from hexane/ 2-propanol lipid extracts with acetone allows the analysis of PG in these lipid extracts, thereby extending the application of this method of extraction. Besides better sensitivity, this method is less laborious and less expensive compared with purification on C 18 cartridges. We also evaluated PG stability during extraction and storage. The use of 0.005% BHT during PG extraction decreased the variability of analysis and limited 6-oxo-PGF 1a oxidation. Importantly, PG were rapidly destroyed during the storage of powdered tissue; however, PG were stable in hexane/2-propanol extracts. Lastly, our data support the need to euthanize animals by head-focused microwave irradiation rather than by decapitation and provide direct evidence that PG are not trapped or destroyed in microwaved brains. | 5,635 | 2008-04-01T00:00:00.000 | [
"Chemistry",
"Medicine"
] |
Analysis and Enhancement of BWR Mechanism in MAC 802.16 for WiMAX Networks
WiMAX [Worldwide Interoperability for Microwave Access] is the latest contender as a last mile solution for providing broadband wireless Internet access and is an IEEE 802.16 standard. In IEEE 802.16 MAC protocol, Bandwidth Request (BWR) is the mechanism by which the Subscriber Station (SS) communicates its need for uplink bandwidth allocation to the Base Station (BS). The performance of the system is affected by the collisions of BWR packets in uplink transmission, that have the direct impact on the size of the contention period in uplink sub frame, uplink access delay and uplink throughput. This paper mainly deals with Performance Analysis and Improvement of Uplink Throughput in MAC 802.16 by the Application of a New Mechanism of Circularity. The implementation incorporates a generic simulation of the contention resolution mechanism at the BS. An analysis of the total uplink access delay and also uplink throughput is performed. A new paradigm of circularity is employed by selectively dropping appropriate control packets in order to obviate the bandwidth request collisions, which yields the minimum access delay and thereby effective utilization of available bandwidth towards the uplink throughput. This new paradigm improves contention resolution among the bandwidth request packets and thereby reduces the delay and increases the throughput regardless of the density and topological spread of subscriber stations handled by the BS in the network.
INTRODUCTION
The IEEE 802.16 MAC layer plays an important role in the OSI model.It is a sub layer of the data link layer, the other being the logical link control layer (LLC), and acts as a link between the lower hardware oriented and the upper software oriented layers.IEEE 802.16 consists of the access points like BSs (Base Station) and SSs (Subscriber Stations).All data traffic goes through the BS, and the BS can control the allocation of bandwidth on the radio channel.According to demand of subscribers stations Base Station allocates bandwidth.Hence 802.16 are a Bandwidth on Demand system.Basically there are two modes of operation in 802.16 i.e.P2MP (Point to Multi Point) and Mesh Mode of operation.In P2MP mode of operation a base station can communicate with subscriber station and/or base stations.Each SS is identified by a 48-bit IEEE MAC address and a BS is identified by a 48-bit Base Station ID (Not MAC address).Each connection with BS and SS in a session is identified by a 16-bit CID (Connection Identifier) In P2MP mode of operation communication between BS and SS is established based on Req / Grant mechanism (which is CSMA/CA in case of 802.11).In Mesh Mode operation a subscriber station can directly communicate with another subscriber's station within its communicating range.It is ad-hoc in nature [1].
We have considered the point-to-multipoint mode of operation of the IEEE 802.16 network.In this mode, the communication occurs only between the SS and the BS.The BS directly controls the data that is transmitted between the different SSs.In addition to the control of communication between SSs, a BS can send information to other BSs as well.This allows SSs that are not connected to the same BS, to exchange data.Initially when a SS is switched on, it performs the network entry procedure [2].
The procedure can be divided into the following phases: Scan for downlink channel and establish synchronization with the BS Obtain transmit parameters (from UCD message) Perform ranging Negotiate basic capabilities Authorize SS and perform key exchange Perform registration Establish IP connectivity Establish time of day Transfer operational parameters Set up connections The following figure 1 shows the network entry procedure The BS in turn returns certain response messages in order to complete the different steps.The first such mechanism is Initial Ranging.Here, a series of Ranging-Request and Ranging-Response messages are exchanged.Also the processes of Negotiating Basic Capabilities and Registration involve their own request messages.These are called the SBC-REQ and REG-REQ messages respectively.After a SS has gained entry into the network of a BS, if it has data to send, it starts the Bandwidth Request (BWR) procedure.
In our project, we focus on the contention-based BWR mechanism and its performance metrics [3].
A. Salient features of WiMAX
WiMax basically offers two forms of wireless service [4]: 1. Non-line-of-sight: This service is a WiFi sort of service.Here a small antenna on your computer connects to the WiMax tower.In this mode, WiMax uses a lower frequency range --2 GHz to 11 GHz (similar to WiFi). 2. Line-of-sight: In this service, where a fixed dish antenna points straight at the WiMax tower from a rooftop or pole.The line-of-sight connection is stronger and more stable, so it's able to send a lot of data with fewer errors.Line-of-sight transmissions use higher frequencies, with ranges reaching a possible 66 GHz.The entire WiMax scenario is as shown in Figure 2. WiMax is a wireless broadband solution that offers a rich set of features with a lot of flexibility in terms of deployment options and potential service offerings.Some of the more salient features that deserve highlighting are as follows: OFDM-based physical layer Very high peak data rates Scalable bandwidth and data rate support Scalable bandwidth and data rate support Link-layer retransmissions Support for TDD and FDD WiMax uses OFDM
II. STATEMENT OF THE PROBLEM
Bandwidth Request (BWR) is the mechanism by which the SS communicates its need for uplink bandwidth allocation to the BS.A single cell in WiMax consists of a base station (BS) and multiple subscriber stations (SSs).The BS schedules the traffic flow in the WiMax i.e., SSs do not communicate directly.The communication between BS and SS are bidirectional i.e., a downlink channel (from BS to SS) and an uplink channel (from SS to BS).The downlink channel is in broadcast mode.The uplink channel is shared by various SS's through time division multiple access (TDMA).The subframe consists of a number of time slots.The duration of subframe, slots and the number are determined by the BS scheduler.The downlink subframe contains uplink map (UL map) and downlink map (DL map).The DL map contains information about the duration of sub frames and which time slot belongs to a particular SS as the downlink channel.The UL map consists of information element (IE) which includes transmission opportunities [5].Bandwidth Request refers to the mechanism by which the SS ask for bandwidth on the uplink channel for data transmission.Compared to RNG-REQ, these request packets are of multiple types They can be stand-alone or piggybacked BWR message.The requests must be made in terms of the number of bytes of data needed to be sent and not in terms of the channel capacity.This is because the uplink burst profile can change dynamically.There are two methods for sending bandwidth request.Contention Free method and Contention Based method.In contention free bandwidth request method, the SS will receive its bandwidth automatically from BS.In contention based bandwidth request method, more than one subscriber can send their request frames to same base station at same time.Hence there will be chances of collision, which is resolved by Truncated Binary Exponential Backoff Algorithm.BE and nrtPS services are two cases of contention based request method.In the uplink subframe of the TDD frame structure of 802.16, there are a number of Contention Slots (CSs) present for the purposes of BWR.In contention based bandwidth request mechanism, an SS attempts to send its BWR packet in one of these contention slots in the uplink subframe to the BS.If a BWR packet is successfully received by the BS and bandwidth is available, then the bandwidth is reserved for the SS and it can transmit its data without contention in the next frame.In case multiple subscriber stations send their request messages to the same BS at the same time, there will be a collision.So, here the contention is resolved by using the truncated binary exponential backoff procedure.The minimum and maximum backoff windows are decided by the BS.Also, the number of bandwidth request retries is 16.The backoff windows are always expressed in terms of powers of two.This algorithm solves retransmission strategy after a collision.It keeps track of the number of collisions [6].
A Subscriber Station can transmit its bandwidth request http://ijacsa.thesai.orgusing bandwidth request contention slots known as BWR contention slots.Subscriber stations can access the channel using RACH method i.e.Random Access Channel method.A subscriber station that wants to transmit data first enters into the contention resolution algorithm.In this scheme we consider different number of contention slots for each frame and each subscriber station has 16 transmission opportunities at maximum.The Initial Backoff window size is 0-7 and the final maximum backoff window size is 0-63.While accessing the channel randomly this way, there will be collisions among these request packets.Suppose the backoff window at a certain time for an SS is 0 to 15 (0 to 2^4-1) and the random number picked is 8.The SS has to defer a total of 8 BWR Contention Slots before transmitting the BWR packet.This may require the SS to defer BWR Contention Slots over multiple frames.In case a collision is detected, the backoff window is doubled.Now a random number is picked between 0 and 31 and the deferring is continued.This procedure can be repeated for a maximum of 16 times after which the data that was to be sent is discarded and the whole process is restarted from the very beginning.Base station can allocate bandwidth to subscriber station in three ways: GPC (Grant per Connection Mode), GPSS (Grant per Subscribers Station), and Polling.GPC is a bandwidth allocation method in which bandwidth is allocated to a specific connection within a subscriber station.GPSS is a bandwidth allocation method in which requests for the bandwidth is aggregated for all connections within a subscriber station and is allocated to the subscriber station as that aggregate.The bandwidth requests are always made for a connection.Polling is the process by which the BS allocates to the SSs bandwidth specifically for the purpose of making bandwidth requests.These allocations may be to individual SSs or to groups of SSs.Polling is done on either an SS or connection basis.Bandwidth is always requested on a CID basis and bandwidth is allocated on either a connection (GPC mode) or SS (GPSS mode) basis, based on the SS capability [7].
A. Analysis mode module
The purpose of this module is to analyze the communication between BS and SS's, and to obtain the access delay and Throughput of the network.
The following Network Architecture parameters are used for the simulation process.
Along with the above network parameters, we also need to give the seed value for the simulation purpose.Seed value is actually taken by the Random Number Generation (RNG) process.There are 64 well-defined seed values available.We can find these seed values in network simulator application.By using these values we will carry out the simulation.
The parameters mentioned above are used in Tool Command Language script.Tcl scripting is used to design and simulate the WiMAX networks with varying architectures.Tcl gives us a lot of options that allow us to have a great degree of control over the simulation of networks.We use WiMAX Control Agent in order to produce a detailed account of the activities going on during the simulations.
Subscriber Stations (SSs) use the contention minislots for transmitting their requests for bandwidth.The Base Station allocates bandwidth for the SSs in the next frame, if bandwidth is available.Because of the reservation procedure, the SSs are guaranteed collision free data transmission.The contention is resolved in the uplink channel for bandwidth request based on a truncated binary exponential backoff, with the initial backoff window and the maximum backoff window controlled by the base station (BS).The values are specified as part of the Uplink Channel Descriptor (UCD) message, describe the physical layer characteristics of an uplink and are equal to power-of-two.The SS will enter a contention resolution process, if it has data for transmission.
Figure 3 shows the contention resolution process for this module.
B. Enhancement mode module
The purpose of this module is to analyze the communication between BS and SS's, and obtain the delay incurred in BWR and Throughput of the network by using Circularity Principle.For this Module, the Network Architecture parameters are the same as we set up in Analysis mode.We use these parameters in Tool Command Language.In addition to this, we have to input, Circularity value which is needed to carry out the enhancement process.Here we need to set this value at the back-end of the network simulator.
Figure 4 shows the contention resolution process for this module.The procedure is same as we see in the previous module but only difference is, here we are enclosed the new Circularity principle.Circularity concentrates on the modification of existing BWR scheme so as to minimize BWR collisions and hence improving the throughput [8].
Circularity is defined as a number which enables the identification of specific groups of events or packets.Each event or packet under consideration is numbered in a sequential manner.An event or packet with a number which is a multiple of the circularity value is said to be circularitysatisfied.So we are setting a counter to find Circularity satisfied packet and we are dropping it.So, a finite delay is introduced before the occurrence of circularity satisfied events or the sending of circularity satisfied packets.This additional delay reduces the probability of packet collisions.The selfless behavior of certain SSs may increase the individual BWR delays but on the whole the delay incurred in the entire network will be reduced.All the other calculation remains the same as we see in Analysis module.
C. Comparison mode module
The purpose is to analyze the graph which shows that how the Enhancement mode is better than the existing scheme.For this Module, the Network Architecture parameters are the same as we set up in Analysis mode.We use these parameters in Tool Command Language.In addition to this, we have to input, Circularity value which is needed to carry out the enhancement process.Here we need to set this value at the back-end of the network simulator.
In this module, we are comparing the results of two previous modules.Before the processing of this module, we need to run the simulation by setting different number of mobile nodes for analysis and enhancement modules and note down the results.The obtained delay and throughput results are written in a file.The extension of this file should be filename.xgand need to input to the Xgraph package to plot the graph.The output file will be an image file of the extension png. Figure 5 shows the flow chart for comparing the Access delay results of two previous modules.1) The Network Simulator 2 (NS2): NS2 is a tool that helps you better understand certain mechanisms in protocol definitions, such as congestion control, that are difficult to see in live testing [9].It is recommended NS2 as a tool to help understand how protocols work and interact with different network topologies.We can also patch the source code in case the protocol you want to simulate is not supported and live with low-quality graphics tool [10].Figure 7 shows the network animator.2) TCL (Tool Command Language) Tcl is a small language designed to be embedded in other applications (C programs for example) as a configuration and extension language [11].Tcl is specially designed to make it extremely easy to extend the language by the addition of new primitives in C. Like Lisp, Tcl uses the same representation for data and for programs.
V. SIMULATION SETUP
The Simulation consists of two parts: Simulation of BWR scheme without Circularity using NS-2 Changing the backend and re-simulating (With circularity) The following parameters are used for the simulation of the existing Bandwidth Request scheme.
A. Simulation of BWR Scheme without Circularity
The parameters mentioned are used in the Tool Command Language (TCL) script that we have written.This script also uses the WiMAX Control Agent in order to produce a detailed account of the activities going on during the simulations.In the resulting output file, we search for the timing details of specific events in order to extract the Bandwidth Request delay.
The start and stop traffic times of the BWR procedure for all the Subscriber Stations (SS) in the scenario are stored in files.Using a C program, we find the average BWR delay per node, after calculating the total time taken by all the nodes to complete their respective BWR processes.
Such simulations can be carried out for different numbers of SS each time by the use of shell scripts.Then the average BWR delay is recorded along with number of SS involved in each such simulation.
B. Changing the backend and re-simulating (With circularity)
In order to enhance the Bandwidth Request scheme, we make some modifications to the backend of ns-2, which is implemented in C++ language.During the BWR procedure, there will be many SS contending to send their requests to join the network.The packets sent by different SS may collide at some instants and they will have to be resent.We try to reduce the collisions between packets of different SS by making the SSs less selfish.We have made two such changes, one in each of the files mentioned above [12].
VI. RESULTS
We have run the simulation for 6 mobile nodes and we can see the output as in the figure 8.The calculator function takes the traced file, track the sent times details and stored in the intermediate file by name sent times-f.The figure 9 shows the screenshot of sent time details.The outputs for the following sequence of subscriber stations (SSs) with and without circularity are observed and as shown in table.1 Figure 11 shows the graph of Access delay across various size of network with and without circularity.
We can see that, access delay is reduced in the case of enhanced network where we used the concept of circularity.As we see in the graph, the delay is gradually increased for both existing and new plans.But, we find there is better performance with the new scheme.X-axis: No.Of subscriber stations Y-axis: Delay http://ijacsa.thesai.org
D. Comparison of Throughput (For 10 trials output)
Figure 14 shows the comparison of throughput for both with and without circularity of 10 trials.
Figure 14
In figure 14 we have calculated the throughput from the previous access delays, which have been taken for ten trials.We can see the better performance in the case of circularity.
VII. CONCLUSION AND FUTURE ENHANCEMENT
The project involves the design of MAC IEEE 802.16.Here, new concept of circularity has been included in the existing contention resolution algorithm for MAC 802.16.In the existing MAC layer, there is certain amount of wastage in the available bandwidth.A concept of circularity is introduced whereby selected BWR slots are dropped in a controlled way in our new enhanced MAC protocol.We have seen the results of minimized uplink access delay, improved throughput and there by reduction in contention slots per frame.Hence circularity principle can be used to enhance the performance of MAC 802.16.We tried to reduce the collisions and hence have shown that concept of circularity can lead to higher throughput on an average of 12% more than the normal.For current design we have assumed the circularity on all SSs.This scheme can be modified in some particular SSs wherein we apply circularity concept to establish it is also more efficient than this scheme.
Number of Base Stations - 1
Number of Sink Nodes -1 Number of Subscriber Stations -6,12,…,60 Traffic Start Time -20 Sec Traffic Stop Time -40 Sec Simulation Start Time -0 Sec Simulation Stop Time -50 Sec Channel Type -Wireless Channel MAC Type -Mac/802.16/BS
Figure 5 Figure 6
Figure 5 Figure 6 shows the flow chart for comparing the Throughput results of two previous modules.
Figure 6 .
Figure 6.IV.HARDWARE AND SOFTWARE REQUIREMENTS A. Hardware Interface Pentium 4 processor. 512 MB RAM. 20 GB Hard Disc Memory
Channel Type -Wireless Channel Radio Propagation Model-TwoRayGround Network Interface Type Phy/WirelessPhy/OFDM MAC Type -802_16 Interface Queue Type -DropTail Priority Queue Link Layer Type -LL Antenna Model -Omni Antenna Maximum Packets in Interface Queue -50 Routing Protocol -DSDV (Routing is done through the Base Station) Routing Protocol-AODV (Routing is done through the Base Station) Network Architecture Parameters: Number of Base Stations -1 Number of Sink Nodes -1 Number of Subscriber Stations -Varied from 4 to 64 Base Station Coverage -20 meters Traffic Start Time -20 Traffic Stop Time -40 Simulation Stop Time -50
Figure 8
Figure 8 The calculator function takes the traced file, track the received times details and stored in the intermediate file by name recvtimes-f.The figure 10 shows the screenshot of Received time details. A. Comparison of access delay (For single instance) Input given: Seed value = 144443207. No.Of SSs=6, 12, 18…….…60. WOC: Without circularity WC: With Circularity | 4,837 | 2010-01-01T00:00:00.000 | [
"Computer Science",
"Engineering"
] |
Rotation of the c Subunit Oligomer in EF0EF1 Mutant cD61N*
ATP synthases (F0F1-ATPases) mechanically couple ion flow through the membrane-intrinsic portion, F0, to ATP synthesis within the peripheral portion, F1. The coupling most probably occurs through the rotation of a central rotor (subunits c10εγ) relative to the stator (subunits ab2δ(αβ)3). The translocation of protons is conceived to involve the rotation of the ring of c subunits (the c oligomer) containing the essential acidic residue cD61 against subunits ab2. In line with this notion, the mutants cD61N and cD61G have been previously reported to lack proton translocation. However, it has been surprising that the membrane-bound mutated holoenzyme hydrolyzed ATP but without translocating protons. Using detergent-solubilized and immobilized EF0F1 and by application of the microvideographic assay for rotation, we found that the c oligomer, which carried a fluorescent actin filament, rotates in the presence of ATP in the mutant cD61N just as in the wild type enzyme. This observation excluded slippage among subunit γ, the central rotary shaft, and the c oligomer and suggested free rotation without proton pumping between the oligomer and subunit a in the membrane-bound enzyme.
Direct evidence for the relative rotation of c 10 ␥⑀ against ab 2 ␦(␣) 3 under the conditions of ATP synthesis is still lacking, because it has not yet been feasible to energize the oriented immobilized enzyme within a native-like ion-tight membrane environment. Instead, the rotation of the c oligomer was investigated by attaching the reporter (a fluorescently labeled actin filament) to c 10 of detergent-solubilized and immobilized F 0 F 1 and checking for ATP hydrolysis-driven rotation (14 -16). The presence of detergent was inevitable in these approaches (just as in the one presented here). All of the groups observed that the activity was now insensitive to DCCD 1 and nearly insensitive to venturicidin, in contrast to the behavior of the membrane-bound enzyme. Upon the removal of the detergent, coupling was restored (16). Apparently, the enzyme became functionally uncoupled in the presence of the detergent.
Our method to attach fluorescent actin filaments to the c oligomer via engineered Strep-tags not only was monospecific for the c oligomer of F 0 , it turned out to be quite robust (15), for example, in that it allowed to wash away the detergent after immobilization without the complete loss of rotary activity of immobilized F 0 F 1 . After the washing of both untreated and DCCD-treated EF 0 EF 1 , the yield of rotating filaments with DCCD-treated EF 0 EF 1 dropped to zero as expected in view of the inhibitory effect of DCCD, but it remained to some extent in controls. A partial loss of the rotary activity in the controls was probably caused by mechanical removal of immobilized enzymes/filaments from the surface. Hence, although this result was compatible with the notion that the observable rotating filaments were connected to fully DCCD-sensitive EF 0 EF 1 (coupled enzyme), it did not fully exclude that the rotation of the c oligomer relative to subunit a was decoupled from proton control between subunits a and c by the presence of detergent (decoupled enzyme) in all samples whether they were DCCDtreated or not. To clarify this situation, we repeated the experiment with the EF 0 EF 1 mutant cD61N. It lacks the acidic residue on subunit c, which is essential for proton translocation. The mutant is known to assemble normally but to be completely blocked in proton translocation both by F 0 F 1 and by exposed F 0 . Therefore, the mutant strain is unable to support the growth on non-fermentable carbon sources. However, despite ATP-driven proton pumping being completely blocked, the ATP hydrolytic activity of the membrane-bound enzyme remains unaffected (22,23). In today's understanding of the rotary enzyme, this observation implies either that the rotation of the central shaft, subunit ␥, became uncoupled from the rotation of the c oligomer or that the c oligomer remained mechanically coupled to and corotated with subunit ␥ but was "freewheeling" relative to the stator subunits ab 2 ␦ (␣) 3 . Here we show the latter to be the case. EF 1 EF 0 (cD61N) is as effective in the filament rotation assay as the control. Although this finding fully agrees with the previously proposed protonic uncoupling of detergent-solubilized F 0 F 1 (16,20), it also suggests the free mobility of the c oligomer against the stator, mainly subunit a, not only in the detergent-solubilized but also in the membrane-embedded mutant enzyme.
MATERIALS AND METHODS
Chemicals and Enzymes-All of the restriction enzymes were purchased from New England Biolabs or MBI Fermentas (St. Leon-Rot, * This work was supported by grants from the Deutsche Forshungsgemeinschaft (SFB 431/D1) (to W. J. and S. E.) and by the Human Sciences Frontier Project (to W. J.). The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Molecular Genetics-The complete cysteine-less plasmid pSE1 (-His tag, Strep-tag at the C terminus of c) (15) was used as starting material. Site-directed mutagenesis was performed by standard PCR using the oligonucleotide primers 5Ј-ATTCTGATTGCTGGTCTGTTGCCG-3Ј, 5Ј-ATCGGGATAGCATTCACCAGACCCATAACG-3Ј, 5Ј-GGATACGGCC-AGTACACTTAACTTTCATG-3Ј, and 5Ј-GGGTCTGGTGAATGCTATC-CCGATCGC-3Ј. The BamHI/XhoI fragment of pSE1 was substituted with the corresponding fragment carrying the cD61N mutation by restriction and religation. Successful cloning was confirmed by nucleotide sequencing. The resulting plasmid was called pKG1. pKG1 carried a His 6 tag at the N termini of subunits , a C-terminal Strep-tag at subunits c, a point mutation in subunit c (D61N), and all of the Cys residues were replaced by Ala (24).
Preparation of EF 0 EF 1 -E. coli strain DK8 (25) was transformed with pKG1, and cells were grown on minimal medium containing 10% (v/v) LB and 0.5% (w/v) glucose. Cells were collected at A 600 ϭ 0.8. The membranes were isolated and purified essentially according to Wise (26), and membrane proteins were extracted as described previously (15). After the addition of avidin, the octylglycoside extract of membranes from 25 g of collected cells containing 140 mg of total membrane protein was diluted with buffer A (20 mM TES (pH 7.5), 5 mM MgCl 2 , 1 mM K-ADP, 15% (v/v) glycerol) to 1% octylglycoside (total volume, 100 ml) and then was applied batchwise to 5 ml of streptactin-Sepharose (settled volume, 5 mg streptactin/ml). Washing and elution were performed as described previously (15). Protein-containing fractions (2 mg of protein) were combined, and batchwise was adsorbed onto 1 ml of Ni-NTA Superflow. After washing, up to 100 g of pure EF 0 EF 1 eluted from the column. Protein determinations were carried out according to Sedmak and Grossberg (27) and SDS-gel electrophoresis with the Pharmacia Phast system (8 -25% gradient gels). Staining was carried out with Coomassie Blue followed by silver (28). ATPase activity was measured with 0. (15) in buffer C (7-min incubation); 8) wash with buffer C; and 9) 20 mM glucose, 0.2 mg/ml glucose oxidase, 50 g/ml catalase, 5 mM ATP in buffer C. The deliberate omission of either one single component of the chain Ni-NTA-horseradish peroxidase, EF 0 EF 1 , streptactin, and biotin-F-actin prevented the binding of fluorescent F-actin as evident from the absence of fluorescent filaments within in the flow cell. This ensured that the actin filaments were attached to subunit(s) c in the correct manner. Also, the rotating filaments only could be observed in the presence of ATP (15), whereas in its absence (or with ADP present), this number dropped to zero without affecting the number of immobilized filaments.
Video Microscopy-An inverted fluorescence microscope (IX70, lens PlanApo 100x/1.40 oil, fluorescence cube MWIG, Olympus, Hamburg, Germany) was equipped with a silicon-intensified tube camera (C2400-08, Hamamatsu, Herrsching, Germany) and connected to a VHS-PAL video recorder (25 frames/s). With this setup, the filaments of 5-m length appeared as 3-cm long rods on a 14-inch monitor. A freshly chromatographed sample of EF 0 EF 1 was loaded into the flow cell and labeled with fluorescent actin filaments. The rotation of single filaments was observed for up to 3 min. A single molecule rotation was followed up to 30 min after loading. Video data were captured (frame grabber FlashBus, Integral Technologies, Indianapolis, IN) and further processed by using the software ImagePro Plus 4.0 (Media Cybernetics, Silver Spring, MD) and Matlab 5.2 (The Math Works, Natick, MA).
Other Methods-ATPase activity was measured at protein concentrations of 10 g/ml in 50 mM Tris/HCl (pH 8.0), 3 mM MgCl 2 , 10 mM Na-ATP, 1% octylglycoside. After incubation for 5 min at 37°C, the reaction was stopped by the addition of trichloroacetic acid, and the released P i was determined colorimetrically (29).
RESULTS AND DISCUSSION
EF 0 EF 1 mutant SE1 (15) was used as starting material. In this mutant, all wild type cysteines are substituted by alanines (24), each  subunit carries an engineered His 6 tag at its N terminus, and each c subunit carries an engineered Strep-tag at its C terminus. The desired point mutation within subunit c (Asp613 Asn) was introduced by PCR and confirmed by nucleotide sequencing. The resulting plasmid was called pKG1. Because the cD61N mutation causes uncoupling, EF 0 EF 1 -KG1 had to be prepared from cells grown on medium supplemented with LB and glucose. This yielded 30 -100 g of EF 0 EF 1 -KG1/8l culture volume. Typical activities after purification were 90 units/mg. Fig. 1 shows the results of an SDS-electrophoresis with purified EF 0 EF 1 -KG1, EF 0 EF 1 -SE1, and a control (EF 0 EF 1 -KH7 (11)).
As expected, ATPase activity from membranes isolated from DK8/pKG1 was not inhibited by DCCD in contrast to controls, which were reversibly (i.e. after the addition of 0.5% N,Ndimethyldodecylamine-N-oxide) inhibited by 70% after incubation with 50 M DCCD for 1 day at room temperature. Also, venturicidin A (20 and 100 M, 30-min incubation) did not inhibit the membrane-bound ATPase activity from EF 0 EF 1 -KG1, in contrast to wild-type-like controls (EF 0 EF 1 -SE1, EF 0 EF 1 -KH7). This finding is of limited value though in that the mutation might have compromised the venturicidin binding site (30). Fig. 2 summarizes the results of the filament rotation assay (8). Panel A shows typical time courses as ob- 1 -KH7 (11)) after purification by streptactin-Sepharose and nickel-nitrilotriacetic acid affinity chromatography. Pharmacia Phast gradient gel 8 -25% silver/silicon tungstic acid stain (28) was used. The size difference between subunits c from EF 0 EF 1 -KG1, EF 0 EF 1 -SE1, and EF 0 EF 1 -KH7 is because of the C-terminal Strep-tag engineered into EF 0 EF 1 -KG1 and EF 0 EF 1 -SE1. tained with EF 0 EF 1 -KG1. Panel B shows the dependence of the filament rotational rate from filament length. It is evident that EF 0 EF 1 -SE1 (15) and EF 0 EF 1 -KG1 were indistinguishable.
How do these results complement the proposal that detergent solubilized F 0 F 1 is uncoupled from proton control (16), possibly by partial displacement of subunits a and b from their locations in the native enzyme (20)?
The exact structural consequences of the cD61N mutation are not known. They are expected to be small, because both the size and the polarity of Asp and Asn are very similar. Still the lack of an essential protonable group is sufficient to completely block proton conductance in both directions, passive under ATP synthesis and actively driven by ATP hydrolysis (23).
Assuming that ATP synthesis is driven by the rotation of subunits ␥⑀c n , the failure to conduct protons is expected to prevent both rotation and ATP synthesis. However, ATP hydrolysis catalyzed by the membrane-bound enzyme is only diminished but not completely blocked (by 50% in the cD61N mutant and not at all in the cD61G mutant (23)). This finding in view of the structure of F 0 F 1 either implies some sort of displacement of subunits ␥⑀ from their c oligomer counterpart (with F 0 F 1 still kept together by the stator subunits a, b, and ␦) or continued corotation of ␥⑀c n without concomitant proton pumping. The latter is the case as we show here. Thus, "uncoupling" in EF 0 EF 1 -KG1 is brought about by ATP hydrolysisdriven freewheeling of the c oligomer.
The interaction of subunits ␥⑀ and the c oligomer both in the wild-type enzyme and the mutant EF 0 EF 1 -KG1 withstands the strong mechanical strain between the ATP-hydrolyzing motor and either the drag force exerted on the actin filament or in situ the proton-motive force. In the cD61N mutant, the interactions between ␥⑀ and the c oligomer are expected to be as strong as in the wild type enzyme, because the mutation is comparatively small and not likely to affect F 0 -F 1 interactions at a distance of around 2.7 nm. Accordingly, we did not observe a more pronounced tendency of F 0 to dissociate from F 1 than with the wild type enzyme during preparation (data not shown).
To summarize, 1) the membrane-bound cD61N mutant hydrolyzes ATP without proton translocation; 2) the ␥⑀-c oligomer interactions are strong enough to withstand considerable mechanical strain; and 3) solubilized wild type and mutant enzyme rotate ␥⑀c n upon ATP hydrolysis. These findings together indicate ATP hydrolysis-driven rotation of the c oligomer not only with solubilized but also with membrane-bound enzyme and irrespectively of the native or non-native location of subunits a and b. The expected sterical hindrances for the rotation of the c oligomer relative to subunits a and b would be smallest for the cD61G mutant and perhaps a little more pronounced for the cD61N mutant in accordance with the reported ATPase activities of the respective membrane-bound mutant enzymes (23).
How do these implications relate to the assumed rotary mechanism of F 0 F 1 ? Proton transport through the F 0 portion of ATP synthase relies at least on two essential amino acid residues, Asp-61 on subunit c and Arg-210 on subunit a (E. coli numbering). A mechanism on how proton translocation might drive the rotation of the ring of c subunits (the c oligomer) relative to subunits a and b has been detailed previously (1,3,4,(17)(18)(19)(20).
This model now would seem to be valid for all ATP synthases, because the proposed location of the acidic residue in subunit c of the sodium translocating ATP synthase close to the cytoplasmic side of the membrane (31) had to be abandoned as shown by recent cryoelectron microscopic data. 2 The model features four assumptions. 1) The acidic residue cD61 is positioned at the center of the membrane. It is accessible for protons from both aqueous phases by two parallel but laterally off-set access channels. 2) There is a stochastic rotation of the c oligomer relative to subunit a driven by thermal impact (Langevin force). 3) It is limited by an electrostatic constraint, namely that the acidic residue on subunit c (Asp-61) is forcedly electroneutral (protonated) when facing the lipid core. 4) It is forcedly anionic (deprotonated) when opposing the permanently positively charged residue aR210, which is juxtaposed cD61 (for a detailed discussion cf. Refs. [31][32][33]. The c oligomer thus rotationally fluctuates relatively to subunit a and progresses in one single direction by protonation of one AspϪ through one channel followed by the loss of another proton from a protonated Asp into the other channel located at the opposite side of the membrane. The model implicitly assumes that the interacting essential side chains are properly oriented without the requirement of large protein flexibility other than the thermal motion of the "rigid" c oligomer relative to subunit a. This model both explains wild type features and the behavior of the cD61N mutant, i.e. the loss of passive and active proton translocation along with conservation of the ATPase activity of the membrane-bound enzyme, which corotates the c oligomer with or without proton pumping. However, the occurrence of the corotation in the mutant in vivo contradicts the fourth proposal above, because the postulated transient but essential 2 W. Kü hlbrandt and P. Dimroth, personal communication. juxtaposition of a positive (aR210 ϩ ) and negative (cD61 Ϫ ) charge is lacking in cD61N and cD61G.
In this context, the behavior of point-mutated strains containing aR210A is more difficult to understand. Both in accordance with expectations as predicted from the model and experiments, aR210A does not pump protons but allows for passive proton translocation (34). However, its membrane-bound ATP hydrolysis activity is largely inhibited. Because the mutation does not affect the F 1 part, the only explanation for this inhibition would be the blockage of the c oligomer rotation. These observations become better understandable by taking into account the proposed rotation of the helix with Asp-61 in subunit c and with Arg-210 in subunit a relative to the other helices in these subunits "swiveling" (35). 3 Proton translocation by F 0 would seem to involve both intersubunit as well as intrasubunit rotational movements. | 3,967.6 | 2002-08-30T00:00:00.000 | [
"Biology",
"Chemistry"
] |
Release Characteristics of Diltiazem Hydrochloride Wax-Matrix Granules – Thermal Sintering Effect
: The aim of this study was to investigate the release characteristics of matrix (non-disintegrating) granules consisting of diltiazem hydrochloride (model drug) and glyceryl behenate (a wax matrix forming polymer) for sustained release application using sintering technique. The granules of diltiazem hydrochloride-wax matrix were prepared by melt granulation technique. This was formed by triturating the drug powder with a melted glyceryl behenate (drug: wax ratio, 3:1). The granules were subsequently sintered at 60 and 70 0 C for 1, 1.5 and 3h. The unsintered and sintered wax matrix granules of diltiazem hydrochloride were evaluated for physicochemical parameters and in vitro dissolution studies. The dissolution data were subjected to analysis using different mathematical models namely – zero order flux, first order, Higuchi square root of time, then Korsmeyer and Peppas model. Fourier-Transform Infrared Spectroscopy (FTIR) was carried out to investigate any chemical interactions between the drug and the added recipients before and after sintering. There was increased drug release retardation of diltiazem hydrochloride-wax matrix granules with sintering. The retardation depended on the temperature and duration of sintering. For instance, formulations sintered at 60 and 70°C for a period of 1.5h gave maximum release (m ∞ ), time to attain maximum release (t ∞ ) and dissolution rate (m ∞ /t ∞ ) of 96.1%, 95.2%, 5h, 9h, 19.2 % h -1 and 10.6 % h -1 respectively. The drug release was by Higuchi controlled diffusion mechanism and it followed Fickain diffusion mechanism (n<0.45). Sintering technique enhanced the extent of drug retardation from the systems studied. There was no chemical interaction between the model drug and the added recipients as shown in the FTIR studies.
KEYWORDS: Thermal Sintering technique, sustained release, Fourier-Transform Infrared Spectroscopy
Currently, significant attention is being focused on the development of sustained release dosage forms due to its numerous advantages over conventional dosage forms. Some of these advantages include: maintenance of a steady plasma level of the drug over a prolonged time period, reduction in adverse side effects, patient convenience and compliance e.t.c (Aulton, 2002). Sintering technique is defined as the bonding of adjacent particle surfaces in a mass of powder, or in a compact by the application of heat (Rakesh and Ashok, 2009). Thermal sintering involves the heating of a compact at a temperature below the melting point of the solid constituents in a controlled environment under atmospheric pressure. The changes in the hardness and disintegration time of tablets stored at elevated temperatures have been described as a result of thermal sintering effect (Satyabrata et al., 2010). Recently, Flowerlet et al., (2010) developed an oral sustained release dosage formulation of metformin hydrochloride matrix tablets by sintering the polymer matrix with organic vapour such as acetone. Thermal sintering process has been used for the fabrication of sustained release matrix dosage forms for the stabilization and retardation of drug release from different systems (Cohen et al., 1984). Previously, Rowe et al (1973), have reported that the process of thermal sintering affect the pore structure and strength of plastic matrix tablets.
Polymer films with different permeability have been explored to modify drug release from drug particles. Some examples mentioned in the literature include: films with the drug as a solution in a polymer matrix, e.g. monolithic devices (Oppenheim 1981;Douglas et al., 1987;Davis and Illum, 1988) polymer coated reservoir devices (Lehmann, et al., 1979), polymeric colloidal particles (microparticles or nanoparticles) either in the form of reservoir or matrix devices (Oppenheim, 1981;Douglas et al., 1987;) and osmotically "controlled" devices (Zentner et al., 1985;Muhammad et al., 1991). These methods are however very complicated and expensive since it requires the use of organic solvents as coating fluid. Moreover, these organic solvents are hazardous to the environment. Waxes have been used either as matrix former or as a coating polymer to sustain the release of drugs (Zhou et al., 1996;Zhang et al., 2001;Uhumwangho and Okor, 2006). An alternative simple approach, which was considered in the present study, is melt granulation whereby the drug powder is triturated with a melted wax serving as a hydrophobic retard release agent. The resulting granules consist of the drug particles dispersed in a wax continuous matrix.
Diltiazem hydrochloride (DZH) is a nondihydropyridine member of the group of drugs known as benzothiazepines, which are a class of calcium channel blockers. It is used in the treatment of hypertension, angina pectoris, and some types of arrhythmia (Buckley et al, 1990). Its chemical formular is [(2S,3S)-5-(2-dimethylaminoethyl)-2-(4methoxyphenyl)-4-oxo-2,3-dihydro-1,5benzothiazepin-3-yl] acetate, with a molecular weight of 414.16. Its bioavailability is about 30% to 40% due (Hermann et al., 1983;Smith et al., 1983). The aim of this study was to prepare waxmatrix granules by melt granulation technique using DZH as a model drug. These wax-matrix granules were later sintered thermally at different temperatures and time duration. Consequently, the effect of sintering temperature and duration on the drug release profiles and physicochemical parameters were investigated.
Materials:
The active ingredient used in the study was diltiazem hydrochloride (Cipla Ltd, Goa, India). The matrix former used was glyceryl behenate (Dr Rheddy's Laboratory, India), a fine white solid powder with melting point of 83 0 C. Magnesium stearate (Qualikems Fine Chemical Pvt Ltd, India) was used as the lubricant. Other materials used were analytical grade.
Melt granulation technique: Glyceryl behenate (30 g) was melted in a stainless steel container in a water bath at a temperature higher than its melting point (i.e. 83 0 C). A sample of DZH powder (90 g) was added to the melted wax and thoroughly mixed with a glass rod. It was then allowed to cool to room temperature (35 ± 2 0 C). The mass was pressed through a sieve of mesh 10 (aperture size; 710 µm) to produce wax-matrix granules.
Sintering of the matrix granules: The matrix granules were then subjected to thermal treatment by placing them on aluminum foil and subjecting to sintering at different temperatures (Kondaiah 2002;Luk and Jane, 1996) i.e. 60 and 70 0 C for different durations (1, 1.5 and 3h) in a hot air oven (Labhosp, Mumbia, India).
Packing property of the matrix granules: The packing properties were determined by measuring the difference between bulk density (BD) and the tapped density (TD) using standard procedure. In the procedure, 20g of matrix granule sample was placed in a 250ml clean, dry measuring cylinder and the volume, V 0 occupied by the sample without tapping was determined. An automated tap density tester (model C-TDA2, Campbell Electronics, Mumbai, India) was used for tapping the granules according to USP Chapter 616 Method I (Manish et al, 2001). After 100 taps the occupied volume, V 100 was noted. The bulk and tap densities were calculated from these volumes (V 0 and V 100 ) using the formula. Density = Weight/Volume occupied by sample. From the data, Hausner ratio and compressibility index were determined (US Pharmacopeia, 2006).
Flow property of matrix granules:
The flowability of the granules was determined by measuring the angle of repose formed when a sample of the granules (40g) was allowed to fall freely from the stem of a funnel to a horizontal bench surface. The radius (r) and the height (H) of the powder heap were determined and then the angle of repose (θ) was calculated (Maheshwari et al., 2003).
Hardness-Friability Index (HFI):
This was calculated on the basis of the results of the friability test. In the procedure, 20 g of matrix granules were placed in the drum of an Erweka friabulator (Heusenstamm, Germany) rotating at 20 rev per min for 10 min. The matrix granules were then screened through a 60# sieve to remove the fines generated (Nasipuri and Omotosho, 1985;Eichie et al., 2005;Singh et al., 2007). Hence, the hardness-friability index was calculated using the equation below: where F A and F B are weights after and before friability determination respectively.
Encapsulation of the matrix granules: Samples of matrix granules before and after sintering (drug content, 90mg) were filled manually into plain hard gelatin capsules. The capsules were kept in airtight containers before their use in in-vitro dissolution studies.
In vitro dissolution test: One capsule filled with the matrix granules was placed in a cylindrical basket (aperture size 425µm: diameter 20mm; height 25mm), and immersed in 900ml of leaching fluid (0.1N hydrochloric acid maintained at 37 ±2 o C). The fluid was stirred at 100rpm (Model Disso 2000, Lab India). Samples of the leaching fluid (5ml) were withdrawn at selected time intervals with a syringe fitted with a cotton wool plug and replaced with an equal volume of drug-free dissolution fluid. The samples were suitably diluted with blank dissolution fluid and were analysed for content of diltiazem at λ max , 236nm by using an Elico SL 210 UV-Visible double beam spectrophotometer (Elico, India). The samples were filtered with Whatman No. 3 filter paper before assay and the amounts released were expressed as a percentage of the drug content in each dissolution medium. The dissolution test was carried out in quadruplicate and the mean results reported. Individual results were reproducible to ± 10% of the mean.
Determination of rate order kinetics and mechanism:
The dissolution data were analyzed on the basis of zero order, (cumulative amount of drug released vs. (Higuchi, 1963;Korsmeyer et al., 1983;Peppas, 1985;Harland et al., 1988).
The kinetic models order equations are: Zero order: m = k 0 t First order: log m 1 = log m 0 -0.43 k 1 t M = k H t 1/2 Korsmeyer and Peppas dissolution model= log m =log k 2 + nlogt; where m is the percentage (%) amount of drug released in time t; m 1 is the residual amount (%) of drug in time t; m 0 is the initial amount of drug (100%) at the beginning of the first order release; k 0 , k 1, k H and k 2 are the release rate constants for the zero, first order, the Higuchi models and Korsmeyer and Peppas dissolution models respectively. The n is the diffusion release exponent that could be used to characterize the different release mechanism. Value of n below 0.45 indicates Fickian diffusion mechanism and n value between 0.45 and 0.89 indicates anomalous transport, often termed as first-order release. If the n value reaches 0.89 or above, the release can be characterized by case II and super case II transport, which means the drug release rate does not change over time and the drug is released by zero-order mechanism. The correlation coefficient (r) for each rate order was also calculated.
Fourier Transform Infra Red (FTIR):
The FTIR spectrum of the different samples were recorded in an Infra Red spectrometer (Nicolet Magna 4R 560, MN, USA) using potassium bromide discs prepared from powdered samples. Infrared spectrum was recorded in the region of 4000 to 400 cm -1 .
Statistical analysis: All data obtained were subjected to student t-test (p < 0.05) to test for significance of difference.
Effect of sintering on physicochemical parameters of unsintered and sintered wax-matrix granules:
The effects of sintering on the physicochemical parameters of unsintered and sintered matrix granules are presented in table 1. It was observed that all the matrix granules were free flowing with angle of repose ≤ 29 0 and Carr's index ≤19.3%. (Gordon et al., 1990). There was a slight decrease in these values i.e. angle of repose and Carr's index (See table 1) as temperature and duration of sintering increased, although, the difference did not vary significantly (p>0.05). On the other hand, it was observed that all the sintered matrix granules had high HFI value when compared with the unsintered matrix granules (See table 1). However, the differences varied significantly (p<0.05). More so, with increase in temperature and duration of sintering, the HFI values increased correspondingly (See Table 1). The increase in hardness with increase in temperature and duration of sintering might be attributable to the fusion of the wax matrix particles or the formation of welded bonds among the matrix particles after cooling. Previously, some researchers reported that asperity melting and formation of welded bonds resulted in high tensile strength of tablets, this occurs with compression at high temperature (Pilpel and Esezobo, 1977;Kurup and Pilpel, 1979;Esezobo and Pilpel, 1986).
Dissolution profiles of matrix granules:
The dissolution profiles of the unsintered and sintered matrix granules at 60 and 70 0 C at different time durations are presented in Fig 1. It was observed that the unsintered matrix granules were able to retard the drug for 2h. Generally, as the temperature and duration of sintering of the matrix granules increased, the time to attain maximum release (t ∞ ) increased correspondingly.
For instance, when matrix granules was sintered at 60 0 C for 1.5 and 3h (i.e. formulations GB 3 and GB 4 ) the maximum release (m ∞ ) and time to attain maximum release (t ∞ ) were 96.1%, 94.2%, 5h and 6h respectively, while their corresponding values at 70 0 C for time duration of 1.5 and 3h (i.e. formulations GB 6 and GB 7 ) were 95.2%, 96.2%, 9h and 12h (See table 2). Hence, sintering temperature and duration markedly affected the drug release properties of the wax-matrices granules . The dissolution rate (m ∞ /t ∞ ) also decreased as the sintering temperature and duration of sintering increased (Table 2). This finding is in conformity with previous literature (Rao et al., 2001;Rao et al., 2003). The retardation in drug release on sintering may be due to softening of the wax particles during sintering and hence penetrated the empty spaces, forming a continuous layer around the drug particles in the matrix granules (Singh et al., 2007). This resulted in a decrease of the drug particles surface to the dissolution medium resulting in drug retardation from the matrix granules. It may also be attributed to the increase in HFI (See Table 1) which might decrease porosity and hence a reduction in influx of the dissolution medium into the drug particles in the matrix granules. However, formulation GB 7 which was sintered at 70 0 C for 3h duration was able to retard the drug for a period of 12h. Drug release mechanism: A good knowledge of the drug release kinetics will provide a proper understanding of the drug release mechanism. Four mathematical models were used for analysis: zeroorder kinetics, first-order kinetics, Higuchi mechanism, and Korsmeyer and peppas model (Higuchi, 1963;Korsmeyer et al., 1983;Peppas, 1985;Harland et al., 1988). The values of the correlation coefficients (r) and the release rate constants are presented in Table 3). This indicates that the release of diltiazem hydrochloride from these systems followed Fickian diffusion mechanism (Korsmeyer et al., 1983). FTIR: Formulation GB 7 was considered for FTIR studies since it was able to retard the drug for a period of 12h. This study was carried out in order to investigate if there was any chemical interaction between added excipients and DZH in the formulation (GB 7 ) before and after sintering. The FTIR of the pure drug, glyceryl behenate, unsintered and sintered matrix granules were recorded (See Fig 2a, b, c and d respectively). The IR spectrum of DZH showed characteristic peaks at 1743.04 cm -1 (ester-C=O) and 1679.0 cm -1 (amide-C=O). However, for the glyceryl behenate alone (without drug or other excipients), IR spectrum showed signals at 2956 cm -1 (for aliphatic, C-H stretch), and 1739.02 cm -1 (for ester, C=O stretch). These spectra were compared with the IR spectrum of the unsintered and the sintered wax-matrix granules (GB 7 ). It was observed that the IR spectra showed both the principal peaks of DZH (1743 and 1649cm -1 ) and glyceryl behenate (1739cm -1 for ester), suggesting that there was no chemical interaction between the DZH and added excipients (such as glyceryl behenate) in both sintered and unsintering matrix granules.
Conclusion: Sintering technique enhanced the extent of drug retardation from the systems studied. Formulation GB 7 sintered at 70 0 C for 3h was able to sustain the drug for a period of 12h with a maximum release of 96.2%. The FTIR studies showed that the model drug was not affected by the temperature and time duration used for sintering. | 3,757.6 | 2011-08-02T00:00:00.000 | [
"Materials Science"
] |
Coherent Polarization Shift Keying Modulated Free Space Optical Links Over a Gamma-Gamma Turbulence Channel
Problem statement: The optical signal propagating through the Free Spa ce Optical (FSO) channel suffers from irradiance and phase fluctuati ons caused by the atmospheric turbulence, which results in Bit Error Rate (BER) performance degrada tion. Approach: In this study the performance of the Multilevel Coherent Polarization Shift Keying ( M-POLSK) based FSO communication system operating over the gamma-gamma turbulence channel is investigated. To mitigate the turbulence induced fading, the convolutional coding and spatia l diversity techniques are employed. The upper BER bounds are derived using the transfer function technique. Results: For example, with a SNR of 30 dB, the BERs for uncoded and coded M-POLSK are 0.047 and 1.4 ×10 -4 , respectively in the weak turbulence regime. When the Maximum Ration Combining (MRC) technique employing four detectors are used in the receiver, the power gains of ~31.4, ~29.5 and ~57.9 dB are achieved for weak, moderate and strong turbulence regimes, respectivel y. Conclusion: We have also shown that the spatial diversity offers increased link margin as t he scintillation level rises. Compared to the angul ar modulation, the proposed M-POLSK scheme offers high immunity to the phase noise, thus reducing the power penalties.
INTRODUCTION
Unlike Radio Frequency (RF) based wireless systems which suffer from bandwidth constraints, FSO systems offers full-duplex gigabit rate throughput. This makes it a suitable technology for delivering broadband wireless services for certain applications including the metropolitan area network, enterprise/local area networks, optical fiber backup, enterprise connectivity and the last mile access networks (Uysal et al., 2006). FSO offers a number of advantages over the RF technology, including higher data rate, an unregulated spectrum, high immunity to the electromagnetic interference, high security, a small size transceiver, low cost and a lower power consumption (Popoola and Ghassemlooy, 2009;Popoola et al., 2008). In indoor applications, optical radiation is confined within rooms (assuming no windows and transparent barriers), thus making eavesdropping a difficult task. For outdoor applications, a laser transmitter with a highly directional and a cone-shaped beam profile normally installed high above the street level thus makes interception difficult. Therefore, anyone trying to tap into the communication link can be easily detected and any equipment placed within the narrow optical foot print could easily be identified.
However, the FSO link performance suffers from a number of phenomena such as the misalignment due to the building sway caused by the wind, thermal expansion and weak earthquakes (Uysal et al., 2006;Arnon, 2003;Tang et al., 2011). Another important issue with the outdoor FSO system is the susceptibility of the optical link to the atmospheric conditions. The laser beam propagating through the channel suffers from the high attenuation due to the atmospheric scatters such as haze, fog and rain, which limit the link range and the system reliability. Fog compared with rain and haze is the biggest contributor to the path loss. The attenuation due to thick fog and haze can reach up to 300 dB km −1 thus limiting the link range to 100 m (Ramirez-iniguez et al., 2008). Smoke also has a similar effect as fog on the propagating optical signal (Ramireziniguez et al., 2008).
Even in clear sky conditions, the optical signal suffers from the atmospheric turbulence, which is also known as the scintillation (Popoola and Ghassemlooy, 2009;Kamalakis et al., 2006). Scintillation originates from the inhomogeneities in the refraction index of the atmosphere caused by the variation in the temperature and the pressure. Scintillation leads to significant fluctuations on the amplitude and phase of the optical field (i.e., channel fading) (Popoola and Ghassemlooy, 2009). The knowledge of statistical distribution of the atmospheric turbulence is necessary to fully study and predict FSO performance operating over a clear atmospheric condition.
The performance impairments due to the scintillation can be mitigated by adopting several approaches including the aperture averaging and the diversity techniques (Uysal et al., 2006;Khalighi et al., 2009;Zhu and Kahn, 2003), the adaptive optics (Weyrauch and Vorontsov, 2004), the saturated optical amplifiers (Abtahi et al., 2006), the modulation techniques and the error control coding (Uysal et al., 2006;Zhu and Kahn, 2003). In (Uysal et al., 2006;Zhu and Kahn, 2001;2003) the performances of coded FSO links for the log-normal and gamma-gamma channel modelsunder atmospheric turbulence have been investigated. Study also presents an approximate upper bound for the Pairwise Error Probability (PEP) and the upper bounds on the BER using the transfer function technique for the coded FSO links with Intensity Modulation/Direct Detection (IM/DD). The diversity techniques comprising space, time, or frequency (wavelength) have been adapted to improve performance impairments due to the scintillation. With the spatial diversity technique, where a single receiver with a large Field of View (FOV) is replaced by a group of detectors with a narrow FOV, the possibility of all the detectors suffering from the deep fade simultaneously is much reduced. Moreover, the spatial diversity scheme limits the amount of background light from unwanted sources that impinges on the specific detector, which otherwise could be received by the single receiver with a wide FOV (Khalighi et al., 2009).
The type of modulation schemes in FSO systems is crucial to ensure the maximum power efficiency. The coherent system based on the angular modulation; such as Binary Phase Shift Keying (BPSK) and Differential Phase Shift Keying (DPSK) are highly sensitive to the phase noise effects (Betti et al., 1995). Alternatively, it has been shown that POLSK offers higher immunity to the phase noise and the atmospheric turbulence. The polarization states of the laser beam propagating through the FSO channel can be maintained over a long link range (Sugianto and Davis, 2006).
MATERIALS AND METHODS
The aim of this study is to evaluate the performance of the Multilevel POLSK (M-POLSK) modulated FSO system with the coherent detection operating over the gamma-gamma atmospheric turbulence channel. For this purpose, the performance improvement by the error control coding and the spatial diversity will be also considered. However, the code should be short and simple in order to keep the complexity of this approach reasonably low. The system performance will be compared with the coherent BPSK and DPSK in terms of the average BER. The noise, comprising of both the background radiation and the thermal noise, is modeled as the additive white Gaussian process. We also assume that the transmitter and the receiver have the perfect link alignment.
Gamma-gamma turbulence model: The analysis for the atmospheric turbulence has been carried out by a number of researchers and several theoretical models have been developed to characterize its behaviour. The simplest and most widely reported model is the log normal turbulence, which is mathematically convenient and tractable. The log normal model is based on the Rytov approximation, which requires the unperturbed phase gradient to be large compared to the magnitude of the scattering field wave (Zhu and Kahn, 2003;Popoola and Ghassemlooy, 2009). However, the log normal model only covers the weak turbulence regime with a single scattering event. For the turbulence in the saturation regime with multiple scatterings, the log normal model becomes invalid (Uysal et al., 2006;Osche, 2002;Karp, 1988). The strength of turbulence can be described by the log intensity variance σ 2 l and the log normal model is only valid for σ 2 l . Another important parameter for describing the turbulence strength is the scintillation index, which is the log intensity variance normalized by the square of the mean irradiance. The experimental results have indicated that the scintillation index does not only saturate, but also decreases after it researches the maximum value while the strength of turbulence continues rising (Karp, 1988). In the saturation regime and beyond with the link length of several kilometres the intensity fluctuation is experimentally verified to obey the Rayleigh distribution (Karp, 1988;Popoola and Ghassemlooy, 2009). To express the turbulence effects across all regimes, the gamma-gamma turbulence model is considered in study.
The gamma-gamma model first proposed by Andrews et al. (2001) is valid for all turbulence regimes from weak to strong regimes. It is based on the assumption that the fluctuation of the laser beam propagating through the turbulence medium consists of the refraction (I 1 ) and scattering (I 2 ) effects. Subsequently, the normalized irradiance is expressed as the normalized product of two independently statistical random processes I 1 and I 2 given by Eq. 1: where, I 1 and I 2 represent the refraction and scattering effects, respectively and both are governed by the gamma distribution Al-Habash et al., 2001). Thus, the Probability Density Function (PDF) of the gamma-gamma model for the received irradiance fluctuation is derived as Eq. 2: where, ( ) ⋅ Γ represents the gamma function and K n (.) is the modified Bessel function of the 2nd kind of order n. The parameters α and β characterize the optical power fluctuation PDF which are related to the atmospheric conditions. Assuming that the optical radiation at the receiver is a plane wave, α and β can be expressed as Eq. 3a-b (Popoola and Ghassemlooy, 2009;Andrews et al., 2001): 12 5 l l 5 6 2 2 12 5 l 0.51 1 0.69 exp m -2/3 during daytime and night (Goodman, 1985;Uysal et al., 2006).
M-Polsk modulation principles:
A. transmitter: Figure 1 illustrates the block diagram of the M-POLSK transmitter. The state of the polarization of the laser beam is controlled by a Polarization Controller (PC) before being fed into the Polarization Beam Splitter (PBS). The Transmitting Laser (TL) beam is linearly polarized and has a π/4 polarization with respect to the principle axe of the external Phase Modulator (PM).
The emitted optical field of the carrier is expressed by a complex vector ( ) t 0 E s in the transverse plane, which is given as Eq. 4 (Cusani et al., 1992): where, P, ω and ϕ(t) are the power, the angular frequency and the phase noise of the emitted optical carrier, respectively. The two vectors x and ŷ and denote the direction along which the field is polarized. Note that the square root of the field power directly provides the amplitude.
The signal 0 E (t) is decomposed by the PBS into two orthogonally polarized components with the equal amplitudes. The amplitude and phase of the optical component polarized along the ɵ x axis are modulated externally by the data while the ɵ y component is transmitted as the reference carrier. The applied voltage to the LiNbO 3 based external phase modulator is equal to either zero or V π . The applied voltage V π induces π phase shift in the ɵ x -component and zero phase shift in the ɵ y -component, thus leading to a π/2 rotation of the polarization of the optical carrier. The amplitude modulation combined with the phase modulation in ɵ x component is described as an eightlevel modulation where the time axis is divided into symbol intervals. Each symbol is associated to a value of the optical field and during a symbol interval the transmitted field is constant. The transitions between subsequent symbol intervals are supposed to be instantaneous. Under these conditions, the transmitted optical field at the output of the Polarization Beam Combiner (PBC) is expressed as Eq. 5: where, the modulation function γ∈(0,π) is for b k ∈(1,0) and ε∈(1,3,5,7) is for {b k1 b k2 }∈(10,11,01,00), respectively. The vector m(t) is expressed as Eq. 6: Where: b k = (0,1) = Transmitted bit T = Symbol period and the rectangular pulse shaping function rect T (t) = The rectangular pulse shaping function is equal to one for (t)∈(0,T) and to zero elsewhere Receiver: Figure 2 illustrates the block diagram of the proposed optical coherent heterodyne receiver. The ideal Optical Band-Pass Filter (OBPF) with a narrow bandwidth typically 1 nm is used to limit the background ambient light. The optical field of the local oscillator lo E (t) is linearly polarized at π/4 with respect to the receiver reference axes. An Automatic Frequency Control (AFC) is used to compensate for the slowfrequency fluctuations occurring in the Local Oscillator (LO), whose control signal is derived from the intermediate frequency electric signal. Generally, the AFC is a closed-loop circuit acting on the bias current (Betti et al., 1995).
The received optical field and are uncorrelated and can be expressed as Eq. 7a-b: where, P r and ϕ s (t) are the power and the phase noise of the received optical signal, respectively. Both P r and ϕ s (t) are time-variant due to the atmospheric turbulence.
The parameters P lo , ω lo and ϕ lo (t) represent the power, angular frequency and the phase noise of the local oscillator, respectively and lo ω ≠ ω .
The received optical signal r E (t) is split by the PBS into ɵ x and ɵ y components which are then mixed with the corresponding optical fields emitted from the local oscillator. Therefore, the decomposed orthogonally polarized components x E (t) and y E (t) with equal amplitudes are given as Eq. 8a-b: Following optical-to-electrical conversion, the signals c x (t) and c y (t) at the output of two identical Photo Diodes (PD) are expressed as Eq. 9a-b (Betti et al., 1995): where, R represents the photodiode responsively, ω IF = ω-ω lo and ϕ IF (t) = ϕ s (t)-ϕ lo (t) are the intermediate angular frequency and the phase noise, respectively. The noise terms (n x (t) and n y (t)) represent the background radiation and the thermal noise which are assumed to be statistically independent, stationary Gaussian processes with zero-mean and a variance of 2 n 1 No, No 2 σ = being the double-sided noise power spectral density consisting of the background radiation noise and the thermal noise. The electrical signals c x (t)and c y (t) are passed through the ideal Band-Pass Filters (BPF) to reject the constant term and to limit the additive noise. The bandwidth of the BPF is expressed as B bp = 2(R s +k F B L ) with the center frequency at ω IF , where R s is the symbol rate and B L is the sum of the transmitting and local oscillator lasers' line width. The parameter k F must be chosen to transmit the signals undistorted through the filters (Cusani et al., 1992). The BPF in the lower branch is assumed to have a very narrow bandwidth in order to only pass the carrier signal with negligible distortion. Therefore, the electrical currents at the output of the BPFs are expressed as Eq. 10a-b: where, n xb (t)∼(0,σ n 2 ) is additive Gaussian noise at the output of the BPF. The additive narrowband noise components can be expressed by using the simple trigonometric identities given as Eq. 11 (Proakis, 2001): where, n I xb (t) and n Q xb (t)are the phase and the quadrature components, respectively, which are bandlimited Gaussian with zero mean and a variance of σ n 2 . After passing through a Low Pass Filter (LPF), the higher frequency harmonics have been removed. Thus, the baseband current c(t) is given as Eq. 12: where, * indicates the convolution operation, h lp (t) is the impulse response of the low-pass filter with a bandwidth of B lp = R s +k F B L . The electric signal c(t) is integrated over the symbol period T, sampled at time t = T. Hence, the output of the correlation-type demodulator (Proakis, 2001) The decision rule which maximizes the correlation metrics is applied to determine the average probability of error. It follows that the detector compares the demodulator output V i with seven Threshold (TH) levels: 0, ±R 2 PP lo /2, ± R 2 PP lo , ± 3R 2 PP lo /2. Therefore, a decision is made in favor of the amplitude level closest toV i.
Error rate analysis:
It has been assumed that the data transmission is independent and identically distributed (i.i.d.). For equally probable signals, the decision rule which maximizes the correlation metrics is applied to determine the average probability of error. Compared with the encoded BPOLSK (Tang et al., 2010) the average power for equiprobable coded M-POLSK symbol is increased by a factor of 11, so that the average power of each symbol in the coded M-POLSK system must be reduced by a factor of 11. Therefore, the average power per bit is defined by R 2 P r P lo = P av /22.
Since an error can only occur in one direction, the BER conditioned on the received optical power before the decoder is expressed as Eq. 14: r lo 2 r lo x 7 R P P / 2 In addition, simplifying (14) where, Q(.) is the Gaussian-Q function and r = P av /No is the electrical Signal to Noise Ratio (SNR) at the input of the demodulator.
The PEP is the basic method for the union bounds calculation, which is used as the main criterion for code design (Sandalidis, 2011;Simon and Alouini, 2005). Under the assumption of the maximum likelihood soft decoding with perfect Channel State Information (CSI), the conditional PEP subject to the fading coefficients I=I 1, I 2 , ,… ,I k is expressed as Eq: 16 (Zhu and Kahn, 2003;Uysal et al., 2006): where, ɶ ɶ ɶ 1 n x (x ,...x ) = and 1 n x (x ,...x ) = stand for the choosing coded sequence and the transmission sequence, respectively and Ω is the set of bit intervals' locations where X and ɶ x differ from each other. The alternative function form for the Gaussian-Q function is Eq. 17 (Sandalidis, 2011;Simon and Alouini, 2005): Where: E(.) = The expectation operation |Ω| = The cardinality of Ω corresponding to the length of error event Note that Eq. 19 has no closed form solution. The unconditional PEP Eq. 19 is derived for uncoded M-POLSK modulated FSO communication systems operating over gamma-gamma turbulence channel. The unconditional PEP expression is the tool for the derivation of upper bounds on the error probability of the coded M-POLSK communication system.
Maximum likelihood sequence detection:
In order to reduce the effects of the turbulence induced fading on the received optical signal, a convolution coded M-POLSK-FSO communication system has been considered. The union upper bound on the average BER with uniform error probability codes can be found as Eq. 20 (Sandalidis, 2011;Simon and Alouini, 2005): where, N is an indicator taking into account the number of bits in error, n is the number of information bits per transmission, the transfer function T(D(θ),N) is in conjunction with the particular state diagram of a coded modulation and D(θ) depends on the derived PEP. Here we have applied a convolutional code with the rate of 1/3 and the constraint length of 3, as illustrated in Fig. 8.2-2 of (Proakis, 2001). The function generators of the convolutional encoder are given as and g 1 = (100), g 2 = (101) and g 3 = (111). The transfer function is expressed as Eq. 21: The BER is thus obtained as Eq. 22: D(θ) is defined based on the underlying PEP expression. In this study, using the integrand of PEP expression given by Eq. 20, the approximation D(θ) formula for the channels under consideration is Eq. 23: Spatial diversity techniques: Employing multiple photo-detectors can mitigate the turbulence induced fading in the received signal, thus leading to further improvement in the error performance. To avoid any correlation in the received irradiance the detectors are sufficiently spaced as shown in Fig. 3. Since the transverse correlation size ρ 0 of the laser radiation operating over the atmospheric turbulence channel is nearly a few centimeters, the parameter ρ 0 can be assumed to be greater than the spacing between the detectors (Popoola and Ghassemlooy, 2009). Since the spacing between the PDs is much shorter than the wireless link range, the difference in the propagation delay across the receiver array would be negligible (Popoola and Ghassemlooy, 2009). Note that the received optical power is assumed to be constant and time invariant during 0 T τ < , where the coherence time 0 τ of the atmospheric fluctuation is in the order of milliseconds (Shin and Chan, 2004). The received signal from each branch is scaled by a gain factor {G i } H i=1 . The output of the combiner is the sum of the weighted and co-phased signals as illustrated in Fig. 3. Each receiver aperture size of the H-photo detector is (1/H) th of the aperture area of the single receiver. Accordingly, the background noise variance on each branch is proportional to the receiver aperture area, which is reduced by a factor of H. Whereas the thermal noise on each branch is not affected. It follows that the total noise variance at the combiner output is 2 2 2 sp Thermal Bg H σ = σ + σ . The background noise is not considered here because the ideal OBPF with a narrow FOV is applied at the receiver. Hence, 2 2 2 2 Bg Thermal sp Thermal H and σ < σ σ ≅ σ the variance of the overall noise with a zero mean becomes as Eq. 24: The total received optical power during the symbol duration at the output of the combiner is given as Eq. 25: The optimum post detection electrical SNR r T at the M-POLSK demodulator input becomes as Eq. 26:
RESULTS
To evaluate the system performances of the proposed coded M-POLSK based FSO communication link, the error probability of the system employing the coherent BPOLSK, BPSK and DPSK schemes are illustrated. For the purpose of like-to-like comparison, the average optical signal power E[RP r P lo ] is normalized to unity and the electrical SNRs are made equal for different modulation schemes. Furthermore, the channel turbulence under consideration is from weak to strong regimes. The values of α and β at any given regimes can be calculated with the corresponding value of σ 2 l using Eq. 3. The values of all the parameters used in calculations are illustrated in Table 1. Diameter of the receiver D<<L and d=0 Link length L = 3 km σl 2 = 1.03 α = 2.902 β = 2.51 weak L = 4 km σl 2 = 1.75 α = 2.296 β = 1.822 Moderate L = 6 km σl 2 = 3.67 α = 2.064 β = 1.342 Strong The BER expressions for BPOLSK with and without turbulence are given as Eq. 30a-b (Tang et al., 2010): Following the approach adopted in (Zhu and Kahn, 2002), the error probabilities of the DPSK modulated coherent system in the absence and presence of the turbulence channel is given as Eq. 31a-b: The conditional BER expressions for the coherent BPSK modulation technique without and with the phase tracking errors are given as Eq. 32a-b (Betti et al., 1995): where, ∆Ø denotes the phase tracking error due to the PLL circuit and r l = 1/σ 2 ∆Ø with the phase tracking error variance σ ∆Ø . Therefore, the theoretical unconditional BER for the BPSK scheme in the gamma-gamma turbulence channel is derived as Eq. 32c:
DISCUSSION
The error performances of coherent BPOLSK, DPSK and BPSK schemes can be predicted for any given value of SNR across all turbulence regimes using Eq. 30, 31 and 32 as shown in Fig. 4 The SNR requirements to achieve a BER of 10 −6 without turbulence are ~10.5, ~10.7 and ~13.5 dB for BPSK (without phase tracking errors), DPSK and BPOLSK, respectively. The BPSK-FSO system offers the best performance in terms of error probability followed by the DPSK scheme for all turbulence scenarios. The BPOLSK provides the worst performance in a turbulence channel. This is due to the fact that only half of the emitted optical power is allocated for the information embedded optical carrier whereas the other half is used for the transmission of the optical reference carrier. It follows that the BPOLSK scheme requires no carrier recovery circuit at the receiver and both the carrier and information signals suffer the same phase noise. However, BPSK and DPSK incur penalties due to the phase tracking errors. The BER results in Fig. 5 are computed based on Eqs. 19 and 22 to allow comparisons of the performances of the uncoded and coded M-POLSK schemes as well as the uncoded BPOLSK scheme (Fig. 4) The BER based on the derived PEP yields a very good performance, which is achieved without the need for the bandwidth expansion. It is not practical and even not feasible for many applications to increase the power margin in the link budget in order to eliminate the deep fades observed under turbulence. This motivates the employment of powerful scintillation-mitigation techniques, such as coding and/or diversity techniques.
Using Eq. 29 the power gain (SNR σl,H -SNR σl,1 ) to achieve a BER of 10 −6 for the MRC technique is depicted in Fig. 6. The MRC technique (H = 4) outperforms the single receiver by ∼31.4, ∼29.5 and ∼57.9 dB respectively in weak, moderate and strong turbulence regimes, respectively. The power gain is less in the moderate turbulence regime than in the weak regime. This is because of the deep fades resulting from a loss of spatial coherence of the laser radiation. The power gain reaches up to ~69 dB when ten detectors are used in strong turbulence regime. The power gain is higher in strong fading conditions since adding more detectors will efficiently reduce the chance of a catastrophic fading. Another observation from Fig. 6 is that as the number of detectors (H) increases, the power gain starts flatten out. For example, increasing the number of detectors from four to five only achieves ~2, ~3 and ~3.6 dB more in power gain from weak to strong turbulence regimes, respectively. Thus, the optimum number of the detectors is 2≤ H ≤4. As a consequence, the power gain is achieved with the rise in system complexity and cost.
CONCLUSION
This study has outlined the theoretical analysis of a coherent M-POLSK modulated FSO communication system operating over the gamma-gamma turbulence channel. To mitigate the turbulence induced fading the convolution coding and the spatial diversity with the MRC technique have been applied. The upper BER bound based on the derived PEP has been obtained using the transfer function. The BER yields a very good performance, which is achieved without the need for increasing the SNR. For example, with a SNR of 30 dB, the BERs for uncoded and coded M-POLSK schemes are 0.047 and 1.4×10 −4 respectively, in the weak turbulence regime. Around 69 dB power gain is achievable when ten detectors are used in strong turbulence regime. The spatial diversity with MRC technique (H = 4) outperforms the uncoded M-POLSK employing the single receiver by ∼31.4, ∼29.5 and ∼57.9 dB respectively in weak, moderate and strong turbulence regimes. We also have shown that the spatial diversity offers increased link margin as the scintillation level rises. The performances of BPOLSK, BPSK and DPSK based FSO systems have been evaluated across all turbulence regimes. The BPSK without phase tracking error outperforms BPOLSK in terms of the SNR to achieve the same BER performance for a range of turbulence regimes. However, the BPSK scheme suffers the penalties due to the phase tracking errors. The performance degradation increases with the phase error variances. | 6,372.8 | 2011-04-01T00:00:00.000 | [
"Physics"
] |
The Beurling Estimate for a Class of Random Walks
: An estimate of Beurling states that if K is a curve from 0 to the unit circle in the complex plane, then the probability that a Brownian motion starting at ¡ † reaches the unit circle without hitting the curve is bounded above by c † 1 = 2 . This estimate is very useful in analysis of boundary behavior of conformal maps, especially for connected but rough boundaries. The corresponding estimate for simple random walk was flrst proved by Kesten. In this note we extend this estimate to random walks with zero mean, flnite (3 + – ) ¡ moment.
Introduction
The Beurling projection theorem (see, e.g., [1,Theorem V.4.1]) states that if K is a closed subset of the closed unit disk in C, then the probability that a Brownian motion starting at − avoids K before reaching the unit circle is less than or equal to the same probability for the angular projection K = {|z| : z ∈ K}.
If K = [0, 1], a simple conformal mapping argument shows that the latter probability is comparable to 1/2 as → 0+. In particular, if K is a connected set of diameter one at distance from the origin the probability that a Brownian motion from the origin to the unit circle avoids K is bounded above by c 1/2 . This estimate, which we will call the Beurling estimate, is very useful in analysis of boundary behavior of conformal maps especially for connected but rough boundaries. A similar estimate for random walks is useful, especially when considering convergence of random walk to Brownian motion near (possibly nonsmooth) boundaries. For simple random walk such an estimate was first established in [5] to derive a discrete harmonic measure estimate for application to diffusion limited aggregation. It has been used since in a number of places, e.g., in deriving "Makarov's Theorem" for random walk [7] or establishing facts about intersections of random walks (see, e.g., [8]). Recently it has been used by the first author and collaborators to analyze the rate of convergence of random walk to Brownian motion in domains with very rough boundaries. Because of its utility, we wish to extend this estimate to walks other than just simple random walk. In this note we extend it to a larger class of random walks.
We state the precise result in the next section, but we will summarize briefly here. As in [5], we start with the estimate for a half-line. We follow the argument in [6]; see [2,3] for extensions. The argument in [6] strongly uses the time reversibility of simple random walk. In fact, as was noted in [3], the argument really only needs symmetry in x component. We give a proof of this estimate, because we need the result not just for Z + but also for κZ + where κ is a positive integer. The reason is that we establish the Beurling estimate here for "(1/κ)-dense" sets. One example of such a set that is not connected is the path of a non-nearest neighbor random walk whose increments have finite range; a possible application of our result would be to extend the results of [8] to finite range walks. While our argument is essentially complete for random walks that are symmetric in the x component, for the nonsymmetric case we use a result of Fukai [3] that does the estimate for κ = 1. Since κZ + ⊂ Z + this gives a lower bound for our case, and our bound for the full line then gives the upper bound.
The final section derives the general result from that for a half-line; this argument closely follows that in [5]. We assume a (3 + δ)-moment for the increments of the random walk in order to ensure that the asymptotics for the potential kernel are sufficiently sharp (see (5)). (We also use the bound for some "overshoot" estimates, but in these cases weaker bounds would suffice.) If one would have in (5) a weaker bound, c/|z| b for some b > 1/2, an analogue of (33) would hold and this would suffice to carry out the argument in section 5. So the method presented here should require only (2.5 + δ) moment.
Preliminaries
Denote by Z, R, C the integers, the real numbers and the complex numbers, respectively. We consider Z and R as subsets of C. Let Z + = {k ∈ Z : k > 0}; N = {k ∈ Z : k ≥ 0}, Z − = Z \ N. Let L denote a discrete two-dimensional lattice (additive subgroup) of C. Let X 1 , X 2 , . . . be i.i.d. random variables taking values in L and let S n be the corresponding random walk. We say that X 1 , X 2 , . . . generates L if for each z ∈ L there is an n with P(X 1 + · · · + X n = z) > 0. Let be the first entrance time of B after time 0, and the first entrance time of B including time 0, respectively. We abbreviate T {b} , T 0 {b} by T b , T 0 b respectively. Denote by C n = {z ∈ L : |z| < n} the discrete open disk of radius n, and let τ n := T 0 C c n be the first time the random walk is not in C n .
The purpose of this paper is the prove the following result.
Theorem 1 Suppose L is a discrete two-dimensional lattice in C and X 1 , X 2 , . . . are i.i.d. random variables that generate L such that E[X 1 ] = 0 and for some δ > 0, Then for each positive integer κ, there exists a c < ∞ (depending on κ and the distribution of X 1 ) such that for every (1/κ)-dense set A and every 0 < k < n < ∞, We start by making some reductions. Since B ⊂ A clearly implies P(τ m < T 0 A ) ≤ P(τ m < T 0 B ), it suffices to prove the theorem for minimal (1/κ)-dense sets A = {w j : j ∈ κN} and, without loss of generality, we assume that A is of this form. By taking a linear transformation of the lattice if necessary, we may assume that L is of the form where z * ∈ C \ R and that the covariance matrix of X 1 is a multiple of the identity. (When dealing with mean zero, finite variance lattice random walks, one can always choose the lattice to be the integer lattice in which case one may have a non-diagonal covariance matrix, or one can choose a more general lattice but require the covariance matrix to be a multiple of the identity. We are choosing the latter.) Let p be the (discrete) probability mass function of X 1 . Then our assumptions are {z : p(z) > 0} generates L and for some δ, σ 2 > 0, Let p * (z) = p(z) be step probability mass function of the time-reversed walk; and note that p * also satisfies (1)-(3). We denote by P * (A) the probability of A under steps according to p * . We call a function f p-harmonic at w if Let X 1 , X 2 , . . . be independent L-valued random variables with probability mass function p, and let S n = S 0 + n i=1 X i , n ≥ 0 be the corresponding random walk. Denote by P x (resp., E x ) the law (resp., expectation) of (S n , n ≥ 0) when S 0 = x, and we will write P, E, for P 0 , E 0 .
Let a(z) denote the potential kernel for p, and let a * (z) denote the potential kernel using p * . Note that a is p * -harmonic and a * is p-harmonic for z = 0 and ∆ p * a(0) = ∆ p a * (0) = 1. In [4] it is shown that under the assumptions (1) -(3) there exist constantsk, c (these constants, like all constants in this paper, may depend on p), such that for all z, Since a * (z) = a(−z), this also holds for a * . For any proper subset B of L, let G B (w, z) denote the Green's function of B defined by This equals zero unless w, z ∈ B. We will write G n for G Cn . If w, z ∈ B, and G(w) where T = T 0 B c . This is easily verified by noting that for fixed z ∈ B, each of the three expressions describes the function (w) satisfying: The following "last-exit decomposition" relates the Green's function and escape probabilities: It is easily derived by focusing on the last visit to B strictly less than T 0 B c . For the remainder of this paper we fix p, κ and allow constants to depend on p, κ. We assume k ≤ n/2, for otherwise the inequality is immediate. The values of universal constant may change from line to line without further notice. In the next two sections will prove that (Here, and throughout this paper, we use to mean that both sides are bounded by constants times the other side where the constants may depend on p, κ.) In the final section we establish the uniform upper bound for all minimal (1/κ)-dense sets.
Green's function estimates
We start with an "overshoot" estimate.
Lemma 2 There is a c such that for all n and all z with |z| < n, From the central limit theorem, we know that P z {τ n > r + n 2 | τ n > r} < α < 1. Therefore, τ n /n 2 is stochastically bounded by a geometric random variable with success Therefore, and The second inequality follows immediately from applying log(1+x) ≤ x to x = (|S n |−n)/n. Remark. With a finer argument, we could show, in fact, that E z [|S τn |] ≤ n + c. By doing the more refined estimate we could improve some of the propositions below, e.g., the O(n −1/3 ) error term in the next proposition is actually O(n −1 ). However, since the error terms we have proved here suffices for this paper, we will not prove the sharper estimates.
If |z| < n, Also, for every b < 1, there exist c > 0 and N such that for all n ≥ N , Proof. The first expression follows from (5), (7) and Lemma 2 since a(0) = 0. The next two expressions again use (7), Lemma 2,and (5). For the final expression, first note it is true for b = 1/4, since for 0 ≤ |z|, |w| < n/4, G n (z, w) ≥ G 3n/4 (0, w − z). For b < 1, the invariance principle implies that there is a q = q b > 0 such that for all n sufficiently large, with probability at least q the random walk (and reversed random walk) starting at |z| < bn reaches C n/4 before leaving C n . Hence, by the strong Markov property, if |z| < bn, |w| < bn, G n (z, w) ≥ q inf |z |<n/4 G n (z , w). Similarly, using the reversed random walk, if |w| < bn, |z | < n/4, G n (z , w) ≥ q inf |w |<n/4 G n (z , w ). 2
Lemma 5 There is a c < ∞ such that for every z ∈ C n and every minimal (1/κ)-dense set A, w∈A G n (z, w) ≤ c n.
Proof. By Lemma 3, If A is a minimal (1/κ)-dense set, then #{w ∈ A : |z−w| ≤ r} ≤ cr, for some c independent of z. Hence, The main purpose of this section is to obtain estimates in Proposition 12 and Lemmas 13 and 14 which will be used in the proof of Theorem 1 in section 5.
Proof. Let q(n) = P(τ n ≤ T [−n,n]κ ) and note that if k ∈ [−n/2, n/2] κ , then The last-exit decomposition (8) tells us But (11) and (12) imply that which gives q(4n) = O(1/n). The lower bound can be obtained by noting P(ρ n < T Z ) ≤ P(τ n < T [−n,n]κ ) which reduces the estimate to a one-dimensional "gambler's ruin" estimate in the y-component. This can be established in a number of ways, e.g., using a martingale argument. 2 Lemma 7 There exist c > 0 and N < ∞ such that if n ≥ N and z ∈ C 3n/4 , 1{S j ∈ A[n/4, n/2]}, be the number of visits to A[n/4, n/2] before leaving C n . Then (11) and (12) show that there exist c 1 , c 2 such that for n sufficiently large, In particular, if z ∈ C 3n/4 , Lemma 8 There exist 0 < c 1 < c 2 < ∞ and N < ∞ such that if n ≥ N , , z ∈ C 9n/10 \ C n/10 .
Proof. This follows immediately from Lemma 3 and G n (z, 0) = P z (T 0 < τ n ) G n (0, 0). 2 Recall that P * stands for the probability under step distribution p * .
By reversing the path we can see that Also note that P κm * (S j = 0, j − 1 < ρ n ∧ T κ{...,−1,0,1,...,m−1} ) = by translation invariance. Now, This together with (14) implies the lemma. 2 Remark. The above result implies the following remarkable claim: if the step distribution of the walk is symmetric with respect to y-axis then, under P, the events E + n and E − n are independent.
Remark. Versions of this lemma have appeared in a number of places. See [6,2,3].
Proof. In the case κ = 1, this was essentially proved by Fukai [3]. Theorem 1.1 in [3] states that P(n 2 < T N ) 1 for any zero-mean aperiodic random walk on lattice Z 2 with 2 + δ finite moment. Note that we can linearly map L onto Z 2 , and by this cause only multiplicative constant change (depending on L) in the conditions (1)-(3), which imply the assumptions needed for (19) to hold. The conversion from n 2 to ρ n is not difficult and his argument can be extended to give this. Note that this gives a lower bound for other κ, where c depends on L and transition probability p only. Hence, the two terms in the product in Lemma 9 are bounded below by c/ √ n but the product is bounded above by c 1 /n. Hence, each of the terms is also bounded above byc/ √ n, and this proves the statement. 2 Proof. We prove (a), and note that (b) can be done similarly. It is equivalent to show P(T κN+n < T 0 ) ≥ c log n Note that since τ n ≤ T κN+n , Lemma 3 yields the upper bound on the above probability of the same order. For the lower bound note that invariance principle implies by Lemma 3. Use Markov property and Lemma 7 applied to disk centered at n = (n, 0) of radius 9n/10 to get P(T κN+n < T 0 |τ n < T 0 , Re(S τn ) ≥ 4n/5, |S τn | − n ≤ n/5) ≥ c, uniformly in n. An easy overshoot argument yields P(τ n < T 0 , Re(S τn ) ≥ 4n/5, |S τn |−n ≤ n/5) P(τ n < T 0 , Re(S τn ) ≥ 4n/5), which implies the lemma. 2 Proposition 12 If j, n ∈ Z + , Proof. (a) A simple Markov argument gives P(τ n ≤ T κN ) ≤ P(τ n ≤ T κZ + ) ≤ P(S T κN = 0) −1 P(τ n ≤ T κN ), and hence the first two quantities are comparable. Since τ n ≤ ρ n , (18) gives P(τ n ≤ T κN ) ≥ c/ √ n. For the upper bound, let A − = A − n be the event that Re(S τn ) ≤ 0. By the invariance principle, P(A − ) ≥ 1/4. However, we claim that P(A − | τ n ≤ T κN ) ≥ P(A − ). Indeed, by translation invariance, we can see for every j > 0, P jκ (A − ) ≤ P(A − ), and hence by the Strong Markov property, P(A − | τ n > T κN ) ≤ P(A − ). Therefore, The invariance principle can now be used to see that for some c, and hence P(ρ n ≤ T κN ) ≥ (c/4) P(τ n ≤ T κN ).
(b) Let T = T −n ∧ T κN . Since P −n (S T = −n) ≥ c/ log n by Lemma 11(a), it suffices by the strong Markov property to show that By considering reversed paths, we see that P −n (S T = 0) = P * (S T = −n).
(e) This is done similarly to (d), using (c) instead of (b). 2 Lemma 13 There exist 0 < c 1 < c 2 < ∞ and N < ∞, such that if n ≥ N, m = n 4 , and Remark. When w ∈ C 4n \ C 3n (i) implies a lower bound of the same order in (ii).
Proof. (i) Let T = τ m ∧ η n . We will show that Consider the martingale M j = π σ 2 [a * (S j∧T ) −k] − log n, and note that M j = log |S j∧T | − log n + O(|S j∧T | −1 ). Therefore, The optional sampling theorem implies that (the estimate (10) can be used to show that the optional sampling theorem is valid). Note that The last inequality uses Lemma 2. Therefore, and hence it suffices to show that Clearly, Also, and hence E w [M T ; |S T | < n] = O(log 2 n/n). Combining these estimates with (26) and (27) gives (28) and therefore (25).
(ii) Let q = q(n, A) be the maximum of P w (τ m < T A[n/2,n] ) where the maximum is over all w ∈ C 4n . Let w = w n be a point obtaining this maximum. Letη n be the first time that a random walk enters C n and let η * n be the first time after this time that the walk leaves C 2n . Then by a Markovian argument and an easy overshoot argument we get where α = 1 − c < 1 for c the constant from Lemma 7. The O(n −1 ) error term comes from considering the probability that |S η * n | ≥ 4n. By letting z = w we get P w (τ m < T A[n/2,n] ) P w (τ m < T A[n/2,n] , τ m <η n ) = P w (τ m <η n ) We now show that (i) implies Namely, by the same argument as in (i), applied to n/2 instead of n and m = n 4 still, one gets P z (τ m <η n ) 1 log n , for z ∈ C 2n \ C 3n/2 .
The uniform upper bound can easily be extended to all z ∈ C 2n using strong Markov property and overshoot estimate (10). Now for z ∈ C 4n \ C 3n we have so that the upper bound in (i) together with strong Markov imply (29) for z ∈ C 4n \ C 3n . The remaining case z ∈ C 3n \ C 2n is implied again by strong Markov inequality and an overshoot estimate. 2 Recall that we may assume k ≤ n/2.
(Here and below we use the easy estimate: | 4,760 | 2004-03-18T00:00:00.000 | [
"Mathematics"
] |
A Metropolized adaptive subspace algorithm for high-dimensional Bayesian variable selection
A simple and efficient adaptive Markov Chain Monte Carlo (MCMC) method, called the Metropolized Adaptive Subspace (MAdaSub) algorithm, is proposed for sampling from high-dimensional posterior model distributions in Bayesian variable selection. The MAdaSub algorithm is based on an independent Metropolis-Hastings sampler, where the individual proposal probabilities of the explanatory variables are updated after each iteration using a form of Bayesian adaptive learning, in a way that they finally converge to the respective covariates' posterior inclusion probabilities. We prove the ergodicity of the algorithm and present a parallel version of MAdaSub with an adaptation scheme for the proposal probabilities based on the combination of information from multiple chains. The effectiveness of the algorithm is demonstrated via various simulated and real data examples, including a high-dimensional problem with more than 20,000 covariates.
Introduction
Variable selection in regression models is one of the big challenges in the era of highdimensional data where the number of explanatory variables might largely exceed the sample size. During the last two decades, many classical variable selection algorithms have been proposed which are often based on finding the solution to an appropriate optimization problem. As the most famous example, the Lasso (Tibshirani, 1996) relies on an 1 -type relaxation of the original 0 -type optimization problem. Convex methods like the Lasso are computationally very efficient and are therefore routinely used in high-dimensional statistical applications. However, such classical methods mainly focus on point estimation and do not provide a measure of uncertainty concerning the best model, per se, although recent works aim at addressing these issues as well (see e.g. Wasserman and Roeder, 2009, Meinshausen and Bühlmann, 2010and Lee et al., 2016. On the other hand, a major advantage of a fully Bayesian approach is that it automatically accounts for model uncertainty. In particular, Bayesian model averaging (Raftery et al., 1997) and the median probability model (Barbieri and Berger, 2004) can be used for predictive inference. Furthermore, posterior inclusion probabilities of the individual covariates can be computed to quantify the Bayesian evidence. Important 0 -type criteria like the Bayesian Information Criterion (BIC, Schwarz, 1978) and the Extended Bayesian Information Criterion (EBIC, Chen and Chen, 2008) can be derived as asymptotic approximations to a fully Bayesian approach (compare e.g. Liang et al., 2013). It has been argued that 0 -type methods posses favourable statistical properties in comparison to convex 1 -type methods with respect to variable selection and prediction (see e.g. Raskutti et al., 2011 andNarisetty andHe, 2014). Since solving the associated, generally NP-hard, discrete optimization problems by an exhaustive search is computationally prohibitive, there have been recent attempts in providing more efficient methods for resolving such issues, as for example, mixed integer optimization methods (Bertsimas et al., 2016) and Adaptive Subspace (AdaSub) methods (Staerk, 2018;Staerk et al., 2021).
The challenging practical issue of a fully Bayesian approach is similar to that of optimizing 0 -type information criteria: computing (approximate) posterior model probabilities for all possible models is not feasible if the number of explanatory variables p is very large, since there are in general 2 p possible models which have to be considered. Often, Markov Chain Monte Carlo (MCMC) methods based on Metropolis-Hastings steps (e.g. Madigan et al., 1995), Gibbs samplers (e.g. George and McCulloch, 1993;Dellaportas et al., 2002) and "reversible jump" updates (e.g. Green, 1995) are used in order to obtain a representative sample from the posterior model distribution. However, the effectiveness of MCMC methods depends heavily on a sensible choice of the proposal distributions being used. Therefore, such methods may suffer from bad mixing resulting in a slow exploration of the model space, especially when the number of covariates is large. Moreover, tuning of the proposal distribution is often only feasible after manual "pilot" runs of the algorithm.
Adaptive MCMC methods aim to address these issues by updating the proposal parameters "on the fly" during a single run of the algorithm so that the proposal distribution automatically adjusts according to the currently available information. Recently, a number of different adaptive MCMC algorithms have been proposed in the Bayesian variable selection context, see e.g. Nott and Kohn (2005), Lamnisos et al. (2013), Ji and Schmidler (2013), Griffin et al. (2014), Griffin et al. (2021) and Wan and Griffin (2021). In this work we propose an alternative, simple and efficient adaptive independent Metropolis-Hastings algorithm for Bayesian variable selection, called the Metropolized Adaptive Subspace (MAdaSub) algorithm, and compare it to existing adaptive MCMC algorithms. In MAdaSub the individual proposal probabilities of the explanatory variables are sequentially adapted after each iteration. The employed updating scheme is inspired by the AdaSub method introduced in Staerk et al. (2021) and can itself be motivated in a Bayesian way, such that the individual proposal probabilities finally converge against the true respective posterior inclusion probabilities. In the limit, the algorithm can be viewed as a simple Metropolis-Hastings sampler using a product of independent Bernoulli proposals which is the closest to the unknown target distribution in terms of Kullback-Leibler divergence (among the distributions in the family of independent Bernoulli form).
The paper is structured as follows. The considered setting of Bayesian variable selection in generalized linear models (GLMs) is briefly described in Section 2. The MAdaSub algorithm is motivated and introduced in Section 3. By making use of general results obtained by Roberts and Rosenthal (2007), it is shown that the MAdaSub algorithm is ergodic despite its continuing adaptation, i.e. that "in the limit" it samples from the targeted posterior model distribution (see Theorem 1). Alternative adaptive approaches are also briefly discussed and conceptually compared to the newly proposed algorithm. In Section 4, a parallel version of MAdaSub is presented where the proposal probabilities can be adapted using the information from all available chains, without affecting the ergodicity of the algorithm (see Theorem 3). Detailed proofs of the theoretical results of Sections 3 and 4 can be found in the Supplement to this paper. The adaptive behaviour of MAdaSub and the choice of its tuning parameters are illustrated via low-and high-dimensional simulated data applications in Section 5, emphasizing that the speed of convergence against the targeted posterior depends on an appropriate choice of these parameters. In Section 6 various real data applications demonstrate that MAdaSub provides an efficient and stable way for sampling from high-dimensional posterior model distributions. The paper concludes with a discussion in Section 7. An R-implementation of MAdaSub is available at https: //github.com/chstaerk/MAdaSub.
The setting
In this work we consider variable selection in univariate generalized linear models (GLMs), where the response variable Y is modelled in terms of p possible explanatory variables X 1 , . . . , X p . More precisely, for a sample of size n, the components of the response vector Y = (Y 1 , . . . , Y n ) T are assumed to be independent with each of them having a distribution from a fixed exponential dispersion family with g E(Y i | X i, * ) = µ + p j=1 β j X i,j , i = 1, . . . , n , where g is a (fixed) link function, µ ∈ R is the intercept and β = (β 1 , . . . , β p ) T ∈ R p is the vector of regression coefficients. Here, X = (X i,j ) ∈ R n×p is the design matrix; it's i-th row X i, * corresponds to the i-th observation and it's j-th column X * ,j ≡ X j corresponds to the values of the j-th predictor. For a subset S ⊆ {1, . . . , p}, the model induced by S is defined by a GLM of the form (1) but with design matrix X S ∈ R n×|S| in place of X ∈ R n×p and corresponding vector of coefficients β S ∈ R |S| , where X S denotes the submatrix of the original design matrix X containing only the columns with indices in S.
For brevity, we often simply refer to the model S. Without further notice, we assume that we always include an intercept µ in the corresponding GLM with design matrix X S . We In a fully Bayesian approach we assign prior probabilities π(S) to each of the considered models S ∈ M as well as priors π(µ, ψ, β S | S) for the parameters of each model S ∈ M, where ψ denotes a possibly present dispersion parameter (e.g. the variance in a normal linear model). After observing data D = (X, y), with X ∈ R n×p and y ∈ R n , the posterior model probabilities are proportional to π(S | D) ∝ π(y | X, S) π(S) , S ∈ M , where π(y | X, S) = f (y | X, S, µ, ψ, β S ) π(µ, ψ, β S | S) dµ dψ dβ S is the marginal likelihood of the data y under model S, while f (y | X, S, µ, ψ, β S ) denotes the likelihood of the data y under model S given the parameter values µ, ψ, β S and the values of the explanatory variables X. Note that the marginal likelihood π(y | X, S) is generally only available in closed form when conjugate priors are used.
Remark 2.1. A prominent example in normal linear models is a conjugate prior structure, where the prior on the variance ψ = σ 2 is given by Jeffreys prior (independent of the model S) and the prior on the vector of coefficients β S in model S ∈ M is given by a multivariate normal distribution, i.e. β S | S, σ 2 ∼ N |S| (ϑ S , σ 2 g W S ), π(σ 2 ) ∝ 1 σ 2 , where ϑ S ∈ R |S| , g > 0 and W S ∈ R |S|×|S| are hyperparameters. After centering each of the covariates X j , j ∈ P, the improper prior π(µ) ∝ 1 is a common choice for the intercept µ (again, independent of the model S). With no specific prior information, the prior mean of β S can be set to the zero vector (ϑ S = 0). The matrix W S is often chosen to be the identity matrix I |S| of dimension |S| or to be W S = (X T S X S ) −1 yielding Zellner's g-prior (Zellner, 1986). The first choice corresponds to Ridge Regression and implies prior independence of the regression coefficients, while the second choice with g = n corresponds to a unit information prior. In case no specific prior information is available about the possible regressors, a natural choice for the model prior is an independent Bernoulli prior of the form where ω = π(j ∈ S) is the prior probability that variable X j is included in the model, for all j ∈ P. One can either set the prior inclusion probability ω to some fixed value or consider an additional hyperprior for ω, with the latter option yielding more flexibility. A convenient choice is the (conjugate) beta prior ω ∼ Be(a ω , b ω ), where a ω > 0 and b ω > 0 can be chosen in order to reflect the prior expectation and prior variance of the model size s = |S|, S ∈ M (see Kohn et al., 2001 for details). In practice, one often imposes an a-priori upper bound s max on the model size (with s max ≤ n) by setting π(S) = 0 for |S| > s max (cf. Liang et al., 2013;Rossell, 2021), while for fixed control variables X j one can enforce the inclusion of such variables by setting π(j ∈ S) = 1.
In the general non-conjugate case the marginal likelihood is not readily computable and numerical methods may be used for deriving an approximation to the marginal likelihood.
Laplace's method yields an asymptotic analytic approximation to the marginal likelihood (Kass and Raftery, 1995). Similarly, different information criteria like the Bayesian Information Criterion (BIC, Schwarz, 1978) or the Extended Bayesian Information Criterion (EBIC, Chen and Chen, 2008) can be used directly as asymptotic approximations to fully Bayesian posterior model probabilities under suitable choices of model priors. Under a uniform model prior, i.e. π(S) = 1 2 p for all S ∈ M, the BIC can be derived as an approximation to −2 log(BF(S)) = −2 log(PO(S)), where BF(S) = π(y | X, S)/π(y | X, ∅) denotes the Bayes factor of model S ∈ M versus the null model ∅ ∈ M and PO(S) denotes the corresponding posterior odds (Schwarz, 1978;Kass and Wasserman, 1995). In a high-dimensional but sparse situation, in which only a few of the many possible predictors contribute substantially to the response, a uniform prior on the model space is a naive choice since it induces severe overfitting. Therefore, Chen and Chen (2008) propose the prior where γ ∈ [0, 1] is an additional parameter. If γ = 1, then π(S) = 1 p+1 p |S| −1 , so the prior gives equal probability to each model size, and to each model of the same size; note that this prior does also coincide with the beta-binomial model prior discussed above when setting a ω = b ω = 1, providing automatic multiplicity correction (Scott and Berger, 2010).
If γ = 0, then we obtain the uniform prior used in the original BIC. Similar to the derivation of the BIC one asymptotically obtains the EBIC with parameter γ ∈ [0, 1] as where f (y | X, S,μ S ,ψ S ,β S ) denotes the maximized likelihood under the model S ∈ M (compare Chen and Chen, 2012). Under the model prior (6) and a unit-information prior on the regression coefficients for each model S ∈ M, one can asymptotically approximate the model posterior by In this work we consider situations where the marginal likelihood π(y | X, S) is available in closed form due to the use of conjugate priors (see Remark 2.1) or where an approximation to the posterior π(S | D) is used (e.g. via equation (8) with the EBIC or any other 0 -type criteria such as the risk inflation criterion, cf. Foster and George, 1994;Rossell, 2021).
This assumption allows one to focus on the essential part of efficient sampling in very large model spaces, avoiding challenging technicalities regarding sampling of model parameters for non-conjugate cases. It also facilitates empirical comparisons with other recent adaptive variable selection methods, which focus on conjugate priors (Zanella and Roberts, 2019;Griffin et al., 2021). Furthermore, conjugate priors such as the g-prior as well as normalized 0 -type selection criteria such as the EBIC in equation (8) have shown to provide concentration of posterior model probabilities on the (Kullback-Leibler) optimal model under general conditions even in case of model misspecification (Rossell, 2021), as well as model selection consistency for the true model in GLMs without misspecification (Chen and Chen, 2012;Liang et al., 2013).
The MAdaSub algorithm
A simple way to sample from a given target distribution is to use an independent Metropolis-Hastings algorithm. Clearly, the efficiency of such an MCMC algorithm depends on the choice of the proposal distribution, which is in general not an easy task (see e.g. Rosenthal, 2011). In the ideal situation, the proposal distribution for an independence sampler should be the same as the target distribution π(S | D), leading to an independent sample from the target distribution with corresponding acceptance probability of one. Adaptive MCMC algorithms aim to sequentially update the proposal distribution during the algorithm based on the previous samples such that, in case of the independence sampler, the proposal becomes closer and closer to the target distribution as the MCMC sample grows (see e.g. Holden et al., 2009, Giordani andKohn, 2010). However, especially in high-dimensional situations, it is crucial that the adaptation of the proposal as well as sampling from the proposal can be carried out efficiently. For this reason, we restrict ourselves to proposal distributions which have an independent Bernoulli form: if S ∈ M is the current model, for some vector r = (r 1 , . . . , r p ) ∈ (0, 1) p of individual proposal probabilities.
Serial version of the MAdaSub algorithm
The fundamental idea of the newly proposed MAdaSub algorithm (given below as Algorithm 1) is to sequentially update the individual proposal probabilities according to the currently "estimated" posterior inclusion probabilities. In more detail, after initializing the vector of proposal probabilities j of variables X j are updated after each iteration t of the algorithm, such that r (t) j finally converges to the actual posterior inclusion probability π j = π(j ∈ S | D), as t → ∞ (see Corollary 2 below). Therefore, in the limit, we make use of the proposal which is the closest distribution (in terms of Kullback-Leibler divergence) to the actual target π(S | D), among all distributions of independent Bernoulli form (9) (see Clyde et al., 2011). Note that the median probability model (Barbieri and Berger, 2004;Barbieri et al., 2021), defined by S MPM = {j ∈ P : π j ≥ 0.5}, has the largest probability in the limiting proposal (10) of MAdaSub, i.e. arg max V ∈M q(V ; r * ) = S MPM . Thus, MAdaSub can be interpreted as an adaptive algorithm which aims to adjust the proposal so that models in the region of the median probability model are proposed with increasing probability.
For j ∈ P, the concrete update of r (t) j after iteration t ∈ N is given by where, for j ∈ P, L j > 0 are additional parameters controlling the adaptation rate of the algorithm and 1 S (i) denotes the indicator function of the set S (i) . If j ∈ S (t) (i.e. 1 S (t) (j) = 1), then variable X j is included in the sampled model in iteration t of the algorithm and the proposal probability r (t) j of X j increases in the next iteration t + 1;
similarly, if j / ∈ S (t) (i.e. 1 S (t) (j) = 0), then the proposal probability decreases. The additional "truncation" step 2 (a) in the MAdaSub algorithm ensures that the truncated individual proposal probabilitiesr (t) j , j ∈ P, are always included in the compact interval I = [ , 1 − ], where ∈ (0, 0.5) is a pre-specified "precision" parameter. This adjustment simplifies the proof of the ergodicity of MAdaSub. Note that the mean size of the proposed model V from the proposal q(V ;r) in equation (9) withr ∈ [ , 1− ] p is at least E|V | ≥ ×p; thus, in practice we recommended to set ≤ 1 p , so that models of small size including the null model can be proposed with sufficiently large probability. On the other hand, if is chosen to be very small, then the MAdaSub algorithm may take a longer time to convergence in case proposal probabilities of informative variables are close to ≈ 0 during the initial burn-in period of the algorithm. Simulations and real data applications show that the choice = 1 p works well in all considered situations (see Sections 5 and 6). The updating scheme of the individual proposal probabilities is inspired by the AdaSub method proposed in Staerk (2018) and Staerk et al. (2021) and can itself be motivated in a Bayesian way: since we do not know the true posterior inclusion probability π j of variable X j for j ∈ P, we place a beta prior on π j with the following parametrization where r is the prior expectation of π j and L j > 0 controls the variance of π j via Var(π j ) = 1 If L j → 0, then Var(π j ) → r , which is the variance of a Bernoulli random variable with mean r (0) j . If L j → ∞, then Var(π j ) → 0. Now, one might view the samples S (1) , . . . , S (t) obtained after t iterations of MAdaSub as "new" data and interpret the information learned about π j as t approximately independent Bernoulli trials, where j ∈ S (i) corresponds to "success" and j / ∈ S (i) corresponds to "failure". Then the (pseudo) posterior of π j after iteration t of the algorithm is given by with posterior expectation E(π j | S (1) , . . . , S (t) ) = L j r (0) and posterior variance The interpretation of r (0) j as the prior expectation for the posterior inclusion probability π j motivates the choice of r (0) j = π(j ∈ S) as the actual prior inclusion probability of variable X j . If no particular prior information about specific variables is available, but the prior expected model size is equal to q ∈ (0, p), then we recommend to set r (0) j = q p and L = L j = p for all j ∈ P, corresponding to the prior π j ∼ Be(q, p − q) in equation (12). In this particular situation, equation (15) reduces to Even though it seems natural to choose the parameters r (0) j and L j of MAdaSub as the respective prior quantities, this choice is not imperative. While the optimal choices of these parameters generally depend on the setting, various simulated and real data applications of MAdaSub indicate that choosing r (0) j = q p with q ∈ [2, 10] and L j ∈ [p/2, 2p] for j ∈ P yields a stable algorithm with good mixing in sparse high-dimensional set-ups irrespective of the actual prior (see Sections 5 and 6). Furthermore, if one has already run and stopped the MAdaSub algorithm after a certain number of iterations T , then one can simply restart the algorithm with the already updated parameters r (T ) j and L j + T (compare equation (16)) as new starting values for the corresponding parameters.
Using general results for adaptive MCMC algorithms by Roberts and Rosenthal (2007), we show that MAdaSub is ergodic despite its continuing adaptation.
The proof of Theorem 1 can be found in Section A of the Supplement, where it is shown that MAdaSub satisfies both the simultaneous uniform ergodicity condition and the diminishing adaptation condition (cf. Roberts and Rosenthal, 2007). As an immediate consequence of Theorem 1 we obtain the following important result.
Corollary 2. For all choices of r (0) ∈ (0, 1) p , L j > 0 and ∈ (0, 0.5), the proposal probabilities r (t) j of the explanatory variables X j in MAdaSub converge (in probability) to the respective posterior inclusion probabilities π j = π(j ∈ S | D), i.e. for all j ∈ P it holds that r (t) j P → π j as t → ∞.
Comparison to related adaptive approaches
In this section we conceptually compare the proposed MAdaSub algorithm (Algorithm 1) with other approaches for high-dimensional Bayesian variable selection, focusing on adaptive MCMC algorithms most closely related to the new algorithm (see Section D of the Supplement for details on further related methods).
In a pioneering work, Nott and Kohn (2005) propose an adaptive sampling algorithm for Bayesian variable selection based on a Metropolized Gibbs sampler, showing empirically that the adaptive algorithm outperforms different non-adaptive algorithms in terms of efficiency per iteration. However, since their approach requires the computation of inverses of estimated covariance matrices, it does not scale well to very high-dimensional settings. Recently, several variants and extensions of the original adaptive MCMC sampler of Nott and Kohn (2005) have been developed, including an adaptive Metropolis-Hastings algorithm by Lamnisos et al. (2013), where the expected number of variables to be changed by the proposal is adapted during the algorithm. Zanella and Roberts (2019) propose a tempered Gibbs sampling algorithm with adaptive choices of components to be updated in each iteration. Furthermore, different individual adaptation algorithms have been developed in Griffin et al. (2014) as well as in the follow-up works of Griffin et al. (2021) and Wan and Griffin (2021), which are closely related to the proposed MAdaSub algorithm. These strategies are based on adaptive Metropolis-Hastings algorithms, where the employed proposal distributions are of the following form: if S ∈ M is the current model, then the probability of proposing the model V ∈ M is given bỹ where η = (A 1 , . . . , A p , D 1 , . . . , D p ) T ∈ (0, 1) 2p is a vector of tuning parameters with the following interpretation: For j ∈ P, A j is the probability of adding variable X j if it is not included in the current model S and D j is the probability of deleting variable X j if it is included in the current model S. An important difference is that the adaptation strategies in Griffin et al. (2021) specifically aim to guard against low acceptance rates of the proposal (18), while MAdaSub aims at obtaining a global independent proposal with the largest possible acceptance rate, focusing on regions close to the median probability model. for multi-armed bandits in reinforcement learning, which has recently been investigated in the context of non-parametric Bayesian variable selection (Liu and Ročková, 2021). In contrast to MAdaSub, Thompson Variable Selection (TVS) does not provide samples from the posterior distribution but is designed to minimize the regret (i.e. the difference between optimal and actual rewards); as a consequence, the sampling probabilities in TVS are not guaranteed to converge to the posterior inclusion probabilities.
Parallelization of the MAdaSub algorithm
In this section we present a parallel version of the MAdaSub algorithm which aims at increasing the computational efficiency and accelerating the convergence of the chains. The simplest approach to parallelization would be to independently run the MAdaSub algorithm in parallel on each of K ∈ N different workers, yielding K individual chains which, in the limit, sample from the posterior model distribution (see Theorem 1). However, it is desirable that the information learned about the adaptive parameters can be shared efficiently between the different chains, so that the convergence of the adaptive parameters to their optimal values can be accelerated, leading to a faster convergence of the chains to their common limiting distribution.
We propose a parallel version of MAdaSub, where the workers sample individual MAda-Sub chains in parallel, but the acquired information is exchanged periodically between the chains and the adaptive proposal probabilities are updated together (see Algorithm 2 in Section B of the Supplement for full algorithmic details). More specifically, let S (k,1) , . . . , S (k,T ) denote the models sampled by MAdaSub (see Algorithm 1) for the first T iterations on worker k, for k ∈ {1, . . . , K}. Then, for each worker k ∈ {1, . . . , K}, we define the jointly updated proposal probabilities after the first round (m = 1) of T iterations bȳ where r (k,0) j denotes the initial proposal probability for variable X j and L (k) j the corresponding adaptation parameter (both can be different across the chains).
After the joint update, each MAdaSub chain is resumed (withr (k,1) j as initial proposal probabilities and L (k) j + T K as initial prior variance parameters for j ∈ P) and is run independently on each of the workers for T additional iterations in a second round (m = 2); then the proposal probabilities are updated jointly again tor (k,2) j , and so on (up to m = R rounds in Algorithm 2 of the Supplement). The joint updates of the proposal probabilities after m ∈ N rounds of T iterations are given bȳ Similarly to the serial version of MAdaSub, the adaptive learning of its parallel version can be naturally motivated in a Bayesian way: each worker k = 1, . . . , K can be thought of as an individual subject continuously updating its prior belief about the true posterior inclusion probability π j of variable X j through new information from its individual chain; additionally, after a period of T iterations the subject updates its prior belief also by obtaining new information from the K − 1 other subjects. If the (possibly different) priors where r is the prior expectation of subject k about π j and L (k) j > 0 controls its prior variance, then the (pseudo) posterior of subject k about π j after m rounds of T iterations of the parallel MAdaSub algorithm is given by (compare to equation (14)) with posterior expectation (compare to equation (15)) corresponding to the joint update in equation (20).
Although the individual chains in the parallel MAdaSub algorithm make use of the information from all the other chains in order to update the proposal parameters, the ergodicity of the chains is not affected.
Corollary 4. For each worker k ∈ {1, . . . , K} and all choices of r (k,0) ∈ (0, 1) p , L (k) j > 0, j ∈ P and ∈ (0, 0.5), the proposal probabilitiesr (k,m) j of the explanatory variables X j converge (in probability) to the respective posterior inclusion probabilities π j = π(j ∈ S | D), i.e. for all j ∈ P and k = 1, . . . , K it holds thatr Thus, the same convergence results hold for the parallel version as for the serial version of MAdaSub. The benefit of the parallel algorithm is that the convergence of the proposal probabilities against the posterior inclusion probabilities can be accelerated via the exchange of information between the parallel chains, so that the MCMC chains can converge faster against the full posterior distribution. There is a practical trade-off between the effectiveness regarding the joint update for the proposal probabilities and the efficiency regarding the communication between the different chains. If the number of rounds R is chosen to be small with a large number of iterations T per round, the available information from the multiple chains is not fully utilized during the algorithm; however, if the number of rounds R is chosen to be large with a small number of iterations T per round, then the computational cost of communication between the chains increases and may outweigh the benefit of the accelerated convergence of the proposal probabilities.
If T max denotes the maximum number of iterations, we observe that choosing the number of rounds R ∈ [10, 100] with T = T max /R iterations per round works well in practice (see Sections 5 and 6 as well as Table G.4 of the Supplement).
Illustrative example
We first illustrate the adaptive behaviour of the serial MAdaSub algorithm (Algorithm 1) in a relatively low-dimensional setting. In particular, we consider an illustrative simulated dataset D = (X, y) with sample size n = 60 and p = 20 explanatory variables, by gener- ∼ N (X i, * β 0 , 1), i = 1, . . . , n. We employ the g-prior with g = n and an independent Bernoulli model prior with inclusion probability ω = 0.5, resulting in a uniform prior over the model space (see Remark 2.1). In the MAdaSub algorithm we set r (0) j = 1 2 for j ∈ P, i.e. we use the prior inclusion probabilities as initial proposal probabilities. We first consider the choice L j = p (for j ∈ P) for the variance parameters of MAdaSub, corresponding to equation (17 , corresponding to the targeted proposal distribution, which is, as stated above, the closest independent Bernoulli proposal to the target π(· | D) in terms of Kullback-Leibler divergence (Clyde et al., 2011).
Note that the non-adaptive independence sampler with posterior inclusion probabilities as proposal probabilities (r (t) j = π(j ∈ S | D)) is only considered as a benchmark and cannot be used in practice, since the true posterior probabilities are initially unknown and are to be estimated by the MCMC algorithms. Furthermore, we also present comparisons with a standard local "Markov chain Monte Carlo model composition" (MC 3 ) algorithm (Madigan et al., 1995), which in each iteration proposes to delete or add a single variable to the current model. (black) and of the sizes |S (t) | of the sampled models (red) along the first 5,000 iterations (t) for non-adaptive sampler with prior marginals as proposal probabilities, for MAdaSub (with L j = p), for non-adaptive sampler with posterior marginals as proposal probabilities and for local add-delete MC 3 sampler (from top to bottom).
to zero. On the other hand, the non-adaptive sampler with posterior marginals as proposal probabilities leads to fast mixing with corresponding acceptance rate of approximately 0.54.
Even though the MAdaSub algorithm starts with exactly the same "initial configuration" as the non-adaptive sampler with prior marginals, it quickly adjusts the proposal probabilities accordingly, so that the resulting acceptance rate approaches the target value of 0.54 from the non-adaptive sampler with posterior marginals. In particular, when inspecting the evolution of the sampled model sizes in Figure 1, the MAdaSub algorithm is very difficult to distinguish from the sampler with posterior marginals after a very short burn-in period (see also Figure E.1 of the Supplement).
To illustrate the behaviour of the MAdaSub algorithm with respect to the variance parameters L j , additionally to the choice L j = p we examine two further runs of MAdaSub for non-adaptive independence sampler with prior marginals (blue) and posterior marginals (red) as proposal probabilities, for add-delete MC 3 sampler (gray), as well as for MAdaSub with L j = p (black), L j = p/n (orange) and L j = 100p (purple) for j ∈ P.
with the same specifications as before, but with L j = p/n and with L j = 100p, respectively. Figure 2 indicates that the original choice L j = p is favourable, yielding a fast and "sustainable" increase of the acceptance rate (see also j are continuously adjusted towards the current empirical inclusion frequencies f (11) j | ≤ δ. Even when automatic stopping may be applied, we additionally recommend to investigate the convergence of the MAdaSub algorithm via the diagnostic plots presented in this section and in Section E of the Supplement.
Low-dimensional simulation study
In this simulation study we further investigate the performance of the serial MAdaSub algorithm in relation to local non-adaptive and adaptive algorithms. In particular, we analyse how the algorithms are affected by high correlations between the covariates.
We consider a similar low-dimensional setting as in the illustrative data application with p = 20 covariates and sample size n = 60. To evaluate the performance in a variety of different data situations, for each simulated dataset the number s 0 of informative variables is randomly drawn from {0, 1, . . . , 10} and the true active set S 0 ⊆ P of size |S 0 | = s 0 is randomly selected from the full set of covariates P = {1, . . . , p}; then, for each j ∈ S 0 , the j-th component β 0,j of the true coefficient vector β 0 ∈ R p is simulated from a uniform distribution β 0,j ∼ U (−2, 2). As before, the covariates are simulated using a Toeplitz correlation structure, while the response is simulated from a normal linear model with error variance σ 2 = 1. We consider three different correlation settings by varying the correlation ρ between adjacent covariates in the Toeplitz structure: a low-correlated setting with ρ = 0.3, a highly-correlated setting with ρ = 0.9 and a very highly-correlated setting with ρ = 0.99. For each of the three settings, 200 different datasets are simulated as described above; in each case, we employ a g-prior with g = n on the regression coefficients and a uniform prior on the model space.
For each simulated dataset we apply MAdaSub with 20,000 iterations, using L j = p for j ∈ P and = 1 p . In order to investigate the influence of the initial proposal probabilities r and setting r 9} to prevent the premature focus of the algorithm on some covariates (if π marg j ≈ 1) or the avoidance of other covariates (if π marg j ≈ 0).
Here, the marginal posterior odds PO j are crude approximations to the true posterior odds, derived under the assumption of posterior independence of variable inclusion. The local MC 3 algorithm (Madigan et al., 1995) is applied as before as well as with additional swap moves to potentially improve the mixing (as in Griffin et al., 2021). Using the Rpackage scaleBVS (Zanella and Cabezas Gonzalez, 2020), we apply the adaptive weighted tempered Gibbs sampling algorithm of Zanella and Roberts (2019) to obtain (weighted) frequency estimates (as for the other algorithms) and Rao-Blackwellized estimates of posterior inclusion probabilities (PIPs). Exact PIPs are again derived using the BAS algorithm to the true PIPs, where PIP convergence is defined to occur at the smallest iteration t c for which max j∈P |f if t c ≥ 20,000, then the number of iterations for convergence is displayed as 20,000 in
Similar to the low-dimensional simulations, covariates are generated from a Toeplitz correlation structure with ρ = 0.6 and the response is simulated via y i ind.
are the same for all chains k. For the parallel version, we consider different random initializations of proposal probabilities r (k,0) j = q (k) /p, j ∈ P, with q (k) ∼ U (2, 10) and variance parameters L Table G.1 of the Supplement, comparing the performance of MAdaSub also with the adaptive approaches in Griffin et al. (2021). Table 1 shows that in all considered settings the median estimated time-standardized effective sample size for both MAdaSub versions is several orders larger than for the MC 3 algorithm. For low SNRs (e.g. SNR = 0.5), both MAdaSub versions tend to show larger improvements compared to the MC 3 algorithm than for high SNRs (e.g. SNR = 3). Note that for high SNRs, the posterior distribution tends to be more concentrated around the true model S 0 = {1, . . . , 10}, so that local proposals of the add-delete-swap MC 3 algorithm may also be reasonable. On the other hand, for low SNR, the posterior tends to be less concentrated, so that global moves of MAdaSub have a larger potential to improve the mixing compared to the MC 3 algorithm. The acceptance rates of MAdaSub are also larger in small SNR scenarios, as the posterior model distribution tends to be better approximated by independent Bernoulli proposals. However, in all considered settings, the acceptance rates of MAdaSub are reasonably large with median acceptance rates between 5.1% and 54.2% (see Table 1) and are considerably larger compared to the MC 3 algorithm with median acceptance rates between 0.6% and 5.8% (detailed results not shown).
For low SNRs (SNR ≤ 1), serial updating in MAdaSub tends to yield larger (for p = 500) or similar (for p = 5000) time-standardized effective sample sizes compared to parallel updating, as both versions appear to have converged to stationarity with similar acceptance rates, while the parallel version tends to yield larger computation times as a result of communicating chains. For large SNRs (SNR ≥ 2), MAdaSub with parallel updating performs favourable since the proposal probabilities tend to converge faster than with serial updating, which leads to considerably larger acceptance rates and outweighs the computational cost of communicating chains. Previous results for the same simulation set-up indicate that the two alternative individual adaptation algorithms of Griffin et al. (2021) tend to yield the largest improvements compared to the MC 3 algorithm for higher SNR (particularly for SNR = 2). The proposal (18) of these algorithms allows for larger moves than the add-delete-swap proposal in MC 3 , but -in contrast to the independence proposal of MAdaSub -the proposal (18) still locally depends on the previously sampled model. Overall, MAdaSub shows a competitive performance compared to the adaptive algorithms of Griffin et al. (2021), with advantages of MAdaSub in low SNR settings and advantages of the adaptive algorithms of Griffin et al. (2021) in high SNR settings (see Table G.1 of the Supplement).
6 Real data applications
Tecator data
We first examine the Tecator dataset which has already been investigated in Griffin and Brown (2010), Lamnisos et al. (2013) and Griffin et al. (2021). The data has been recorded by Borggaard and Thodberg (1992) computation times can be found in Section H of the Supplement. As the covariates represent 100 channels of the near-infrared absorbance spectrum, adjacent covariates are highly correlated and it is not surprising that they have similar posterior inclusion probabilities.
If one is interested in selecting a final single model, the median probability model (which includes all variables with posterior inclusion probability greater than 0.5, see Barbieri and Berger, 2004) might not be the best choice in this particular situation, since then only variables corresponding to the "global mode" and no variables from the two other "local modes" in Figure 4 are selected. Alternatively, one may choose one or two variables from each of the three "local modes" or make use of Bayesian model averaging (Raftery et al., 1997) for predictive inference.
PCR and Leukemia data
We illustrate the effectiveness of MAdaSub for two further high-dimensional datasets. In particular, we consider the polymerase chain reaction (PCR) dataset of Lan et al. (2006) with p = 22,575 explanatory variables (expression levels of genes), sample size n = 60 (mice) and continuous response data (the dataset is available in JRSS(B) Datasets Vol. 77(5), Song and Liang, 2015). Furthermore, we consider the leukemia dataset of Golub et al. (1999) with 6817 gene expression measurements of n = 72 patients and binary response data (the dataset can be loaded via the R-package golubEsets, Golub, 2017). For the PCR dataset we face the problem of variable selection in a linear regression framework, while for the leukemia dataset we consider variable selection in a logistic regression framework. We have preprocessed the leukemia dataset as described in Dudoit et al. (2002), resulting in a restricted design matrix with p = 3571 columns (genes). Furthermore, in both datasets we have mean-centered the columns of the design matrix after the initial preprocessing.
Here we adopt the posterior approximation induced by EBIC γ with γ = 1 (see equation (8)), corresponding to a beta-binomial model prior with a ω = b ω = 1 as parameters in the beta distribution (see Section 2). For both datasets we run 25 independent serial MAdaSub chains with 1,000,000 iterations and 25 parallel MAdaSub chains exchanging serial MAdaSub chains (Algorithm 1, top) and 25 parallel MAdaSub chains exchanging information after every round of 20,000 iterations (Algorithm 2, bottom). Bold lines represent median frequencies with 5%-and 95%-quantiles (shaded area) over the chains within each round, for most informative variables X j (with final estimate f j ≥ 0.05 for at least one chain).
information after each of R = 50 rounds of T = 20,000 iterations (yielding also 1,000,000 iterations for each parallel chain). For each serial and parallel chain k = 1, . . . , 50, we set = 1 p and randomly initialize the proposal probabilities r (k,0) j = q (k) /p, j ∈ P, with q (k) ∼ U (2, 5) and the variance parameters L (k) j = L (k) , j ∈ P, with L (k) ∼ U (p/2, 2p). For the leukemia dataset we make use of a fast C++ implementation for ML-estimation in logistic regression models via a limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm, which is available in the R-package RcppNumerical (Qiu et al., 2016). For both datasets, the 50 MAdaSub chains are run in parallel on a computer cluster with 50 CPUs, yielding overall computation times of 2,836 seconds for the PCR data (2,310 seconds for a single chain) and 1,402 seconds for the leukemia data (995 seconds for a single chain). Note that in very high-dimensional settings such as for the PCR data (with p = 22,575), the classical MC 3 algorithm (Madigan et al., 1995) does not yield stable estimates due to slow mixing (cf. Griffin et al., 2021), while the BAS algorithm (Clyde, 2017) using sampling without replacement is computationally intractable. Further results in Griffin et al. (2021) show that several competing adaptive algorithms -including sequential Monte Carlo algorithms of Schäfer and Chopin (2013) The reliable estimation of posterior inclusion probabilities is particularly important for Bayesian inference, since the median probability model (MPM) -including all variables with posterior inclusion probability larger than 0.5 -has been shown to yield optimal predictions for uncorrelated covariates (Barbieri and Berger, 2004) and also a favourable performance for correlated designs (Barbieri et al., 2021) Since MAdaSub is based on adaptive independent proposal distributions, in each iteration of the algorithm the proposed model is (almost) independent of the current model, so that "distant" moves in the model space are encouraged. This can be advantageous in comparison to Gibbs samplers and Metropolis-Hastings algorithms based on local proposal distributions, which may yield larger acceptance rates but are more prone to be stuck in local modes of the posterior model distribution. In future work one may also consider combinations of the adaptive independent proposals in MAdaSub with adaptive local proposals as for example in Lamnisos et al. (2013) and Zanella and Roberts (2019). While MAda-Sub yields competitive results without the use of Rao-Blackwellization compared to the related adaptive algorithms of Griffin et al. (2021), the incorporation of Rao-Blackwellized estimates of posterior inclusion probabilities in the burn-in phase or as initial proposal probabilities may further increase the speed of convergence of MAdaSub. Finally, the extension of MAdaSub to settings with non-conjugate priors is interesting to be investigated, for example by considering data augmentation approaches with additional latent variables or by incorporating reversible-jump moves (Green, 1995;Wan and Griffin, 2021).
A Ergodicity of the MAdaSub algorithm
In this section we present a detailed proof for the ergodicity of the serial MAdaSub algorithm (see Theorem 5), i.e. we show that "in the limit" MAdaSub samples from the targeted posterior model distribution π(· | D) despite the continuing adaptation of the algorithm.
We will make use of a general ergodicity result for adaptive MCMC algorithms by Roberts and Rosenthal (2007). In order to state the result directly for the specific setting of the MAdaSub algorithm, we first introduce some notation.
where q(S ;r) is the probability of proposing the model S and α(S | S;r) is the corresponding acceptance probability.
denote the t-step transition kernel of MAdaSub when the vector of proposal probabilitiesr is fixed (i.e. not adapted during the algorithm). Similarly, let denote the t-step transition kernel for the first t iterations of MAdaSub, given only the initial conditions S (0) = S andr (0) =r.
The following theorem provides the ergodicity result of Roberts and Rosenthal (2007, Theorem 1) adjusted to the specific setting of MAdaSub.
Theorem A.1 (Roberts and Rosenthal, 2007). Consider the MAdaSub algorithm with initial parameters r (0) ∈ (0, 1) p , L j > 0 and ∈ (0, 0.5). Suppose that for each fixed vector of proposal probabilitiesr ∈ [ , 1 − ] p , the one-step kernel P (· | · ;r) of MAdaSub is stationary for the target distribution π(· | D), i.e. for all S ∈ M we have Further suppose that the following two conditions hold: (a) The simultaneous uniform ergodicity condition is satisfied, i.e. for all δ > 0, there exists an integer T ∈ N such that denotes the total variation distance between two distributions P 1 and P 2 defined on some common measurable space (Ω, A).
(b) The diminishing adaptation condition is satisfied, i.e. we have max S∈M P · S;r (t) − P · S;r (t−1) wherer (t) andr (t−1) are random vectors of proposal probabilities induced by the MAdaSub algorithm (see Notation A.1).
Then the MAdaSub algorithm is ergodic, i.e. for all S ∈ M andr ∈ [ , 1 − ] p we have Furthermore, the weak law of large numbers holds for MAdaSub, i.e. for any function where E[g | D] = S g(S)π(S | D) denotes the posterior expectation of g.
In the following we will show that MAdaSub satisfies both the simultaneous uniform ergodicity condition and the diminishing adaptation condition, so that Theorem A.1 can be applied.
Proof. Here we make use of a very similar argumentation as in the proof of Lemma 1 in Griffin et al. (2021). We show that M is a 1-small set (see Roberts and Rosenthal, 2004, Section 3.3), i.e. there exists β > 0 and a probability measure ν on M such that Then by Theorem 8 in Roberts and Rosenthal (2004), the simultaneous uniform ergodicity condition is satisfied.
In order to prove that M is 1-small (note that M is finite), it suffices to show that there exists a constant β 0 > 0 such that P (S | S;r) ≥ β 0 for all S, S ∈ M and allr ∈ [ , 1 − ] p .
Indeed, for S, S ∈ M andr ∈ [ , 1 − ] p it holds This completes the proof.
In order to show that the diminishing adaptation condition is satisfied for the MAdaSub algorithm, we will make repeated use of the following simple observation.
Proof. Since a (t) j t∈N 0 are bounded sequences, there are constants L j > 0 so that |a (t) j | ≤ L j for all t ∈ N 0 and j ∈ {1, . . . , m}. We proceed by induction on m ∈ N: equation (35) obviously holds for m = 1. Now suppose that the assertion holds for m − 1 and we want to show that it also holds for m. Then we have Lemma A.3. Consider the application of the MAdaSub algorithm on a given dataset D with some tuning parameter choices r (0) ∈ (0, 1) p , L j > 0 and ∈ (0, 0.5). Then, for j ∈ P, we have Furthermore, for all S, S ∈ M it holds In particular, MAdaSub fulfils the diminishing adaptation condition.
Proof. For j ∈ P we have With Lemma A.2 (set m = p and note that the number of variables p = |P| is fixed for the given dataset) we conclude that for V ∈ M it holds Let S, S ∈ M and suppose that S = S . Then we have P (S | S;r (t) ) − P (S | S;r (t−1) ) = q(S ;r (t) )α(S | S;r (t) ) − q(S ;r (t−1) )α(S | S;r (t−1) ) .
→ 0 for all S ∈ M. Therefore, we also have α(S | S;r (t) ) − α(S | S;r (t−1) ) ≤ C(S ) q(S;r (t) ) C(S) q(S ;r (t) ) − C(S ) q(S;r (t−1) ) C(S) q(S ;r (t−1) ) where we made use of Lemma A.2 with m = 2 and a (t) Again by using Lemma A.2 and combining equations (38), (39) and (40) we conclude that Finally, we consider the case S = S . Then it holds Thus we have shown that equation (37) holds for all S, S ∈ M. In particular, we conclude that the diminishing adaptation condition is satisfied for MAdaSub (recall that almost sure convergence implies convergence in probability).
Proof. The MAdaSub algorithm fulfils the simultaneous uniform ergodicity condition (see Lemma A.1) and the diminishing adaptation condition (see Lemma A.3). Furthermore, for each fixedr ∈ [ , 1 − ] p , the corresponding transition kernel P (· | · ;r) is induced by a simple Metropolis-Hastings step and therefore has the desired target distribution π(· | D) as its stationary distribution. Hence, by Theorem A.1 the MAdaSub algorithm is ergodic and fulfils the weak law of large numbers.
Corollary 6. For all choices of r (0) ∈ (0, 1) p , L j > 0 and ∈ (0, 0.5), the proposal probabilities r (t) j of the explanatory variables X j in MAdaSub converge (in probability) to the respective posterior inclusion probabilities π j = π(j ∈ S | D), i.e. for all j ∈ P it holds that r (t) j P → π j as t → ∞.
Proof. Since MAdaSub fulfils the weak law of large numbers (Theorem 5), for j ∈ P it holds that Hence, for j ∈ P, we also have
B Algorithmic details of parallel version of MAdaSub
Algorithm 2 Parallel version of MAdaSub Input: • Number of workers K ∈ N.
• Number of rounds R ∈ N.
• Number of iterations per round T ∈ N.
C Ergodicity of parallel version of MAdaSub
In this section we extend the ergodicity result for the serial MAdaSub algorithm (Algorithm 1) of Section A to the parallel version of MAdaSub (Algorithm 2).
Proof. The proof of the simultaneous uniform ergodicity condition for each of the parallel chains is along the lines of the proof for the serial version of MAdaSub (see Lemma A.1).
As before, we can conclude with Theorem A.1 that each parallel chain is ergodic and fulfils the weak law of large numbers, provided that the diminishing adaptation condition is also satisfied for each of the parallel chains.
In order to show the diminishing adaptation condition for the chain on worker k ∈ {1, . . . , K} it suffices to show that for j ∈ P it holds where denotes the proposal probability of variable X j after t iterations of the chain on worker k; the remaining steps of the proof are analogous to the proof of diminishing adaptation for the serial version of MAdaSub (see Lemma A.3). Note that in equation (42) we make use of the convention that b i=a c i = 0 for b < a; additionally, c ∈ N denotes the greatest integer less than or equal to c ∈ R. Furthermore, note that for t = mT with m ∈ N it holds r (k,t) j =r (k,m) j for j ∈ P, k ∈ {1, . . . , K}.
Using the triangle inequality (compare proof of Lemma A.3) and noting that for all t, T ∈ N we have t T − t−1 T ≤ 1, we conclude that for k ∈ {1, . . . , K} it holds Thus, we have shown that equation (41) holds and this completes the proof.
Proof. Since each chain in the parallel MAdaSub algorithm fulfils the weak law of large numbers (Theorem 7), for j ∈ P and k ∈ {1, . . . , K} it holds that Hence, for j ∈ P and k ∈ {1, . . . , K}, we also havē to be ensured that no model is sampled twice and therefore, after each iteration of the algorithm, the sampling probabilities of some of the remaining models have to be renormalized.
D Further approaches related to MAdaSub
Additionally, BAS differs from the other methods discussed in Section 3.2 since it is not an MCMC algorithm and may yield biased estimates of posterior inclusion probabilities after a limited number of iterations.
Another related adaptive method for Bayesian variable selection has been proposed by Ji and Schmidler (2013). They consider an adaptive independence Metropolis-Hastings algorithm for sampling directly from the posterior distribution of the regression coefficients β = (β 1 , . . . , β p ) T , assuming that the prior of β j for j ∈ P is given by a mixture of a point-mass at zero (indicating that the corresponding variable X j is not included in the model) and a continuous normal distribution (indicating that variable X j is "relevant"). G Additional results for the high-dimensional simulation study of Section 5.3
Mixtures
In this section we present additional results for the high-dimensional simulation study of Section 5.3 of the main document.
(n, p) Algorithm SNR = 0. reported in Table 1 of the paper for the 20 variables with the largest estimated PIPs, here the median is taken over all variables, even though the majority of variables receives very small posterior probability. *Results for exploratory individual adaptation (EIA) and adaptively scaled individual adaptation (ASI) algorithms are taken from Table 1 in Griffin et al. (2021). Comparisons between MAda-Sub and algorithms of Griffin et al. (2021) should be interpreted in a holistic way, as the used computational systems, implementations and the specific simulated datasets for each setting may differ.
A,B / Acc.r (20) A,B / Acc.r (20) A,B / Acc.r (20) A,B / Acc. MAdaSub for high-dimensional simulation setting with n = 500 and p = 500, with fixed choices of r (k,0) j = 10/p for all serial and parallel chains k. Performance of MAdaSub algorithms (A) with serial and parallel updating schemes compared to add-delete-swap MC 3 algorithm (B) in terms of median estimated ratiosr (20) A,B of the relative time-standardized effective sample size for PIPs over the 20 variables with the largest estimated PIPs, and in terms of median acceptance rates (Acc.). SNR = 0.5 SNR = 1 SNR = 2 SNR = 3 Initializationr (20) A,B / Acc.r (20) A,B / Acc.r (20) A,B / Acc.r (20) A,B / Acc. = L (k) ∼ U (p/2, 2p) for each chain k. Performance of parallel MAdaSub algorithm (A) compared to adddelete-swap MC 3 algorithm (B) in terms of median estimated ratiosr (20) A,B of the relative timestandardized effective sample size for PIPs over the 20 variables with the largest estimated PIPs and in terms of median acceptance rates (Acc.).
A,B / Acc. / Timer (20) A,B / Acc. / Timer (20) A,B / Acc. / Timer (20) A,B of the relative time-standardized effective sample size for PIPs over the 20 variables with the largest estimated PIPs, in terms of median acceptance rates (Acc.) and in terms of median computation times (in seconds). fixed (the same) initialisations of the tuning parameters r also Table G.2). Despite this, to avoid optimistic biases in the evaluation of the proposed algorithm (cf. Buchka et al., 2021), in Table 1 of the main document we still report the results for the parallel version with the originally considered random initializations of both tuning parameters r larger numbers of rounds R), then the convergence of the proposal probabilities is accelerated, leading to larger acceptance rates (for SNR ≥ 1); however, the higher frequency of communication between the chains comes at the prize of larger computation times. For settings with high signal-to-noise ratios (SNR ≥ 2), the resulting median estimated ratios of the relative time-standardized effective sample size are largest for R ∈ [20,100]. Note that we considered the number of parallel chains to be the same as the number of assigned CPUs (i.e. 5 parallel chains with 5 CPUs, see Section 5.3), which is the most natural choice. However, in practice the "optimal" choice of the number of rounds R may also depend on the number of available CPUs for parallel computation (especially in case this number is considerably different from the number of parallel MAdaSub chains).
H Additional results for Tecator data application of Section 6.1 Here we provide additional results regarding the efficiency of the serial MAdaSub algorithm under the same setting as in Lamnisos et al. (2013), where several adaptive and non-adaptive MCMC algorithms are compared using normal linear models for the Tecator data. In particular, Lamnisos et al. (2013) consider a classical MC 3 algorithm (Madigan et al., 1995), the adaptive Gibbs sampler of Nott and Kohn (2005) and adaptive and nonadaptive Metropolis-Hastings algorithms based on the tunable model proposal of Lamnisos et al. (2009). In the comparative study of Lamnisos et al. (2013) each algorithm is run for 2,000,000 iterations, including an initial burn-in period of 100,000 iterations. Furthermore, thinning is applied using only every 10th iteration, so that the finally obtained MCMC sample has size 190,000. For comparison reasons, after a burn-in period of 100,000 iterations, we run the serial MAdaSub algorithm for 190,000 iterations, so that the considered MCMC sample has the same size as in Lamnisos et al. (2013). In the serial MAdaSub algorithm we set r (0) j = 5 100 for j ∈ P, i.e. we use the prior inclusion probabilities as the initial proposal probabilities in MAdaSub; further, we set L j = p for j ∈ P and = 1 p . Since the acceptance rate of MAdaSub is already sufficiently large in the considered setting yielding a well-mixing algorithm, we do not consider additional thinning of the resulting chain. In fact, the acceptance rate of the serial MAdaSub chain is approximately 0.38 for the 190,000 iterations (excluding the burn-in period). We note that in this example the relatively large number of 100,000 burn-in iterations is not necessarily required for MAdaSub and is only used for comparison reasons. Lamnisos et al. (2013) report estimated median effective sample sizes of the different samplers for the evolution of the indicators γ (t) j T t=1 for j ∈ P, where γ (t) j = 1 S (t) (j) indicates whether variable X j is included in the sampled model S (t) in iteration t. The estimated median effective sample size for the 190,000 iterations of the serial MAdaSub algorithm is approximately 38,012 (using the R-package coda), which is slightly larger than the values for the competing algorithms reported in Lamnisos et al., 2013 (the largest one is 37,581 for the "optimally" tuned Metropolis-Hastings algorithm). Note that when using 1,900,000 iterations with thinning (every 10th iteration after 100,000 burn-in iterations) as in the other algorithms, the estimated median effective sample size for MAdaSub is much larger (178,334), yielding almost independent samples of size 190,000.
We finally provide details on the computational costs of the serial and parallel versions of MAdaSub for the analysis of the Tecator data presented in Section 6.1 of the main document. The computation time for each of the 5000 iterations of the serial MAdaSub algorithm is approximately 3.5 seconds (using an R implementation of MAdaSub on an Intel(R) Core(TM) i7-7700K, 4.2 GHz processor); thus, even without parallelization, one obtains accurate posterior estimates with the serial MAdaSub algorithm within seconds using a usual desktop computer (e.g. after 10,000 or 15,000 iterations, see Figure 4 of the main document). Lamnisos et al. (2013) report that the computation times for each of the other considered MCMC methods were in the order of 25,000 seconds for the total number of 2,000,000 iterations (using a MATLAB implementation). Although the computation times are not directly comparable, these results indicate that the serial MAdaSub algorithm is already very efficient. The timings for MAdaSub are also of a similar order as for the recent adaptive algorithms of Griffin et al. (2021), who report that short runs of 6000 iterations of the exploratory individual adaptation algorithm yield stable estimates for the Tecator data with computation times of about 5 seconds . When using a computer cluster with 50 CPUs, the overall computation time for all considered 50 MAdaSub chains (each with a large number of 290,000 iterations) is 460 seconds, while the computation time for a single chain is 231 seconds on the same system. This shows that, even though 25 of the 50 MAdaSub chains communicate with each other after every 5,000 iterations, the parallelization yields a substantial speed-up in comparison to a serial application of 50 independent chains. I Additional results for PCR and Leukemia data applications of Section 6.2 To further illustrate the stability of the results, we examine three independent runs of the serial MAdaSub algorithm for the PCR and leukemia data, each with T = 1,000,000 iterations, setting r (0) j = q p as initial proposal probabilities with different expected search sizes q: for the first run we set q = 2, for the second run q = 5 and for the third run q = 10.
Further tuning parameters are set to L j = p and = 1/p for each of the three MAdaSub runs. and of 25 parallel MAdaSub chains exchanging information every 20,000 iterations (Algorithm 2, bottom) in terms of empirical variable inclusion frequencies f j for most informative variables X j (with final f j ≥ 0.1 for at least one chain). | 15,076.6 | 2021-05-03T00:00:00.000 | [
"Computer Science",
"Mathematics"
] |
Environmentally Friendly Pyrometallurgical Scheme for Vacuum Separation of Non-Ferrous Metals from Waste Products in Incineration Plants
Residues from the municipal solid waste processed in incineration plants in European countries are an important raw material to obtain valuable components, including non-ferrous metals. State and private companies specializing in the processing of waste incineration slag as products most often receive concentrates of non-ferrous metals, which, on average, contain, in mass. %: 20÷60 Cu; 10÷30 Zn; 5÷15 Pb; ~ 1 Al; ~ 1 Sn; ~ 1 Fe, up to 50 g/t Аu and up to 3,000 g/t Ag. Concentrates are sent for processing to smelters without taking the cost of zinc into account. The paper presents the study on the separation of metallic zinc into a separate product (zinc concentrate) from the collective concentrate of non-ferrous metals by a vacuum-thermal method, the safest from the environmental point of view. The study was performed with non-ferrous metal concentrate of +0.3-0.8 mm in size, containing wt. %: 68.07 - Cu; 12.4 - Zn; 14.78 - Pb; 0.99 - Al; 1.2 - Sn; 0.15 - Fe, up to 2.0 kg/t - Ag. The material was heat treated at 800÷900℃ with the residual pressure in the system of less than 0.13 kPa. Zinc concentrate was obtained, containing more than 96% of the main component. At the same time, the Cu content increased by 14.09% in the residue from the heat-vacuum treatment. Other metals (Pb, Al, Sn) including noble metals were also concentrated in the residue. The results of the study show that it is possible to separate zinc into a separate product from non-ferrous metal concentrates containing more than 10% Zn in the initial material by the proposed method.
Introduction
Every year, the amount of municipal solid waste (MSW) increases, in particular, developed countries and megacities around the world are faced with this problem [1][2][3][4]. Disposal of the ever-increasing amount of MSW is not only an environmental problem but also a social and economic one [5][6][7]. Disposal of MSW practiced over the past decades is widely recognized as a futureless direction, both from the environmental and economic sides [8][9][10]. One of the solutions for this problem is the construction of waste incineration plants which, along with waste disposal, receive energy (in the form of steam or hot water) [11,12] and materials that serve as a secondary source of valuable components [13,14].
Waste disposal technology at thermal waste treatment plants is accompanied by the production of slags containing up to 10% of metal scrap that is a secondary raw material for the extraction of non-ferrous metals, including ferrous metals -about 7-8%, non-ferrous metals -remained 2-3% [15,16].
The metal content in slag and ash from MSW combustion averages 25 kg per ton of MSW [17]. The resulting slag is sent for mechanical processing (grinding) and subsequent sorting, based on the different physical properties of the slag constituents. The material is washed, the iron is removed by magnetic separation, the "light" (aluminum) and "heavy" components of the slag (copper, brass, lead, zinc, silver, gold, etc.) are separated [18,19]. The obtained concentrate of "heavy" non-ferrous metals contains up to 37% Cu, up to 13% Zn (as brass), up to 4% Pb and Sn (as bronze), meets the requirements for secondary copper raw materials and is sent to copper-smelting plants for copper extraction [20,21], as a rule, by the pyrometallurgical method. Similar technologies [14,22] are used in the largest companies for the disposal and processing of waste incineration plant slags in Europe and Switzerland [23].
Many scienti c studies are devoted to the problem of MSW processing, in particular in incineration plants, with subsequent extraction of valuable components from the slag and ash. There are innovative technologies that enable su ciently complete extraction of valuable components from the slag and ash from MSW combustion into non-ferrous metal concentrate [14,[24][25][26][27]. The objectives of the study included the development of an environmentally safe, reagentfree, pyrometallurgical scheme for the vacuum separation of non-ferrous metals from waste products of incineration plants. Previously, similar studies were performed at the Institute of Metallurgy and Ore Bene ciation to obtain high-purity selenium from copper-smelting waste [28,29]. The authors studied various two-component systems, including the thermodynamics of formation and evaporation of lead-tin alloys to determine the optimum conditions for vacuumthermal zinc extraction [30].
Materials and reagents
The collective concentrate of non-ferrous metals is obtained on an innovative technological line for the processing of slags formed as a result of thermal utilization of residual solid domestic waste at incineration plants. The basis of the process is the dry mechanical process that allows the processing of about 120,000 tons of slag annually. The output products (non-ferrous metal concentrate) consist of a mixture of non-ferrous and noble metals. The concentrate is non-magnetic and has electrical conductivity. Table 1 shows the material composition of the collective concentrate after bene ciation of metals on the technological line for dry mechanical processing of slags. We can see from the data in Table 1 that zinc in su cient quantities is contained in the collective concentrate of non-ferrous metals, and its cost is not taken into account when the concentrate is supplied to the copper processing plant. The idea of the project was to develop an environmentally safe technological scheme for vacuum distillation separation of non-ferrous metals present in the collective concentrate into separate products, in particular: zinc separation into zinc concentrate.
Non-ferrous metal concentrate with a particle size of +0.3-0.8 mm was used as a test material shown in Fig. 1.
Experimental methods
The content of major elements in the concentrate and the products obtained after heat treatment of the material was determined by chemical method with the help of an atomic emission spectrometer Optima 8300 DV "Perkin Elmer" (made in the USA) and by X-ray uorescent method with a wave-dispersive combined spectrometer Axios "PANalytical" (made in the Netherlands). The phase composition of the initial materials was determined in a D8 Advance "BRUKER" X-ray diffractometer (made in Germany) in Cu-Kα radiation and a JEOL JXA-8230 scanning electron microscope (made in Japan).
Separation of zinc into a separate product was performed with the help of a laboratory vacuum apparatus with a vertical arrangement of a quartz reactor. The scheme of the laboratory setup is shown in Figure 2. The unit consists of an electric tube furnace Nabertherm RT 50-250/11 (1) with a quartz reactor installed inside (2). A set of ve graphite crucibles (4) The temperature in the system was additionally controlled using a chromel-alumel thermocouple installed above the sample of the test material. The vacuum in the system was created using a Pfeiffer Vacuum HiPace® 10 series turbomolecular vacuum pump (made in Germany) with a pumping rate of 10 l / s. The residual pressure in the system was monitored using a Pirani VSM77D vacuum gauge (made in Germany). The degree of distillation of the volatile components of the concentrate was determined by the weight loss of the sample using an analytical balance Shimadzu AUW-220 (made in Japan).
Characterization of collective non-ferrous metal concentrates
The content of the main components in the concentrate determined by chemical analysis with the atomic emission spectrometer Optima 8300 DV "Perkin Elmer", is shown in Table 2. The source material was fused in a graphite crucible in an induction vacuum electric furnace to determine the elemental composition by X-ray uorescence analysis to average the composition, and a tablet was formed from the material using an industrial press. The results obtained on a wave-dispersive combined spectrometer Axios "PANalyical" are shown in Table 3. The alkali, alkaline-earth, and rare-earth metals (Mg, Ca, K, Y) found in trace amounts by the X-ray uorescence method in the concentrate sample in the pressed tablet (in the original material without heat treatment, not present in the remelted ingot) were most likely slagged as a result of melting the material in the induction furnace at high temperatures.
The quantitative content of elements in the studied material by X-ray uorescent method was determined under standard procedures using the obtained spectra without the use of standards for calibration. Obtained overestimated values of the sum of certain elements "before normalization" (above 100%) indicate the high intensity of the spectra, which indirectly indicates the reliability of the results obtained.
The initial material of the sample was sent for mineralogical analysis and scanning electron microscopy to determine the phase composition both inside the metal grains and at their boundaries. Figure 3 shows the images of the thin sections of the sample concentrate, obtained on a scanning electron microscope JEOL JXA-8230.
Separation of zinc into a separate product
The separation of zinc into a separate product from a concentrate of non-ferrous metals with a particle size of + 0.3-0.8 mm was performed in the temperature range: 800 ℃ and 900 ℃ with residual pressure in the system <0.13 kPa (<1 mm Hg). The experimental results are shown in Table 4. The chosen temperature interval is justi ed by the elimination of signi cant material overheating and, consequently, lower energy consumption during zinc distillation, as well as by the reduction of lead transfer into the vapor phase and its further co-condensation with zinc. Residues from zinc distillation from the collective concentrate sample were formed into " tablets" using an industrial press and sent for X-ray uorescence analysis. Figure 4 shows photographs of the residues after thermal vacuum treatment of the concentrate and the resulting zinc condensate at the bottom of a graphite crucible.
The bulk of the zinc at 900℃ was condensed on the walls of the quartz retort in the colder zone from the location of the graphite crucibles (Table 4). X-ray uorescence analysis showed that in the zinc obtained as a result of liquid-phase condensation (collected on the walls of the retort), the content of the main component is 98.21%, the main impurity elements, wt%: 0.15 -Pb; 0.15 -Mg; 0.13 -Al; 0.35 -Si; 0.2 -Cl. The content of other impurity elements is less than 0.02%.
The resulting sublimates of zinc condensate were remelted into an ingot (to average the composition) to determine the content of the main component (Zn) and impurity elements. Melting was performed in an induction vacuum furnace at atmospheric pressure of 480-520°C. The foam (ZnO) formed on the surface of the ingot was removed mechanically with a tantalum stick.
The resulting ingot is machined to give a smooth surface. A photograph of the obtained ingot of metallic zinc is shown in Figure 5. Table 5 shows the content of elements determined by X-ray uorescence analysis. Table 5 The content of elements in a metal zinc ingot obtained from sublimates during vacuum heat treatment of a sample of a collective concentrate of non-ferrous metals at t = 800 ℃ and t = 900℃ Table 6 shows the content of elements determined by the X-ray uorescence analysis method in the residues from the thermal vacuum treatment of the collective concentrate of non-ferrous metals at temperatures of 800 ℃ and 900℃. Table 7 shows the results of the X-ray phase analysis of the formed foam. Analysis performed on a D8 Advance (BRUKER) diffractometer, Cu radiation -K α .
Material balance of zinc distribution by processed products
Material balance of zinc and main accompanying elements distribution under the products of vacuum-thermal treatment of collective non-ferrous metal concentrate is presented in Table 8. It is shown that in principle, it is possible to extract more than 93% of zinc from a sample of non-ferrous metals concentrate using an environmentally friendly reagent-free vacuum-thermal method into a separate product (zinc concentrate) containing more than 96% Zn. Valuable components (Cu, Pb, Ag) are concentrated in the evacuation residues and are suitable for further processing by classical methods. The environmental friendliness of vacuum-thermal technologies is determined by a signi cant decrease in the number of waste process gases, the sanitary cleaning of which is not di cult, by a decrease in the temperature of heat treatment resulting in the reduction of energy costs.
Declarations Figure 1 Photos of non-ferrous metal concentrate with +0.3-0.8 mm particle size Figure 2 Schematic diagram of the laboratory vacuum unit 1 -tubular electric furnace; 2 -quartz reactor; 3 -graphite crucible (base); 4 -a set of crucibles with a channel for steam passage; 5 -a sample of the starting material; 6 -alundum support; 7 -rubber stopper.
Figure 3
The results of the study of the concentrate sample with the grain size of +0.3-0.8 mm on scanning electron microscope JEOL JXA-8230 (magni cation x70) Figure 4 Photographs of products obtained after stripping zinc from a sample of a collective concentrate of non-ferrous metals а) loading crucible with concentrate after zinc stripping at t = 800 ℃; b) upper crucible with metallic zinc condensate; c) compressed concentrate in the form of a tablet for analysis after zinc stripping at t =900℃. | 2,973.6 | 2021-11-16T00:00:00.000 | [
"Materials Science"
] |
Integrated photodetectors for compact Fourier-transform waveguide spectrometers
Extreme miniaturization of infrared spectrometers is critical for their integration into next-generation consumer electronics, wearables and ultrasmall satellites. In the infrared, there is a necessary compromise between high spectral bandwidth and high spectral resolution when miniaturizing dispersive elements, narrow band-pass filters and reconstructive spectrometers. Fourier-transform spectrometers are known for their large bandwidth and high spectral resolution in the infrared; however, they have not been fully miniaturized. Waveguide-based Fourier-transform spectrometers offer a low device footprint, but rely on an external imaging sensor such as bulky and expensive InGaAs cameras. Here we demonstrate a proof-of-concept miniaturized Fourier-transform waveguide spectrometer that incorporates a subwavelength and complementary-metal–oxide–semiconductor-compatible colloidal quantum dot photodetector as a light sensor. The resulting spectrometer exhibits a large spectral bandwidth and moderate spectral resolution of 50 cm−1 at a total active spectrometer volume below 100 μm × 100 μm × 100 μm. This ultracompact spectrometer design allows the integration of optical/analytical measurement instruments into consumer electronics and space devices.
Extreme miniaturization of infrared spectrometers is critical for their integration into next-generation consumer electronics, wearables and ultrasmall satellites. In the infrared, there is a necessary compromise between high spectral bandwidth and high spectral resolution when miniaturizing dispersive elements, narrow band-pass filters and reconstructive spectrometers. Fourier-transform spectrometers are known for their large bandwidth and high spectral resolution in the infrared; however, they have not been fully miniaturized. Waveguide-based Fourier-transform spectrometers offer a low device footprint, but rely on an external imaging sensor such as bulky and expensive InGaAs cameras. Here we demonstrate a proof-of-concept miniaturized Fourier-transform waveguide spectrometer that incorporates a subwavelength and complementary-metal-oxide-semiconductor-compatible colloidal quantum dot photodetector as a light sensor. The resulting spectrometer exhibits a large spectral bandwidth and moderate spectral resolution of 50 cm −1 at a total active spectrometer volume below 100 μm × 100 μm × 100 μm. This ultracompact spectrometer design allows the integration of optical/analytical measurement instruments into consumer electronics and space devices.
Miniaturization of infrared spectrometers will lead to their wider use in consumer electronics-such as mobile phones enabling food control, the detection of hazardous chemicals and wearable electronics. Besides the highly interesting infrared fingerprint and functional group regions (2.5-20.0 μm), a Fourier-transform near-infrared spectrometer operating between 0.76 and 2.50 μm can be used for the counterfeit detection of medical drugs 1 , or the detection of Earth's greenhouse gases such as methane and CO 2 (ref. 2 ); however, higher sensitivity and specificity are usually achieved in the mid-wave infrared region.
Furthermore, ultracompact spectrometers are also highly desired for space applications such as femtosatellites (space devices with a maximum weight below 100 g) 3 and can be useful for novel snapshot hyperspectral cameras (each pixel of a camera consists of an individual spectrometer) requiring ultracompact spectrometers for each pixel to achieve a small pixel pitch 4,5 .
Extensive miniaturization efforts on various elements of spectrometers such as dispersive elements, narrow band-pass filters and Fourier-transform and reconstructive spectrometers have been Article https://doi.org/10.1038/s41566-022-01088-7 100 μm × 100 μm × 100 μm. This work demonstrates an ultracompact short-wave spectrometer design combining large bandwidth and moderate spectral resolution with a spectral sensitivity in the infrared light region.
The schematic in Fig. 1 shows the miniaturization of the detection scheme by monolithically integrating the optical sensor on top of a waveguide. The multimode waveguide was inscribed in a LiNbO 3 substrate with a depressed-index cladding structure fabricated by femtosecond laser irradiation. In the experiments, only the fundamental mode has been excited by carefully aligning the laser input with the waveguide. The flat substrate surface on top of the buried waveguide enables the deposition of electrodes without risking discontinuity of the electrodes compared with silicon-based waveguides, often having an elevated waveguide on top of the substrate. The specifically designed shape of the waveguide cladding confines near-infrared light but intentionally increases the power leakage along the Z direction to increase interactions with the detectors on the surface. Within the waveguide, a stationary wave is created by back-reflection of the waveguide-coupled light at a mirror surface (or by the superposition of two counterpropagating waves entering at both ends of the waveguide). In typical waveguide spectrometers, metal nanorods in proximity to the waveguide probe the intensity profile of the stationary wave and scatter the light proportionally to the local intensity of the stationary wave. The scattered light is subsequently imaged by a commercial camera 9,10,[16][17][18][19][20] . Here a detector consisting of a gold bottom electrode with a subwavelength dimension perpendicular to the waveguide and of a length reaching over the complete width of the waveguide is fabricated instead of metal nanorods. For a proof-of-concept device, a HgTe QD photoconductor type was chosen as no band alignments of QD layers are required. The photoconductor was fabricated in a vertical-stacked configuration (as typically used for photodiodes), reducing the footprint area of the sensor. In analogy to metal nanoprobes utilized in typical waveguide spectrometers 9 , the bottom electrode in the photodetector scatters out light from the evanescent field of the stationary wave (that is, simultaneously functioning as an electrode and light scatterer). Subsequently, the light is partially absorbed in the HgTe QD layer creating photoinduced electron-hole pairs. These charge carriers are separated by an applied electric field, resulting in a demonstrated, thoroughly compared in another review article 3 . However, the scaling of spectrometers, so far, comes at a tradeoff between spectral bandwidth, resolution and/or limitation to the visible spectral range [6][7][8] . Fourier-transform infrared spectrometers combine large spectral bandwidth and resolution in the infrared, but they have not been fully miniaturized yet. Although the interferometric platform of Fourier-transform spectrometers has been downscaled, for example, as optical waveguide spectrometers with impressively high spectral resolution, bandwidth and operation in the infrared region, they still rely on an external imaging sensor for signal detection 9,10 . This means that currently, the overall waveguide spectrometer cannot be smaller than commercially available detectors, which are bulky and expensive for highly sensitive infrared cameras. Although the idea of addressing the challenge of further waveguide spectrometer miniaturization by the monolithic integration of subwavelength photodetectors on top of a waveguide spectrometer is not new 3,9 , it has yet to be realized.
Subwavelength, infrared photodetectors rely on non-scalable device fabrication 11 or require cryogenic cooling (expensive and bulky) 12 . The scaling of commercial infrared detectors such as InGaAs and mercury cadmium tellurides down to subwavelength dimensions and their integration with optical waveguides is challenging. However, notably, infrared photodetectors based on solution-processable colloidal quantum dots (QDs) offer distinct opportunities: they can be fabricated on various substrates, and the spectral response can be tuned by the QD size and composition. For example, the absorption spectrum of mercury telluride (HgTe) QDs can cover the visible and infrared light region approaching the terahertz region by varying the QD size [13][14][15] . HgTe-QD-based photodetectors are typically fabricated either as photoconductors or photodiodes and, to the best of our knowledge, have not been monolithically integrated into waveguide spectrometers.
Here we demonstrate the fabrication of a waveguide-integrated, HgTe-QD-based photoconductor. The room-temperature-operated photodetector exhibits a spectral response up to a wavelength of 2 μm. Furthermore, the wire-shaped, subwavelength-sized photodetector was monolithically integrated with an optical waveguide realizing a proof-of-concept Fourier-transform micro-spectrometer with a spectral resolution of 50 cm −1 at an active spectrometer volume below Article https://doi.org/10.1038/s41566-022-01088-7 photocurrent. As the detector is placed just in the evanescent field of the waveguide, the detector can only absorb a fraction of light intensity. This is very well desired as it allows the creation of a stationary wave within the waveguide, which requires that the reflected light intensity is comparable to the incident light intensity. QDs within the evanescent field of the waveguide but outside the photoconductor structure probably lead to some parasitic light absorption reducing the overall light intensity. The parasitic light absorption probably does not contribute to the photoconductor device signal, as the high resistivity of the QD film limits the charge diffusion from neighbouring HgTe QDs. The total QD photodetector thickness, including both electrodes, is below 300 nm (atomic force microscopy measurement of QD layer thickness is shown in Extended Data Fig. 1). Downscaling of the vertical dimension of the imaging sensor by a factor of 1,000 is achieved compared with state-of-the-art waveguide spectrometers using external InGaAs cameras and appropriate optics (typically resulting in a thickness of around 30 cm). Adding the thickness of the buried, leaky waveguide (front view of the optical bright-field image is shown in Extended Data Fig. 2) to the QD photoconductor thickness results in an overall spectrometer device thickness below 100 μm. With an overlap of the electrodes of 70 μm and a mirror travel range of 100 μm, the resulting dimensions of the ultracompact spectrometer are below 100 μm × 100 μm × 100 μm, which includes the optical system and imaging sensor (but excludes the electrical circuit). We have excluded the piezoelectric stage from the spectrometer volume calculation, as other device architectures without a moving mirror exist, for example, a stationary wave created by counterpropagating waves 10 or with a fixed mirror position and an array of nanoprobes 20 . In this proof-of-concept research study, a single photodetector was characterized, which requires a phase modulation, for example, utilizing a piezo-stage-mounted movable mirror. Figure 2a illustrates the fabrication process of the detector (detailed description is provided in the Methods section). The bottom electrode is fabricated with standard electron-beam lithography. The HgTe QD film is deposited in a layer-by-layer manner by alternating spin-coating steps of QD dispersion followed by a ligand exchange solution containing 1,2-ethanedithiol. The fabrication of a suitable top electrode with submicrometre dimensions on top of a QD film is challenging and, to the best of our knowledge, not developed yet. For example, lithography via a shadow mask lacks alignment precision and results in feature sizes considerably larger than 1 μm. Furthermore, standard high-resolution electron-beam lithography requires the deposition of a resist such as poly(methyl methacrylate) (PMMA) by spin coating and subsequent annealing of the resist typically at 180 °C. Unfortunately, the heating of most QD films to such high temperatures compromises the structural and chemical integrity of QDs (for example, oxidation). A workaround, inspired by graphene transfer, prepares the PMMA double layer by spin coating and annealing it on a 100 nm copper buffer layer on a SiO 2 substrate. This stack was placed in a beaker containing a copper etchant solution (optical images are shown in Extended Data Fig. 3). Overnight and starting from the edges, the copper is completely etched due to the capillary forces of the solution. Once the copper is completely etched, the PMMA detaches and floats at the liquid/air interface. After rinsing of the already annealed PMMA sheet, it is picked up with the half-fabricated HgTe QD photoconductor by fishing it from the liquid/air interface. After drying at ambient conditions, the sample can be treated with standard electron-beam lithography. Further development may use roll-to-roll PMMA transfer by lamination from a donor substrate with a low-adhesive surface treatment. Importantly, the possibility of detector fabrication is not limited to LiNbO 3 substrates, but can be extended to various flat substrates including SiO 2 on silicon, demonstrating the compatibility with complementary metal-oxide-semiconductor on-chip integration. Figure 2b shows the absorbance of tetrapodic-shaped HgTe QDs (transmission electron microscopy image is shown in Extended Data Fig. 4) in solution and compares it with the photoresponse of a corresponding HgTe QD photoconductor consisting of a compact QD film. The spectral dependence of the photoresponse is acquired by illuminating the device from top in a monochromator setup. A bathochromic shift of about 40 meV is observed, which is expected due to the increased electronic coupling of the QDs in films and after ligand exchange with shorter ligands. The detector exhibits a spectral photoresponse in the infrared comparable to commercially available InGaAs photodetectors with a quantum-confined excitonic peak at 1.8 μm. Figure 2c shows the noise current of the detector measured in the dark, exhibiting a 1/f noise behaviour commonly observed in photoconductors [21][22][23][24] . The active device area depends on the transparency of the thin gold electrodes and the extension of the electric field (applied between the electrodes) reaching into the QD film. Although the gold electrodes overlap over a length of 70 μm and a width of 60 nm, contributions to the photocurrent may mainly originate from the edges of the device and only limited contributions may come from photons reaching the HgTe QD film through the 60-nm-thick gold electrode. For an estimation of the photoresponsivity and specific detectivity, the overlap of the electrodes can be used as the device area resulting in 0.6 A W -1 and 3 × 10 9 Jones, respectively (a detailed calculation is provided in the Methods section). However, the active device area may substantially differ when the detector is illuminated (from the side) through the waveguide, and the photosignal may benefit from plasmonic field enhancement of the subwavelength device structure.
A schematic of the setup is shown in Fig. 3a (optical image of the setup is shown in Extended Data Fig. 5 and an optical image of the device is shown in Extended Data Fig. 6): a 1,570 nm laser (300 μW output power) is modulated by a mechanical chopper (50% open areas) and coupled into a LiNbO 3 waveguide. The modulation of light by the chopper allows to recover the signal with a low-noise lock-in amplifier. A stationary wave is created within the waveguide due to the back-propagation of the light reflected from a mirror on the opposite end of the waveguide. Thus, the modulated photosignal depends on the relative position of the subwavelength photodetector: it gives a maximum of the photosignal at antinode positions and a minimum photosignal at node positions of the stationary wave. A slight decrease in conductivity was observed within the first week (after device fabrication), which stabilized afterwards, giving a constant conductivity over the course of at least three months (the sample was stored in an inert atmosphere in between measurements). The current-voltage curves (Fig. 3b) show an ohmic device behaviour with a resistance of about 30 MΩ once a stabilized device performance was observed with a notably increased conductivity under illumination. The mirror is mounted on a piezostage and the travel range along the waveguide axis is calibrated by using the waveguide spectrometer as an interferometer with a calibration wavelength of 1,550 nm (Extended Data Fig. 7). For spectroscopic experiments, the calibrated mirror is moved away from the waveguide increasing the optical path difference. The stationary wave shifts with respect to the mirror position and the subwavelength photodetector goes through nodes and antinodes of the stationary wave. The resulting photosignal is shown in Fig. 3c with a 100 μm mirror travel range; a zoomed-in view of the results in Fig. 3c is shown in Fig. 3d. A typical mirror scan experiment was acquired in about 160 min and only minor signal fluctuations are observed (Fig. 3c). The corresponding fast Fourier transformation is also shown (Fig. 3e). The wavelength of the coupled laser is well determined with the ultracompact spectrometer. The resolution of the Fourier-transform infrared and waveguide spectrometers is the inverse of the optical path difference (that is, two times the mirror displacement). A travel range of the mirror by 100 μm results in a spectral resolution of 50 cm −1 (13 nm resolution at a wavelength of 1,570 nm). In comparison to other spectrometer types, a spectral resolution of 50 cm −1 may not be very high; however, all the spectrometers are subject to a tradeoff among the spectral resolution, bandwidth and spectrometer volume. In this regard, the presented waveguide spectrometer reaches the fundamental limits and further miniaturization may require smaller waveguide cross sections. When a higher spectral resolution is desired, a longer optical path difference can be chosen 17,25,26 , which will inherently increase the waveguide length and spectrometer volume. The maximal detectable wavelength of the presented waveguide spectrometer is determined by the absorption spectrum of the HgTe QD film, reaching about 2 μm in our case. The minimal unambiguously detectable wavelength is limited by the transmission of LiNbO 3 in the ultraviolet region of about 400 nm once the chosen sampling interval satisfies the Nyquist-Shannon sampling theorem.
We can simplify the optical waveguide scheme: instead of modulating the waveguide-coupled light with a bulky mechanical chopper or a shutter, the photosignal can also be effectively modulated by Fig. 8; raw data of the mirror-modulated photosignal are shown in Extended Data Fig. 9). Signal modulation by the vibration of the mirror allows for a more compact spectrometer design and allows us to directly couple multiple laser light sources to the optical waveguide. Figure 4a shows a schematic of the setup with laser light simultaneously coupled from a 1,570 and 1,310 nm laser with optical laser output powers of 300 and 330 μW, respectively. The recorded photosignal is shown in Fig. 4b,c, exhibiting a well-resolved beating pattern and Fig. 4d shows the corresponding fast Fourier transformation of the photosignal. The signal of both lasers is of similar intensity, in agreement with the corresponding laser powers. The spectral resolution is about 100 cm −1 (50 μm mirror displacement) translating into 25 and 18 nm resolution at a wavelength of 1,570 and 1,310 nm, respectively. The monolithic integration of subwavelength infrared photodetectors has a tremendous effect on the scaling of Fourier-transform waveguide spectrometers, but may also be of interest for miniaturized Raman spectrometers, waveguide-based biosensors and lab-on-a-chip devices 27 , as well as the development of high-resolution snapshot hyperspectral cameras 4 .
Further improvements in integrated subwavelength photodetectors may come with the implementation of photodiodes exhibiting higher light sensitivity, and the extension of spectral sensitivity into the mid-wavelength infrared region by utilizing larger HgTe QDs 15,21,22,28,29 and intraband absorption 30,31 . Furthermore, instead of a single photodetector, a photodetector array, ideally with a subwavelength period, can be fabricated. However, the subwavelength periodic arrays may exhibit electronic and photonic crosstalk between the photodetectors-which can limit the detector periodicity to a period larger than the wavelength. In this case, the integration of a Mach-Zehnder modulator may be useful 10 . Furthermore, the moving mirror can be replaced, for example, with a stationary mirror deposited at the end of a waveguide 20 , or alternatively, by a loop-shaped waveguide design 9 . In addition, PMMA transfer may be further developed towards a roll-to-roll lamination process by adjusting the adhesive strength between the sacrificial substrates and the desired HgTe QD layer.
To summarize, monolithically integrated subwavelength photodetectors are crucial to achieve the full miniaturization potential of Fourier-transform waveguide spectrometers. A fabrication method of such detectors involves introducing circumventing temperature-sensitive processing steps. A subwavelength photodetector based on HgTe QDs has been monolithically integrated onto a LiNbO 3 waveguide with a spectral sensitivity up to a wavelength of 2 μm and room-temperature operation. The monolithic integration of the photodetector downscales the thickness of the imaging sensor by a factor of 1,000, resulting in a large-bandwidth, ultracompact (below 100 μm × 100 μm × 100 μm) infrared micro-spectrometer with a moderate spectral resolution of 50 cm −1 . The presented results pave the way towards micro-spectrometers in consumer electronics, space applications and hyperspectral cameras.
Online content
Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/s41566-022-01088-7.
All the chemicals were used as received, unless otherwise stated. Oleylamine was dried and degassed under reduced pressure at a temperature of 120 °C for 1 h before its use.
Trioctylphosphine telluride (TOP:Te) was synthesized by stirring 5.08 g tellurium (0.04 mol) in dry trioctylphosphine (20 ml) for three days yielding a 2 M TOP:Te solution. The solution was filtered through a 0.45 μm polytetrafluoroethylene syringe filter resulting in a clear, yellowish solution.
HgTe QD synthesis
Caution Highly toxic compounds. Highly toxic compounds are used and appropriate precautions have to be implemented. The reaction was adapted from another work 13 with slight modification. Briefly, 27 mg (0.1 mmol) HgCl 2 and 4 ml oleylamine were heated to 100 °C under inert conditions and under continuous stirring at 1,000 rpm. The reaction was kept for 30 min at 100 °C to ensure the complete solvation of HgCl 2 . Subsequently, the reaction was cooled to 70 °C, and a mixture of 65 μl TOP:Te (0.13 mmol) in 700 μl oleylamine was quickly injected. After 90 s of QD growth, the reaction was quenched in a mixture of 200 μl 1-dodecanethiol, 200 μl tri-n-octylphosphine and 4 ml tetrachloroethylene. The HgTe QD dispersion was purified by precipitation of QDs with 6 ml methanol and centrifugation at 4,000 rpm (~2,200 maximum relative centrifugal force) for 1 min. The supernatant was discarded and the QDs were dispersed in 1 ml tetrachloroethylene. Three drops of oleylamine and three drops of 1-dodecanethiol were added to the dispersion followed by the addition of 1 ml acetone and three drops of a mixture of 10 ml 2-propanol and 50 mg didodecyldimethylammonium bromide to increase the QD stability 32 . For QD precipitation, 800 μl methanol was added, followed by centrifugation at 4,000 rpm (~2,200 maximum relative centrifugal force) for 1 min. The supernatant was discarded and the QDs were dispersed in chlorobenzene and filtered through a 0.2 μm polytetrafluoroethylene syringe filter.
Waveguide fabrication
The waveguide was fabricated by using an amplified Ti:sapphire femtosecond laser system (Spitfire, Spectra Physics): it delivered 120 fs pulses (Fourier-transform limited) at a central wavelength of 795 nm and operated at a repetition rate of 1 kHz. The beam power was finely controlled by a half-wave plate and a linear polarizer, followed by a calibrated neutral density filter and was focused by a ×40 (numerical aperture, 0.65) microscope objective. The sample was placed in a computer-controlled XYZ stage (0.05 μm precision) to scan the sample in the focal region of the objective, describing the desired trajectories to fabricate a 'U'-shaped cladding consisting of about 30 parallel damage tracks. A mean beam power of 0.17 mW (estimated after the microscope objective) was set as the optimum value for fabrication, and the scanning velocity was set to 500 μm s -1 to obtain continuous tracks along the waveguide (good spatial overlap between consecutive pulses) but minimizing the stress induced in the crystal by irradiation.
Device fabrication
For the bottom electrode fabrication on top of the waveguide, briefly, a PMMA double layer was fabricated by spin coating 50 K PMMA 4% in anisole at 4,000 rpm for 45 s, followed by 3 min annealing at 180 °C. Subsequently, 950 K PMMA 2.25% in anisole was spin coated at 4,000 rpm for 45 s followed by 5 min annealing at 180 °C. Espacer 300Z was spin coated at 4,000 rpm for 45 s and subsequently annealed for 3 min at 110 °C. The desired structures were exposed by electron-beam lithography (30 kV, 10 μm aperture, 4 nm step size, dose of 350 μC cm -2 ). After exposure, the sample was stirred in water for 30 s, developed for 60 s in a mixture of MIBK:2-propanol (1:3), rinsed for 30 s in 2-propanol and dried with a nitrogen drying gun. Subsequently, 2 nm chromium and 40 nm gold were deposited by electron-beam-assisted thermal evaporation. After liftoff at 50 °C in acetone, the sample was rinsed in 2-propanol and dried with a nitrogen drying gun. The sample was cleaned in an oxygen plasma cleaner for 60 s at 1 mbar.
The QD thin film was fabricated by layer-by-layer deposition at ambient conditions: HgTe QD dispersion was spin coated at 3,000 rpm for 45 s, followed by spin coating a ligand exchange solution (10 ml 2-propanol, 200 μl HCl(aq) and 200 μl 1,2-ethanedithiol) at 3,000 rpm for 45 s. Then, 2-propanol was spin coated at 3,000 rpm for 45 s for rinsing the sample. This process was repeated four more times, resulting in a QD layer thickness of 170 nm.
A second substrate was prepared by electron-beam-assisted thermal evaporation of 100 nm copper on top of a Si/SiO 2 wafer. A PMMA double layer was spin coated on top of copper: 50 K PMMA 4% in anisole at 4,000 rpm for 45 s followed by 3 min annealing at 180 °C. Subsequently, 950 K PMMA 2.25% in anisole was spin coated at 4,000 rpm for 45 s followed by 5 min annealing at 180 °C. After spin coating, the PMMA was scratched away from the edges of the sample. This allows access of the copper etchant solution to the sandwiched copper layer. The PMMA/Cu/SiO 2 /Si sample was placed in a water-based ammonium peroxodisulfate solution (25 g per 100 ml). Overnight, the copper was completely etched away, and the PMMA floated on top of the copper etchant solution. The copper etchant solution was then replaced with ultrapure water. The water was further replaced three more times over 4 h with fresh water to ensure a clean backside of the floating PMMA.
The floating PMMA was fished with the HgTe QD/waveguide sample. The transferred PMMA/HgTe QD/waveguide sample was dried at ambient conditions, which took about 10 min. The design of the top electrode was written by electron-beam lithography (30 kV, 10 μm aperture, 4 nm step size, dose of 350 μC cm -2 ) into the PMMA double layer. After development for 60 s in a developer (MIBK:2-propanol (1:3)), rinsing with 2-propanol and drying with a nitrogen drying gun, 60 nm gold was deposited by electron-beam-assisted thermal evaporation. Subsequently, a liftoff was performed in 50 °C warm acetone; afterwards, the sample was rinsed in 2-propanol and dried with a nitrogen drying gun.
Waveguide illuminated sample setup
The sample was mechanically fixed on a substrate holder. A free-space laser (1,510-1,587 nm; 6328 tunable diode laser, New Focus) was mechanically modulated with an optical 50/50 chopper and coupled into an optical fibre. The end of the optical fibre was stripped from its cladding, cleaned, cleaved and mounted on an XYZ mechanical stage (M-VP-25 XL, Newport) to align the optical fibre with the LiNbO 3 waveguide. On the other end of the waveguide, a gold-coated mirror was mounted on a 100-μm-travel-range piezo-stage (P-517.3CL, Physik Instrumente).
The sample was contacted with two micromanipulators and typically biased with 50 mV (2614B, Keithley). The modulated photosignal was amplified over a 100-kΩ-load resistor and measured with a lock-in amplifier (SR860, Stanford Research Systems), receiving the lock frequency from a mechanical chopper (27 Hz). The d.c. output voltage signal of the lock-in amplifier was programmed to deliver a driving Nature Photonics Article https://doi.org/10.1038/s41566-022-01088-7 voltage for the piezo-stage. One part of the measured photosignal is dependent on the mirror position, whereas the second part is stray light in the sample, which is not dependent on the mirror position. The undesired background was subtracted from the photosignal. The mirror travel distance was multiplied by 2 to obtain the optical beam path difference, followed by fast Fourier transformation.
In the case that two lasers were coupled, a fibre-coupled free-space laser (1,510-1,587 nm; 6328 tunable diode laser, New Focus) and a fibre-coupled laser (1,270-1,330 nm; TLB-6724-P, New Focus) were coupled with a wavelength-division multiplexer (1,310 and 1,550 nm; WD1350A, Thorlabs) into a single optical fibre. Also, in this experiment, the sample was contacted with two micromanipulators and biased with 50 mV (2614B, Keithley). The fibre-coupled light could not be modulated by a mechanical chopper, and therefore, the modulation was performed by vibrating the mirror. The lock-in output voltage was programmed to deliver a driving voltage (d.c. with a sinusoidal a.c. component) for the piezo-stage. The a.c. component of the stage was about 100 nm (r.m.s.). The modulation frequency was also supplied by the lock-in amplifier and we chose 27 Hz. In this experiment, the measured photosignal (measured over 100 kΩ resistor by the lock-in amplifier) is the derivative of the stationary wave due to the a.c. modulation of the stationary-wave position underneath the photodetector. Undesired stray light does not contribute to the overall photosignal as it is not frequency modulated by the mirror or reflected away from the photodetector. As the photosignal oscillates around zero, a phase jump by 180° is observed with the lock-in amplifier. These 180° phase jumps were normalized to jump from 1 to −1 (δ norm = cos ( (δ−δ 0 )× 180 )). The normalized phase was multiplied with the amplitude to give the phase-corrected photosignal. The mirror travel distance was multiplied by 2 to obtain the optical beam path difference, followed by fast Fourier transformation.
Photoresponse setup
Light from a broad light source was mechanically modulated (MC2000B-EC, Thorlabs) and optically monochromated (SpectraPro HRS-300, Princeton Instruments; gratings, 150 Grooves mm −1 and blaze wavelength of 0.8 μm; 150 Grooves mm −1 and blaze wavelength of 2.0 μm). Higher-frequency orders were filtered out with long-pass filters (780, 1,000 and 1,500 nm). The beam was collimated and divided into a reference beam characterized by a reference detector (UM-9B-L, Gentec-EO) and an illumination beam for the sample. The sample was biased with 50 mV (2614B, Keithley) and the photosignal was measured over 100-kΩ-load resistance with a lock-in amplifier (SR865, Stanford Research Systems).
Noise setup
The sample was biased with a battery-powered current amplifier (SR570, Stanford Research Systems), and the drain current was amplified with the same amplifier and subsequently measured with a data acquisition board (USB-6281, National Instruments) at a sampling rate of 625 kHz. A 40 kHz low-pass filter was employed. The d.c.-current offset of the drain current was removed, and power spectral densities of 385 one-second-long time traces were calculated and subsequently averaged. The 50 Hz net frequency was manually removed from the result.
Calculation of responsivity and specific detectivity
The irradiance impacts perpendicular on the photodetector through free space. Here R = where I ds is the drain current (9.2 × 10 −11 A) and i n /I ds is the currentnormalized noise current (4 × 10 −4 Hz −0.5 ).
Toxic and environmental concerns of mercury-containing devices
If the complete waveguide surface area (<100 μm × 100 μm) is covered with a 180-nm-thick HgTe film (not taking QD ligands and packing density of the QDs into account), it would result in a volume of 1.8 × 10 −9 cm 3 HgTe equivalent to about 10 ng of mercury. This is far less compared with canned tuna (about 200 μg kg -1 on average) 33 . Although our device requires a reasonably small amount of highly toxic mercury, we hope that in the long run, all the toxic elements in the device will be replaced with more benign elements. Furthermore, the release of mercury into the environment should be minimized by implementing rigorous recycling protocols. | 7,148.4 | 2022-10-24T00:00:00.000 | [
"Physics",
"Engineering"
] |
Accessibility Dynamics and Regional Cross-Border Cooperation (CBC) Perspectives in the Portuguese—Spanish Borderland
: Accessibility plays a major role in achieving sustainable transport, and therefore urban and regional sustainability. The urban public transport system promotes mobility and realizes a large part of urban movements. Moreover, improving accessibility in order to promote sustainable transport requires the application of new concepts and indicators as a powerful tool in the process of creating a balanced urban transport system. In this regard, one of the main goals of this research is to present an overview of the relevant accessibility indicators and assessment of accessibility in regional Cross-Border Cooperation (CBC) in order to transcendence challenges and obstacles for sustainable transportation in these regions along of Portuguese-Spanish border. This paper focuses on the accessibility of cross-border cooperation scenarios along the border regions of Alto Alentejo (Portugal) and Badajoz (Spain) where the Case Study Research Method (CSR) made it possible to recognize accessibility as a key factor in territorial success. Also, accessibility analysis can assess improvements as well as regional imbalances. In addition, this methodology can be used to identify missing links, which requires new investments enabling long-term sustainability.
Introduction
In recent decades, EU policies have been moving towards increasing cross-border cooperation in order to exploit all the potential of border areas [1][2][3][4][5]. Although the Trans-European Transport Network (TEN-T) has made a tremendous contribution to increasing the provision of transport infrastructure and improving transport services, it often seems that peripheral and border regions are poorly connected and their accessibility is reduced relative to central regions [6][7][8]. The situation is similar to the international level, which results in many internal borders of the EU becoming its inner periphery [9,10].
Most of the cross-border region, as well as Alto Alentejo (Portugal) and Extremadura-Badajoz (Spanish side of the border) are marked by an overall weak urban network, low-density settlements, continued population losses and fragility in the economic structure, as well as weaker connections between users and services. In fact, many experiences in cross-border public services have not been implemented successfully in these territories, mainly due to the following obstacles: political borders, many administrative obstacles, and effects related to economic discontinuities and natural obstacles [11,12].
A well-planned accessible and public transportation network between cities is pivotal for their sustainable development [13][14][15]. Accessibility is central to the concept of achieving more sustainable urban transportation and improving the sustainability of cities and regions [16][17][18][19]. In fact, many European CBC Projects have demonstrated their success [20][21][22]. Recent studies and academicians recognize accessibility as one of the most significant factors for territorial development regarding CBC projects in cross border regions [23][24][25][26][27][28][29][30].
Considering the classification criteria of inner periphery presented in [8] these border regions (Alto Alentejo and Extremadura-Badajoz) meet all of them: higher travel time to regional centers is needed, poor access to services-of-general-interest, municipalities having low economic performance, constraining the purchasing power of the population and also the access to services [11,12]. Based on the exposed, this article aims to assess and research the relevance of the accessibility concept in the Spanish-Portuguese border regions of Alto-Alentejo and Extremadura-Badajoz. Besides, this paper aims to propose a theoretical framework which consider the one segment (accessibility) of multidimensionality of the concept of sustainable transportation in borderlands -helping to provide the basis for the regional main-actors and decision makers.
Drawing upon professional, academic and ESPON projects [12,31,32] this article analyses the actual indicators of accessibility, and also assesses the accessibility levels as a factor to achieve more sustainable regional transport in this border territory.
Although significant progress has been made in Spain and Portugal cross-border transportation in the last decades in term of developed TENt networks and many CBC projects, cross border public transport and the provision of public services have received less attention that accessibility in this area makes unsustainable. Therefore, the following hypotheses were formulated: Different accessibility concepts as a territorial aspect of different modes of transport have different dynamics and perspectives in cross-border cooperation at regional and local level. Therefore, the following hypotheses were formulated: Which trends in regional accessibility have been the most relevant? How can we know that accessibility being sustainable and what can we do about it in the border area? Which indicators of accessibility can be a performance metric for sustainable transport? What services are provided in the case study areas? What are negative factors cause the slow development of CPS in the case study areas? What is the development of potential and future needs for CPS in the case study regions?
Literature Review
The current patterns and dynamics that are going on in the border regions remains unclear after economic barriers were eliminated [33][34][35][36][37]. "The processes of the European Union (EU) integration and enlargement have produced a new regional socioeconomic map in Europe. Border regions, in particular, have been put in a state of flux" [33]. Peyrony and Denert [35], in their consideration of Cross-Border Planning emphasize how it is important for EU regions to have their own institutional policy for border regions. According to [36] "cross-border integration does not derive from the mere opening of national borders that it supposedly helps at the same time to remove, but stems from the strategic Sustainability 2020, 12,1978 3 of 20 behavior of actors who actively mobilize borders as resources". Thus, [38] conducted an Internet public consultation (2015-2016) on the border obstacles that showed that EU citizens are considered "legal and administrative" type of barriers (language and transport) major obstacles in their daily movement across the border [33] (Figure 1). policy for border regions. According to [36] "cross-border integration does not derive from the mere opening of national borders that it supposedly helps at the same time to remove, but stems from the strategic behavior of actors who actively mobilize borders as resources". Thus, [38] conducted an Internet public consultation (2015-2016) on the border obstacles that showed that EU citizens are considered "legal and administrative" type of barriers (language and transport) major obstacles in their daily movement across the border [33] (Figure 1).
On the other hand, many CBC projects across EU boundaries, have proved to be very successful. [16]. Example of good practice are the Projects b-solutions, where the Association of European Border Regions (AEBR) and The Directorate-General for Regional and Urban Policy [38] strive to be closer to local administrations in border areas with the initiative to collect information with a bottoms-up approach in which CBC practitioners can expose what obstacles they encounter when trying to realize projects with the neighboring countries. Starting from such previous experiences, [22] presented a selected sample, incorporating a global analysis sample of best-selected experiences in order to confirm and reinforce previous global views. One of the analyzed active Euroregions is Alentejo-Centro-Extremadura Euroregion (EUROACE).
Based on recent studies and research [1][2][3]18,[38][39][40][41], the activation of cross-border spaces depends on many factors that enhance cross-border interaction: cooperation's across modes of transport and operators as well as the accessibility of public transport services with appropriate scheduling for users in both CBC forming areas [19].
The accessibility of the transport system is a prerequisite for social and economic development, as it implies access to basic goods and services. In order to be sustainable, transport must be of high quality, safe, accessible to all, contributing to greater mobility, environmentally and economically sustainable, requiring accessible and environmentally and economically satisfactory transport systems [19].
Basic principles of development (enhancing well-being and equity) and sustainability (preserving natural and human capital) should be imperative for sustainable transport trends and policies [19,42,43], but, we often have a situation of open borders with uncoordinated public transport [44]. Without effective cross border passenger transport the principle of free movement of people within the EU cannot be fully realized: "especially passenger transport is not provided, then those EU citizens who cannot afford personal transport have no chance to enjoy the right of mobility, employment, and the other services in the neighbor country. For CB commuting public transport is of great importance, and in case of the existence of administrative barriers are needed strong economic factors [34,45].
According to [7], border regions are often peripheral and less developed in terms of transport infrastructure than the rest of the country for a number of reasons: sometimes these are the nature of On the other hand, many CBC projects across EU boundaries, have proved to be very successful. [16]. Example of good practice are the Projects b-solutions, where the Association of European Border Regions (AEBR) and The Directorate-General for Regional and Urban Policy [38] strive to be closer to local administrations in border areas with the initiative to collect information with a bottoms-up approach in which CBC practitioners can expose what obstacles they encounter when trying to realize projects with the neighboring countries. Starting from such previous experiences, [22] presented a selected sample, incorporating a global analysis sample of best-selected experiences in order to confirm and reinforce previous global views. One of the analyzed active Euroregions is Alentejo-Centro-Extremadura Euroregion (EUROACE).
Based on recent studies and research [1][2][3]18,[38][39][40][41], the activation of cross-border spaces depends on many factors that enhance cross-border interaction: cooperation's across modes of transport and operators as well as the accessibility of public transport services with appropriate scheduling for users in both CBC forming areas [19].
The accessibility of the transport system is a prerequisite for social and economic development, as it implies access to basic goods and services. In order to be sustainable, transport must be of high quality, safe, accessible to all, contributing to greater mobility, environmentally and economically sustainable, requiring accessible and environmentally and economically satisfactory transport systems [19].
Basic principles of development (enhancing well-being and equity) and sustainability (preserving natural and human capital) should be imperative for sustainable transport trends and policies [19,42,43], but, we often have a situation of open borders with uncoordinated public transport [44]. Without effective cross border passenger transport the principle of free movement of people within the EU cannot be fully realized: "especially passenger transport is not provided, then those EU citizens who cannot afford personal transport have no chance to enjoy the right of mobility, employment, and the other services in the neighbor country. For CB commuting public transport is of great importance, and in case of the existence of administrative barriers are needed strong economic factors [34,45].
According to [7], border regions are often peripheral and less developed in terms of transport infrastructure than the rest of the country for a number of reasons: sometimes these are the nature of the areas themselves, sometimes the lack of a critical mass that could justify investment in transport, lack cooperation of the authorities, which leads to non-efficiently policies [8]. Maggi et al. [46] and Lopez et al. [47], emphasize that there is a need for cooperation between states and it would reduce the occurrence of "missing networks and isolated areas in the future" [8]. This is impossible if each country solves its own problems. The relationship between accessibility and development has been exploited especially when it comes to evaluating investments in major infrastructure projects [4]. The most used definition of accessibility is: "accessibility indicators describe the location of an area concerning opportunities, activities or assets existing in other areas and in the area itself, where 'area' may be a region, a city or a corridor" [48].
There is no single approach to measuring accessibility. Accessibility indicators "have generally been used to evaluate the performance of transport networks" and play "a key role in evaluating the competitive advantage of some locations due to the quality of their transport infrastructure" [28]. The classification has been developed by [49]. They suggested four basic perspectives: (1) infrastructure-based measures (focusing on time, congestion and operating speeds in the transport network (road or rail), (2) activity-based measures, (3) person-based measures (opportunities attainable by an individual, i.e., the individual's 'freedom to participate in activities under given constraints') [28]. (4) utility-based measures ('measured at the individual level and assuming that users aim to maximize the benefit of their travel after accounting for the cost' [48][49][50]. On the other hand, [14,50] consider the subjective perception as a key element for the evaluation of accessibility. Handy and Niemeier [14] argue that there is a need to incorporate 'how residents perceive and evaluate their community' and 'the uses and perceptions of the residents, workers, and visitors of an area' [51].
Furthermore, the population potential indicator or the daily accessibility indicator measure reachable population or activities, while the location indicator or network efficiency indicator use the population of destinations as the weighting of travel cost measures [47,52].
Potential accessibility is one of the most important indicators for measuring accessibility by using different modes of transport [30]. This indicator was developed by ESPON and recalculated in 2006 to retroactively adjust to NUTS3 calculations so that it can be possible to compare results for two years. However, the most of data available in ESPON's public database and most of them are outdated and are available mainly for the 1999 version of NUTS [10,31]. The potential of accessibility indicators not only measures transport networks, but also takes into account travel time (dependency function) and reachable population (activity function), thus giving overall accessibility to each region [28,30].
The concept, pattern and accessibility models have been developed through a large number of studies and projects. The main ones, among many other project and strategies, includes: [32] as an innovative ESPON project (include 18 European CBC areas), has applied results from ESPON with a focus on accessibility and connectivity. In the [53], the analysis of accessibility and infrastructures within EUROACE region in the Spanish-Portuguese border space was also conducted [16,23,29,[54][55][56].
Cross-border public services have become increasingly important by opening up the European internal market [57,58]. Increasing interest in CPS may also be influenced by an observable "come-back" of municipal public service provision in Europe that gives rise to a need for better coordinating service provision across national borders [58]. The ESPON project [12], through one analytical concept of case studies, made it possible to clearly define or delineate the exact nature and scope of cross-border public service delivery activities. The results of the analyzes show that more than five or ten CPSs can be found at the borders of Benelux, France, Germany, Switzerland) and the Nordic countries, with two exceptions along the Czech-German (Elba-Labe region) and Austrian-Germany (Salzburg), which is not the case with other borders. This analysis emphasizes the importance of considering the real status and needs of CPS in terms of overcoming future challenges.
Methodology
Considering the aim of the research, a methodological framework based on a case study analysis method [59], as well as other direct and indirect method analysis, have also been applied to the study areas. The indicators for the case study accessibility analyzes are shown in Table 1. This indicator takes into account travel time (dependency function) and reachable population (activity function), thus giving overall accessibility to each region market [31,32]. The accessibility analysis uses data available in the ESPON database [10,13] for different modes of transport (the database was updated in 2006, which allowed us to analyze for two different and comparative years). However, several accessibility indicators used at regional and urban level (which are necessary for further accessibility analyzes at Euro-city level) are not available. Also, daily availability indicators for 2001 and 2006 are not available in the ESPON database [10].
Case Study Analyses
Following the method used previously by [16,23,29], and based on a previous study that explores expert attitudes and perceptions towards the identification of a set of critical factors for the success of CBC projects were assessed, described and analyzed, enabling the identification of 14 critical factors to achieve success in development projects based on CBC principles. In that research 20 European CBC case studies (Newry (IE [23]. After identifying critical factors for territorial success on the basis of a case analysis, the acquired critical factors for the Euro city Elvas-Badajoz study area (NUTS3 level: Alto Alentejo -Badajoz) were applied in further analysis.
According to [60], this typology of case study may be considered as within the category Hypothesis-Generating Case Studies, after the method was used in order to "examine one or more cases for the purpose of developing more general theoretical propositions, which can then be tested through other methods" [29].
The methodology was developed through four main phases ( Figure 2). The methodology was developed through four main phases ( Figure 2). The final phase of the methodological framework is the analysis and assessment of regional accessibility and the provision of public services in cross-border cooperation. The phases are: data collection; criteria for selecting case studies; analysis of case studies, which could be schematized as follows.
Besides the aforementioned pre-established criteria, the selected projects were required so as to meet seven specific principles, some of which were adapted from the study developed by [23]: • Cities must have a record of previous work on CBC.
• The CBC project should consider the integration of environmental, sociocultural, and economic development goals, as part of a singular development strategy. • Cities should demonstrate relationships with multiple stakeholders organized in a group association created to develop and strengthen aspects inherent to CBC, and development objectives. • The distance between cities could not be greater than 60 km. • At least one of the cities should be a medium-sized city. • There should be considerable connectivity-movement between cities. • There should be considerable the low formal number of CPS • Eurocity marketing and advertisements must be previously identified as a critical factor for territorial success.
As mentioned before, the following criteria were used to analyze the Iberian area, after which the results of the case study analysis and the factors of territorial success determined the choice of the Iberian study area, Alto Alentejo-Badajoz (NUTS level 3). These cross-border regions are characterized by low density, poorly developed transport infrastructure and services, lack of critical mass of the population, which hampers the development of mobility when it comes to the realization of public transport [12,61]. Accessibility assessment as a critical factor is further analyzed on NUTS 3 level in the borders regions of Alto Alentejo (Portuguese) and Badajoz (Spain). According to the [31], the potential accessibility is an indicator that relates two functions: the activities and the travel time. As for the travel time between centroids, by different modes of transportation with the population (road, train, and air) was synthesizing values of the potential accessibility for each NUTS 3 of the ESPON space.
Analyses and identification of the current CPS in the region, their topics, governance arrangements and barriers for them to work and further possibilities are based on the ESPON project cross-border public services, and target analyses [12] based on the ESPON CPS 2018 on-line survey. Case study areas Alentejo-Extremadura -Andalusia and their future perspectives have been analysed in-depth. Analyses are done through 11 criteria [12] for defining CPS and field of intervention in some policy area. The final phase of the methodological framework is the analysis and assessment of regional accessibility and the provision of public services in cross-border cooperation. The phases are: data collection; criteria for selecting case studies; analysis of case studies, which could be schematized as follows.
Besides the aforementioned pre-established criteria, the selected projects were required so as to meet seven specific principles, some of which were adapted from the study developed by [23]: • Cities must have a record of previous work on CBC.
•
The CBC project should consider the integration of environmental, sociocultural, and economic development goals, as part of a singular development strategy.
•
Cities should demonstrate relationships with multiple stakeholders organized in a group association created to develop and strengthen aspects inherent to CBC, and development objectives.
•
The distance between cities could not be greater than 60 km.
•
At least one of the cities should be a medium-sized city.
•
There should be considerable connectivity-movement between cities. • There should be considerable the low formal number of CPS • Eurocity marketing and advertisements must be previously identified as a critical factor for territorial success.
As mentioned before, the following criteria were used to analyze the Iberian area, after which the results of the case study analysis and the factors of territorial success determined the choice of the Iberian study area, Alto Alentejo-Badajoz (NUTS level 3). These cross-border regions are characterized by low density, poorly developed transport infrastructure and services, lack of critical mass of the population, which hampers the development of mobility when it comes to the realization of public transport [12,61]. Accessibility assessment as a critical factor is further analyzed on NUTS 3 level in the borders regions of Alto Alentejo (Portuguese) and Badajoz (Spain). According to the [31], the potential accessibility is an indicator that relates two functions: the activities and the travel time. As for the travel time between centroids, by different modes of transportation with the population (road, train, and air) was synthesizing values of the potential accessibility for each NUTS 3 of the ESPON space.
Analyses and identification of the current CPS in the region, their topics, governance arrangements and barriers for them to work and further possibilities are based on the ESPON project cross-border public services, and target analyses [12] based on the ESPON CPS 2018 on-line survey. Case study areas Alentejo-Extremadura-Andalusia and their future perspectives have been analysed in-depth. Analyses are done through 11 criteria [12] for defining CPS and field of intervention in some policy area.
Data Analyses
Potential accessibility indicators for 2001 [31] were obtained according to the Accessibility Model based on Schurman et al. which uses the centroids of the NUTS-3 region as origin and destinations to Sustainability 2020, 12,1978 7 of 20 calculate minimum paths, i.e., minimum travel times between NUTS-3 region centroids. The value of the potential accessibility indicator for each NUTS-3 region is calculated by summing the population in all other regions. [10,16,17,28,31,53].
The analysis was developed for a case study where several data sources are used to evaluate the actual accessibility situation (summarized in Table 1). These data will also show that accessibility as a critical factor reflects cross-border cooperation projects and sustainable transport.
Research results from ESPON's targeted and applied analysis were used for this analysis. Road, rail, air, daily access and multimodal accessibility indicators are analyzed and summarized. [31,53,62].
We emphasize that the potential accessibility indicators for years 2001 and 2006 in the present ESPON database cannot be directly compared to the potential accessibility indicators for 2011 because these are applied analyses for two different ESPON projects [31,53]. Data for 2011 used because for a later period the data are not readily available in the ESPON database (see Table 1). All indicator values are expressed as an index, i.e., associated with ESPON average [10,16].
Regarding data analyses for cross-border public services there are not many experiences of cross-border services, namely in public services provision, due to the obstacles (Online ESPON CPS Survey 2018) [10]:
•
Obstacles associated with political borders linked to legal and administrative questions; • Effects associated with economic discontinuities and natural obstacles (weak urban network, and low density of population and settlements).
Garrinhas [63] added a third obstacle linked to cultural barriers coming from language differences. In order to assess the development of cross-border public services, in this article we used results of the targeted analysis undertaken by ESPON on this topic is used throughout CPS Target analyses [10,12,53].
Potential Accessibility Indicators
Concerning travel time and other indicators, the exact methodology is available in the ESPON database metadata. It is also available in the final report of the European Spatial Planning Observation Network (ESPON) project where potential accessibility for all modes of transport was obtained. Values for multimodal accessibility were obtained synthesizes all different modes-a comprehensive indicator. According to ESPON, multimodal accessibility is the accessibility potential "of a log sum that is collected across the road, rail and air" [10,31]. Potential accessibility in the ESPON database has been calculated and displayed for two different years, values were standardized to the ESPON average for 2001 and 2006. Each ESPON average is set to 100, and regional values are transformed accordingly. The change in accessibility index was used, which means that it is possible to see the development of infrastructure in this period. Differences in index values show a change in the position of regions relative to other regions. "Positive values express improvement in the relative quality of localization, while negative values express a loss in relative locational quality" [10].
For this indicator, the 2001 accessibility values are standardized to the ESPON average for that year and from 2006. Each ESPON average is set at 100, and regional values are transformed accordingly. A change in accessibility index was used. Differences in index values show a change in the position of regions relative to other regions. "Positive values express improvement in the relative quality of localization, while negative values express a loss in relative locational quality" [10,53].
In [10,31], "potential accessibility is an indicator linking the activities to be achieved with the travel time required to achieve them." It functions as follows: 'Ai' (1) is the availability of area 'I', 'Vj' is activity V to be reached in area 'j', and 'c ij' is the generalized cost of reaching area 'j' from area 'I'. "Ai" is the total number of activities available on "j", tends to be easy to switch from "I" to "j". "The interpretation is that the more attractive destinations in areas 'j' and the more accessible areas 'j' than area 'I', the greater the area 'i' [10,31].
In the [31], the potential accessibility is an indicator that relates the activities to be reached with the travel time it takes to reach them. 'Ai' is the total of the activities reachable at 'j' weighted by the ease of getting from 'I' to 'j'. "The interpretation is that the greater the number of attractive destinations in areas 'j' is and the more accessible areas 'j' are from the area 'I', the greater is the accessibility of area 'i' [10,31]: Destination size is measured by population or economic indicators such as GDP. Potential accessibility is a construct of two functions: the activity function representing the activities or opportunities to be reached and the impedance function representing the effort, time, distance or cost needed to reach them [10,62].
In this accessibility model, the minimum travel time across a network between the NUTS-3 region centroids is calculated. For each NUTS-3 region, the value of the potential accessibility indicator is calculated by summing up the population in all other European regions, including those outside ESPON space, weighted by the travel time to go there [10,16,31].
The values of accessibility indicators, the changes over time, and the absolute level of accessibility and index change of accessibility are presented in Result chapter.
Daily Accessibility Indicators
Daily accessibility indicators present the number of people that can be reached within 5 h travel time by fastest mode of road and rail)
Study Area
For this article, the geographical delimitation of the studied area includes: on the Portuguese side, the Alto Alentejo that corresponds to statistical NUTS 3 Alto Alentejo and on the Spanish side, NUTS3 region Badajoz (Figure 3). While on the Spanish side we observe an increase in population, and in Portugal a decrease in natural population growth rates, the whole CBA area can be said to be at a level close to stagnation [10,12,61]. Demographic framework is shown in Table 2. Historical and cultural factors are the basis of the cooperation between these territories separated by only 20 km. In the last century, until the seventies, the political regimes of both countries limited the formal border crossing of people and goods, so smuggling was the main way to overcome this limitation.
Besides the economic motivations, there were also political ones. But in the last three decades, changes in the political regimes and EU integration have promoted cross-border mobility [12]. The Elvas-Badajoz axis was historically linked to all these historical facts, working as an "entrance-exit door" for Spanish-Portuguese people. "More recently, a new dynamic of flows and cooperation has emerged in these territories, gaining personality in the Euro city arrangement signed in 2013. Currently, Campo Maior has been joined with both cities creating the new Eurocity Badajoz-Elvas-Campo Maior" [12].
The importance of the primary sector in both territories, reinforces the lower human habitation along the border. These specific characteristics, define economic and demographic discontinuities and reinforce the legal and administrative obstacles and the language barriers. According to the ESPON DEMIFER Project (2010), the Alto Alentejo is considered an "ageing challenge region" while Extremadura is considered a "challenge of labour force region" [10,61]. While on the Spanish side we observe an increase in population, and in Portugal a decrease in natural population growth rates, the whole CBA area can be said to be at a level close to stagnation [10,12,61]. Demographic framework is shown in Table 2. Historical and cultural factors are the basis of the cooperation between these territories separated by only 20 km. In the last century, until the seventies, the political regimes of both countries limited the formal border crossing of people and goods, so smuggling was the main way to overcome this limitation.
Accessibility
Besides the economic motivations, there were also political ones. But in the last three decades, changes in the political regimes and EU integration have promoted cross-border mobility [12]. The Elvas-Badajoz axis was historically linked to all these historical facts, working as an "entrance-exit door" for Spanish-Portuguese people. "More recently, a new dynamic of flows and cooperation has emerged in these territories, gaining personality in the Euro city arrangement signed in 2013. Currently, Campo Maior has been joined with both cities creating the new Eurocity Badajoz-Elvas-Campo Maior" [12].
The importance of the primary sector in both territories, reinforces the lower human habitation along the border. These specific characteristics, define economic and demographic discontinuities and reinforce the legal and administrative obstacles and the language barriers.
Accessibility
Throughout the analysis of the results of potential accessibility by road, rail, air and multimodal (Table 3), it is possible to identify cross-border differences in this territorial profile. "For each NUTS-3 region, the population in all destination regions is weighted by the travel time required" [10,16] to reach the destination. "The weighted population is summed up to the indicator value for the accessibility potential of the origin region. All indicator values are expressed as an index, i.e., related to the ESPON average" [10,16].
Aiming to summarize the collected data of the case study area, two tables have been developed related to potential indicators by road, rail, air, multimodal accessibility and by analyzing daily indicators, respectively.
Values of Badajoz's average potential accessibility by all modes of transport is higher than Alto Alentejo's. However, the values of potential accessibility for Elvas (PT182) and Badajoz (ES431) appear to improve over time [10,16]. Figure 4 presents the absolute value of potential road accessibility in 2006 expressed as the index value. The EU27 average is set at 100 [10]. The clear increase in road potential accessibility related to completed road projects is presented by the accessibility situation in Table 3 and Figure 4.
In terms of potential rail accessibility, ES431 shows a higher rail accessibility potential (index), especially in the 2011 year, while PT182 describes lower values. Regarding the Potential Accessibility Index 2001-2006, there is a slight increase in Badajoz and Elvas. As a result of infrastructure improvements, after the implementation of EU projects, the differences have more than ten points of the index in 2011.
Potential air accessibility gives a different situation from the accessibility by inland modes: both regions have high values, slightly higher in Badajoz than in Elvas. Regarding multimode indicators, the situation is similar due to the fact that their international airports improved their accessibility.
Changes in the index of accessibility show the status of potential accessibility during two different years, reflecting the situation and changes in the infrastructure in that period [10]. Regarding the temporal change during the 2001-2006 period, Badajoz demonstrates slightly higher index-change for road and rail, while Elvas has the worse position by one index point. Slightly negative values of the standardized index can be found in Elvas and Badajoz for air and multimode. According to [64] positive index values represent the better relative quality of the location, while negative values reduce the quality of the location [64]. Table 4 shows the change of the index values of potential accessibility between 2001 and 2006.
Aiming to summarize the collected data of the case study area, two tables have been developed related to potential indicators by road, rail, air, multimodal accessibility and by analyzing daily indicators, respectively.
Values of Badajoz's average potential accessibility by all modes of transport is higher than Alto Alentejo's. However, the values of potential accessibility for Elvas (PT182) and Badajoz (ES431) appear to improve over time [10,16]. Figure 4 presents the absolute value of potential road accessibility in 2006 expressed as the index value. The EU27 average is set at 100 [10]. The clear increase in road potential accessibility related to completed road projects is presented by the accessibility situation in Table 3 and Figure 4. Through the analysis of daily accessibility indicators (amount of population that can be reached within 5 h travel time by road-rail), Table 5 shows the results which reflect a higher value for daily accessibility by road than rail in 2011. Those differences are higher in Extremadura-Badajoz than in Alto Alentejo-Elvas. The number of population that can be reached within 5 h travel time by fastest mode of the road is 6152400, and only 1972900 by train. These differences are substantial for Elvas but not as high as in Badajoz.
Since 1991 a process of border deactivation has been performed following the instructions of European integration, the development of CBC, and the implementation of programs and Structural Funds, particularly the INTERREG and in line with its condition of the internal community border.
About border deactivation, the minimization of transaction costs is a proven fact, owing to free transit, the elimination of customs, controls, and barriers, and the significant progress made in road infrastructure and cross-border transportation and communication networks. These are determinant factors (and constraints) of the remarkable expansion observed in the traffic of goods, services, and people.
In this process, CBC and its institutions, with their advantages and disadvantages, have played a fundamental role in the territorial channeling of financial resources. Thus, the influence of CBC in the political, administrative, and social landscape of this border area is undeniable. CBC institutions have created a new strand of relations, interactions, and common interests that were previously nonexistent. Thus, they have laid the groundwork for the future and encouraging joint ventures [65].
When it comes to external accessibility, many TENt projects have greatly contributed to the integration of the Iberian Peninsula with the central parts of the EU. They are an important contribution to the ongoing efforts to improve connectivity between the EU center and its peripheral regions and to strengthen the position of the Iberian Peninsula as a Western European gate, this refers to external accessibility. Also until 2004, much of the TENT budget was invested in cross-border sections, this is shown by changing the results of regional accessibility indicators in the 2001-2011 table. The high-speed rail link from the Sines seaport to Madrid passing through the CBA will also have positive effects on the whole region [10,66].
On the other hand, there is internal accessibility in low density territory characterized by low accessibility values due to lack of infrastructure and services [10]. In that case, one could consider the improvement low-density accessibility program based on taking advantage of capacities that are already there, new "multimodal intelligent and flexible transportation"+1 networks, and "alternative forms of service provision" [10].
Cross-border co-operation development policies need to address this issue in terms of promoting a sustainable economy and the attractiveness of these regions through increased accessibility based on a join approach about the transport accessibility [10,16].
Cross-border Public Services
Mobility patterns and cross border public transportation connection in the region need to be analyzed (this could mean analyzing commuting flow and their intensity, or possibilities for common ticket prices or timetables) [10,12] (Table 6). Table 6. Provided CPS Source: ESPON CPS, 2018 [12].
CPS Name in the Policy Area
Border Key Selection Criteria
SP-PT
Service provision in a labor market with a relatively low number of cross-border commuters. Aiming more at promoting cross-border working in a large geographical area along the border. The CPS has been established recently in 2017.
SP-PT
Prevention of risks and improvement of the management of natural resources and promote adaptation to climate change in all sectors Sustainability 2020, 12, 1978 13 of 20 Three CPS were chosen by the regional entity in the Alentejo region to illustrate the future CPS in the region: • Invasive species management system, of climate change, and environmental protection; • Cross-border multimodal freight transport platform, in the field of transport and mobility; • Cross-border mobility observatory, in the field of transport and mobility.
Transport is one of the identified areas by the Regional Commission of Alentejo (CCDR Alentejo, Interview 2017) and by the regions as having great potential to remove cross-border cooperation hurdles. Harmonization and coordination of technical and legal standards and achieving inter-operability in the transport sector as well as the provision of multimodal travel information are high priorities [10,12].
The promotion of networking and flow initiatives and public transport, through the introduction of joint solutions that can be boosted by the use of ICT, is also a priority. Regarding cross-border multimodal freight transport platform priorities, the opportunity to have more rapid access to the sea, through the port of Sines, is of major importance to the border territory and that is dependent on the improvement of the Sines-Badajoz multimodal transport corridor [12,67].
Regarding [9] Eurocity Elvas Badajoz is a solution for overcoming the need to get critical mass for the CPS and the EUROBEC emerges as a project that contributes to Eurocity consolidation and acts through the creation of a solid governance structure open to citizens, with multilevel action. During the previous years of cooperation between Badajoz and Elvas, a large number of projects and actions in the cultural, sports, social, employment, mobility, and infrastructures fields, have been developed. As previously pointed out, the border territory of Alentejo and Extremadura is characterized by demographic and economic activity scarcity. "The recent addition of Campo Maior is a positive aspect of Eurocity enrollment because the capacity for providing services in this border territory is higher and that provides more critical mass to carry out concrete cooperation activities, giving more equilibrium to population distribution and possible demand" [12,67].
An important key feature of this CPS cooperation EUROBEC project is the need to consolidate the structures of governance to formulate the best way to integrate other institutions which operating in this project and improving institutional capacity and efficiency of public administration through CBC [12].
In strategic terms, in addition to passenger transport, the high-speed rail link from Lisbon to Madrid also includes freight services from the port of Sines to Madrid, passing through the CBA directly affecting the greater logistical importance of the Elvas-Badajoz transit axis [10]. In terms of internal accessibility, it is necessary to invest in the development of an integrated low-density accessibility program and in that way also take advantage of existing transportation infrastructure capacity [10].
CBC and its institutions, with their advantages and disadvantages, have played a fundamental role in the financial resources allocation. Thus, the influence of CBC in the political, administrative, and social landscape of the Spain -Portugal borderland is undeniable. CBC institutions have created a new strand of relations, interactions, and common interests that were previously nonexistent. Thus, they have laid the groundwork for the future and encouraging joint ventures [65]. Therefore, in the future, nationals governments should invest not only in national projects, but their priorities should also be cross-border links outside their national borders.
Moreover, transport infrastructure projects could have a substantial impact on the potential accessibility of cross-border regions. The improved use of opportunities provided by the existing INTERREG in this area can play an important coordination role and help solve cross-border accessibility challenges. From a methodological aspect, attention has should be given when looking at changes over time.
According that, the relation between sustainable transport, key issues, and particular performance of accessibility indicators are summarized in the following Table 7 and contains overviews of performance accessibility indicators, on the regional level in CBC areas as well as the possible future challenges facing transport policymakers which contribute to achieving more sustainable transport of passengers. Table 7. Accessibility as one of the pillars of sustainable transport (general and specific performance indicators for regional level). Adapted from [18].
Sustainable targets
• Therefore, planning sustainable accessibility is both a challenge and an opportunity. It is a challenge because there are still many prejudices and practical obstacles that usually cannot be solved at the regional level, and have no priority at the national level. It is an opportunity because it is a basic building block of sustainable transport and it should be further facilitated.
Discussion and Conclusions
This research allows for the analysis of accessibility factors between cities, which in the case studies of European cross-border cooperation projects are considered critical for achieving territorial success [18,23,24,68]. This factor identified in the Eurocity Elvas-Badajoz case study [16,17] through the assessment of the many levels of CBA for accessibility showed the importance of accessibility analysis in cross-border cooperation areas and their change and trends at the Portuguese-Spanish border.
If we look at the quality of the interaction between different modes of transport, through the applied transport policies between 2001 and 2006, we can say that significant improvements are evident, but that there are still inequalities in accessibility values by region and by modes of transport.
Regarding the temporal change during the 2001-2006 period, Badajoz demonstrates a slightly higher index-change for road and rail, while Elvas has the worse position by one index point. A somewhat negative standardized index is found in Elvas and Badajoz for air and multimode. We can conclude that differences have more than a ten-point index in 2011, as a consequence of investing in infrastructure through EU infrastructure projects.
Regarding public transport and regional sustainability, the problem is low quality of public transport and low level of connectivity with TEN-T corridors and transport nodes. Also, there is a difference in the development of mobility systems, some regions have neither the knowledge nor the capacity to plan these systems.
According to the Transport Sustainable Development Principles (2015) [19]: "Transport system improvements should aim to ensure equal access to citizens to reach desired destinations (services, health, recreation) and access (employment, education), regardless of individual wealth, age, gender or possible health conditions resulting in impaired mobility ', which has not been confirmed in the CBA cross-border region of Alto Alentejo -Extremadura-Badajoz.
The results of previous studies [16,17], where public transport/ urban movement, political commitment and cooperation between cities and health have been assessed as issues that have not been adequately addressed, question the creating the project of Eurocity. Including the results obtained during this research, we can conclude that sustainable transport in this cross-border area is a serious problem, which requires the implementation of sustainable solutions in the future.
In strategic terms, the high-speed rail link from Lisbon to Madrid would diminish the remote location of the region, i.e., it would increase external accessibility, also including freight services from the Port of Sines to Madrid, passing through the CBA directly affecting the greater logistical importance of the Elvas-Badajoz transit axis [10]. In terms of internal accessibility, it is necessary to invest in development of public transport and implementing an integrated low-density accessibility program and in that way also take advantage of existing transportation infrastructure capacity) [10].
Similar results were obtained in later published studies regarding the Portuguese-Spanish border area [5,44,[69][70][71][72]. Major differences have been identified between the two sides of the border: Spanish citizens have higher values of accessibility, which lead to higher standards than the Portuguese border population. This unbalance within this borderland, results in a deviation from the desired territorial sustainability. Disparities of accessibility by road, rail, air and multimodal still exist in this area. Despite efforts to increase the infrastructural endowment and thus change the low value of accessibility in recent decades, the periphery of these regions has done its part, as peripheral regions will remain peripheral from the point of view expressed throughout Europe [10]. The Spanish Portugal border area defining as an area where "Potential Accessibility is high at international level and low at the national level") [8] (Figure 5). Portugal border area defining as an area where "Potential Accessibility is high at international level and low at the national level") [8] ( Figure 5).
Figure 5.
Potential Accessibility is high at international level and low at national level. Source: EC-Cross-border transport infrastructure in the EU (2018) [8].
In this border area, the problem is also asymmetric decision level on the cross-border cooperation between a regional entity in Spain, and a central entity in Portugal what present the common difficulty in the provision of a CPS [12]. Regarding ESPON CPS project, the development of the multimodal platform is on the way and its importance could be empowered by the construction of a new rail segment and the requalification of the previous rail line on the Portuguese side, connecting the Badajoz platform to the port of Sines, but also being able to serve the ports of Lisbon and Setúbal. "The requalification of the rail line on the Spanish side, connecting Badajoz to Mérida and Navamoral, could contribute to extending the area of service of this platform and could contribute to a desirable modal transfer from road to rail freight transport. In any case, the schedule Figure 5. Potential Accessibility is high at international level and low at national level. Source: EC-Cross-border transport infrastructure in the EU (2018) [8].
In this border area, the problem is also asymmetric decision level on the cross-border cooperation between a regional entity in Spain, and a central entity in Portugal what present the common difficulty in the provision of a CPS [12]. Regarding ESPON CPS project, the development of the multimodal platform is on the way and its importance could be empowered by the construction of a new rail segment and the requalification of the previous rail line on the Portuguese side, connecting the Badajoz platform to the port of Sines, but also being able to serve the ports of Lisbon and Setúbal. "The requalification of the rail line on the Spanish side, connecting Badajoz to Mérida and Navamoral, could contribute to extending the area of service of this platform and could contribute to a desirable modal transfer from road to rail freight transport. In any case, the schedule of those future infrastructural investments will not make the development of this CPS impossible. Despite the asymmetry in the level of the public entities that participate in this CPS organization, the conjugation of the national objectives and regional ones have made it easier to start it" [12].
The implementation of the mobility observatory has the objective is to inform mobility flows and policies in the border area, in particular in the Eurocity territorial scope. However, it will require "some technical capacities and its effectiveness will depend on the capacity to set up the best strategic option to develop sustainable mobility in the border area". Thus, the regional entity for transports and mobility of Extremadura (SP) and the Instituto da Mobilidade e Transporte (PT) should agree on a legal framework for passenger transport as a cross-border public service. In the CB area, the existence of public transport has the effect of increasing mobility and only strong economic interests can influence to overcome the administrative obstacles for the realization of this mode of transportation [5,45].
Increased accessibility in the CB area can be significantly influenced by transport projects, as well as the benefits and possibilities of INTERREG implementation, and when it comes to the methodological aspect it should be observed how things will go over time [10,66].
The effective passenger transport supply in Elvas-Campo Maior-Badajoz Eurocity is strongly constrained by the passenger transport legislation framework because what could be understood as an urban passenger transport service, is considered as an international passenger transport with all the limitations and impositions to operators and to operate [73][74][75][76]. This is not only a Spain -Portugal borderland problem, but some European actions should also be taken in order to overcome the limitations that this CPS work highlights. | 11,326 | 2020-03-05T00:00:00.000 | [
"Geography",
"Environmental Science",
"Engineering"
] |
Overlapping Ownership, Endogenous Quality, and Welfare
This paper investigates how overlapping ownership a¤ects quality levels, consumer surplus,
rms pro
ts and welfare when the industry is a vertically di¤erentiated duopoly and quality choice is endogenous. This issue is particularly relevant since recent empirical evidence suggests that overlapping ownership constitutes an important feature of a multitude of vertically di¤erentiated industries. We show that overlapping ownership while detrimental for welfare, may increase or decrease the quality gap, consumer surplus and
rmspro
ts. In particular, when the overlapping ownership structure is such that the high quality
rm places a positive weight on the low quality
rms pro
ts, the incentives of the high quality
rm to compete aggressively reduce. This may increase the equilibrium quality of the low quality
rm, which in turn may lead to higher consumer surplus, despite higher prices. JEL Classi
cation: L13; L41. Keywords: Overlapping Ownership, Vertical Di¤erentiation. Duarte Brito<EMAIL_ADDRESS>gratefully acknowledges
nancial support from Fundação para a Ciência e a Tecnologia (UID/ECO/04007/2019). Ricardo Ribeiro<EMAIL_ADDRESS>gratefully acknowledges
nancial support from Fundação para a Ciência e a Tecnologia (UID/GES/00731/2019). Helder Vasconcelos<EMAIL_ADDRESS>gratefully acknowledges
nancial support from Fundação para a Ciência e a Tecnologia (UID/ECO/04105/2019). All remaining errors are of course our own.
We contribute to this strand of the literature by studying the e¤ects of overlapping ownership on the quality choices, consumer surplus, pro…ts and welfare of a vertically di¤erentiated duopoly. This issue is particularly relevant since recent empirical evidence suggests that overlapping ownership constitutes an important feature of a multitude of vertically di¤erentiated industries. See, for example, Schmalz (2018), Newham, Seldeslachts and Banal-Estanol (2018) and Backus, Conlon and Sinkinson (2019) for evidence on the airline, banking, supermarket and pharmaceutical industries. 2;3 We show that when the overlapping ownership structure is such that the high quality …rm places a positive weight on the low quality …rm's pro…ts, the incentives of the high quality …rm to compete aggressively reduce. This may increase the equilibrium quality of the low quality …rm, which in turn may lead to higher consumer surplus, despite higher prices.
The model, the equilibria and the conclusions are presented in sections 2, 3 and 4, respectively. 1 Brito, Ribeiro and Vasconcelos (2019a) show that overlapping ownership can induce product prices and output levels that are even higher and lower, respectively, than those in a monopoly.
2 For a characterization of the importance of overlapping ownership in those industries please see Tables 2, 3 and 4 in Schmalz (2018), Table 1 in Newham, Seldeslachts and Banal-Estanol (2018) and Figure 12 in Backus, Conlon and Sinkinson (2019). 3 We can identify features of an airline such as bag handling, gate location, connecting layover times, ‡ight schedules, in- ‡ight services, legroom, seat characteristics, and ‡ight frequency with the quality of an airline (Barbot, 2004;Brueckner and Flores-Fillol, 2019). We can identify the probability of failure of a bank with the quality of the bank (Vives, 2016). We can identify features of a supermarket such as product assortment, store location, product availability, car parking space, and opening hours with the quality of a supermarket (Aslan, 2019). We can identify the brand name of a pharmaceutical product (even though generics are legislated to be therapeutically identical to branded products) with the perceived quality of the product (Cabrales, 2003).
All proofs are presented in the online mathematical appendix.
Theoretical Model
We follow Wauthy (1996)'s approach and notation. Two duopolists, …rm 1 and …rm 2, sell products of di¤erent quality to a continuum of consumers that have di¤erent valuations for quality. We assume that each consumer is identi…ed by a parameter that characterizes the utility when purchasing from …rm i = L; H, as follows: u i = s i p i , where s i and p i denote the quality and price of …rm i.
is uniformly distributed over the support [ ; + ], and + = is assumed to be su¢ ciently large so that the market is not covered in equilibrium. We focus on the non-trivial case in which s H > s L , with s H and s L denoting the quality level of the high (H) and low (L) quality …rm, respectively.
The utility of not purchasing any product (outside option i = 0) is normalized to zero: u 0 = 0. 4 We assume that quality is costless and can take values in interval [0; s + ] in the lines of Choi and Shin (1992) and Wauthy (1996). This simpli…es the analysis considerably. Assuming …xed or variable costs of quality as in Motta (1993) makes the model intractable and it is no longer possible to solve explicitly for the equilibrium quality levels. This constitutes a very interesting potential area for future research.
We also assume that, due to overlapping ownership, …rm i's objective function places a weight w i < 1 on …rm j's pro…t (with the weight on own pro…t normalized to 1). These assumptions imply that the objective function of …rm i = L; H is b i = i + w i j = p i D i + w i p j D j , where i and D i denote the pro…t and demand of …rm i. 5
Game, Timing and Equilibrium
Consumers and …rms play the following game. At the beginning, nature draws the valuations of each consumer for quality. Next, …rms address a two-stage decision problem. In the …rst (second) stage, each …rm chooses the quality (price) of its product. Finally, each consumer selects the option (i = H; L; 0) that provides the highest utility. We focus on the sub-game perfect Nash equilibrium (SPNE) of the game and begin by addressing the consumers decision problem. 4 If, alternatively, the market was fully covered, the outcome would be maximum di¤erentiation, regardless of the ownership structure and prices would increase in the presence of overlapping ownership. 5 We are agnostic about whether overlapping ownership is induced by common-ownership, cross-ownership or both and about which particular type of weight is used. See Brito et al. (2018) for a review of the implications of each type of ownership on the objective function of …rms. See Backus, Conlon and Sinkinson (2019) and Brito et al. (2019b) for a discussion of di¤erent alternative weights.
Consumers Decision Problem
It is straightforward to show that consumers with (i) HL = p H p L s H s L will purchase the high quality product; (ii) p L s L = L0 < HL = p H p L s H s L will purchase the low quality product; and (iii) < L0 = p L s L will choose not to purchase. This yields the following demand functions: (1)
Firms Decision Problem
The SPNE of the game involving the …rms' decision problem is obtained by backward induction.
In the second stage, the two …rms (simultaneously) set the prices that maximize their objective function given the quality levels. Lemma 1 presents the corresponding equilibrium.
Lemma 1 The equilibrium prices, as a function of the quality levels, are: Given the quality levels s H and s L , both equilibrium prices increase in w L and w H . The fact that each …rm places a positive weight on the rival's pro…t makes them price less aggressively. The price di¤erence p H p L increases with w H and decreases with w L because own equilibrium price is more a¤ected by an increase in the weight given to the rival than the rival's price.
Having addressed the equilibrium in the pricing stage, we now address the quality stage. The two …rms (simultaneously) set quality levels anticipating the price equilibrium above. Lemma 2 presents the corresponding equilibrium. 6 Lemma 2 In equilibrium, …rms set the following quality levels: Corollary 1 For any (w L ; w H ) 2 (0; 1) 2 , s H is invariant to w H and w L , while s L is increasing in w H and decreasing in w L . 6 The condition for an uncovered market is In order to discuss the implications of Corollary 1 on consumer surplus, …rms'pro…ts and welfare, we begin (for tractability) by analyzing some particular cases before addressing the general case.
Benchmark Case
In the absence of overlapping ownership, Lemmas 1 and 2 imply that: This yields, as in Choi and Shin (1992) and Wauthy (1996), that the lower quality …rm chooses quality and price levels which are 4=7 and 2=7, respectively, of those of the higher quality …rm. As a consequence, HL = 5 12 + and L0 = 1 8 + , which yields that D H = 7 + 12( + ) and D L = 7 + 24( + ) . In turn, consumer surplus is CS = 7s + +2 24( + ) and, since costs are zero, …rms' pro…ts are H = In this case, the overlapping ownership structure is such that only the high quality …rm places a positive weight on the low quality …rm's pro…ts. Lemmas 1 and 2 imply that: This yields, as established by Corollary 1, that the high quality …rm chooses the same equilibrium quality (and price) as in the benchmark case while the low quality …rm has an incentive to increase its equilibrium quality (and price) and narrow the quality gap. The reason being that the high quality …rm will now price less aggressively (given it internalizes the externality imposed on the rival), which makes the demand of the low quality …rm more sensitive to its quality level. 7 As a consequence, HL increases while L0 remains unchanged: HL = 5 w H 12 4w H + and L0 = 1 8 + , which 7 In the benchmark case, the choice of quality level by the low quality …rm is the result of two countervailing e¤ects. The …rst (direct) e¤ect induces the …rm to increase its quality level since higher quality increases demand. The second (strategic e¤ect) induces the …rm to decrease its quality level since higher quality leads the rival (the high quality …rm) to lower its price, which in turn decreases demand for the …rm. In case 1, overlapping ownership increases the …rst e¤ect (since it makes the demand of the low quality …rm more sensitive to its quality level, as the high quality …rm will price less aggressively) and may increase or decrease the second e¤ect (since it can make the price of the high quality …rm more or less sensitive to the quality level of the low quality …rm, depending on the quality levels). The impact on the …rst e¤ect dominates and so the quality level of the low quality …rm, increases.
Figure 1
Demand Impacts in Case 1 yields that some demand will now be diverted from the high quality …rm to the low quality …rm, as depicted in Figure 1. Proposition 1 discusses the impact on consumer surplus, …rms pro…ts and welfare.
Proposition 1 If w L = 0: higher price, but are more than compensated by the higher quality, while the latter now purchase a lower quality, but are more than compensated by the lower price.
We now address the impact on …rms'pro…ts. The pro…t of the high quality …rm decreases with w H because some demand is diverted from the high quality …rm to the low quality …rm while p H does not change. The high quality …rm accepts this loss in pro…t since it now places a positive weight on the pro…t of the low quality …rm, which increases with w H because some demand is diverted from the high quality …rm to the low quality …rm while p L increases.
Finally, we address the impact on welfare. Despite the positive impact on consumers, welfare decreases with w H as the result of the following trade-o¤ (since price is irrelevant in terms of welfare). On the one hand, some consumers continue to buy the low quality product, whose quality increases with w H . On the other hand, some consumers switch from the high quality product to the low quality one. The second e¤ect, which is felt by consumers with a higher valuation for quality, dominates.
3.2.3 Case 2: w H = 0 and w L > 0 In this case, the overlapping ownership structure is such that only the low quality …rm places a positive weight on the high quality …rm's pro…ts. Lemmas 1 and 2 imply that: This yields, as established by Corollary 1, that the high quality …rm chooses the same equilibrium quality (and a higher price) while the low quality …rm has an incentive to decrease its equilibrium quality (and increase price for w L < 0:25605/decrease price for w L > 0:25605), widening the quality gap. The reason being that such lower quality level bene…ts the high quality …rm, which is now internalized by the low quality …rm. 8 As a consequence, HL and L0 increase: HL = (c) Welfare decreases with w L .
We begin by addressing the impact on consumer surplus. Now, when comparing the equilibrium decisions when w L = 0 with those when w L > 0 one can divide consumers into …ve distinct groups, 8 In case 2, overlapping ownership may increase or decrease the two e¤ects discussed in footnote 7 (since it can make the demand of the low quality …rm and the price of the high quality …rm more or less sensitive to the quality level of the low quality …rm, depending on the quality levels). Moreover, it introduces a third (direct) e¤ect, whichdominates and -induces the low quality …rm to decrease its quality level, since a lower quality increases the demand for the high quality …rm, now internalized by the low quality …rm. The high quality …rm responds to this increased demand by increasing its price. We now address the impact on …rms' pro…ts. The pro…t of the high quality …rm increases with w L since the decrease in s L allows the …rm to increase p H , which more than compensates the resulting decrease in demand. The pro…t of the low quality …rm may increase or decrease with w L because demand decreases (the diversion to the outside option more than compensates the diversion from the high quality …rm) while p L may increase or decrease.
Finally, we address the impact on welfare. Welfare decreases with w L because (since price is irrelevant in terms of welfare) some consumers switch from the low quality product to the outside option, some consumers continue to buy the low quality product, whose quality decreases, and some consumers switch from the high quality product to the low quality one.
Case 3: w H
In this case, both …rms place a positive and symmetric weight on the rival pro…t, which combines the two previous cases. Lemmas 1 and 2 imply that: This yields that the high quality …rm chooses the same equilibrium quality (and a higher price) while the low quality …rm has an incentive to decrease its equilibrium quality (and increase price for w < 0:569 86/decrease price for w > 0:569 86). This, in turn, suggests that the dominating e¤ect when both …rms places a positive and symmetric weight on the rival pro…t is the one resulting from w L , which is, in fact, established in Proposition 3.
Proposition 3 If w H = w L = w: (a) Consumer surplus decreases with w; (b) The high (low) quality …rm's pro…t increases (can either increase or decrease) with w; (c) Welfare decreases with w:
General Case
The cases above illustrate that overlapping ownership (a) may increase or decrease consumer surplus (in particular, it decreases consumer surplus if w L is signi…cantly di¤erent from zero); 9 (b) may increase or decrease …rms'pro…ts; and (c) decreases welfare.
Conclusions
In this paper, we have analyzed the implications of overlapping ownership in a standard vertical di¤erentiation duopoly model. We have shown that overlapping ownership while detrimental for welfare, may increase or decrease the quality gap, consumer surplus and …rms'pro…ts. In particular, when overlapping ownership leads the manager of the high quality …rm to place some weight on the low quality …rm's pro…ts, the low quality level increases and consumers will bene…t from this. The reason being that when the rival prices less aggressively, quality di¤erentiation is not as relevant and the low quality …rm narrows the quality gap.
Online Mathematical Appendix
In this mathematical appendix, we present the proofs of the results presented in the main text.
Proof of Lemma 1
The …rst-order conditions for maximization of each …rm's objective function are: from where the result follows directly.
Proof of Corollary 1
The proof follows directly from: The denominator is always positive and the second term in the numerator is an inverted parabola with a minimum when wL = 0 or wL = 1. In the former case it is equal to 1 and in the latter case it is equal to 8 (1 wH ). Therefore, @s L @w H > 0.
As for @s L @w L we have that: The denominator is always positive and the numerator is an inverted parabola with an unconstrained maximum at wH = 25w L 9w 2 L +3w 3 L +13 4(w L +1)(4w L w 2 L +1) > 1. Therefore, the numerator is maximized at wH = 1 and takes value 6 (1 wL) 3 < 0, meaning that @s L @w L < 0.
Proof of Proposition 2
Given the equilibrium price and quality expressions one can easily compute consumer surplus, …rms'pro…ts and welfare, which are presented below divided by s + +2 : ; with derivatives: < 0: | 4,107.6 | 2019-11-27T00:00:00.000 | [
"Economics"
] |
Nucleosome Organization around Pseudogenes in the Human Genome
Pseudogene, disabled copy of functional gene, plays a subtle role in gene expression and genome evolution. The first step in deciphering RNA-level regulation of pseudogenes is to understand their transcriptional activity. So far, there has been no report on possible roles of nucleosome organization in pseudogene transcription. In this paper, we investigated the effect of nucleosome positioning on pseudogene transcription. For transcribed pseudogenes, the experimental nucleosome occupancy shows a prominent depletion at the regions both upstream of pseudogene start positions and downstream of pseudogene end positions. Intriguingly, the same depletion is also observed for nontranscribed pseudogenes, which is unexpected since nucleosome depletion in those regions is thought to be unnecessary in light of the nontranscriptional property of those pseudogenes. The sequence-dependent prediction of nucleosome occupancy shows a consistent pattern with the experimental data-based analysis. Our results indicate that nucleosome positioning may play important roles in both the transcription initiation and termination of pseudogenes.
Introduction
Pseudogenes are produced from protein-coding genes during evolution. Though highly homologous with their parent genes, pseudogenes are unable to synthesize functional protein due to the defects in their sequences. There are two major types of pseudogenes: duplicated pseudogenes and processed pseudogenes (or retropseudogenes). The former type is created by genomic duplication and the latter by retrotransposition [1,2]. For each type, the abnormalities occurred in either the protein-coding regions or the regulatory regions of parent genes leading to the loss of protein-coding ability of pseudogenes. Duplicated pseudogenes are often distributed in the flanking of the parent genes and may still maintain the upstream regulatory sequences of their parents due to their duplicative origin. Processed pseudogenes are usually characterized by absence of intron-like segments, decayed poly A tail, frame shifts, and premature stop codons. Processed pseudogenes are thought to be nonautonomous retrotransposons which are probably mobilized by long interspersed elements (LINEs), a kind of autonomous retrotransposons in the genome [3,4]. Processed pseudogenes occur in a great number of eukaryotes, especially in mammalian genomes [5,6].
Many unexpected discoveries of biological functions for pseudogenes challenge the popular belief that pseudogenes are nonfunctional and simply molecular fossils. A nitric oxide synthase (NOS) pseudogene functions as a regulator of the paralogous protein-coding neuronal nitric oxide synthase (nNOS) gene by producing antisense RNA that forms a duplex with some of the gene's mRNA [7,8]. The Makorin1-p1 pseudogene in mouse regulates the stability of the mRNA of its homologous Makorin1 gene probably by producing RNA which competes for the freely available repressor molecules that inhibit the homologous gene expression [9]. Some pseudogenes can also compete with their parent genes for microRNA binding, thereby modulating the repression of the functional gene by its cognate miRNA [10]. The transcription of MYLKP1 pseudogene, which is upregulated in cancer cells, creates a noncoding RNA (ncRNA) that inhibits the mRNA expression of its parent MYLK gene [11]. Moreover, recent studies have documented that a subset of pseudogenes generates endogenous small interfering RNAs (endo-siRNAs) and suppresses gene expression by means of the RNA interference pathway in mouse oocytes [12,13], subsequently in rice [14], most lately in African Trypanosoma brucei [15], a unicellular eukaryote. These observations suggested that pseudogenes might be an alternative source of natural antisense transcripts that regulate the activity of sense transcripts of their parent genes. Besides, pseudogenes may have a whole set of functions related to intracellular immunobiology [2,16,17].
The variety of known or suspected pseudogene functions discovered to date suggests that pseudogenes as a whole have a wide range of previously unsuspected functions. Of the functions, RNA-level functions are of great importance and are most frequently discussed. The prerequisite of understanding the RNA-level functions of pseudogenes is to explore their transcriptional activity. It has been shown that the nucleosome, a fundamental composing unit of the chromatin structure in eukaryotes, affects gene transcription in that it modulates the accessibility of underlying genomic sequence to proteins [18]. How does nucleosome positioning affect pseudogene transcription? Seeking to answer the question, we analyze the nucleosome organization around the pseudogenes in human. Nucleosome occupancy is measured by both a sequence-dependent computational model and experimental data [19]. The computational model emphasizes the sequence-dependency of nucleosome positioning, while the nucleosome occupancy inferred from in vivo experimental data reflects the joint effect of DNA sequence and other external factors, such as chromatin remodeler, DNA methylation, histone modification, and polymerase II binding, on nucleosome positioning [19][20][21]. The two methods may have different implications for the dependency of pseudogene transcription on chromatin structure.
Transcribed and Nontranscribed Pseudogenes.
A total of 201 consensus pseudogenes, including 124 processed pseudogenes and 77 duplicated pseudogenes, were identified in ENCODE regions [22]. Of the ENCODE pseudogenes, 38 pseudogenes have evidence of transcription, and others are considered to be nontranscribed. The sequences and annotation information (genomic position, strand, and positions of start positions and end positions) of the pseudogenes mapping to the human genome (hg18) were retrieved from UCSC (http://www.genome.ucsc.edu/). The type and transcriptional information of the pseudogenes were downloaded from the pseudogene database (http://www.pseudogene .org/). The number of transcribed pseudogenes in ENCODE regions is too small, so we refer to the genome-wide transcribed processed pseudogenes that were identified by Harrison et al. [23]. The annotation of the 192 transcribed processed pseudogenes that corresponds to the human genome (version hg18) was taken from the pseudogene database (http://www.pseudogene.org/). The transcribed processed pseudogenes were identified by mapping three sources of expressed sequences (Refseq mRNAs, Unigene consensuses, and ESTs from dbEST) onto the processed pseudogenes.
Oligonucleotide microarray data was used to further verify the expression of the selected transcribed pseudogenes [23]. The sequences surrounding the start sites and end sites of the transcribed pseudogenes were retrieved from the human complete genome (hg18) by using the positional information of the pseudogenes. The statistics of the pseudogenes are listed in Table 1.
Human Nucleosome Occupancy.
Experimental databased nucleosome occupancy profile mapping to the human genome (hg18) was taken from Schones et al. [19]. It was based on maps of nucleosome positions in both resting and activated human CD4+ T cells generated by direct sequencing of nucleosome ends using the Solexa high-throughput sequencing technique. The two nucleosome profiles (resting and activated) have a resolution of 10 bp. We applied cubic spline fitting to each of the profiles to obtain nucleosome occupancy at each genomic site. We also estimated nucleosome occupancy by a sequence-dependent computational model described in detail in the Methods section.
Conformational Energy Calculation.
Conformational energy is to be calculated on the basis of the geometrical description of DNA double helix structure. According to Cambridge Convention [24], each base pair of DNA is viewed as a rigid board, and its position relevant to its neighbor is specified by roll, tilt, twist, slide, shift, and rise. Nucleosomal DNA bending appeared to be due to periodic variations in both roll and tilt in the crystal structure 1kx5 [18]. The periodic changes reflected the helix twisting that altered the rotational position of each base-pair step (or dinucleotide step) relative to the dyad. In addition to the general trend of periodic changes, variations in the roll and tilt at each basepair step were also dependent on the property of individual dinucleotide.
Nucleosomal DNA deformation is viewed as forced bending. It is assumed that torque is uniformly distributed along the DNA. We consider DNA bending to be analogous to the bending of a rod of multiple segments with variable stiffness. For a bending force exerted by the histone octamer on a segment of the DNA, the conformational energy at each step along the sequence depends on both the corresponding dinucleotide flexibility and the phasing of the dinucleotide with respect to the dyad. According to simple elastic model, deformations of roll and tilt from their equilibrium values at dinucleotide step are described as The bending energy is then calculated by where ( ) and ( ) are, respectively, the actual roll and tilt angle at dinucleotide step , 0 ( ) and 0 ( ), which are dependent on the dinucleotide at step , are, respectively, the roll and tilt without torque, ( ) and ( ) are the dinucleotidedependent force constants, and Ω is the accumulated twist ( ) at the center of step , counted from the dyad position. For 147 bp nucleosomal core DNA, its structure is symmetrical with respect to the dyad that is located at the centeral nucleotide, and the dinucleotide steps from the dyad are labeled as = ±1, ±2, ±3, . . . , ±73 towards downstream and upstream directions. The step ±1 is half step away from the dyad; thus the accumulated twist is calculated as follows: The bending energy for the central -bp segment of a nucleosomal DNA is the sum of corresponding dinucleotide steps: where is a positive odd number and less than or equal to 147. In (4), is determined by utilizing its relationship with the total bending angle of the core DNA. In the crystal structure of core particles, about 10 bp at each end has no contact with the histone octamers, and therefore the sequence dependency of nucleosome positioning is reflected merely in the central 129 bp part of the nucleosomal DNA. The central 129 bp part of the nucleosomal core DNA bends around histone octamer about 579 ∘ ( ) under the stress of , and the is due to contribution of and at every step: Combining (1) and (5) leads to The empirical parameters of our model for conformational energy calculation consist of force constants ( and ) and roll and tilt angles ( 0 and 0 ) for 10 dinucleotides at the equilibrium state ( Table 2). The dinucleotide-dependent parameters 0 and 0 averaged over a large pool of DNAprotein complexes and force constants and are taken from the paper of Morozov et al. [25]. A constant = 34.8 ∘ , average twist for the 1kx5 X-ray crystal structure of nucleosome-bound DNA, was used for all dinucleotide steps.
Nucleosome Occupancy Estimation.
According to Boltzmann distribution, the potential of forming a nucleosome which centers at position in a DNA segment of bp is defined as where = 1/ , is Boltzmann constant, is the room temperature, = 147 (nucleosome size), and is the deformation energy of the underlying DNA of the nucleosome which occupies positions − ( − 1)/2 through + ( − 1)/2. For simplicity, we assume = 1 in calculation. Nucleosome occupancy at the base-pair position is measured by the average of the nucleosome formation potentials over -bp window: In this study, = 51, of which performance was validated in our other study (unpublished).
Normalized nucleosome occupancy at every base-pair is calculated by the log-ratio between the corresponding absolute nucleosome occupancy and the average nucleosome occupancy ⟨ ⟩ per base-pair across the genome as
BioMed Research International
Distance relative to start position An obvious nucleosome depletion detected upstream of the start positions of transcribed pseudogenes, suggesting that the nucleosome depletion at the region may promote the pseudogene transcription by exposing the underlying sequence in a linker region, which is accessible for transcription factor binding. A similar depletion at the region downstream of the end positions of transcribed pseudogenes might imply the role of nucleosome positioning in transcription termination by facilitating the sequence to form hairpin structure to terminate transcription. Note that the nucleosome depleted regions detected upstream of the start positions and downstream of the end positions of transcribed pseudogenes match well with the transcription start region and transcription end region of the pseudogenes, respectively.
Experimental Nucleosome Occupancy around
As compared with transcribed pseudogenes, nucleosome depletion both upstream and downstream of the nontranscribed pseudogenes is unexpected since nucleosome depletion in those regions is thought to be unnecessary in light of the nontranscriptional property of those pseudogenes.
Sequence-Dependent Prediction for Nucleosome
Occupancy around Pseudogenes. The overall distribution trend of experimentally determined nucleosome occupancy around both start positions and end positions of pseudogenes is reproduced successfully by our computational model ( Figure 2). It has been demonstrated in the previous study that predicted occupancy has a better correlation with in vitro nucleosome occupancy than in vivo occupancy [26], as our prediction depends solely on the physical properties of DNA and reflects the sequence-dependent nucleosome-forming ability. In the present paper, the depletion of nucleosomes
The Effect of Sequence Degeneration of Pseudogenes on Nucleosome Formation.
Pseudogenes provide a natural resource of relics for researchers to explore the chromatin response to sequence mutations that are enriched in pseudogenes. Specifically, a number of structurally similar but not identical pseudogenes can be produced from a single functional gene during evolution. In particular, each of the high-transcriptional ribosomal protein genes tends to have many, in some cases over 100, pseudogenes. A simple way to test the possible change of nucleosome distribution over pseudogenes is to correlate the nucleosome occupancy over the pseudogenes with their evolutionary distances. To do this, we first downloaded the annotation (hg16-based) for 2536 ribosomal protein (RP) pseudogenes [27] from the pseudogene database (http://pseudogene.org/) and then remapped them onto the hg18 human genome using Lift program accessed at http://www.genome.ucsc.edu/. 2401 RP pseudogenes were successfully mapped. From them, duplicated pseudogenes and pseudogenic fragments that account only a small percentage of pseudogenes were removed. Finally, we retained 1931 processed pseudogenes whose sequences and annotations (GC content, DNA identity to their ancestral genes, etc.) are available at http://pseudogene.org/. We computed the average nucleosome occupancy over each pseudogene from the hg18-based experimental nucleosome reads data (the same to the procedure described in Section 2.1.2). Sequence-dependent predictive model was also applied to the pseudogenes to get average nucleosome occupancy over each one. The correlations among the variables for each RP pseudogene family were computed (Table 3).
Our data clearly illustrate that predicted nucleosome occupancy over pseudogenes tends to positively correlate with their DNA identity, suggesting that the ability of the pseudogenes to form nucleosome(s) tends to decline in the process of their evolution. However, we did not detect a positive correlation between experimental nucleosome occupancy and DNA identity. There are three possible reasons for this. Firstly, the effects of some nonsequence factors which are likely to play a larger role in nucleosome positioning in human than in simple eukaryotes, such as yeast, exceed the sequence-induced effect on nucleosome positioning [19]. Secondly, it is also possible that the mutations occurring in some pseudogenes are so little and trivial that they cannot bring about a significant effect on the nucleosome-forming ability of pseudogenes. Thirdly, the high substitution rates in nucleosome-enriched regions [28] are likely to result in the weak negative correlation between nucleosome occupancy and pseudogene identity.
We also found a significant correlation between pseudogenes' divergence and their predicted nucleosome occupancy, indicating again the decreasing trend of nucleosomeforming ability of pseudogenes during their degradation process. Furthermore, there is a strong positive correlation of predicted nucleosome occupancy of pseudogenes with their GC content, consistent with the previous finding that GC content dominates intrinsic nucleosome occupancy [29]. The GC-dependency of nucleosome occupancy and the decrease a The "Identity" and "Divergence" of pseudogenes from the coding sequences of their functional RP genes were taken from Zhang et al. 2002 [27]. The "Divergence" was computed with the program MEGA2, using the Kimura two-parameter model and pairwise deletion. b Among 79 RP pseudogene families, there are two RP pseudogene families whose lengths are not up to 129 bp, a minimum required size for nucleosome occupancy prediction. c The average of the significant Spearman correlation coefficients and the number of positive significant correlations were indicated in the parenthesis.
of GC content of pseudogenes with time [6] could explain the reduced intrinsic preference of pseudogenes for nucleosomeforming during evolution.
Conclusion
In this report, we analyzed the organization of nucleosomes around pseudogenes and compared between transcribed and nontranscribed pseudogenes. Experimental data-based analysis shows nucleosome depletion both upstream of the start positions and downstream of the end positions of transcribed pseudogenes, suggesting that nucleosome positioning plays an important role in both transcription initiation and transcription termination of pseudogenes. A similar depletion of nucleosomes is detected for nontranscribed pseudogenes, which is likely to be caused by sequence-dependent nucleosome-inhibitory effect. We also applied a sequencedependent model for calculating nucleosome occupancy to pseudogenes and obtained consistent pattern with experimental nucleosome organization. | 3,764.6 | 2015-05-04T00:00:00.000 | [
"Biology"
] |
Adsorption Sites of Hydrogen Atom on Pure and Mg-Doped Multi-Walled Carbon Nanotubes
Hydrogen adsorption sites on pure multiwalled carbon nanotube (MWCNT) and Mg-doped MWCNTs material system have been investigated using molecular dynamics (MD) simulations as well as quantum chemical calculations. Through combining MWCNTs with Mg, the hydrogen adsorption sites energy on this Mg-MWCNTs system is found to be larger than that of the pure MWCNTs. Additionally, it was found that, through Mg-doping, new adsorption sites for hydrogen molecules are created in comparison with undoped nanotubes. It is also found that H atom is preferably adsorbed at every place near magnesium atom.
Introduction
Hydrogen is an attractive alternative energy carrier for future fuel needs.The use of hydrogen as a fuel requires development in different industry segments, including production, delivery, and storage.One of the most critical factors facing hydrogen economy is transportation and on-vehicle storage of hydrogen [1][2][3][4][5][6][7][8][9].The major contribution to the problem is from low gas density of hydrogen.
Metal hydrides are specific combinations of metallic alloys, which possess the unique ability to absorb hydrogen (hydrogenation) and release it later (dehydrogenation), either at room temperature or on heating.The percentage of gas reversibly absorbed to weight of the metal is around 2%, but hydrides offer a valuable solution to hydrogen storage [10,11].Magnesium hydride (MgH 2 ) is inexpensive and has a maximum storage capacity of 7.6 wt% H 2 .
Various forms of carbon such as fullerene, nanotubes, graphene, and activated carbon with high surface area may be used for the storage of hydrogen.Single-walled carbon nanotubes can store 2.5-3 wt% hydrogen [3,12].Research has focused on the areas of improving manufacturing techniques and reducing costs as carbon nanotubes move toward commercialization [3].Others have proposed storing hydrogen in fullerenes or in activated carbon at low temperatures [12][13][14][15].
Recently, McAfee and Poirier declare that hydrogen storage via carbon nanotubes requires exohedral adsorption in atomic form for which no more than one H atom adsorbate is bound per carbon nanotubes substrate C atom [31,32].This yields a theoretical maximum storage capacity of 7.75%, which is above the 2010 target, in which the US Department of Energy (DoE) has set a benchmark goal for on-board gravimetric hydrogen storage capacities of 6% by weight hydrogen by 2010 and 9% by 2015 [33].
However, combination of carbon nanotubes and metal hydrides in single nanostructure system may give a promising candidate for hydrogen storage.
Therefore, the aim of this research study is to investigate the hydrogen adsorption sites on Mg-doped MWCNT (denoted Mg-MWCNTs) as a model material through the methodology of quantum mechanical (QM) calculations using general gradient approximation-density functional theory (GGA-DFT).
Computational Methods
In the current study, hydrogen atom has been simulated as adsorbate on pure MWCNTs and Mg-MWCNTs to find the energy adsorption sites and to investigate the preferential adsorption of the hydrogen atom onto MWCNTs and Mg-MWCNTs.The computational study was made using For cite and Adsorption locator in Accelrys Materials Studio software [34][35][36].In order to investigate the adsorption of atomic hydrogen on MWCNTs, we perform a series of total energy calculations using adsorbate locator module (max force 0.002 Ha/A, energy 1 × 10 −5 Ha, max displacement = 0.005 A, and max step size = 0.3 A) utilizing GGA:BLYP function.For substitutional doping, we replace, randomly, some carbon atoms by Mg atoms (1.23% Mg/C by atom) followed by geometric optimization to study their effects on hydrogen adsorption using Forcite module with the following parameters: (energy = 2 × 10 −5 kcal/mol, force = 0.001 kcal/mol/A, and displacement = 1 × 10 −5 A).The geometry optimization process is carried out using an iterative process, in which the atomic coordinates are adjusted until the total energy of a structure is minimized.Geometry optimization is based on reducing the magnitude of calculated forces until they become less than preselected tolerance, (0.01 eV/A in our case).The forces on the atoms are calculated from the potential energy expression and will, therefore, depend on the force field that is selected.
Results and Discussions
To obtain the configuration of the hydrogen adsorption on the MWCNT system, first, we fully optimized the geometry of the MWCNT before placing Mg atoms on it.Next, we simulated the doping of Mg on various positions on the MWCNT.
We studied two types of materials as depicted in Figure 1: perfect MWCNTs (Figure 1(a)) and Mg-MWCNT (Figure 1(b)) to study Mg effects on hydrogen adsorption sites.MWCNTs were built with the following parameters: (CNT (6 × 6)) with diameter = 8.14 A, length = 9.84 A, the number of walls is 3, and the wall separation is 3.347 A).
The fully optimized atomic structure of a perfect semiconducting arm-chair (6,6) MWCNT and Mg-MWCNTs containing a single H atom adsorbate at different sites is shown in Figures 2 and 3, respectively.
We tried to find the effects of Mg-doping on the hydrogen adsorption behavior of Mg-MWCNTs.The calculations of the adsorption energies indicated that two distinct adsorption sites are created by the doped Mg atoms: one is the region where the distribution status of electrons is influenced by the doped Mg atoms (region 1) and the other one is the region of positively charged Mg atoms (region 2), created due to the transfer of electrons from Mg atoms to MWCNTs.When hydrogen is adsorbed on top of a C atom in carbon nanotube, the covalent C-H bond is formed, and the neighboring C-C binding is weakened.When hydrogen is adsorbed on top of Mg atom (region 2) in the Mg-doped carbon nanotubes, H atom transfers some electronic charges to Mg atom and forms coordination-like bond between them.While Mg-doped carbon nanotube (region 1) is an electron-rich structure, it has no tendency to accept electrons from adsorbed atoms, and it will form mainly ionic Mg-H bond.Table 1 illustrates the adsorption energy of hydrogen atom for pure MWCNTs systems and Mg-MWCNT systems.The H adsorption energies for Mg-MWCNTs are larger than that of the pure MWCNTs.This result shows that the H adsorption capability of the Mg-doped system is superior to the pure MWCNT system.
Conclusions
We have shown through computational simulations that Mg-MWCNTs can be good hydrogen storage medium.This study suggests that a systematic increase of binding energy of hydrogen can be achieved by moderate substitutional doping of MWCNTs with Mg atoms.
Figure 3 :
Figure 3: Top views of the fully relaxed structures of different adsorbed sites of H atom adsorbed to Mg-doped arm-chair (6, 6) MWCNT.
Table 1 :
Adsorption energy of H for many pure MWCNTs systems and Mg-MWCNTs systems. | 1,499.4 | 2012-01-01T00:00:00.000 | [
"Materials Science",
"Chemistry",
"Engineering",
"Physics"
] |
Research on Electromagnetic Susceptibility of Electronic Modules in Component-Level HEMP PCI Test
: The study of electromagnetic sensitivity of electronic modules is crucial for the selection of a component-level pulse current injection (PCI) waveform, which will determine whether a component-level PCI test is equivalent to a system-level pulse illumination test of the system to which the electronic module belongs. For electromagnetic sensitivity analysis, the equivalence between the injection waveform and a typical high-altitude electromagnetic pulse (HEMP) conducted disturbance waveform in a component-level PCI test is studied. Based on an RF low noise amplifier (LNA) test board, component-level PCI tests were performed using 20 ns/500 ns double exponential wave and square-wave pulse with multiple pulse-widths. The damage threshold was analyzed and determined by using vector norm and its internal damage was observed and validated by optical microscopic analysis. The conclusions are demonstrated as follows: first, during square-wave PCI tests of RF LNA, the electromagnetic sensitive parameter action is divided into three regions by pulse-width range, called ∞ -norm, 2-norm and competitive failure-dominating regions; second, the electromagnetic damage effect of the RF LNA is mainly caused by the burning of its two cascaded transistors, forming a pulse energy transmission channel with short-circuit impedance from the input port to the ground; third, the 100 ns-width square waveform can be determined as the equivalent injection waveform of a HEMP conducted waveform, and the pulse peak value of injected current is determined as the electromagnetic sensitive parameter for square-wave PCI tests of the RF LNA. The conclusions verified the feasibility of establishing the equivalence between different pulse waveforms according to the electromagnetic sensitivity analysis based on the vector norm theory and effect
Introduction
With the development of electromagnetic pulse generation technology such as highaltitude electromagnetic pulse (HEMP), lightning electromagnetic pulse (LEMP) and highpower microwave (HPM), electronic systems face serious survival threats [1,2]. How to accurately assess the survivability and vulnerability of electronic systems exposed to complex electromagnetic environments must be solved. Doing so will help prevent electromagnetic risks and improve the protective design technology of electronic systems. Probability descriptions designed to detail the vulnerability of electronic systems attacked by certain EMP [3,4] usually employ the system-level vulnerability assessment method based on Bayesian networks (BN), with the risk factors of electromagnetic environment effect (E3) and reliability theory taken into account in the stress-strength model. The damage threshold distribution of the main coupling port of the system is obtained by system-level effect threshold tests and statistical distribution fitting methods. However, for practical assessment application, the number of system-under-test (SUT) samples is often limited to less than the sample number required for ordinary statistical distribution fittings [5][6][7][8].
Many electromagnetic effect test cases illustrate that the permanent effect such as system function failure or performance degradation occur when electronic systems are exposed to E3, which is usually caused by the failure of one or more vulnerable components of the electronic system [1,9,10]. Compared with electronic systems, its components have the advantages of low cost and large sample size. Therefore, the component-level pulsed current injection (PCI) test for the vulnerable modules can provide huge quantities of damage threshold test data for distribution fitting, which may provide a method to assist in determining the system-level damage threshold distribution with small sample size in system-level SUTs. The key challenge of this approach is to select the injection waveforms for the component-level PCI so that the effect mechanism is equal to the system-level pulsed illumination or PCI test. Taking a wireless communications system as an illustration of an electronic system, note that the antenna system is the main coupling channel when exposed to EMP and that a low noise amplifier (LNA) is one of the most vulnerable RF components in RF circuits. In the practical EMP coupling process, after the energy enters the RF frontend circuits through the antenna, the waveforms of the electromagnetic response that reach the port of the vulnerable RF module will become more complex and difficult to measure as energy transferred among RF components. To extract the typical characteristics of the complex transient coupled responses from wave shapes and then design the simplified injection waveform according to these extracted parameters is one of the common ways to solve the problem of injection waveform selection. In fact, there are many parameters of a complex transient coupled wave, such as amplitude, peak value, rising time, energy, average power, etc. [11]. Hence, establishing the equivalence between different waveforms is the key issue in selecting suitable simplified injection wave for component-level PCI tests. To validate feasibility, the electromagnetic sensitivity of vulnerable components is studied, focusing mainly on establishing the equivalence among two types of waveforms in a component-level PCI test.
A square wave with different pulse widths, which is generated easily by a PCI generator, is employed as an injection wave due to its simplicity. A double exponential wave is a typical waveform of a HEMP conducted disturbance [12,13]. It is used in this paper as another injection waveform to compare with the square waves to find its equivalent waveform. To find the major electromagnetic parameters which register on the effect tests are called the selection of electromagnetic sensitivity parameters. A vector norm is an efficient mathematical tool used to represent the complex transient wave and compare complex waveforms, such as 2-p norm and ∞-norm representing the energy and peak of waveforms [14], respectively. In this paper, vector norm theory is used to analyze the injection waveform.
The paper is organized as follows. Section 2 describes a self-developed electronic system and its HEMP vulnerability analysis and determines the LNA composed of two GaAs heterojunction bipolar transistors (HBT) as the vulnerable component for research. A series of PCI tests with different injection waveforms are carried out and the test data analysis with vector norm theory is made in Section 3. Section 4 discusses the effect mechanism result with optical microscopic analysis. Section 5 concludes the paper.
The VHF Wireless Communication System and Vulnerability Analysis
The energy contained in a HEMP environment is mainly concentrated below 100 MHz. Because the high frequency or very high frequency (HF/VHF) radio is within HEMP frequency range, the effects of function failure or performance degradation occurred often during the pulse illumination test [15,16]. As shown in Figure 1, a small prototype of a VHF electronic system with superheterodyne transceiver, consisting of antenna, RF board, baseband board, and computer, etc., was developed. The RF board consisted of transmitting channel and receiving channel [17]. The transmitting channel mainly contained a mixer, a low pass filter and primary and secondary power amplifiers. The receiving channel mainly contained a LNA and a mixer. A RF switch was used to control the channel selection for the transceiver, and the impedance matching was designed with L-C circuits to solve the impedance mismatch between antenna and RF circuits. As the antenna was exposed to the outdoor environment, the antenna and the RF front end were the main front-door coupling channels. An electromagnetic pulse through the antenna system coupling induced pulse current, which entered the RF front end, transmitted pulse energy along the RF channel step-by-step, and impacted the RF electronic modules.
A PCI test was performed on the SUT with a HEMP double-exponential wave. The results demonstrated that the communication-receiving sensitivity of the SUT decreased, and the analysis of the effect mechanism demonstrated that it was all caused by the damage of the RF LNA component on the RF board [17]. Note that the RF switch had failed in previous tests due to its semiconductor materials and its proximity to the antenna port. However, its damage threshold is much higher than that of LNA based on test results. To assess the survivability and vulnerability of the electronic system, we focused more on the study of SUT performance degradation or functional failure under the impact of the lowest HEMP environmental strength, which is considered the worst case of the SUT.
A pulse illumination test was also performed on the SUT using a vertically polarized bounded wave simulator. The results of the illumination test verified the conclusions obtained in the PCI test. The test configurations of the PCI and pulse illumination tests are illustrated in Figure 2. In PCI tests, the PCI generator uses coaxial cable directly connected to the RF port of the SUT as the output line. After each test, the antenna is reconnected to the SUT for communication debugging [18].
In addition, the effect of LNA damage often occurs in wireless radios excited by a HEMP. Therefore, the main coupling channel of the SUT is its RF front-end, and its vulnerable component is LNA when the SUT is exposed to HEMP.
Problem Description
It is difficult to obtain sufficient experimental data for the fitting of damage threshold distribution by conducting a system-level illumination test. On the one hand, it is limited by the number of samples of the SUT, and on the other hand, it is limited by many factors such as the instability of the excitation source in the illumination test and the step interval of the excitation source output. After determining the vulnerable components, how to obtain the threshold distribution curve by carrying out a large sample PCI test on the vulnerable components for computing the system-level damage threshold distributions, the key problem to be solved was identified. Before solving this problem, we should establish the relationship between the component-level PCI waveform and the actual coupled response of the pulse illumination test. Acknowledging that the effect phenomenon and mechanism of vulnerable components are similar to the damage effect and mechanism of the system-level illumination test allowed us to establish their equivalent relationship. The major difference between these two environments is that the component-level PCI waveform can be selected from the simple and typical standard wave, such as a square wave, with different pulse width. The coupled response reached the vulnerable deviceunder-test (DUT) port in the pulse illumination test is so complex that is hard to simulate it with pulse generating technology. How to utilize vector norm theory and mechanism analysis to establish their equivalence is a key issue, which is an electromagnetic parameter selection problem.
Therefore, simplified standard waveforms and a typical HEMP conduced waveform are selected in this paper for the PCI tests of the vulnerable component LNA. They are waveforms with square waves of multiple pulse-widths and double exponential waveforms with 20 ns/500 ns, respectively, for carrying out a PCI test. The correlation between waveform parameters and effect mechanism are studied using vector norm theory.
The LNA and the PCI Test Method
The model of the RF LNA used in the SUT is RF3376 with materials belonging to GaAs HBT [19]. The circuit of RF3376 is a two-stage amplifier cascade structure as shown in Figure 3a, which is packaged in an RF integrated chip. Based on the impedance matching and bias circuits provided in the manufactures' datasheet, we designed a test board as the DUT for the component-level PCI test as illustrated in Figure 3b. RF3376, which is suitable for frequency range DC~6 GHz with signal gain factor 22 dB, and 5 V DC power supply, is widely used in wireless communication products due to its low cost. This subsection describes the test configuration and waveforms injected in the RF3376 component-level PCI test. The PCI test configuration is shown in Figure 4. Injected current and load current are monitored with two coaxial current probes, respectively, and a 50 ohms load is connected to the DUT output port. The injected pulse generated by the pulse generator are square wave with different pulse-widths of 50/100/200/400/600/1000 ns, and double exponential pulse with 20 ns rising time and 500 ns pulse width. For each DUT sample, the injection voltage level is changed from low to high until the effect appears. The standard output waves of a pulse generator with ideal loads are calibrated as shown in Figure 5. The standard injected waves occur when the square pulse generator is connected to 50 ohm loads and the HEMP pulse generator is connected to 0 ohm loads respectively.
The criterion for determining whether the effect phenomenon occurs in a PCI test is based on the shape of the injection waveform. PCI tests on RF3376 have shown varying degrees of degradation in the amplifier gain performance when the injection voltage level is greater than 150 V, indicating that the component is very vulnerable. In the actual pulse illumination test, the pulse voltage loaded to the RF port of the SUT through antenna coupling the HEMP can reach several kilovolts, and the RF3376 is completely damaged. Therefore, this paper focuses on the phenomenon of complete damage effect under the harsher high voltage level. Furthermore, when the injection voltage level is equal to or higher than the RF3376 complete damage threshold, the injection waveform shape is completely different from that of the injection waveform below the failure threshold. Therefore, we take the injection waveform of this typical shape as the failure criterion and believe that once this type of waveform appears, complete damage will occur in the DUT. The comparison of the injection waveforms higher and lower than the threshold waveform of the complete damage effect are shown in Figure 6. As illustrated in Figure 6a, for a double-exponential wave, the injection waveform shape is very close to the standard injected pulse connected to a short-circuit load when complete damage occurs. Figure 5b shows that there is a short-circuit channel to GND inside the DUT, which makes the impedance of the DUT's input port close to 0 Ohms. The oscillation of the injection waveform when only gain loss occurs can also demonstrate the input port of the DUT has certain impedance characteristics, and the injection waveform presents the impedance mismatch between pulse generator and the DUT.
Result after PCI with Different Pulses
The experiment, showed a consistency of test data of all samples in each injection environment, which is convenient for statistical analysis. Table 1 and Figure 7 show some test data and measured waves under typical injection environment, respectively. According to Table 1, the load current, that is, the residual pulse current after passing through the DUT is at an average level of 1 A. With the comparison of peak values for injected wave and residual wave (Figure 7), it can be conjectured that a ground discharge channel exists in the DUT. The main pulse energy entering the DUT from the pulse source is released along the ground discharge channel into the ground, protecting the back-end load from pulse impact, which can be seen from the injection waveforms in Figure 7. The shapes of the square wave and the double exponential waveform also verify the near-short-circuit ground channel in the DUT. After the functionality test, these samples (DUT) suffered very serious destruction. The major damage modes of semiconductor devices include open circuit and short circuit. Due to the different physical mechanism, the location of the damage point and its severity will influence the I-V characteristics and performance indicators such as gain or noise factor, etc., for the device. In this paper, destruction can be considered as very serious damage, and performance degradation like gain decline can be considered as slight damage.
Due to the difference in electromagnetic properties of device materials, they may have different electromagnetic sensitivities to pulse peak value, pulse integral energy, rate of rising edge and rectification impact [1,20]. Vector norm theory has been widely used to characterize EMP waveform characteristics and effect mechanism, such as the U.S. military standard MIL-STD 188-125, IEC standard 61000-4-33 and other international specifications and standards [20,21].
Vector norm theory generally adopts mathematical vectors or matrices to express its features and properties, which are defined as: Therefore, f (t) is the injection current waveform of the INPUT port of DUT. As shown in Table 2, 2-norm and ∞-norm are used to study the electromagnetic sensitivity characteristics of the DUTs, which represent the energy and peak value of the injected current wave respectively. The blue and red scatter points in Figure 8 are the sample failure threshold data represented by ∞-norm and 2-norm, respectively, and the trend curve reflecting the correlation between failure threshold and pulse width is obtained by the fitting method. When the pulse width is less than or equal to 200 ns, the ∞-norm value used to represent the current peak value is similar, indicating that the electromagnetic sensitive parameter leading to the effect is mainly the current peak value, and the corresponding effect mechanism is mainly breakdown. When the pulse width is located in 800 ns to 1000 ns, the trend of the red curve shows that the 2-norm representing energy tends to be stable, indicating that the electromagnetic sensitive parameter is mainly energy, and its effect mechanism is mainly burnout. With the increase of pulse width, the trend of ∞-norm falls and 2-norm rises, showing that energy plays a more important role than peak value. This is the transition zone from peak to energy, which is called the transition zone of electromagnetic sensitive parameter competition failure. Therefore, based on this discovery of the effect laws, the pulse-width zone is distinguished and includes ∞-norm dominating, 2-norm dominating and competitive failure dominating regions, respectively.
Mechanism for the Damage of the LNA
In this subsection, electrical parameter tests of I-V characteristics and optical microscopic analysis are performed on the damaged samples. Figure 9 shows a schematic diagram of the circuits in the RF3376. The amplifier consists of two GaAs BHT transistors that are cascaded with a common collector. The RF signal reached the receiver, entered into DUT through the RF IN port and was amplified by the two-stage amplifier, before outputting at the RF OUT port. The RF IN port was selected as the injection port in the PCI tests, and the RF OUT port was followed by a 50 ohms standard load. In each injection environment, a typical damaged sample was selected for comparative analysis. As shown in Figure 10a, the pin pairs of IN-GND and OUT-GND of all damaged samples show short-circuit low resistance characteristics, indicating that short-circuit channels appeared inside due to pulse impact. As shown in Figure 10b, the main damaged parts of all the damaged samples are the two cascaded transistors of DUT. According to the damage degree, as the pulse width of the injection waveform increases, the burning degree of the transistor becomes more serious, indicating that the energy norm (2-norm) has a more obvious influence on the device destruction with the increase of the pulse width. These results verify the effect laws obtained in Section 3. However, in the study of the semiconductor device damage mechanism, the low resistance channel always reflects damage induced by the breakdown effect of DUT, which causes an instant increasing pulse current that leads to the burnout. Therefore, as an intermediate process, it is difficult to find evidence of the breakdown effect in samples with a serious degree of burnout. The sample #YQ-7 (Pulse width 1000 ns) with the most serious damage degree was taken as an example to study the short-circuit channel caused by pulse impact, as shown in Figure 11. The two transistors suffered the most serious damage. After the pulse energy entered the RF IN port, it reached the signal ground GND along B1 → E1 → B2 → E2, then forming the main pulse transmission channel 1, whose material was carbonized and presents a short-circuit characteristic. In addition, the bypass R2 resistor burned out, forming pulse transmission channel 2. The appearance of pulse channel 1 leads to shortcircuit characteristics of RF IN and GND pins, and the pulse channel 2 and the burnout of PN junction of the first-stage transistor leads to short-circuit characteristic of RF OUT and GND pins, which agrees with the test results of I-V characteristics.
Waveform Equivalence and EM Parameter Determination
According to Figure 10b, the damage degree of the EMP environmental damaged sample #DE-11 is the lightest damaged degree in the PCI test, lower than the damage result of the square wave with 100 ns pulse width. Based on the Figure 7 injection waveform test results, due to the impedance mismatch caused by the short-circuit feature of the damaged DUT port, the output amplitude of the square-wave pulse generator became huge with a long-attenuated oscillation period, which will carry powerful energy to impact the DUT. However, the output of the EMP pulse generator will become close to the standard double-exponential wave when the DUT port is in short-circuit status. According to the difference of the wave shapes, the energy carried in the square-wave pulse is far greater than a double-exponential wave, which is largely responsible for the effect difference between the practical environment waveform and the standard simplified waveform.
With the same pulse width, we can see the energy carried in a square wave and that its impact on RF3376 is significantly higher than the 20 ns/500 ns EMP wave. If the square wave with the same pulse width as the environment wave, is selected as the injected wave instead of the actual coupled environment wave, it will be able to obtain harsher results. However, whether to choose square wave as injection waveform depends on the actual test requirements.
According to Figure 10b, we believe that the effect caused by a double exponential waveform can be approximately equivalent to the square wave environment with 100 ns pulse width for RF3376. As demonstrated in Figure 7a, the 2-norm of the test data of 100 ns square wave and double exponential wave are calculated at 0.0172 and 0.0156, respectively, and the numerical results are similar and at the same level. Based on the analysis results of norm theory and effect mechanism, 20 ns/500 ns double exponential waveform is equivalent to 100 ns square pulse waveform for the RF3376 component. From pulse-width regions divided in Figure 8, the electromagnetic sensitive parameter region of RF3376 is the ∞-norm dominant region, and the electromagnetic sensitive parameter of RF3376 under the 100 ns square-wave injection environment is the current peak.
Conclusions
To utilize a component-level PCI test to assist in system-level tests for damage threshold distribution, it is necessary to study the electromagnetic sensitivity characteristics of the vulnerable electronic components. First, a small electronic system was developed as the research object, and the RF LNA was diagnosed as a vulnerable component by a PCI and pulse illumination test. Then the PCI tests of RF3376 were carried out with square waveforms of different pulse widths and double exponential waveforms of typical a HEMP conducted environment. The action rules of electromagnetic sensitive parameters were obtained by using norm theory. The effect mechanism and damage path were determined by electrical parameter and optical microscopic analysis. Based on the results of norm and mechanism analysis, the equivalent square wave of the double exponential waveform and the electromagnetic sensitive parameter of square-wave injection were determined. The main conclusions are as follows: According to the laws of the damage threshold curves represented by norms varying different square waves, the electromagnetic parameter action is divided into three regions, called ∞-norm, 2-norm and competitive failure dominating regions. The ∞-norm dominant region indicates that the peak value of the injection waveform plays a major role in the damage effect; 2-norm indicates the energy; and the competitive failure region indicates that multiple electromagnetic sensitive parameters such as peak value and energy jointly play a role in the damage effect.
The electromagnetic damage effect of RF3376 is mainly caused by the burning of two transistors in a cascade relationship, forming a pulse energy transmission channel from the component input port to the signal ground GND. The pin pair IN-GND and OUT-GND of the DUT are short-circuited due to the short-circuit impedance characteristics of the channel. The effect mechanism provides the explanation of the injection waveform shape when DUT is completely destroyed and verifies the test results of I-V characteristics.
By analyzing the norm results and damage mechanism of a double exponential environment waveform and a square waveform, the 100 ns square waveform can be determined as the equivalent injection waveform of 20 ns/500 ns double exponential waveform. As a 100 ns square wave is in the ∞-norm dominating region, the pulse peak value of injected current is determined as the electromagnetic sensitive parameter for square-wave PCI tests of RF3376.
In future work, the equivalence of the system-level pulse illumination test and the component-level PCI test based on a simplified injection wave will be investigated further to solve the feasibility problem of using the component-level injection test with large sample size to supplement the system-level test with small sample size.
Conflicts of Interest:
The authors declare no conflict of interest. | 5,730.2 | 2022-02-15T00:00:00.000 | [
"Engineering",
"Physics"
] |
Computational Investigation of Darapladib and Rilapladib Binding to Platelet Activating Factor Receptor . A Possible Mechanism of Their Involvement in Atherosclerosis
Platelet Activating Factor (PAF), the most potent inflammatory mediator, is involved in a wide range of pathophysiological actions. PAF signal transduction is mediated through PAF receptors (PAFR) that are coupled with several isoforms of G-proteins. PAF hydrolysis is mediated through specific enzymes clustered as PAF acetylhydrolases (PAF-AH). The plasma isoform is known as lipoprotein-associated PLA2 (Lp-PLA2), and is considered a marker, or a mediator in the mechanism of atherosclerosis. Darapladib and rilapladib are selective Lp-PLA2 inhibitors. They are, thus, proposed as a novel therapeutic approach for cardiovascular disease (CVD). The data derived from the computational methods used in this paper suggest that darapladib and rilapladib are potential PAFR antagonists, predicted to bind inside the PAF-binding site with a comparable binding affinity to the endogenous agonist (ΔG = –11.1 Kcal mol). Darapladib (ΔG = –10.6 Kcal mol) exhibited a higher affinity than rilapladib (ΔG = –8.2 Kcal mol). The fact that darapladib down-regulates PAFR expression, while PAFR inhibitors down-regulate the expression of CD36, could be the biochemical explanation in the observed necrotic core reduction, both in animals and humans. The reported results in conjunction with bibliographical data lead to the hypothesis that the involvement of darapladib and rilapladib in atherosclerosis could be through direct inhibition of PAF activity as well as modification of PAF metabolism.
Platelet Activating Factor 1.Platelet Activating Factor General Data
Platelet Activating Factor (PAF), a phosphoglycerylether lipid (Scheme 1), is the most potent inflammatory mediator involved in a wide range of pathophysiological actions.PAF is a considered a cell-to-cell messenger acting both intercellular and intracellular (Antonopoulou, Nomikos, Karantonis, Fragopoulou, & Demopoulos, 2008).Even though the majority of ether lipids have been replaced with their esterified analogues during evolution, PAF and some minor phosphoglycerylether lipids were conserved in various organisms due to their important biological roles (Kulikov & Muzya, 1997).While the term PAF was initially attributed to 1-O-alkyl-2-acetyl-sn-glycero-3-phosphocholine (Demopoulos, Pinckard, & Hanahan, 1979), today it is clear that PAF is a member of a large family or structurally related phospholipids with similar pathophysiological activities.These molecules are produced due to enzymatic and chemical oxidation and their main common structural feature is the short chain at sn-2 position (Montrucchio, Alloatti, & Camussi, 2000).
Platelet Activating Factor Metabolism
PAF is synthesized by two distinct pathways, namely the "remodeling" and "de novo" (Snyder, 1995), while it is hydrolyzed by PAF acetylhydrolase (PAF AH).PAF AH is a PLA2 belonging to groups VII and VIII.The plasma isoform, also known as lipoprotein-associated PLA2 (Lp-PLA2, EC 3.1.1.47),has been classified as group VIIA PLA2 (PLA2G7), is calcium independent and circulates bound with LDL and HDL.Two intracellular PAF AHs, namely PAF AH Ib and PAF AH II, have been also characterized (Snyder, 1995;Tselepis & John Chapman, 2002).Increased Lp-PLA2 activity is associated with increased risk of cardiac events, but it is not known whether Lp-PLA2 is a causative agent.
1.1.3Platelet Activating Factor Receptor PAF signal transduction is mediated through PAF receptors (PAFR).PAFR is coupled with several isoforms of G-proteins.The type of cell and ligand determines the G-protein isoform(s) activated by PAFR each time.The ability of PAF to stimulate distinct signaling pathways via multiple G-proteins may explain the diverse biological responses of human cells to it (Ishii & Shimizu, 2000;Honda, Ishii, & Shimizu, 2002).PAFR are "serpentine receptors", with a seven a-helical domains that wave in and out of the plasma membrane seven times.PAFR have been found in all the blood cells and several tissue and organ cells.Soon after the cloning of PAFR, the expression levels of PAFR mRNA in various tissues and organs were determined.
The internalization and desensitization of PAFR is regulated through a phosphorylation site consisted of serine and threonine residues in the C-terminal cytoplasmic tail.PAFR is modified posttranslational by disulfide bonding at C90-C173 and glycosylation at N169, and modifications are necessary for the surface exposure of PAFR (Prescott, Zimmerman, Stafforini, & McIntyre, 2000;Honda et al., 2002).PAF and PAF-like lipids bearing a short oxidized acyl chain at the sn-2 position readily bind to PAFR, but PAFR also interacts with components of the bacterial wall, such as lipopolysaccharides (LPS) (Nakamura et al., 1992) and phosphorylcholine (Cundell, Gerard, Gerard, Idanpaan-Heikkila, & Tuomanen, 1995).These interactions are thought to be an alternative recognition system for innate immunity inducing inflammatory responses to the immune cells.
In humans, the PAFR mRNA is most abundant in neutrophils, monocytes, placenta, lung, dendritic cells and endothelial cells and is the same isoform for all the cell types.The PAFR was initially cloned from the guinea-pig lung by functional expression in Xenopus laevis oocytes.Subsequently, the cloning of human, rat, mouse, porcine, bovine and caprine PAFR was reported (Ishii & Shimizu, 2000;Honda et al., 2002).
Platelet Activating Factor and Atherosclerosis
PAF interplays in critical stages of atherogenesis including thrombosis, inflammation and oxidation.PAF promotes oxidation by stimulating human monocytes/macrophages and neutrophils to produce superoxide anions and hydrogen peroxide that cause LDL oxidation, creating a positive feedback effect, as PAF itself is produced during LDL oxidation.Lp-PLA2 protects LDL against the production and activity of Ox-LDLs by facilitating hydrolysis of PAF-like lipids (Demopoulos, Karantonis, & Antonopoulou, 2003).
In vitro studies involving PAF-like lipids that are mostly fragmented and/or oxidized sn-2 fatty acyl groups and their hydrolysis products, have shown that these molecules can act both as pro-and anti-inflammatory mediators (Berliner, Leitinger, & Tsimikas, 2009;Feige, Mendel, George, Yacov, & Harats, 2010).These studies though do not take into consideration the fact that lyso-PC and free fatty acids are associated with lipoproteins and other plasma carriers making it difficult to calculate their exact concentration and bioavailability in plasma (Öörni & Kovanen, 2009;Rosenson & Stafforini, 2012).These results are further weakened by the fact that many of the observations for lyso-PC can be attributed to contaminating traces of PAF remaining in the lyso-PC preparations used in the studies (Marathe et al., 2001), and the fact that there is no evidence for a specific lyso-PC receptor.
Several PAF agonists/antagonists have been synthesized and isolated from natural sources (Antonopoulou et al., 2008).Some of them are isolated from Mediterranean foods and when co-administered with cholesterol in animals, were able to significantly reduce the amount of esterified cholesterol in aorta without affecting cholesterol plasma levels, and reduce PAF-induced early atherogenesis (Nomikos, Fragopoulou, & Antonopoulou, 2007), as well to cause regression of the existing plaques.
Darapladib and rilapladib (Scheme 1) are selective Lp-PLA2 inhibitors and produce sustained inhibition of plasma Lp-PLA2 activity.Darapladib is a potent, freely reversible, inhibitor of human Lp-PLA2, with an inhibition constant K i of 0.11 nM (Blackie et al., 2003).Rilapladib is also a potent and reversible inhibitor of human Lp-PLA2 with half maximal inhibitory concentration (IC 50 ) in the range of 0.1 to 10 nM (Patent publication numbers: WO2012080497 A2, WO 2012080497 A3 and US20130267544 A1).
Initially darapladib was tested in vivo in atherosclerosis animal models with promising results, as the medication reduced plaque and necrotic core area in swine (Wilensky et al., 2008), and plaque area and inflammatory burden in mice (Hu et al., 2011;Wang et al., 2011).These results suggest that the drug could move on to Phase II ΔG = R T lnK d , where R = 1.987 cal K -1 mol -1 and T = 273 K. Visual inspection of the lowest energy and highest populated model of PAFR-rilapladib complex (Figure 2D) reveled that its lower affinity could be attributed to the lack of interaction between the oxoquinolinyl ring and His248/His249 residues.In such a configuration, the position of the phosphate group of PAF is occupied by the methoxyethyl piperidinyl moiety of rilapladib, which provides no hydrogen bonding interactions with either His248 or His249.The oxoquinolinyl ring is hydrogen bonded with Tyr177 and is buried inside the same site of PAF's choline moiety.The 2,3-difluorophenyl ring of rilapladib is stacked above the oxoquinolinyl moiety interacting with Phe98 and Phe152.Finally, the 4-trifluoromethyl biphenyl group is buried a bit deeper inside the hydrophobic channel with respect to the corresponding moiety of darapladib, with the -CF 3 group at the same position of C-10 of PAF's aliphatic chain.
Interaction of Darapladib and Rilapladib With Lp-PLA2 and PAFR
Taken together, the above results suggest that darapladib may be a potential PAFR antagonist, which is predicted to bind inside the PAF-binding site with a comparable binding affinity (ΔG = -10.6Kcal mol -1 ) with respect to the endogenous agonist (ΔG = -11.1 Kcal mol -1 ).Similarly, rilapladib could also serve as a PAFR antagonist, albeit with lower binding affinity (ΔG = -8.2Kcal mol -1 ).The predicted binding modes of both inhibitors with either Lp-PLA2 or PAFR indicate that their trifluromethyl biphenyl moiety is probably interacting within the same binding sites that accommodate the long alkyl chain of PAF, whereas the pyrimidinyl and oxoquinolinyl rings (of darapladib and rilapladib, respectively) interact with the catalytic residues of Lp-PLA2 and the hydrophilic PAF-binding site.
Lp-PLA2 and PAF Involvement in Atherosclerosis
There is a considerable amount of data reporting Lp-PLA2 as a marker of the risk of coronary heart disease (CHD), with controversial results.Even though Lp-PLA2 tends to be considered an independent marker for CVD, recent studies fail to establish its association with CVD event in apparently health subjects and in patients treated with statins that have their cholesterol levels managed (Rosenson & Stafforini, 2012).
According to our proposed theory where PAF is the initial cause of atherosclerosis and plaque formation (Demopoulos et al., 2003), and the literature data, darapladib and rilapladib are likely to inhibit/reduce atherosclerosis and its development process (therefore all its harmful consequences) also through the inhibition/reduction of PAF effects.
The deposition and binding of LDL-Cholesterol in the subintimal space is considered a key factor for the initiation and development of the atherosclerosis.After their binding to proteoglycans the LDL-Cholesterol are oxidativelly modified (ox-LDL) resulting in high concentrations of really potent inflammatory molecules, like PAF and PAF-like lipids.These molecules act through the specific PAF receptor present in almost all the cells involved in atherosclerosis like smooth muscle cells, cardiomyocytes, neutrophils, monocytes-macrophages, eosinophils, and Kupffer cells.It has also been shown that endothelial cells, express PAFR not only on the cell surface, but also in the large endosomal compartment (Montrucchio et al., 2000;Antonopoulou et al., 2008).
In addition, we and others have published (Nomikos, Fragopoulou, & Antonopoulou, 2007) that the PAF-inhibitors usually inhibit the key-PAF biosynthetic enzymes, and, additionally, either inhibit or activate PAF AH, the key-PAF catabolic enzyme.
Darapladib, Rilapladib and PAF Biological Activity as Well as PAF Levels
Therefore, darapladib and rilapladib are likely to inhibit/reduce atherosclerosis and its development process (therefore all its harmful consequences) through the inhibition/reduction of PAF effects, but also through inhibition of PAF biosynthesis that leads to reduced PAF levels, as do statins (Tsantila et al., 2011).
Unfortunately there are no in vitro experimental data concerning the regulation of the two major PAF biosynthetic enzymes by darapladib and rilapladib that could help us understand the mechanism of PAF levels regulation.
On the other hand darapladib and rilapladib are potent specific inhibitors of Lp-PLA 2 , which is considered the main PAF degrading enzyme.The effect of darapladib on PAF levels has only been studied in mice by two different research groups.Hu et al. showed that darapladib reduced plaque area in LDL receptor (LDLR) deficient mice, without affecting the lipid profile or PAF levels of the mice.The intervention reduced as expected Lp-PLA2 activity along with CRP and IL-6 levels and the expression of the inflammatory genes of MCP-1 and VCAM-1 (Hu et al., 2011).The same results were obtained by Wang et al. in Apo-E deficient mice that also had decreased macrophages' content and increased collagen content in the lesions of the darapladib group (Wang et al., 2011).
These controversial results can be explained by suggesting that PAF hydrolysis is not mediated only through Lp-PLA2.The PAF clearance was measured in mice and showed that the majority of the PAF molecules were hydrolyzed in liver and kidney by the intracellular PAF AH, after being transported as intact molecules.The fact that mice have an 8.6 times increased enzymatic activity relative to humans indicates that this is probably the PAF clearance pathway also in humans (Liu et al., 2011).
These observations give rise to the critical question of whether and to what extend Lp-PLA2 is responsible for the clearance of the other highly inflammatory PAF-like molecules present in oxLDL that have a smaller affinity to the enzyme compared to PAF, but are in much higher concentrations (Markakis et al., 2010).
Possible Actions of Darapladib and Rilapladib in Aorta, That Are Explained by PAFR Inhibition
One critical aspect of the in vivo darapladib administration to diabetic and hypercholesterolemic swine, which is not discussed by the authors, is the down-regulation of PAFR expression by 49% compared to control group not receiving the drug (Wilensky et al., 2008).
It is known that the expression of CD36 is directly associated with the uptake of oxLDL by macrophages (Febbraio & Silverstein, 2007;Rios, Gidlund, & Jancar, 2011) and this uptake is not regulated by intracellular levels of cholesterol, leading to continuous uptake of oxLDL and the differentiation of macrophages into foam cells.The oxLDL molecules increase CD36 expression, exerting a positive feedback effect on the expression of its receptor in human and mouse monocytes/macrophages (Feng et al., 2000;Rios, Jancar, Melo, Ketelhuth, & Gidlund, 2008), an effect that is reversed by PAFR antagonists.Moreover treatment of LDL receptor-deficient mice with PAFR antagonists reduced the formation of fatty streaks lesions (Subbanagounder, Leitinger, Shih, Faull, & Berliner, 1999).
PAFR down-regulation with a possible antagonistic effect from darapladib and rilapladib can give an explanation to the reduction of the nectrotic core in darapladib and rilapladib treated animals and humans.The mechanism can involve the reduction of oxLDL uptake from macrophages through CD36, thus inhibiting extensive foam cell formation and subsequently a smaller necrotic core.
PAF Levels and PAF AH, Lp-PLA2 Expression
Several studies have shown that PAF and PAF inhibitors levels can affect PAF AH expression.LPS and PAF stimulate expression of PAF AH via distinct signaling pathways (Howard, Abdel-Al, Ditmyer, & Patel, 2011).In another study involving human non-adherent monocyte-macrophage cells (Mono-Mac 6; MM6) it was found that both PAF and LPS were able to up-regulate the expression of PAF AH in a dose dependent manner.The specific PAFR inhibitor WEB2170 was able to completely block the PAF stimulated up-regulation of PAF AH and also inhibited the PAF AH production in the tested cell line but also in rats (Howard & Olson, 2000), after LPS stimulation.The p38 MAPK inhibitor, SB203580 inhibited by 60% the up-regulation of PAF AH after LPS stimulation while PAF stimulation was not affected.The co-administration of WEB2170 and SB203580 completely abolished PAF AH expression, indicating that the LPS-induced PAF AH mRNA levels present after SB203580 administration are the result of autocrine activation of the PAF receptor due to LPS-stimulated production of PAF, or the fact that LPS acts through the PAFR.
The PAFR Inhibition by Darapladib and Rilapladib Hypothesis, Concerning Hydrolysis Products of Lp-PLA 2
From the above it could be formulated in more detail the aforementioned hypothesis concerning the harmful consequences of the hydrolysis products of Lp-PLA2 as follows: It is well-known that the general body's response is to increase the levels of Lp-PLA2 when the levels of PAF are increased (i.e.PAF affects the gene expression of Lp-PLA2), as shown in a recent study involving 150 patients with CHD and 120 controls that found a strong positive relationship between elevated plasma PAF or Lp-PLA2 levels and the risk of CHD.This study also provided evidence that there was a strong correlation between plasma PAF and Lp-PLA2 levels, and between plasma PAF and Lp-PLA2 and inflammatory factors IL-6 and hs-CRP levels (Zheng et al., 2012).
So it could thus be suggested that: a) Darapladib and rilapladib through reduction of the PAF biological activity (as PAF inhibitors) and PAF levels (as possible inhibitors of PAF biosynthesis) could reduce Lp-PLA2 biosynthesis and prevent the possible adverse effects of Lp-PLA2 (the pro-inflammatory molecules, such as LPC and oxNEFA), and b) In addition, darapladib and rilapladib inhibit also the effects of the existing Lp-PLA2 and so the harmful consequences of the LPC and the oxNEFA.
Conclusion
In conclusion, the combination of computational modeling data presented in this paper with the bibliography on PAFR inhibitors and their effect on atherosclerosis, recommend that more experiments should be done in order to clarify our hypothesis that the implication of darapladib and rilapladib in atherosclerosis is through the inhibition of PAF actions, but moreover through the modification of PAF metabolism.These experiments must include measurement with basic commonly accepted methodology of the effect of darapladib and rilapladib first on PAFR in ex-vivo models of washed platelet aggregation and second on the in vitro PAF biosynthetic enzymes.
(a) the high d (b) the large o the solvent (F nal clusters | 3,892 | 2014-01-02T00:00:00.000 | [
"Biology"
] |
A Review on Metal Nanoparticles Nucleation and Growth on / in Graphene
In this review, the fundamental aspects (with particular focus to the microscopic thermodynamics and kinetics mechanisms) concerning the fabrication of graphene-metal nanoparticles composites are discussed. In particular, the attention is devoted to those fabrication methods involving vapor-phase depositions of metals on/in graphene-based materials. Graphene-metal nanoparticles composites are, nowadays, widely investigated both from a basic scientific and from several technological point of views. In fact, these graphene-based systems present wide-range tunable and functional electrical, optical, and mechanical properties which can be exploited for the design and production of innovative and high-efficiency devices. This research field is, so, a wide and multidisciplinary section in the nanotechnology field of study. So, this review aims to discuss, in a synthetic and systematic framework, the basic microscopic mechanisms and processes involved in metal nanoparticles formation on graphene sheets by physical vapor deposition methods and on their evolution by post-deposition processes. This is made by putting at the basis of the discussions some specific examples to draw insights on the common general physical and chemical properties and parameters involved in the synergistic interaction processes between graphene and metals.
Free-standing graphene, also known as one layer graphite, was firstly obtained in 2004 [1,2].Then, the scientific and technological research has seen an exceptional continuing grow of the interest in graphene and graphene-based materials since the properties of these materials can drastically revolutionize the modern-day technology.Graphene, in fact, presents several disruptive properties as compared to the standard semiconducting materials which were, until now, at the basis of the technological development.As examples, graphene is characterized by extraordinary carrier mobility (200,000 cm 2 V −1 s −1 [3]), thermal conductivity (~5000 Wm −1 K −1 [4][5][6]), white light transmittance (~97.3%[7]), and specific surface area (~2630 m 2 g −1 [8]).These properties make graphene the key material in the current nanotechnology revolution and the ideal material for the fabrication of functional devices finding applications in electronics, energy generation and storage (batteries, fuel cells and solar cells), plasmonics, sensors, supercapacitors and other nano-devices [1,2,[9][10][11][12][13][14][15][16].
In general, composites fabricated combining graphene and metal NPs attract great attention since they result versatile hybrid materials presenting unconventional properties arising from the atomic-scale mixing of the properties of graphene and NPs.In fact, in addition to graphene, metal NPs are another main character in the nanotechnology field of study.Due to electron confinement and surface effects metal NPs present size-dependent electrical, optical, mechanical properties different from the corresponding bulk counterparts and these properties are routinely exploited in plasmonic, sensing, electrical, catalytic applications [72][73][74].The notable aspect is that these size-dependent properties of metal NPs can be coupled to the properties of graphene to obtain a composite artificial material presenting un-precedent characteristics and performances arising from the (controlled) mixing of the properties of the component elements.For example, nanocomposite materials obtained by metal NPs and thin metal nano-grained films deposited on graphene sheets were successful employed in transistors, optical and electrochemical sensors, solar cells, batteries [17][18][19][31][32][33][34][35][36][37][38][39][40][41][42][43].
A deep understanding and control of the electrical properties of metal/graphene interface is crucial for future applications of this material in electronics and optoelectronics.Current injection at the junction between a three dimensional metal contact and two-dimensional graphene with very different densities of states is an interesting physical problem.Furthermore, the specific contact resistance at the metal/graphene junction [75][76][77][78] currently represents one of the main limiting factors for the performances of lateral and vertical graphene transistors both on rigid and flexible substrates [79][80][81][82][83][84][85].Several solutions have been investigated to minimize this resistive contribution [86][87][88].
In this context, the key point of study is the interaction occurring at the graphene-metal interface .In fact, for example, the electronic properties of graphene are dramatically influenced by interaction with metallic atoms [101][102][103][104]. So, this interaction crucially affects the electronic transport properties of graphene based transistors [105][106][107][108][109][110][111][112][113].In this context, the detailed description and comprehension of the metal-graphene interactions is the key step toward the control of processes and properties of the graphene-metal NPs composite materials and, so, to develop effective applications [59].The graphene-metal NPs composites can be prepared by several methods such as chemical reduction, photochemical synthesis, microwave assisted synthesis, electroless metallization, and physical vapor deposition processes [17][18][19].In particular, this paper reviews the basic aspects of physical vapor based synthesis methods of graphene-metal NPs composites.Physical vapor deposition processes, such as thermal evaporation or sputtering, are traditional methods to produce metal NPs and films on substrates [114][115][116][117][118][119][120][121][122].These methods are acquiring large interest for the production of metal NPs-graphene composites with specific physico-chemical properties exploitable in specific applications (SERS, catalysis, nanoelectronics) [54][55][56][57][58][59][60][61][62][63][64][65][66][67].In fact, they are simple, versatile and high-throughput and the general microscopic thermodynamics and kinetics mechanisms involved in the nucleation and growth processes of atoms on surfaces are well-known.In this sense, physical vapor deposition processes are a convenient way of depositing a range of metallic materials onto graphene sheets.Atoms deposited on a substrate undergo competing kinetic and thermodynamic processes which establish the final NPs or film structure [114][115][116].The adsorbed atoms (or adatoms) transport process involves random hopping phenomena on the surface dictated by the surface diffusivity D (which determines the diffusion length) obeying an Arrhenius law [114][115][116].So, these adatoms, randomly diffuse across the substrate surface until they can join together forming a nucleus or they can stop at some particular surface defect or they can re-evaporate from the surface.This situation is largely influenced by the adatom-substrate interaction and process parameters (substrate temperature, arrival flux, etc.).Materials deposited by physical vapor processes can adopt a variety of morphologies which are tunable by the control of the deposition process parameters.In addition, post-deposition processes can allow a further control of the NPs or films morphology ad structure by inducing further specific thermodynamics and kinetics driven self-organization phenomena.It is evident, so, the key importance assumed by the understanding of the growth kinetics of the metal NPs and films on graphene sheets to infer how the interaction with the graphene and the process parameters influences the metal film morphology and, as a consequence, the overall nanocomposite properties.
On the basis of these considerations, the review is organized as follows: The first part (Section 2) is devoted to adsorption and diffusion of metal atoms on/in graphene and on the influence of these parameters on the metal NPs nucleation and growth processes.This section describes the fundamental microscopic thermodynamics and kinetics processes occurring during vapor-phase depositions (i.e., evaporation or sputtering) of metals on graphene sheets and resulting in the formation of metal NPs or films; particular attention is devoted to theoretical (Section 2.1) and experimental (Section 2.2) studies focused on the interaction, after adsorption, of metals atoms with graphene and on how this interaction influences the adatoms diffusivity and the final metal NPs structure and morphology.Critical discussions on the specific involved microscopic phenomena (adsorption, diffusion, nucleation, ripening, coalescence, etc.) and on the corresponding parameters (surface energies, diffusivity, activation energy, etc.) are presented.
The second part (Section 3) is devoted to the review of data concerning the production of metal NPs arrays on graphene exploiting the dewetting process of deposited metal films.The dewetting process of a metal film deposited on a substrate is the clustering phenomenon of the continuous metal layer driven by the lowering of the total surface free energy.Nowadays, the controlled dewetting of thin metal films on functional substrates is widely used as a low-cost, versatile, high-throughput strategy to produce array of metal NPs on surfaces for several applications such as in plasmonic and nanoelectronics [123][124][125][126][127][128][129][130].Recently, this strategy was applied to thin metal films (such as Au, Ag) for the production of arrays of metal NPs on graphene which were, then, used, for example, in SERS applications [68][69][70][71].We discuss the results of such a strategy pointing out the microscopic parameters involved in the dewetting process of metal films on graphene.
Section 4, shortly discuss some aspects related to the metal-graphene contacts to draw the general requirements for a metal contacts to be suitable to be efficiently used as an electrode to grapheme in nanoelectronics devices.
Finally, the last paragraph (Section 5) summarizes conclusions, open points and perspectives in the graphene-metal NPs composites field of study.
General Considerations
Liu et al. [57,100] systematically studied metal adatoms adsorption on graphene by ab initio calculations, ranging from alkali metals, to sp-simple, transition, and noble metals.In these works, the main aim was the correlation between the adatom adsorption properties and the growth morphology of the metals on the graphene.The authors main finding lies in the fact that the metal growth morphology is determined by the E a /E c parameter (with E a the adsorption energy of the metal on graphene and E c the bulk metal cohesive energy) and by the ∆E parameter (i.e., the activation energy for the metal adatom diffusion on graphene).First of all, experimental data (as we will see in Section 2.2) show that different metals on graphene exhibit very different growth morphologies even if deposited in similar conditions and at similar coverage.For example, considering a single-layer graphene obtained by thermal annealing of SiC, a 0.8 ML deposition of Pb with the sample at 40 K, results in the formation of large crystalline Pb islands [100]; deposition of Fe, in the same conditions, results, instead, in continuous nucleation of large, medium, and small size islands [100]; further experimental data [65] concern deposition of metals on single-layer graphene grown on Ru(0001): Pt and Rh result in finely dispersed small clusters, Pd and Co in larger clusters at similar coverages.To complicate further the situation, for example, Gd atoms deposited on graphene/SiC at room temperature nucleate in two-dimensional islands of fractal morphology [100].In general, therefore, even if the various metals follow a Volmer-Weber growth mode (three-dimensional growth without a wetting layer) on the graphene, a wide-range of morphology for metals nanostructures deposited on graphene are observed.Within this mess of data, Liu et al. [57,100] performed a systematic theoretical study to understand, quantitatively, the key parameters governing the metal clusters growth morphology during deposition.They start from the idea that the interaction of the metal atoms with free-standing graphene determines the specific adatoms diffusion mechanisms establishing, then, how the adatoms nucleate and growth.So, the authors, performed first-principles calculations based on the density functional theory to evaluate the interaction of the metals with graphene.Several results were inferred by these simulations which can be summarized as follows: (a) The adsorption site of metal atom on graphene is the more energetically stable and it depends on the chemical nature of the atom.So, for Mg, Al, In, Mn, Fe, Co, Ni, Gd the adsorption site is the hexagonal center site in the graphene lattice, named the hollow site (H).The adsorption site for Cu, Pb, Au atoms is at the top of a carbon atom, named T site.The adsorption site for Ag, Cr, Pd, Pt atoms is at the middle of a carbon-carbon bond, named B site.The second column in Table 1 summarizes the results of Liu et al. [57,100] about the energetic stable sites in graphene for all the investigated atoms.
(b) The results for the adsorption energy E a of the atoms adsorbed on graphene are plotted in Figure 1a and listed in the third column of Table 1.The value of the adsorption energy ranges from less than 1.0 kcal/mol to 45.0 kcal/mol depending on the chemical nature of the atom.This value is an indication of the strength of the interaction between the adsorbed atom and graphene.For example, the interaction of Mg and Ag atoms with graphene is very weak since the corresponding adsorption energies are in the 0.5-0.6 kcal/mol range.On the contrary, the binding of Pd and Pt atoms on graphene is much stronger since the corresponding adsorption energies are 26.5 and 39.3 kcal/mol, respectively.On the other hand, in general, the adsorption energy of I-IV metals on graphene is intermediate, in the 6-27 kcal/mol.
(c) The calculated values for diffusion barrier energies for several atoms on free-standing graphene are plotted in Figure 1b and listed in the fourth column of Table 1.In general, the following correlation between the adsorption energy and diffusion barrier energy exists: the diffusion barrier increases as a consequence of the increase of the adsorption energy (even if some exceptions are present as in the case of Ni and Pt).In particular, the growth morphology of metals on graphene is connected to the E a /E c and ∆E parameters characterizing the metal atoms-graphene system.Figure 2 reports E a /E c for the analyzed atoms on graphene.So, the combination of ∆E (Figure 1b) and E a /E c (Figure 2) is claimed by Liu et al. [100] as the main reason establishing the growth morphology of the specific metal species on the free-standing graphene.From a general point of view, the occurring of the three-dimensional Volmer-Weber growth mode (i.e., growth of three-dimensional clusters typically almost spherical or semispherical directly on the substrate surface) is determined by the energetic condition E c > E a (i.e., (E a /E c ) < 1): in fact, in this condition the bonding between the deposited atoms is higher than the bonding to the graphene.In particular, the growth morphology of metals on graphene is connected to the Ea/Ec and ΔE parameters characterizing the metal atoms-graphene system.Figure 2 reports Ea/Ec for the analyzed atoms on graphene.So, the combination of ΔE (Figure 1b) and Ea/Ec (Figure 2) is claimed by Liu et al. [100] as the main reason establishing the growth morphology of the specific metal species on the free-standing graphene.From a general point of view, the occurring of the three-dimensional Volmer-Weber growth mode (i.e., growth of three-dimensional clusters typically almost spherical or semispherical directly on the substrate surface) is determined by the energetic condition Ec > Ea (i.e., (Ea/Ec) < 1): in fact, in this condition the bonding between the deposited atoms is higher than the bonding to the graphene.Table 1.Ea (adsorption energy of the metal atom on graphene, kcal/mol), ΔE (diffusion barrier of the metal adatom on graphene, kcal/mol), Ea/Ec (with Ec the bulk metal cohesive energy), and Ec−Ea (kcal/mol).Reproduced from Reference [100] with permission from the Royal Society of Chemistry.However, ∆E establishes the adatoms hopping probability.So, it dictates the rate of the adatoms joining to the closest preformed metal cluster with respect to the rate of adatoms joining to other adatoms to form a new cluster.Therefore, ∆E establishes the surface density of the metal clusters on the graphene.For example, the small value of E a /E c for Fe on graphene establishes a standard three-dimensional Volmer-Weber growth mode for Fe clusters on graphene consistent with the experimental observations [100].However, ΔE establishes the adatoms hopping probability.So, it dictates the rate of the adatoms joining to the closest preformed metal cluster with respect to the rate of adatoms joining to other adatoms to form a new cluster.Therefore, ΔE establishes the surface density of the metal clusters on the graphene.For example, the small value of Ea/Ec for Fe on graphene establishes a standard three-dimensional Volmer-Weber growth mode for Fe clusters on graphene consistent with the experimental observations [100].In addition, the diffusion barrier ΔE for Fe on graphene is high so that a high Fe clusters density is produced with respect, for example, the clusters density for Pb deposited on graphene.In fact, ΔE for Pb is lower than for Fe.As a consequence, the Pb adatoms diffuse faster than the Fe adatoms resulting in larger clusters but with a lower surface density.On the other hand, Gd has (Ea/Ec) but higher than that of Fe or Pb and a diffusion barrier intermediate between that of Fe and Pb.This results in fractal-like morphology of the Gd islands on graphene.A further observation concerns, for example, Dy and Eu: despite similar values of Ea/Ec and ΔE, their growth morphologies are different.Dy forms small three-dimensional clusters while Eu forms flat top crystalline islands with well-defined facets.Therefore, Liu et al. [100] suggest that other factors affect the growth morphology in addition to Ea/Ec ratio and ΔE and identify the main factor in specific characteristics of the adatom-adatom interaction.For example, the repulsive interaction between Dy adatoms, arising from a large electric dipole moment, is larger than Eu adatoms resulting in a higher effective barrier for diffusion.
Nd
We observe that these results can be regarded as a general rough guide in understand the growth morphology of metals on graphene.However, these results neglect some effects which are, instead, observed by experimental analyses such as the difference in the growth morphology of deposited metals by changing the substrate supporting the graphene layer (highlighting, so, an effect of the adatoms interaction with the substrate supporting the graphene) or by changing the number of graphene layer.The theoretical results by Liu et al. [57,100] are, in fact, obtained for free-standing single layer graphene sheets.As we will see in the next sections, some theoretical and experimental works studied the effect of supporting substrate on the adatoms-graphene interaction and its impact on the metals growth morphology.
Besides these general considerations, in the following subsections we focus our attention on the model Au-graphene system since it is, surely, the main studied system from a technological point of In addition, the diffusion barrier ∆E for Fe on graphene is high so that a high Fe clusters density is produced with respect, for example, the clusters density for Pb deposited on graphene.In fact, ∆E for Pb is lower than for Fe.As a consequence, the Pb adatoms diffuse faster than the Fe adatoms resulting in larger clusters but with a lower surface density.On the other hand, Gd has (E a /E c ) but higher than that of Fe or Pb and a diffusion barrier intermediate between that of Fe and Pb.This results in fractal-like morphology of the Gd islands on graphene.A further observation concerns, for example, Dy and Eu: despite similar values of E a /E c and ∆E, their growth morphologies are different.Dy forms small three-dimensional clusters while Eu forms flat top crystalline islands with well-defined facets.Therefore, Liu et al. [100] suggest that other factors affect the growth morphology in addition to E a /E c ratio and ∆E and identify the main factor in specific characteristics of the adatom-adatom interaction.For example, the repulsive interaction between Dy adatoms, arising from a large electric dipole moment, is larger than Eu adatoms resulting in a higher effective barrier for diffusion.
We observe that these results can be regarded as a general rough guide in understand the growth morphology of metals on graphene.However, these results neglect some effects which are, instead, observed by experimental analyses such as the difference in the growth morphology of deposited metals by changing the substrate supporting the graphene layer (highlighting, so, an effect of the adatoms interaction with the substrate supporting the graphene) or by changing the number of graphene layer.The theoretical results by Liu et al. [57,100] are, in fact, obtained for free-standing single layer graphene sheets.As we will see in the next sections, some theoretical and experimental works studied the effect of supporting substrate on the adatoms-graphene interaction and its impact on the metals growth morphology.
Besides these general considerations, in the following subsections we focus our attention on the model Au-graphene system since it is, surely, the main studied system from a technological point of view due to its exceptional performances in technological devices ranging from sensors and biosensors to transistors and solar cells.
Mobility and Clustering of Au on Graphene
Srivastava et al. [92] performed density functional calculations to investigate the bonding properties of Au n (n = 1-5) clusters on perfect free-standing single-layer graphene.In synthesis, their results show that the Au n clusters are bonded to graphene through an anchor atom and that the geometries of the clusters on graphene are similar to their free-standing counterparts.Figure 3 shows, in particular, the results for the stable geometry configurations of the Au 1 , Au 2 , Au 3 , Au 4 , Au 5 on the graphene.According to these results: (a) the energetically stable site for the Au atom on graphene is atop to C atom (at an equilibrium distance of 2.82 Å), in agreement with the finding of Liu et al. [100]; (b) for n > 1, each of the Au n cluster is bonded to the graphene by one Au atom which is closer to the graphene and the overall geometry of the cluster remembers its freestanding configuration.Concerning the Au 5 cluster two different stable configurations are found, i.e., the last two rows in Figure 3.These two configurations differ for taking into in account or not van der Waals interaction: the last configuration for the Au 5 cluster (named Au 5 (P)) is obtained taking into in account the van der Waals interaction.The overall results of the calculations performed by Srivastava et al. are summarized in Table 2.This table reports, for each Au n cluster: h a which is the distance of the Au anchor atom of the cluster from the graphene plane; d ac which is the distance of the Au anchor atom from the nearest-neighbor C atom of the graphene layer; the binding energies BE 1 , BE 2 , BE 3 of the Au n clusters with the graphene, being these energies defined by BE 1 G −E Au_n with E G the energy of the free-standing graphene, E ' G the energy of the graphene after adsorbing the Au n cluster, E Au_n the energy of the isolated Au n cluster, E G+Aun the energy of the system formed by the free-standing graphene and the isolated Au n cluster, n the number of Au atoms in the cluster.With these definitions, BE 1 represents the cohesive energy of the cluster affected by the interaction with the graphene, BE 2 is the energy gained by the system in consequence of the addition of one more atom to the already existing cluster, BE 3 is the energy gained by the system resulting from the interaction of graphene and cluster.
In particular, analyzing the binding energies, the following conclusions can be drawn: the Au n cluster is bonded to the graphene by the Au anchor atom and the bonding energy is dependent both on h a and d ac .Furthermore, the small values of BE 3 are the signature of the weak bond between the Au n clusters and the graphene.This should favor high mobility of Au adatoms and Au n cluster on perfect free-standing graphene.However, this mobility is, also, determined by the diffusion barrier.To analyze this point, we discuss the theoretical findings of Amft et al. [93].They used density functional calculations to study the Au n (n = 1-4) mobility on free-standing single layer graphene and their clustering properties.In particular, they studied the mobility of the Au atoms (Au 1 ) and the mobility of the Au 2 , Au 3 , and Au 4 clusters finding that the diffusion barrier of all studied clusters ranges from 4 to 36 meV.On the other hand, they found that the Au n adsorption energy ranges from −0.1 to −0.59 eV.The diffusion barrier, therefore, results much lower than the adsorption energies.These results confirm the high mobility of the Au 1-4 clusters on graphene along the C-C bonds.The Au 4 cluster shows a peculiarity with respect to the other clusters: it can present two distinct structure, i.e., the diamond-shaped Au values for the adsorption energy and for the diffusion barrier of the Au 1-4 clusters, Amft et al. [93] conclude that the low diffusion barriers for the Au n clusters (with respect to the adsorption energy) suggest a high mobility of the clusters on the graphene also at low temperatures.So, the adsorbed Au n clusters can easily diffuse on the graphene and, upon merging, they form larger clusters to minimize the total energy of the system (since the Au-Au bonding energy is higher than the Au-C one).
Amft et al. [93] conclude that the low diffusion barriers for the Aun clusters (with respect to the adsorption energy) suggest a high mobility of the clusters on the graphene also at low temperatures.So, the adsorbed Aun clusters can easily diffuse on the graphene and, upon merging, they form larger clusters to minimize the total energy of the system (since the Au-Au bonding energy is higher than the Au-C one).Table 2. Anchor atom's distance above graphene plane (ha), distance from nearest-neighbor C atom (dac), binding energies (BE 1 -BE 3 ) of Aun clusters adsorbed on perfect graphene.Reproduced from Reference [92] with permission from the American Physical Society.The theoretical results illustrated in the previous Sections 2.1.1 and 2.1.2are derived for atoms and cluster on free-standing graphene.However, as we will see in Section 2.2, some experimental results pointed out some differences in the growth morphology of metals deposited on graphene by changing the substrate supporting the graphene.So, in the present section we review a theoretical Reproduced from Reference [92] with permission from the American Physical Society.Table 2. Anchor atom's distance above graphene plane (h a ), distance from nearest-neighbor C atom (d ac ), binding energies (BE 1 -BE 3 ) of Au n clusters adsorbed on perfect graphene.Reproduced from Reference [92] with permission from the American Physical Society.The theoretical results illustrated in the previous Sections 2.1.1 and 2.1.2are derived for atoms and cluster on free-standing graphene.However, as we will see in Section 2.2, some experimental results pointed out some differences in the growth morphology of metals deposited on graphene by changing the substrate supporting the graphene.So, in the present section we review a theoretical analysis (as model system analyses) about diffusion and mobility of Au atoms on graphene taking into in account the effect of the substrate supporting the graphene sheet.These theoretical data, so, can be Crystals 2017, 7, 219 9 of 40 directly compared to the theoretical data for adsorption and diffusion of Au atoms on free-standing graphene as reported in the previous sections.
System
Semidey-Flecha et al. [99] used density functional theory calculations to investigate the adsorption and diffusion of Au adatom on the graphene moiré superstructure on Ru(0001).Their results can be synthesized as follows: (a) the FCC region on the graphene moiré is the most stable adsorption site for Au 1 ; (b) the diffusion barrier for Au 1 is determined to be 0.71 eV (much higher than the value of 15 meV evaluated by Amft et al. [93] for Au 1 on free-standing graphene).
The epitaxial growth of graphene on Ru(0001) is usually used to produce supported high-quality large area graphene sheets [65,99,131].In this case, the graphene layer presents the moiré super-structure due to mismatch between the graphene and Ru(0001).In addition, from an experimental point of view, the study of metal atoms (Pd [65], Co [65], Au [65,132], Fe [133], Pt [134]) deposited on graphene/Ru(0001) is a very active field of study in view of catalytic applications.So, the theoretical study of metal atoms bonding and mobility on graphene/Ru(0001) is crucial in reach a control on the metal growth process.In particular, the theoretical analysis by Semidey-Flecha et al. [99] are focused on the diffusion properties of Au atoms on graphene/Ru(0001).
First of all, Figure 4 reports the graphene structures taken into considerations by the authors to run the simulations: (a) free-standing grapheme; (b) graphene on fcc Ru(0001); (c) graphene on hcp Ru(0001); (d) graphene on ridge Ru(0001).Each image reports, also, the indication of the notable sites.
Crystals 2017, 7, 219 9 of 40 analysis (as model system analyses) about diffusion and mobility of Au atoms on graphene taking into in account the effect of the substrate supporting the graphene sheet.These theoretical data, so, can be directly compared to the theoretical data for adsorption and diffusion of Au atoms on free-standing graphene as reported in the previous sections.Semidey-Flecha et al. [99] used density functional theory calculations to investigate the adsorption and diffusion of Au adatom on the graphene moiré superstructure on Ru(0001).Their results can be synthesized as follows: (a) the FCC region on the graphene moiré is the most stable adsorption site for Au1; (b) the diffusion barrier for Au1 is determined to be 0.71 eV (much higher than the value of 15 meV evaluated by Amft et al. [93] for Au1 on free-standing graphene).
The epitaxial growth of graphene on Ru(0001) is usually used to produce supported high-quality large area graphene sheets [65,99,131].In this case, the graphene layer presents the moiré super-structure due to mismatch between the graphene and Ru(0001).In addition, from an experimental point of view, the study of metal atoms (Pd [65], Co [65], Au [65,132], Fe [133], Pt [134]) deposited on graphene/Ru(0001) is a very active field of study in view of catalytic applications.So, the theoretical study of metal atoms bonding and mobility on graphene/Ru(0001) is crucial in reach a control on the metal growth process.In particular, the theoretical analysis by Semidey-Flecha et al. [99] are focused on the diffusion properties of Au atoms on graphene/Ru(0001).
First of all, Figure 4 reports the graphene structures taken into considerations by the authors to run the simulations: (a) free-standing grapheme; (b) graphene on fcc Ru(0001); (c) graphene on hcp Ru(0001); (d) graphene on ridge Ru(0001).Each image reports, also, the indication of the notable sites.Graphene is shown as bonds only.Top and second layer Ru atoms are shown as green and grey spheres, respectively.Reproduced from Reference [99] with permission from the American Institute of Physics.
Figure 5 reports, according to the calculations of Semidey-Flecha et al. [99], the potential surface energy for Au 1 calculated on the same set of (3 × 3) surfaces.These potential surfaces energy furnish the preferential diffusion path for Au 1 as well as the global diffusion barrier.
Figure 5a refers to Au 1 adsorbed on free-standing graphene: it shows that, in this configuration, the most stable sites are the top site on the free-standing graphene (see Figure 4a), for which the adsorption energy is ∆E = −0.11eV.In addition, on the free-standing graphene, Au 1 diffusion preferentially occurs between adjacent top sites with a barrier of E a = 0.002 eV. Figure 5b refers to Au 1 adsorbed on graphene supported on the fcc version of Ru(0001): it shows that the most stable sites are the t2 ones (see Figure 4b), for which the adsorption energy is ∆E = −1.42eV.In this case, Au 1 preferentially diffuses between adjacent t2 sites via the t1 site, with barrier of E a =0.76 eV. Figure 5c refers to Au 1 adsorbed on graphene supported on the hcp version of Ru(0001): it shows that the most stable sites are the t2 ones (see Figure 4c), for which the adsorption energy is ∆E = −1.13eV.In this case, Au 1 preferentially diffuses between adjacent t2 sites via the t1 site, with barrier of E a = 0.66 eV.Finally, Figure 5d refers to Au 1 adsorbed on graphene supported on the ridge version of Ru(0001): it shows that the most stable sites are the tβ ones (see Figure 4d), for which the adsorption energy is ∆E = −0.92eV.In this case, Au 1 preferentially diffuses between adjacent tβ sites with barrier of E a = 0.32 eV.The hexagon identifies the standard graphene hexagon.In each image, the dashed line signs the adatom minimum-energy diffusion path."X" marks the transition state from a local minimum energy site to another.The energy scale is in eV.Reproduced from Reference [99] with permission from the American Institute of Physics.
Figure 5a refers to Au1 adsorbed on free-standing graphene: it shows that, in this configuration, the most stable sites are the top site on the free-standing graphene (see Figure 4a), for which the adsorption energy is ΔE = −0.11eV.In addition, on the free-standing graphene, Au1 diffusion preferentially occurs between adjacent top sites with a barrier of Ea = 0.002 eV. Figure 5b refers to Au1 adsorbed on graphene supported on the fcc version of Ru(0001): it shows that the most stable sites are the t2 ones (see Figure 4b), for which the adsorption energy is ΔE = −1.42eV.In this case, Au1 preferentially diffuses between adjacent t2 sites via the t1 site, with barrier of Ea=0.76 eV. Figure 5c refers to Au1 adsorbed on graphene supported on the hcp version of Ru(0001): it shows that the most stable sites are the t2 ones (see Figure 4c), for which the adsorption energy is ΔE = −1.13eV.In this case, Au1 preferentially diffuses between adjacent t2 sites via the t1 site, with barrier of Ea = 0.66 eV.Finally, Figure 5d refers to Au1 adsorbed on graphene supported on the ridge version of Ru(0001): it shows that the most stable sites are the tβ ones (see Figure 4d), for which the adsorption energy is ΔE = −0.92eV.In this case, Au1 preferentially diffuses between adjacent tβ sites with barrier of Ea = 0.32 eV.
To conclude, Semidey-Flecha et al. [99] report, also, the resulting coarse-grained potential energy surface for Au1 on graphene/Ru(0001), see Figure 6: it allows the determination of the minimum-energy diffusion path (the dashed line) for Au1 from the global minimum-energy adsorption site in the fcc region of one moiré cell to that in an adjacent moiré.For this diffusion path, the authors were able to calculate the Au1 diffusion barrier as Ea = 0.71 eV.So, using this value in the Arrhenius law of the hopping rate r = Aexp(−Ea/kT) and the value A = 10 12 s −1 for the pre-exponential factor, the room-temperature hopping rate is estimated in about 0.1 s −1 .The hexagon identifies the standard graphene hexagon.In each image, the dashed line signs the adatom minimum-energy diffusion path."X" marks the transition state from a local minimum energy site to another.The energy scale is in eV.Reproduced from Reference [99] with permission from the American Institute of Physics.
To conclude, Semidey-Flecha et al. [99] report, also, the resulting coarse-grained potential energy surface for Au 1 on graphene/Ru(0001), see Figure 6: it allows the determination of the minimum-energy diffusion path (the dashed line) for Au 1 from the global minimum-energy adsorption site in the fcc region of one moiré cell to that in an adjacent moiré.For this diffusion path, the authors were able to calculate the Au 1 diffusion barrier as E a = 0.71 eV.So, using this value in the Arrhenius law of the hopping rate r = Aexp(−E a /kT) and the value A = 10 12 s −1 for the pre-exponential factor, the room-temperature hopping rate is estimated in about 0.1 s −1 .
Crystals 2017, 7, 219 10 of 40 Figure 5a refers to Au1 adsorbed on free-standing graphene: it shows that, in this configuration, the most stable sites are the top site on the free-standing graphene (see Figure 4a), for which the adsorption energy is ΔE = −0.11eV.In addition, on the free-standing graphene, Au1 diffusion preferentially occurs between adjacent top sites with a barrier of Ea = 0.002 eV. Figure 5b refers to Au1 adsorbed on graphene supported on the fcc version of Ru(0001): it shows that the most stable sites are the t2 ones (see Figure 4b), for which the adsorption energy is ΔE = −1.42eV.In this case, Au1 preferentially diffuses between adjacent t2 sites via the t1 site, with barrier of Ea=0.76 eV. Figure 5c refers to Au1 adsorbed on graphene supported on the hcp version of Ru(0001): it shows that the most stable sites are the t2 ones (see Figure 4c), for which the adsorption energy is ΔE = −1.13eV.In this case, Au1 preferentially diffuses between adjacent t2 sites via the t1 site, with barrier of Ea = 0.66 eV.Finally, Figure 5d refers to Au1 adsorbed on graphene supported on the ridge version of Ru(0001): it shows that the most stable sites are the tβ ones (see Figure 4d), for which the adsorption energy is ΔE = −0.92eV.In this case, Au1 preferentially diffuses between adjacent tβ sites with barrier of Ea = 0.32 eV.
To conclude, Semidey-Flecha et al. [99] report, also, the resulting coarse-grained potential energy surface for Au1 on graphene/Ru(0001), see Figure 6: it allows the determination of the minimum-energy diffusion path (the dashed line) for Au1 from the global minimum-energy adsorption site in the fcc region of one moiré cell to that in an adjacent moiré.For this diffusion path, the authors were able to calculate the Au1 diffusion barrier as Ea = 0.71 eV.So, using this value in the Arrhenius law of the hopping rate r = Aexp(−Ea/kT) and the value A = 10 12 s −1 for the pre-exponential factor, the room-temperature hopping rate is estimated in about 0.1 s −1 ., "E", and "F" mark the preferential adsorption sites, and "X" marks the highest-energy site.Reproduced from Reference [99] with permission from the American Institute of Physics., "E", and "F" mark the preferential adsorption sites, and "X" marks the highest-energy site.Reproduced from Reference [99] with permission from the American Institute of Physics.
In-Plane Adsorption and Diffusion of Au in Graphene
Another interesting aspect studied by means of theoretical analyses concerns the in-plane diffusion of Au atoms in graphene.Malola et al. [98], in particular, studied this phenomenon using density functional calculations motivated by the experimental data of Gan et al. [58] which experimentally observed in-plane adsorption of Au atoms in vacancies of graphene sheets and measured the rate for the in-plane Au diffusion (as we will discuss in Section 2.2).
The analysis of Malola et al. [98] starts considering that the vacancies formation in the graphene sheets is the essential condition for the Au in-plane adsorption and diffusion since the Au in-plane diffusion is mediated by these vacancies.So, first of all, the authors calculated the carbon vacancy formation energy in free-standing graphene as a function of the number of vacancies corresponding to some selected geometries, see in Figure 7 the empty points.In addition, they calculated the formation energy for Au adsorbed in these graphene vacancies, see in Figure 7 the full points.
In-Plane Adsorption and Diffusion of Au in Graphene
Another interesting aspect studied by means of theoretical analyses concerns the in-plane diffusion of Au atoms in graphene.Malola et al. [98], in particular, studied this phenomenon using density functional calculations motivated by the experimental data of Gan et al. [58] which experimentally observed in-plane adsorption of Au atoms in vacancies of graphene sheets and measured the rate for the in-plane Au diffusion (as we will discuss in Section 2.2).
The analysis of Malola et al. [98] starts considering that the vacancies formation in the graphene sheets is the essential condition for the Au in-plane adsorption and diffusion since the Au in-plane diffusion is mediated by these vacancies.So, first of all, the authors calculated the carbon vacancy formation energy in free-standing graphene as a function of the number of vacancies corresponding to some selected geometries, see in Figure 7 the empty points.In addition, they calculated the formation energy for Au adsorbed in these graphene vacancies, see in Figure 7 the full points.Carbon vacancies formation energy in graphene (empty squares), and formation energies for Au adsorbed in graphene vacancies (full points).For each vacancy, the insets show the selected geometry for the vacancy.Reproduced from Reference [98] with permission from the American Institute of Physics.
For example, the single and double vacancies formation energy is about 8 eV, and then it increases by a rate of about 2 eV/C increasing the number of C atoms to remove.The difference between the two curves in Figure 7 is the Au adsorption energy and it is in the 3-6 eV range on the basis of the number of vacancies being formed.Considering these data, the authors observe that the in-and out-plane bonding energy for Au is higher when adsorbed in double vacancies concluding, so, that the Au-double vacancy should be the most stable configuration.Therefore, Malola et al. [98] used molecular dynamics simulations to simulate the four different diffusion paths presented in Figure 8 for the Au atom in the double vacancy and for each of them calculated the value of the diffusion barrier.
The diffusion barrier of 4.0 eV (diffusion path I) corresponds to the out-of-plane motion of Au.Diffusion path II with 5.8 eV barrier involves out-of-plane motion of C, instead.A diffusion barrier of 7.0 eV corresponds to the in-plane diffusion path III while the path IV has a 7.5 eV barrier.These values are not able to explain the 2.5 eV value experimentally measured by Gan et al. [58] for the in-plane diffusion of Au atoms in graphene by using in-situ transmission electron microscopy (operating at 300 kV) analyses.Then, Malola et al. [98] conclude that the 2.5 eV corresponds to the in-plane radiation enhanced diffusion of the Au atoms in the sense that the in-plane Au atoms diffusion is enhanced by electrons irradiation arising from the electron beam of transmission electron microscopy.The electrons radiation should cause displacement of C atoms generating vacancies which favor Au to overcome the large 4 eV (or higher) energy barrier, resulting in the effective 2.5 eV measured by Gan et al. [58].Carbon vacancies formation energy in graphene (empty squares), and formation energies for Au adsorbed in graphene vacancies (full points).For each vacancy, the insets show the selected geometry for the vacancy.Reproduced from Reference [98] with permission from the American Institute of Physics.
For example, the single and double vacancies formation energy is about 8 eV, and then it increases by a rate of about 2 eV/C increasing the number of C atoms to remove.The difference between the two curves in Figure 7 is the Au adsorption energy and it is in the 3-6 eV range on the basis of the number of vacancies being formed.Considering these data, the authors observe that the in-and out-plane bonding energy for Au is higher when adsorbed in double vacancies concluding, so, that the Au-double vacancy should be the most stable configuration.Therefore, Malola et al. [98] used molecular dynamics simulations to simulate the four different diffusion paths presented in Figure 8 for the Au atom in the double vacancy and for each of them calculated the value of the diffusion barrier.
The diffusion barrier of 4.0 eV (diffusion path I) corresponds to the out-of-plane motion of Au.Diffusion path II with 5.8 eV barrier involves out-of-plane motion of C, instead.A diffusion barrier of 7.0 eV corresponds to the in-plane diffusion path III while the path IV has a 7.5 eV barrier.These values are not able to explain the 2.5 eV value experimentally measured by Gan et al. [58] for the in-plane diffusion of Au atoms in graphene by using in-situ transmission electron microscopy (operating at 300 kV) analyses.Then, Malola et al. [98] conclude that the 2.5 eV corresponds to the in-plane radiation enhanced diffusion of the Au atoms in the sense that the in-plane Au atoms diffusion is enhanced by electrons irradiation arising from the electron beam of transmission electron microscopy.The electrons radiation should cause displacement of C atoms generating vacancies which favor Au to overcome the large 4 eV (or higher) energy barrier, resulting in the effective 2.5 eV measured by Gan et al. [58].[98] with permission from the American Institute of Physics.
General Considerations
A set of experimental data on the growth of a range of metal NPs by vapor-phase depositions of metal atoms on graphene was reported by Zhou et al. [65].In this work, the authors deposited, by thermal evaporation, Pt, Rh, Pd, Co, and Au on a graphene moiré pattern on Ru(0001).Then they performed systematic scanning tunneling microscopy studies to analyze the growth mode of the resulting NPs as a function of the amount (in unity of monolayers, ML) of deposited material and as a function of the annealing temperature of a subsequent annealing process.The authors, in particular, tried to highlight the differences observed for the various metals: in fact, their experimental data show that Pt and Rh form small particles sited at fcc sites on graphene.Instead, in similar coverage conditions, Pd and Co form larger particles.Analyzing these results, the authors conclude that the metal-carbon bond strength and metal cohesive energy are the main parameters in determining the metal clusters formation process and the morphology of the clusters in the initial stages of growth.On the other hand, experimental data on the growth of Au show a further different behavior (Au forms a single-layer film on graphene) suggesting, in this case, that other factors affect the growth of the Au cluster.Figures 9-11 summarize some scanning tunneling microscopy analyses of various metals deposited on the graphene/Ru(0001) substrate, as reported by Zhou et al. [65].[98] with permission from the American Institute of Physics.
General Considerations
A set of experimental data on the growth of a range of metal NPs by vapor-phase depositions of metal atoms on graphene was reported by Zhou et al. [65].In this work, the authors deposited, by thermal evaporation, Pt, Rh, Pd, Co, and Au on a graphene moiré pattern on Ru(0001).Then they performed systematic scanning tunneling microscopy studies to analyze the growth mode of the resulting NPs as a function of the amount (in unity of monolayers, ML) of deposited material and as a function of the annealing temperature of a subsequent annealing process.The authors, in particular, tried to highlight the differences observed for the various metals: in fact, their experimental data show that Pt and Rh form small particles sited at fcc sites on graphene.Instead, in similar coverage conditions, Pd and Co form larger particles.Analyzing these results, the authors conclude that the metal-carbon bond strength and metal cohesive energy are the main parameters in determining the metal clusters formation process and the morphology of the clusters in the initial stages of growth.On the other hand, experimental data on the growth of Au show a further different behavior (Au forms a single-layer film on graphene) suggesting, in this case, that other factors affect the growth of the Au cluster.Figures 9-11 summarize some scanning tunneling microscopy analyses of various metals deposited on the graphene/Ru(0001) substrate, as reported by Zhou et al. [65].In particular, Figure 9 reports Scanning Tunneling Microscopy images for Rh deposited at room-temperature on the graphene/Ru(0001) substrates and increasing the amount of deposited Rh (from 0.05 to 0.80 ML).From a quantitative point of view, using these analyses, the authors inferred that until 0.6 ML the average Rh clusters size increases by increasing the amount of deposited Rh: the Rh cluster size and height significantly increase when the amount of deposited material increase but, correspondently, a much lower increases of the particles density is observed.Similar is the behavior of Pt: for a coverage of 0.1 ML, 2 nm-diameter highly dispersed Pt particles are formed at fcc sites; for a coverage of 1 ML, instead, 5 nm-diameter Pt particles are formed and characterized by a narrow size distribution.Figure 10 shows other Scanning Tunneling Microscopy images: (a) and (b) report images of 0.1 and 0.4 ML Pd deposited on graphene/Ru(0001), respectively.In this case, at a coverage of 0.1 ML, 8-14 nm-diameter three-dimensional Pd particles are formed at fcc sites and with a lower surface density compared to Rh and Pt.(c) and (d) report images of 0.2 and 0.4 ML of Co on graphene/Ru(0001).At a coverage of 0.2 ML, 10 nm-diameter three-dimensional Co particles are formed, while, at a coverage of 0.4 ML, 12 nm-diameter clusters are observed.(e) and (f) report images of 0.2 and 0.6 ML Au on graphene/Ru(0001).At 0.2 ML, small two-dimensional Au particles are formed at fcc sites.However, differently from the previous metals, increasing the coverage (0.6 ML, for example), Au forms a film of NPs covering the graphene moiré pattern.Finally, Figure 11 serves as an example to analyze the thermal stability of the nucleated NPs: it presents images of the Rh NPs on the graphene/Ru(0001) substrate after annealing process from 600 to 1100 K for 600 s.These images show that no significant change can be recognized in the Rh NPs below 900 K. Instead, a NPs coalescence process starts at ∼900 K as indicated by the decreased cluster density and larger dimensions.The NPs coalescence process is more evident after the annealing of the sample at 1100 K.
On the basis of their experimental results, Zhou et al. [65] draw the following conclusions about the growth processes for the investigated metal NPs on the graphene/Ru(0001) substrate: (a) Pt, Rh, Pd and Co: these metals should grow on the graphene as three-dimensional clusters due to the high difference in the surface energy of graphene (46.7 mJ/cm 2 ) and of these metals (in the 1-2 J/cm 2 range).However, the interaction between the metals adatoms and the graphene strongly influences this situation by determining the adatoms mobility.Only a small interaction energy of the adatoms with the graphene (with respect to the adatom-adatom interaction energy) will assure a high adatoms mobility and, so, the occurrence of the three-dimensional growth of the clusters.On the basis of this consideration, the authors attribute the observed differences in the Pt, Rh, Pd and Co NPs growth morphologies to the different strengths of the metal-carbon bond.The increase of the strength of the metal-carbon bond will result in the decreasing of the diffusion coefficient for the metal on graphene at a given flux.As a consequence, the decrease of the diffusion coefficient will result in the increase of the metal clusters nucleation rate allowing to obtain, thus, uniformly dispersed the two-dimensional clusters at the initial growth stage.So, the authors note that the relevant metal-carbon dissociation energies are: 610 kJ/mol for Pt-C, 580 kJ/mol for Rh-C, 436 kJ/mol for Pd-C, and 347 kJ/mol for Co-C, so that the metals with higher bond dissociation energies (Pt and Rh) form highly dispersed clusters while those with lower bond dissociation energies (Pd On the basis of this consideration, the authors attribute the observed differences in the Pt, Rh, Pd and Co NPs growth morphologies to the different strengths of the metal-carbon bond.The increase of the strength of the metal-carbon bond will result in the decreasing of the diffusion coefficient for the metal on graphene at a given flux.As a consequence, the decrease of the diffusion coefficient will result in the increase of the metal clusters nucleation rate allowing to obtain, thus, uniformly dispersed the two-dimensional clusters at the initial growth stage.So, the authors note that the relevant metal-carbon dissociation energies are: 610 kJ/mol for Pt-C, 580 kJ/mol for Rh-C, 436 kJ/mol for Pd-C, and 347 kJ/mol for Co-C, so that the metals with higher bond dissociation energies (Pt and Rh) form highly dispersed clusters while those with lower bond dissociation energies (Pd On the basis of this consideration, the authors attribute the observed differences in the Pt, Rh, Pd and Co NPs growth morphologies to the different strengths of the metal-carbon bond.The increase of the strength of the metal-carbon bond will result in the decreasing of the diffusion coefficient for the metal on graphene at a given flux.As a consequence, the decrease of the diffusion coefficient will result in the increase of the metal clusters nucleation rate allowing to obtain, thus, uniformly dispersed the two-dimensional clusters at the initial growth stage.So, the authors note that the relevant metal-carbon dissociation energies are: 610 kJ/mol for Pt-C, 580 kJ/mol for Rh-C, 436 kJ/mol for Pd-C, and 347 kJ/mol for Co-C, so that the metals with higher bond dissociation energies (Pt and Rh) form highly dispersed clusters while those with lower bond dissociation energies (Pd and Co) form large three-dimensional clusters with low surface densities.On the other hand, however, with the continued atoms deposition, the pre-formed cluster on the graphene surface start to growth in size by incorporating the new incoming atoms and this process is competitive to the nucleation of new clusters on the surface.The joining of two or more metal atoms is characterized by the metals cohesive energy which establishes the strength of the metallic bonds.So, now, the metal-carbon dissociation energy and the metal cohesive energy become competitive parameters in establishing the final cluster growth mode and morphology.So, the authors' picture is improved as follows [65]: the C atoms of the graphene strongly interact with Pt and Rh atoms, largely influencing the initial growth stage leading to the formation of uniformly distributed small particles.On the other hand, the bond strength of Pd and Co atoms to the C atoms is much weaker, so that the metals cohesive energy drive the NPs formation and growth, resulting in the formation of large three-dimensional clusters at initial growth stage.
(b) Effect of the substrate supporting the graphene: in their analysis, Zhou et al. [65] compared their results with other literature results.For example, they compared their results on the growth of Pt on graphene/Ru(0001) with the results of N'Daye et al. [61,64] on the growth of Pt on graphene/Ir (111) in similar conditions of depositions.They highlight some crucial differences in the growth morphology of the Pt clusters and impute these differences to the specific interaction of the metal atoms with the substrate supporting the graphene layer.In summary, Zhou et al. [65] report that the equilibrium spacing between graphene and the Ir (111) surface has been calculated to be 0.34 nm.Instead, the equilibrium spacing between the graphene and the Ru(0001) surface has been calculated to be 0.145 nm.This difference arises from the higher interaction of the graphene with the Ru(0001) than with Ir (111).Thus, in general, increasing the interaction energy between the C atoms of the graphene layer with the substrate on which it is supported, will lead to a decrease in the interaction energy between the C atoms and the deposited metal adatoms.This will result in an increased metal adatoms diffusivity.The consequence is that the metal clusters grown on graphene/Ir (111) are spatially more ordered than on graphene/Ru(0001) and that the transition from two-dimensional to three-dimensional morphology of clusters on graphene/Ru(0001) occurs at much lower amount of deposited material.
(c) Au: due to the weak interaction between Au and C, Au is expected, so, to grow on graphene as three-dimensional isolated Au clusters.Instead, Zhou et al. [65] observed that Au on graphene/Ru(0001) forms a continuous nano-granular film.They attribute this behavior, mainly, to the low Au cohesive energy (i.e., Au tends to wet a metal surface with a larger cohesive energy.Note that the Au cohesive energy is 3.81 eV whereas, for example, the Pt cohesive energy is 5.84 eV).In addition, the nearest-neighbor distance for Au is 0.288 nm which is larger than the graphene lattice parameter (0.245 nm).N'Diaye et al. [61,64] inferred that metal with a nearest-neighbor distance of 0.27 nm can perfectly fit the graphene lattice.So, Au atoms do not fit the graphene lattice, contributing to the lowering of the Au-C interaction energy.Therefore, the Au low cohesive energy and the low Au-C interaction energy contribute in determining the atypical Au growth.
In addition to Zhou et al. [65], N'Diaye et al. [61,64] reported another set of experimental analyses on the growth morphologies of Ir, Pt, W, and Re on graphene/Ir (111) and then Feibelman [75,76] reported additional theoretical analyses on the experimental results of N'Diaye et al.
The main results of N'Diaye et al. [64] rely in the establishment of the condition for which a metal form a superlattice on the graphene/Ir(111) substrate: (1) A large metal cohesive energy; (2) a high interaction energy of the deposited metal atoms with graphene established by the large extension of a localized valence orbital of the deposited metal; and (3) the fitting between the graphene lattice parameter and the nearest-neighbor distance of the deposited metal.In the course of their studies, N'Diaye et al. [64] were able, in addition, to infer several characteristics on the metals growth morphology.From an experimental point of view, first of all, the authors choose to deposit materials with very different cohesive energy so to study the impact of this parameter on their growth morphology.In fact, the cohesive energy for W, Re, Ir and Pt is, respectively, 8.90, 8.03, 6.94, 5.84 eV.
Crystals 2017, 7, 219 16 of 40 Figure 12 shows, for example, Scanning Tunneling Microscopies of graphene flakes grown on Ir (111) after deposition, at room-temperature, of 0.2-0.8ML of various metals.In the areas without graphene, metals form some isolated islands of monolayer height.All deposited materials are pinned to graphene flakes forming NPs.Ir and Pt form similar very ordered superlattices of clusters on the graphene flakes (compare Figure 12a,b).At 0.2 ML both materials exhibit two distinct height levels of the clusters.Also W forms an ordered cluster superlattice (see Figure 12c), however with higher height than that obtained for Ir.These W clusters present distinct height levels.A lower spatial order is obtained, instead, for Re clusters as visible by Figure 12d.For Fe (Figure 12e) and Au (Figure 12f) clusters the spatial order is completely absent so that no superlattice is obtained.The authors attribute the absence of the regular cluster superlattice for these metals to their small cohesive energy and/or small binding energy to graphene: metals with small cohesive energy present a more pronounced wetting behavior on graphene with respect to metal with higher cohesive energy (i.e., metals with small cohesive energy have lower surface energy than the metals with higher cohesive energy).Metals with low bonding strength to graphene present high mobility (with respect to metals with higher bonding strength) so that graphene is not able to trap efficiently these adatoms and small clusters).The authors verified [64] these conclusions by depositing Re, Au and Fe on the graphene/Ir(111) substrate at lower temperatures (200 K), so to decrease the adatoms diffusivity.In this case the formation of the superlattices structures for the Re, Au, and Fe clusters was observed.
Crystals 2017, 7, 219 16 of 40 Figure 12 shows, for example, Scanning Tunneling Microscopies of graphene flakes grown on Ir (111) after deposition, at room-temperature, of 0.2-0.8ML of various metals.In the areas without graphene, metals form some isolated islands of monolayer height.All deposited materials are pinned to graphene flakes forming NPs.Ir and Pt form similar very ordered superlattices of clusters on the graphene flakes (compare Figure 12a,b).At 0.2 ML both materials exhibit two distinct height levels of the clusters.Also W forms an ordered cluster superlattice (see Figure 12c), however with higher height than that obtained for Ir.These W clusters present distinct height levels.A lower spatial order is obtained, instead, for Re clusters as visible by Figure 12d.For Fe (Figure 12e) and Au (Figure 12f) clusters the spatial order is completely absent so that no superlattice is obtained.The authors attribute the absence of the regular cluster superlattice for these metals to their small cohesive energy and/or small binding energy to graphene: metals with small cohesive energy present a more pronounced wetting behavior on graphene with respect to metal with higher cohesive energy (i.e., metals with small cohesive energy have lower surface energy than the metals with higher cohesive energy).Metals with low bonding strength to graphene present high mobility (with respect to metals with higher bonding strength) so that graphene is not able to trap efficiently these adatoms and small clusters).The authors verified [64] these conclusions by depositing Re, Au and Fe on the graphene/Ir(111) substrate at lower temperatures (200 K), so to decrease the adatoms diffusivity.In this case the formation of the superlattices structures for the Re, Au, and Fe clusters was observed.Then, the authors investigated the effect of a subsequent annealing process on the morphology and order of the deposited metal clusters.Some results are reported in Figure 13: it reports the Scanning Tunneling Microscopies of Pt deposited on the graphene/Ir(111) substrate and annealed for 300 s from 350 K to 650 K. Figure 13g quantifies the annealing effect by plotting the temperature dependence of the moiré unit cell occupation probability n as a function of the annealing temperature T for all the investigated metals.Then, the authors investigated the effect of a subsequent annealing process on the morphology and order of the deposited metal clusters.Some results are reported in Figure 13: it reports the Scanning Tunneling Microscopies of Pt deposited on the graphene/Ir(111) substrate and annealed for 300 s from 350 K to 650 K. Figure 13g quantifies the annealing effect by plotting the temperature dependence of the moiré unit cell occupation probability n as a function of the annealing temperature T for all the investigated metals.3. Reproduced from Reference [64] with permission from IOPscience.
The evolution of the cluster superlattice (i.e., decay) is due to the thermally activated diffusion of clusters.The clusters perform a random motion around their equilibrium positions and two or more cluster can coalesce if the temperature is high enough to enough increase the diffusion length.The cluster diffusion, and so the probability for two or more cluster to join, is dictated by the activation barrier Ea which the cluster has to overpass to leave its moiré unit cell.This effect is illustrated by Figure 14 showing a sequence of images taken at 390 K (a-e) or at 450 K (f-j).White circles in the images sequences indicate locations of thermally activated changes, i.e., clusters that having overpassed the activation barrier for diffusion and perform a coalescence process.
In addition, N'Diaye et al. [64] were able to infer quantitative evaluations on the parameters involved in this process: supposing the clusters attempt frequency to overpass the diffusion barrier (i.e., the clusters joining frequency) expressed by an Arrhenius law, i.e., ν = ν0exp(−Ea/kT), and supposing the probability that one cluster encounters another one is proportional to n, the data in Figure 13h can be fitted to extract the clusters activation energy for diffusion (Ea) with the corresponding deviation (ΔEa), and the pre-exponential factor ν0.All these evaluated parameters are summarized in Table 3. Lines represent fits for the hopping rate with diffusion parameters as shown in Table 3. Reproduced from Reference [64] with permission from IOPscience.
The evolution of the cluster superlattice (i.e., decay) is due to the thermally activated diffusion of clusters.The clusters perform a random motion around their equilibrium positions and two or more cluster can coalesce if the temperature is high enough to enough increase the diffusion length.The cluster diffusion, and so the probability for two or more cluster to join, is dictated by the activation barrier E a which the cluster has to overpass to leave its moiré unit cell.This effect is illustrated by Figure 14 showing a sequence of images taken at 390 K (a-e) or at 450 K (f-j).White circles in the images sequences indicate locations of thermally activated changes, i.e., clusters that having overpassed the activation barrier for diffusion and perform a coalescence process.
In addition, N'Diaye et al. [64] were able to infer quantitative evaluations on the parameters involved in this process: supposing the clusters attempt frequency to overpass the diffusion barrier (i.e., the clusters joining frequency) expressed by an Arrhenius law, i.e., ν = ν 0 exp(−E a /kT), and supposing the probability that one cluster encounters another one is proportional to n, the data in Figure 13h can be fitted to extract the clusters activation energy for diffusion (E a ) with the corresponding deviation (∆E a ), and the pre-exponential factor ν 0 .All these evaluated parameters are summarized in Table 3. Table 3. Activation energy for diffusion (Ea) with the corresponding deviation (ΔEa), and the pre-exponential factor ν0 with the corresponding errors (fifth and sixth columns) for the cases of Ir, Pt and W deposited on graphene/Ir (111).Reproduced from Reference [64] with permission from IOPscience.
Clusters
Ea (eV) ΔEa (eV) υ0 (Hz) Ir, 0. Zan et al. [66] used Transmission Electron Microscopy to study the morphological and structural evolution of Au NPs on free-standing single-layer graphene sheet changing the effective deposited Au film thickness from less than 0.1 nm to 2.12 nm.
Figure 15 shows the results of the Au depositions: the preferential sites for the Au clusters nucleation are in correspondence of the Au hydrocarbon contamination, as revealed by the wormlike contrast in the high-resolution Transmission Electron Microscopy images.This is a signature of the very high diffusivity of Au atoms on graphene.Furthermore, the images show that the Au cluster number per unit area increases with increasing evaporated amount of Au, and at a nominal Au thickness larger than 1 nm clusters start to joining by coalescence.Circles indicate where modification occur in successive images; (f-j) Scanning Tunneling Microscopy images (15 nm × 15 nm) of 1.5 ML Ir deposited on graphene/Ir(111) at 350 K (f) and annealed at 450 K for 120 s (g); 240 s (h); 360 s (i); 480 s (j).Reproduced from Reference [64] with permission from IOPscience.Table 3. Activation energy for diffusion (E a ) with the corresponding deviation (∆E a ), and the pre-exponential factor ν 0 with the corresponding errors (fifth and sixth columns) for the cases of Ir, Pt and W deposited on graphene/Ir (111).Reproduced from Reference [64] with permission from IOPscience.Zan et al. [66] used Transmission Electron Microscopy to study the morphological and structural evolution of Au NPs on free-standing single-layer graphene sheet changing the effective deposited Au film thickness from less than 0.1 nm to 2.12 nm.
Clusters
Figure 15 shows the results of the Au depositions: the preferential sites for the Au clusters nucleation are in correspondence of the Au hydrocarbon contamination, as revealed by the wormlike contrast in the high-resolution Transmission Electron Microscopy images.This is a signature of the very high diffusivity of Au atoms on graphene.Furthermore, the images show that the Au cluster number per unit area increases with increasing evaporated amount of Au, and at a nominal Au thickness larger than 1 nm clusters start to joining by coalescence.Table 3. Activation energy for diffusion (Ea) with the corresponding deviation (ΔEa), and the pre-exponential factor ν0 with the corresponding errors (fifth and sixth columns) for the cases of Ir, Pt and W deposited on graphene/Ir (111).Reproduced from Reference [64] with permission from IOPscience.Zan et al. [66] used Transmission Electron Microscopy to study the morphological and structural evolution of Au NPs on free-standing single-layer graphene sheet changing the effective deposited Au film thickness from less than 0.1 nm to 2.12 nm.
Clusters
Figure 15 shows the results of the Au depositions: the preferential sites for the Au clusters nucleation are in correspondence of the Au hydrocarbon contamination, as revealed by the wormlike contrast in the high-resolution Transmission Electron Microscopy images.This is a signature of the very high diffusivity of Au atoms on graphene.Furthermore, the images show that the Au cluster number per unit area increases with increasing evaporated amount of Au, and at a nominal Au thickness larger than 1 nm clusters start to joining by coalescence.Figure 16 shows the observed in-situ coalescence process of some Au clusters.The lighter areas within the clusters correspond to clean graphene patches overlaid by the clusters.As examples two of these overlaid regions are marked by the white lines in Figure 16a: the left one occurs at the coalescence front of two coalescing clusters, the right-hand one in the middle of a cluster.
In addition, Zan et al. [66] motivated by the fact that a standard method to modify and functionalize graphene is by hydrogenation, studied the Au growth morphology on intentionally-hydrogenated free-standing graphene.Figure 16 shows the observed in-situ coalescence process of some Au clusters.The lighter areas within the clusters correspond to clean graphene patches overlaid by the clusters.As examples two of these overlaid regions are marked by the white lines in Figure 16a: the left one occurs at the coalescence front of two coalescing clusters, the right-hand one in the middle of a cluster.
In addition, Zan et al. [66] motivated by the fact that a standard method to modify and functionalize graphene is by hydrogenation, studied the Au growth morphology on intentionally-hydrogenated free-standing graphene.Hydrogenation breaks graphene sp 2 bonds and leads to sp 3 bond formation.Au depositions, 0.2 nm in nominal thickness, were, so, carried out on graphene surfaces that had been hydrogenated and the results compared to those obtained for 0.2 nm Au deposited on pure graphene.As can be seen in Figure 17a, the hydrogenated sample presents a higher Au clusters density and cluster sizes are less dispersed than in the pure graphene sample, as shown in the image in Figure 17b.However, similar to pristine graphene, Au clusters nucleate in the defects represented by the contaminations sites where the hydrogenation occurred.So, the increased hydrogenation of the graphene leads to a more effective adhesion of Au, enhancing the nucleation probability of Au clusters in the contaminations.This picture is confirmed by the observation of the occurring of coalescence of Au clusters under the electron beam of the Transmission Electron Microscopy (a process which is not observed for the Au on the pristine graphene).An example of this process in the hydrogenated sample is shown in Figure 17c,d: these Transmission Electron Microscopies present the evolution of the Au clusters under the electron beam at temporal distance of about 10 s.The agglomeration of the Au clusters (marked by the solid circles and dashed rectangles in Figure 17c,d) occurs rapidly, in the 10 s time range.In contrast, the Au clusters formed on the pristine graphene perform a coalescence process on the graphene during the Au deposition and not in few seconds under exposure to the electron beam.So, evidently, the hydrogenation process of the graphene lowers the diffusion barrier for the pre-formed Au clusters, the electron beam furnishes enough energy to the clusters to overcome this diffusion barrier, and the Au clusters coalescence starts and rapidly occurs (~seconds).Hydrogenation breaks graphene sp 2 bonds and leads to sp 3 bond formation.Au depositions, 0.2 nm in nominal thickness, were, so, carried out on graphene surfaces that had been hydrogenated and the results compared to those obtained for 0.2 nm Au deposited on pure graphene.As can be seen in Figure 17a, the hydrogenated sample presents a higher Au clusters density and cluster sizes are less dispersed than in the pure graphene sample, as shown in the image in Figure 17b.However, similar to pristine graphene, Au clusters nucleate in the defects represented by the contaminations sites where the hydrogenation occurred.So, the increased hydrogenation of the graphene leads to a more effective adhesion of Au, enhancing the nucleation probability of Au clusters in the contaminations.This picture is confirmed by the observation of the occurring of coalescence of Au clusters under the electron beam of the Transmission Electron Microscopy (a process which is not observed for the Au on the pristine graphene).An example of this process in the hydrogenated sample is shown in Figure 17c,d: these Transmission Electron Microscopies present the evolution of the Au clusters under the electron beam at temporal distance of about 10 s.The agglomeration of the Au clusters (marked by the solid circles and dashed rectangles in Figure 17c,d) occurs rapidly, in the 10 s time range.In contrast, the Au clusters formed on the pristine graphene perform a coalescence process on the graphene during the Au deposition and not in few seconds under exposure to the electron beam.So, evidently, the hydrogenation process of the graphene lowers the diffusion barrier for the pre-formed Au clusters, the electron beam furnishes enough energy to the clusters to overcome this diffusion barrier, and the Au clusters coalescence starts and rapidly occurs (~seconds).Figure 16 shows the observed in-situ coalescence process of some Au clusters.The lighter areas within the clusters correspond to clean graphene patches overlaid by the clusters.As examples two of these overlaid regions are marked by the white lines in Figure 16a: the left one occurs at the coalescence front of two coalescing clusters, the right-hand one in the middle of a cluster.
In addition, Zan et al. [66] motivated by the fact that a standard method to modify and functionalize graphene is by hydrogenation, studied the Au growth morphology on intentionally-hydrogenated free-standing graphene.Hydrogenation breaks graphene sp 2 bonds and leads to sp 3 bond formation.Au depositions, 0.2 nm in nominal thickness, were, so, carried out on graphene surfaces that had been hydrogenated and the results compared to those obtained for 0.2 nm Au deposited on pure graphene.As can be seen in Figure 17a, the hydrogenated sample presents a higher Au clusters density and cluster sizes are less dispersed than in the pure graphene sample, as shown in the image in Figure 17b.However, similar to pristine graphene, Au clusters nucleate in the defects represented by the contaminations sites where the hydrogenation occurred.So, the increased hydrogenation of the graphene leads to a more effective adhesion of Au, enhancing the nucleation probability of Au clusters in the contaminations.This picture is confirmed by the observation of the occurring of coalescence of Au clusters under the electron beam of the Transmission Electron Microscopy (a process which is not observed for the Au on the pristine graphene).An example of this process in the hydrogenated sample is shown in Figure 17c,d: these Transmission Electron Microscopies present the evolution of the Au clusters under the electron beam at temporal distance of about 10 s.The agglomeration of the Au clusters (marked by the solid circles and dashed rectangles in Figure 17c,d) occurs rapidly, in the 10 s time range.In contrast, the Au clusters formed on the pristine graphene perform a coalescence process on the graphene during the Au deposition and not in few seconds under exposure to the electron beam.So, evidently, the hydrogenation process of the graphene lowers the diffusion barrier for the pre-formed Au clusters, the electron beam furnishes enough energy to the clusters to overcome this diffusion barrier, and the Au clusters coalescence starts and rapidly occurs (~seconds).
Au and Pt Nanoparticles in Graphene
Another aspect related to the kinetic processes of metal atoms interacting with graphene was analyzed by Gan et al. [58]: they studied, experimentally, the in-plane diffusion characteristics of Au and Pt atoms in graphene and the corresponding nucleation process towards the formation of NPs by using in-situ Transmission Electron Microscopy analyses at high temperature.The analysis by the authors starts by the consideration that carbon vacancies in the graphene layers favor the atoms in-plane diffusion with respect to the on-plane diffusion.
So, to perform the experiments, the authors mixed powders of Au or Pt with graphite powder.Then they obtained a mixed fine deposit by an electric arc discharge system.After dispersing and sonicating the resulting deposit, it was placed on standard grids for in-situ Transmission Electron Microscopy analysis.During the Transmission Electron Microscopy studies, the samples were annealed in the 600-700 • C range to induce the metal atoms diffusion.The used fabrication method produces layers consisting of one or few graphene layers characterized by crystal vacancies allowing the in-plane metal atoms diffusion.As an example, Figure 18a,b show Pt atoms in a four-layers graphene structure held at 600 • C. The image in Figure 18b was acquired 60 s after Figure 18a.Two Pt atoms (indicated by the arrows) merge and form a nucleus.Such nuclei of two or several Au or Pt atoms were often observed by the authors.Then they acquired several images with the viewing direction along the graphene layers.In this condition, the observed metal atom apparently remains immobile during the annealing and overlaps with the contrast of the outermost graphene layers: this fact excludes that the metal atom is located on top of the layer.So, after several observations, the authors conclude that the metal atoms are located in-plane with the graphene sheet occupying vacancies on the carbon sites.
To analyze the atoms diffusion, Figure 19 shows the temporal evolution by reporting plan-view Transmission Electron Microscopy images acquired in the same region of the sample which is held at 600 • C and increasing the time.These images follow, in particular, the evolution of Pt atoms.The arrows in the first images identify some Pt atoms and by the images sequence how these atoms change their position by diffusion can be recognized.Atoms diffusing within the layer are marked by "L".It can be concluded that metal atoms prefer edge locations rather than in-plane sites.It is also visible how the atoms at the edge (marked by "E") move along the edge.Using these real-time analyses, the authors, in particular, were able to measure the diffusion length for several of Au and Pt atoms (quantified along the layer) versus time at different temperatures, obtaining data which follow the square-root law connecting the diffusion length to the diffusion time.
Au and Pt Nanoparticles in Graphene
Another aspect related to the kinetic processes of metal atoms interacting with graphene was analyzed by Gan et al. [58]: they studied, experimentally, the in-plane diffusion characteristics of Au and Pt atoms in graphene and the corresponding nucleation process towards the formation of NPs by using in-situ Transmission Electron Microscopy analyses at high temperature.The analysis by the authors starts by the consideration that carbon vacancies in the graphene layers favor the atoms in-plane diffusion with respect to the on-plane diffusion.
So, to perform the experiments, the authors mixed powders of Au or Pt with graphite powder.Then they obtained a mixed fine deposit by an electric arc discharge system.After dispersing and sonicating the resulting deposit, it was placed on standard grids for in-situ Transmission Electron Microscopy analysis.During the Transmission Electron Microscopy studies, the samples were annealed in the 600-700 °C range to induce the metal atoms diffusion.The used fabrication method produces layers consisting of one or few graphene layers characterized by crystal vacancies allowing the in-plane metal atoms diffusion.As an example, Figure 18a,b show Pt atoms in a four-layers graphene structure held at 600 °C.The image in Figure 18b was acquired 60 s after Figure 18a.Two Pt atoms (indicated by the arrows) merge and form a nucleus.Such nuclei of two or several Au or Pt atoms were often observed by the authors.Then they acquired several images with the viewing direction along the graphene layers.In this condition, the observed metal atom apparently remains immobile during the annealing and overlaps with the contrast of the outermost graphene layers: this fact excludes that the metal atom is located on top of the layer.So, after several observations, the authors conclude that the metal atoms are located in-plane with the graphene sheet occupying vacancies on the carbon sites.
To analyze the atoms diffusion, Figure 19 shows the temporal evolution by reporting plan-view Transmission Electron Microscopy images acquired in the same region of the sample which is held at 600 °C and increasing the time.These images follow, in particular, the evolution of Pt atoms.The arrows in the first images identify some Pt atoms and by the images sequence how these atoms change their position by diffusion can be recognized.Atoms diffusing within the layer are marked by ''L''.It can be concluded that metal atoms prefer edge locations rather than in-plane sites.It is also visible how the atoms at the edge (marked by ''E'') move along the edge.Using these real-time analyses, the authors, in particular, were able to measure the diffusion length for several of Au and Pt atoms (quantified along the layer) versus time at different temperatures, obtaining data which follow the square-root law connecting the diffusion length to the diffusion time.Using these values, Gan.et al. [58] evaluated the activation energy for the graphene in-plane diffusion of the Pt and Au atoms: in fact, considering that D = ga 2 ν 0 exp[−E a /kT], with g ≈ 1 a geometrical factor, a the graphene lattice constant, ν 0 the attempt frequency which can be assumed to be the Debye frequency, then E a is estimated, both for Pt and Au, in about 2.5 eV.This value arises by the combined effect from the covalent bonding between Pt or Au and C atoms and from the activation energy for site exchange of carbon atoms that is given by the vacancy migration energy in graphene (1.2 eV).However, a question arises about these results: the role of the electron beam used for the in-situ Transmission Electron Microscopy analyses on the observed metal atoms diffusion process.In fact, it could determine an enhanced radiation diffusion.This point was, in particular, addressed, from a theoretical point of view, by Malola et al. [84] as discussed in Section 2.1.4.Their theoretical simulations indicate that the lowest-energy path with 4.0 eV barrier involves out-of-plane motion of Au (see Figure 8).Other diffusion paths are characterized by higher energy barriers.So, the 2.5 eV barrier value measured by Gan et al. [58] for the in-plane diffusion of Au atoms in graphene should arise as an electron (300 keV) radiation enhanced diffusion: in fact, assuming Au in double vacancy, at least one of the 14 neighboring C atoms should be removed every 10 s as result of the electron beam interaction.This generation of vacancies favor Au to overcome the large 4 eV (or higher) energy barrier, resulting in the effective 2.5 eV.The radiation enhanced diffusion interpretation is in agreement with the experimental result that the 2.5 eV barrier is found both for Au and Pt which is not expected a-priori considering that C-Pt interaction is stronger than the C-Au one.In fact, on the basis of this fact, the activation energy for the Pt diffusion should be higher.Instead, the C-metal energy interaction is substantially negligible in the diffusion process if it is dominated by radiation enhancement.This value arises by the combined effect from the covalent bonding between Pt or Au and C atoms and from the activation energy for site exchange of carbon atoms that is given by the vacancy migration energy in graphene (1.2 eV).However, a question arises about these results: the role of the electron beam used for the in-situ Transmission Electron Microscopy analyses on the observed metal atoms diffusion process.In fact, it could determine an enhanced radiation diffusion.This point was, in particular, addressed, from a theoretical point of view, by Malola et al. [84] as discussed in Section 2.1.4.Their theoretical simulations indicate that the lowest-energy path with 4.0 eV barrier involves out-of-plane motion of Au (see Figure 8).Other diffusion paths are characterized by higher energy barriers.So, the 2.5 eV barrier value measured by Gan et al. [58] for the in-plane diffusion of Au atoms in graphene should arise as an electron (300 keV) radiation enhanced diffusion: in fact, assuming Au in double vacancy, at least one of the 14 neighboring C atoms should be removed every 10 s as result of the electron beam interaction.This generation of vacancies favor Au to overcome the large 4 eV (or higher) energy barrier, resulting in the effective 2.5 eV.The radiation enhanced diffusion interpretation is in agreement with the experimental result that the 2.5 eV barrier is found both for Au and Pt which is not expected a-priori considering that C-Pt interaction is stronger than the C-Au one.In fact, on the basis of this fact, the activation energy for the Pt diffusion should be higher.Instead, the C-metal energy interaction is substantially negligible in the diffusion process if it is dominated by radiation enhancement.[60] investigated, from an experimental point of view, the nucleation phenomenon of Au NPs on graphene.In particular, they focused the attention on the effect of the substrate supporting the graphene and of the graphene layer number on the NPs nucleation kinetics.The experimental data were discussed within the mean field theory of diffusion-limited aggregation, allowing to evaluate the Au adatom effective diffusion constants and activation energies.
Liu et al. [60], so, prepared graphene samples by mechanical exfoliation of graphite onto SiO 2 /Si substrates or hexagonal boron nitride substrates.Raman spectroscopy was used to analyze the number of graphene layers.Au was deposited on the graphene layers by electron beam evaporation, having care, in addition, to produce reference samples were by depositing Au on graphite substrates.To induce morphological evolution of the Au on the substrates, subsequent annealing processes were performed.At each step of evolution, the authors performed Atomic Force Microscopy analyses to study the samples surface morphology, i.e., the Au NPs morphology, size, surface density and surface roughness.
First of all, the authors deposited 0.5 nm of Au on single-layer (1 L) graphene and bilayer (2 L) graphene supported onto SiO 2 /Si, and onto graphite surfaces maintaining the substrates at room temperature.Then, the Atomic Force Microscopy analyses allowed infer the following conclusions: on the graphite surface, Au NPs coalesce to form ramified islands.The large Au-Au binding energy (∼3.8 eV), drives the Au adatoms diffusion towards the joining and formation of small compact NPs.Once formed, these very small NPs diffuse slowly on the graphite and then they coalescence to form islands.Under the same deposition conditions on the 1 L graphene, Au NPs with a narrower-size distribution and higher surface density are obtained.Instead, concerning the Au NPs obtained on the 2 L graphene, some of these evidence an ongoing evolution from elongated islands structures to ramified structures.This difference with the Au NPs obtained on graphite is the signature of the lower diffusion coefficient of the Au adatoms on 1 L and 2 L graphene than on graphite.Further results are summarized by Figure 20: by depositing 0.1 nm of Au, the observed density of Au NPs is about 1200 µm −2 (Figure 20a) on 1 L graphene.A 350 • C-2 h thermal process leads to the decrease of the surface density of the Au NPs to about 130 µm −2 (Figure 20c).Instead, on the graphite substrate, the thermal process causes a decrease of the Au NPs density from about 180 µm −2 (Figure 20b) to about 3 µm −2 (Figure 20d).These data confirm the thermal-activated nature of the NPs growth mechanism.[60] investigated, from an experimental point of view, the nucleation phenomenon of Au NPs on graphene.In particular, they focused the attention on the effect of the substrate supporting the graphene and of the graphene layer number on the NPs nucleation kinetics.The experimental data were discussed within the mean field theory of diffusion-limited aggregation, allowing to evaluate the Au adatom effective diffusion constants and activation energies.
Liu et al. [60], so, prepared graphene samples by mechanical exfoliation of graphite onto SiO2/Si substrates or hexagonal boron nitride substrates.Raman spectroscopy was used to analyze the number of graphene layers.Au was deposited on the graphene layers by electron beam evaporation, having care, in addition, to produce reference samples were by depositing Au on graphite substrates.To induce morphological evolution of the Au on the substrates, subsequent annealing processes were performed.At each step of evolution, the authors performed Atomic Force Microscopy analyses to study the samples surface morphology, i.e., the Au NPs morphology, size, surface density and surface roughness.
First of all, the authors deposited 0.5 nm of Au on single-layer (1 L) graphene and bilayer (2 L) graphene supported onto SiO2/Si, and onto graphite surfaces maintaining the substrates at room temperature.Then, the Atomic Force Microscopy analyses allowed infer the following conclusions: on the graphite surface, Au NPs coalesce to form ramified islands.The large Au-Au binding energy (∼3.8 eV), drives the Au adatoms diffusion towards the joining and formation of small compact NPs.Once formed, these very small NPs diffuse slowly on the graphite and then they coalescence to form islands.Under the same deposition conditions on the 1 L graphene, Au NPs with a narrower-size distribution and higher surface density are obtained.Instead, concerning the Au NPs obtained on the 2 L graphene, some of these evidence an ongoing evolution from elongated islands structures to ramified structures.This difference with the Au NPs obtained on graphite is the signature of the lower diffusion coefficient of the Au adatoms on 1 L and 2 L graphene than on graphite.Further results are summarized by Figure 20: by depositing 0.1 nm of Au, the observed density of Au NPs is about 1200 μm −2 (Figure 20a) on 1 L graphene.A 350 °C-2 h thermal process leads to the decrease of the surface density of the Au NPs to about 130 μm −2 (Figure 20c).Instead, on the graphite substrate, the thermal process causes a decrease of the Au NPs density from about 180 μm −2 (Figure 20b) to about 3 μm −2 (Figure 20d).These data confirm the thermal-activated nature of the NPs growth mechanism As a comparison, the authors performed similar studies for Au deposited on graphene supported onto hexagonal boron nitride (h-BN): this choice is dictated by the fact that graphene is known to be flatter on single-crystal h-BN than on SiO 2 .So, the upper part of the image 21a shows the surface of h-BN presenting a roughness of 47 pm, while the bottom shows the h-BN surface supporting 1 L graphene, with a roughness of 54 pm.The other Atomic Force Microscopy images in Figure 21 show the resulting Au NPs obtained by the deposition of 0.1 nm of Au on the surface of bare h-BN, on 1 L graphene supported on h-BN and on 1 L graphene supported on SiO 2 .The comparison of these images allow us to conclude that the NPs growth is faster on h-BN and 1 L graphene supported on h-BN than on 1 L graphene supported on SiO 2 .
At this point, once recorded these experimental data, Liu et al. [60] exploited the mean-field nucleation theory to analyze these data so to extract quantitative information on the parameters involved in Au NPs morphological evolution processes.As the amount of deposited materials increases, three kinetic regimes for the Au clusters growth can be recognized: clusters nucleation, clusters growth, and steady-state.At the early stages of deposition, moving adatoms on the substrate explore a certain area in a certain time so that they can encounter each other and and, so, they have some finite probability to join (nucleation process) and form stable nucleii.The number of nuclei increases with time.However, in the same time, new atoms arrive from the vapor-phase and they can be captured by the preexisting nuclei.At enough high deposition time, so, the nuclei growth in cluster of increasing size and new nucleii are not formed: a steady state is reached.In this condition, the mean Au adatoms diffusion length is equal to the mean Au NP spacing and a saturation density for the nuclei is obtained.The authors, then, considered that, according to the mean-field nucleation theory, the nuclei saturation density n is predicted as n(Z)~N 0 η(Z)(F/N 0 ν) i/(i+2.5)exp[(E i + iE d )/(i + 2.5)kT] being Z a parameter depending on the total deposition time, N 0 the substrate atomic density (cm −2 ), η(Z) a dimensionless parameter, F is the rate of arriving atoms from the vapor phase (cm −2 s −1 ), ν an effective surface vibration frequency (∼10 11 -10 13 s −1 ), i the number of Au atoms in the critical cluster, E i the Au atom binding energy in the critical cluster, and E d the activation energy for the Au atom diffusion.As a comparison, the authors performed similar studies for Au deposited on graphene supported onto hexagonal boron nitride (h-BN): this choice is dictated by the fact that graphene is known to be flatter on single-crystal h-BN than on SiO2.So, the upper part of the image 21a shows the surface of h-BN presenting a roughness of 47 pm, while the bottom shows the h-BN surface supporting 1 L graphene, with a roughness of 54 pm.The other Atomic Force Microscopy images in Figure 21 show the resulting Au NPs obtained by the deposition of 0.1 nm of Au on the surface of bare h-BN, on 1 L graphene supported on h-BN and on 1 L graphene supported on SiO2.The comparison of these images allow us to conclude that the NPs growth is faster on h-BN and 1 L graphene supported on h-BN than on 1 L graphene supported on SiO2.
At this point, once recorded these experimental data, Liu et al. [60] exploited the mean-field nucleation theory to analyze these data so to extract quantitative information on the parameters involved in Au NPs morphological evolution processes.As the amount of deposited materials increases, three kinetic regimes for the Au clusters growth can be recognized: clusters nucleation, clusters growth, and steady-state.At the early stages of deposition, moving adatoms on the substrate explore a certain area in a certain time so that they can encounter each other and and, so, they have some finite probability to join (nucleation process) and form stable nucleii.The number of nuclei increases with time.However, in the same time, new atoms arrive from the vapor-phase and they can be captured by the preexisting nuclei.At enough high deposition time, so, the nuclei growth in cluster of increasing size and new nucleii are not formed: a steady state is reached.In this condition, the mean Au adatoms diffusion length is equal to the mean Au NP spacing and a saturation density for the nuclei is obtained.The authors, then, considered that, according to the mean-field nucleation theory, the nuclei saturation density n is predicted as n(Z)~N0η(Z)(F/N0ν) i/(i+2.5)exp[(Ei + iEd)/(i + 2.5)kT] being Z a parameter depending on the total deposition time, N0 the substrate atomic density (cm −2 ), η(Z) a dimensionless parameter, F is the rate of arriving atoms from the vapor phase (cm −2 s −1 ), ν an effective surface vibration frequency (∼10 11 -10 13 s −1 ), i the number of Au atoms in the critical cluster, Ei the Au atom binding energy in the critical cluster, and Ed the activation energy for the Au atom diffusion.Clusters of size smaller than i shrinks while clusters larger than size i grow and form the stable NPs.The authors consider that in the examined experiments, i should be small and, so, they analyze their experimental data on n(z) for i = 1 and i = 2 obtaining the values reported in Figure 22: the Au adatom diffusion energy E d and the corresponding diffusion coefficient D calculated as D = (a 2 ν d /4)exp[−E d /kT] with a the graphene lattice parameter (0.14 nm) and ν d the adatom attempt frequency (∼10 12 s −1 ).
Crystals 2017, 7, 219 24 of 40 Clusters of size smaller than i shrinks while clusters larger than size i grow and form the stable NPs.The authors consider that in the examined experiments, i should be small and, so, they analyze their experimental data on n(z) for i = 1 and i = 2 obtaining the values reported in Figure 22: the Au adatom diffusion energy Ed and the corresponding diffusion coefficient D calculated as D = (a 2 νd/4)exp[−Ed/kT] with a the graphene lattice parameter (0.14 nm) and νd the adatom attempt frequency (∼10 12 s −1 ).
Figure 22.The calculated diffusion energy, Ed, and diffusion constant, D, of Au adatoms on various surfaces: graphite, hexagonal boron nitride (h-BN), single-layer graphene (SLG) on h-BN, SLG on SiO2, and bilayer graphene (BLG) on SiO2.Calculations using different critical sizes i are given in black (i = 1) and red (i = 2) curves for comparison.For graphite, Ed and D are assumed as 50 meV and 7 × 10 −6 cm 2 s −1 , independent of critical size i.Reproduced from Reference [60] with permission from the American Chemical Society.
On the basis of Figure 22 it is clear that the activation energy for the Au adatom diffusion process is higher on 1 L graphene on h-BN, 1 L and 2 L graphene on SiO2 than on graphite and bare h-BN.In addition, it is higher on 1 L graphene on SiO2 than on 2 L graphene on SiO2 which is, in turn, higher than 1 L graphene on h-BN.Now, the question concerning why these differences are observed arises.In this sense, the authors, first of all, note that adatom diffusion is affected by the surface strains which is, in turn, related to the surface roughness.A compressive strain of the surface reduces the energy barrier for the adatom diffusion while a tensile strain tends to increase it.In its free-standing configuration, 1 L graphene displays ripples with about 1 nm height variation.In contrast, when supported and annealed on SiO2/Si substrates, graphene follows the local SiO2 roughness: the graphene−SiO2 van interaction energy is balanced by the elastic deformation energy of graphene with the consequent increase of the graphene roughness with respect to its free-standing configuration.The Atomic Force Microscopy measurements by Liu et al. [60] show that 1 L graphene on SiO2 presents a roughness 8 times higher than bulk graphite.On this rough graphene surface, there will be regions of both concave and convex curvature.The Au adatoms have, locally, different mobility on these different-curvature regions: within regions where they have a lower mobility then their nucleation in small clusters is favored with respect to defect-free graphite.A further aspect is that the energy barrier for the adatoms diffusion increases as the bonding strength of Au with the C atom increases: 2 L graphene is more stable than 1 L graphene due to the π bonding between the layers.In addition, the 2 L graphene has a lower roughness compared to 1 L graphene.Both factors should create weaker Au bonding and, thus, faster diffusion of the Au adatoms on 2 L graphene.About the diffusion of Au atoms on 1 L graphene on h-BN: according to the experimental data the mobility of the Au adatoms on 1 L graphene supported on h-BN should be higher than on 1 L graphene supported on a SiO2 substrate.However, the calculations in Figure 22 lead to the opposite conclusion The calculated diffusion energy, E d , and diffusion constant, D, of Au adatoms on various surfaces: graphite, hexagonal boron nitride (h-BN), single-layer graphene (SLG) on h-BN, SLG on SiO , and bilayer graphene (BLG) on SiO 2 .Calculations using different critical sizes i are given in black (i = 1) and red (i = 2) curves for comparison.For graphite, E d and D are assumed as 50 meV and 7 × 10 −6 cm 2 s −1 , independent of critical size i.Reproduced from Reference [60] with permission from the American Chemical Society.
On the basis of Figure 22 it is clear that the activation energy for the Au adatom diffusion process is higher on 1 L graphene on h-BN, 1 L and 2 L graphene on SiO 2 than on graphite and bare h-BN.In addition, it is higher on 1 L graphene on SiO 2 than on 2 L graphene on SiO 2 which is, in turn, higher than 1 L graphene on h-BN.Now, the question concerning why these differences are observed arises.In this sense, the authors, first of all, note that adatom diffusion is affected by the surface strains which is, in turn, related to the surface roughness.A compressive strain of the surface reduces the energy barrier for the adatom diffusion while a tensile strain tends to increase it.In its free-standing configuration, 1 L graphene displays ripples with about 1 nm height variation.In contrast, when supported and annealed on SiO 2 /Si substrates, graphene follows the local SiO 2 roughness: the graphene−SiO 2 van interaction energy is balanced by the elastic deformation energy of graphene with the consequent increase of the graphene roughness with respect to its free-standing configuration.The Atomic Force Microscopy measurements by Liu et al. [60] show that 1 L graphene on SiO 2 presents a roughness 8 times higher than bulk graphite.On this rough graphene surface, there will be regions of both concave and convex curvature.The Au adatoms have, locally, different mobility on these different-curvature regions: within regions where they have a lower mobility then their nucleation in small clusters is favored with respect to defect-free graphite.A further aspect is that the energy barrier for the adatoms diffusion increases as the bonding strength of Au with the C atom increases: 2 L graphene is more stable than 1 L graphene due to the π bonding between the layers.In addition, the 2 L graphene has a lower roughness compared to 1 L graphene.Both factors should create weaker Au bonding and, thus, faster diffusion of the Au adatoms on 2 L graphene.About the diffusion of Au atoms on 1 L graphene on h-BN: according to the experimental data the mobility of the Au adatoms on 1 L graphene supported on h-BN should be higher than on 1 L graphene supported on a SiO 2 substrate.However, the calculations in Figure 22 lead to the opposite conclusion which the authors impute to increased van der Waals forces between 1 L graphene and SiO 2 with respect to 1 L graphene and h-BN.This condition should lead to the increased mobility of the Au adatoms on 1 L graphene supported on h-BN.
The Dewetting Process
Thin metal films deposited on a non-metal susbstrate are, generally, thermodinamically unstable.Then, if enough energy is furnished to the film so that atomic diffusion occurs, the system tends to minimize the total surface and interface energy: the result is the break-up of the film and the formation of spherical metal particles minimizing the total exposed surface [123][124][125][126][127][128][129][130].The dewetting process starts in structural defects of the films: these are the locations in which holes in the film, reaching the underlaying substrate, nucleate.The holes grow with time and two or more holes join (i.e.coalesce) with the result of leaving the film in filaments structures.These filaments, then, being unstable, decay in spherical particles by a Raileigh-like instability process.The overall result is, so, the formation of an array of metal NPs.In a certain range, the mean size and mean spacing of the formed NPs can be controlled by the thickness of the deposited film or by the characteristic parameters of the process inducing the dewetting phenomenon such as the temperature or time of an annealing process [123][124][125][126][127][128][129][130].The energetic budget needed to start the dewetting process of the film (i.e., to activate the atomic diffusion) can be furnished to the film by standard thermal annealing, or, alternatively, by laser, ion, electron beam irradiations.In addition, for metal films, the dewetting process can occur both in the solid or molten state.
Due to these peculiarities, the dewetting process was, also, exploited to produce, in a controlled way, metal NPs on graphene surface from deposited thin metal films.This approach is effective in the production of shape-and size-selected metal NPs on the graphene surface for some interesting applications involving, for example, the Surface Enhanced Raman Scattering of the NPs as modified by the interaction with the graphene layer.
Dewetting of Au Films on Graphene
Zhou et al. [68] investigated the possibility to produce and to control size, density and shape of Au NPs on graphene by the dewetting process of deposited thin films.So, after depositing the Au films, they performed annealing processes to induce the evolution of the films in NPs and, interestingly, they found that the shape, size and density of the obtained NPs can be controlled by the number of graphene layers and by the annealing temperature.
First of all, the authors [68] transferred n-layer graphene on a SiO 2 substrate after having obtained the n-layer graphene by standard mechanical exfoliation.The number of the graphene layers on the SiO 2 substrate was determined by crossing optical microscope and micro-Raman spectroscopy.After depositing (by thermal evaporation) thin Au films onto the n-layers graphene and onto the SiO 2 surface as reference, annealing processes were performed in the 600 • C-900 • C temperature range for 2 h.Then the authors used Scanning Electron Microscopy analysis to study shape, size and density of the observed NPs as a function of the annealing temperature, thickness of the starting deposited Au film, number of graphene layers supporting the Au film.The following general considerations are drawn by the authors on the basis of the results of these analysis: firstly, if the annealing temperature is in the 600-700 • C range, then the Au film on n-layer graphenes can be tuned into hexagon-shaped Au NPs.
Secondly, annealing at 800 • C produces, instead, coexistence of hexagonal and triangular Au NPs on graphenes.Thirdly, annealing at 900 • C produces irregular-shaped Au NPs on graphenes.Moreover, the density and size of the formed Au NPs on n-layer graphenes are strictly dependent on the number n of graphene layers.In particular, increasing n the NPs mean size increases and the NPs surface density decreases.As an example, Figure 23 Another aspect is that the Au film dewetting process on the n-layer graphenes is thickness-dependent.The influence of the Au film thickness on the shape of the obtained Au NPs is described by the images in Figure 24: it presents Scanning Electron Microscopy images of 1 nm, 1.5 nm and 2 nm thick Au films on n-layers graphene and annealed at 600 °C for 2 h.With the increase of the Au film thickness, the effect of the graphene layers number on the shape of Au NPs becomes more and more weak.When film thickness is below 2.0 nm, after thermal annealing at 600 or 700 °C, almost all the Au NPs show hexagonal shape.Whereas for 5.0 nm Au film or more, although hexagon-shaped Au NPs still exist after annealing at 600 °C, the Au NPs are not well faceted.Another aspect is that the Au film dewetting process on the n-layer graphenes is thickness-dependent.The influence of the Au film thickness on the shape of the obtained Au NPs is described by the images in Figure 24: it presents Scanning Electron Microscopy images of 1 nm, 1.5 nm and 2 nm thick Au films on n-layers graphene and annealed at 600 • C for 2 h.With the increase of the Au film thickness, the effect of the graphene layers number on the shape of Au NPs becomes more and more weak.When film thickness is below 2.0 nm, after thermal annealing at 600 or 700 • C, almost all the Au NPs show hexagonal shape.Whereas for 5.0 nm Au film or more, although hexagon-shaped Au NPs still exist after annealing at 600 • C, the Au NPs are not well faceted.All these experimental data highlight the key role of the graphene layers number in determining size, density and shape of the Au NPs clearly indicates that n establishes the interaction strength between the graphene and the Au atoms affecting, as a consequence, the Au diffusivity and the final Au NPs morphology.To infer information on the parameters governing the Au NPs shape, size and density evolution, the authors [68] take into considerations the following main factors: the Au adatoms are weakly bonded with C atoms on graphene surface (interpreted as a physical adsorption rather than a chemical bonding) and the strength of this bonding is largely influenced by the number of graphene layers [101][102][103][104]. So, with the increase of layer number the inter-layer interaction strength decreases and, consequently, the interaction between Au adatoms and n-layer graphene becomes much weaker, resulting in the thickness-dependent particle size and density of Au NPs on graphenes by the different Au mobility on the graphenes.The surface diffusion of metal adatoms on graphenes can be described by these two equations: D∝exp(−Ea,n/kT) and N∝(1/D) 1/3 , being D the adatoms surface diffusion, N the NPs surface density, Ea,n the activation energy for the adatoms surface diffusion on n-layers graphene.Combining these two equations, the relation N∝exp (Ea,n/3kT) is obtained.So, Zhou et al. [68] conclude that the decrease of surface diffusion barrier with increasing the number of graphene layers n explains the observed experimental data: the diffusion coefficient establishing the diffusion length, determines the joining probability for the adatoms.Therefore, concerning the thermal annealing post-growth processes, it establishes the size and density of the formed NPs by the competition between nucleation and growth phenomena [69].Therefore, different surface diffusion coefficients (by different activation energies Ea,n) of the Au adatoms on the n-layers graphene can result in n-dependent morphologies, sizes, and density of the Au NPs on n-layer graphenes.To support quantitatively these considerations, in a further study, Zhou et al. [69], proceeded to the quantification of the size and density of the Au NPs after the thermal treatment.In particular, the authors proceeded to the following experiment: after depositing a Au film on the SiO2 substrate, on 1-layer, 2-layers, 3-layers, and 4-layers graphene supported on the SiO2 substrate, the authors performed a 1260 °C-30 s annealing to obtain round-shaped Au NPs All these experimental data highlight the key role of the graphene layers number in determining size, density and shape of the Au NPs clearly indicates that n establishes the interaction strength between the graphene and the Au atoms affecting, as a consequence, the Au diffusivity and the final Au NPs morphology.To infer information on the parameters governing the Au NPs shape, size and density evolution, the authors [68] take into considerations the following main factors: the Au adatoms are weakly bonded with C atoms on graphene surface (interpreted as a physical adsorption rather than a chemical bonding) and the strength of this bonding is largely influenced by the number of graphene layers [101][102][103][104]. So, with the increase of layer number the inter-layer interaction strength decreases and, consequently, the interaction between Au adatoms and n-layer graphene becomes much weaker, resulting in the thickness-dependent particle size and density of Au NPs on graphenes by the different Au mobility on the graphenes.The surface diffusion of metal adatoms on graphenes can be described by these two equations: D∝exp(−E a,n /kT) and N∝(1/D) 1/3 , being D the adatoms surface diffusion, N the NPs surface density, E a,n the activation energy for the adatoms surface diffusion on n-layers graphene.Combining these two equations, the relation N∝exp (E a,n /3kT) is obtained.So, Zhou et al. [68] conclude that the decrease of surface diffusion barrier with increasing the number of graphene layers n explains the observed experimental data: the diffusion coefficient establishing the diffusion length, determines the joining probability for the adatoms.Therefore, concerning the thermal annealing post-growth processes, it establishes the size and density of the formed NPs by the competition between nucleation and growth phenomena [69].Therefore, different surface diffusion coefficients (by different activation energies E a,n ) of the Au adatoms on the n-layers graphene can result in n-dependent morphologies, sizes, and density of the Au NPs on n-layer graphenes.To support quantitatively these considerations, in a further study, Zhou et al. [69], proceeded to the quantification of the size and density of the Au NPs after the thermal treatment.In particular, the authors proceeded to the following experiment: after depositing a Au film on the SiO 2 substrate, on 1-layer, 2-layers, 3-layers, and 4-layers graphene supported on the SiO 2 substrate, the authors performed a 1260 • C-30 s annealing to obtain round-shaped Au NPs as shown in Figure 25a but with a different size and surface density N of the NPs on the basis of the number n of the graphene layers.As reported in Figure 25b the authors quantified the size and the surface density of the Au NPs as a function of n.In particular, N versus n was analyzed by the N∝exp (Ea,n/3kT) relation.Although it is difficult to obtain the absolute value of barriers due to the lack of the pre-exponential factor, the authors were able in evaluate the barrier difference between n-layer graphene by the density ratios: Ea,1 − Ea,2 = 3kTln(N1/N2) = 504 ± 44 meV, and similarly, Ea,2 − Ea,3 = 291 ± 31 meV, Ea,3 − Ea,4 = 242 ± 22 meV.
Dewetting of Ag Films on Graphene
Zhou et al. [71] extended their work to the dewetting of Ag films on n-layers graphene.In this case, in addition, a detailed study of the Surface Enhanced Raman Scattering of the Ag NPs was also conducted.The authors deposited Ag films onto n-layer graphenes (supported on SiO2).In this case experiments were conducted maintaining the substrate temperature at 298, 333, and 373 K during the Ag depositions and Scanning Electron Microscopy images were used to study the morphology, size, surface density of the produced Ag NPs on the graphene layers as a function of the substrate temperature.In addition, also in this case, a strict dependence of the Ag NPs morphology, size and surface density on the number of graphene layers n supporting the Ag film was found.Similarly to Au, this was attributed by the authors to the changes in the surface diffusion coefficient of Ag on n-layer graphenes at different temperatures (the substrate temperature during Ag depositions, in this case).In addition, the authors observed that Raman scattering of n-layer graphenes is greatly enhanced by the presence of the Ag NPs.In particular, they found that the enhancement factors depend on the number n of graphene layers.Monolayer graphene has the largest enhancement factors, and the enhancement factors decrease with layer number increasing.Obviously, this is due to the specific structural characteristics of the Ag NPs as determined by n.
In particular, the authors [71] thermally evaporated 2 or 5 nm Ag films onto n-layer graphenes supported on the 300 nm-thick SiO2 layer grown on Si.During the Ag depositions, the substrate is kept at 298 K, or 333 K, or 373 K. On the basis of the substrate temperature and number of graphene layers, different shapes, sizes, and surface density are obtained for the resulting Ag NPs.As an example, Figure 26 reports Scanning Electron Microscopy images of 5 nm-thick Ag film deposited on SiO2, on 1-layer, and 2-layers graphene with the substrate kept at 298 K (a-b), 333 K (c-d), 373 K (e-f).The differences in the formed Ag NPs are just evident at 333K: on one layer graphene, the density of Ag NPs larger than that on bilayer graphene, the NPs spacing is lower, but the NPs diameter are similar in the two samples.At 373 K these differences are enhanced: the Ad NPs present very different sizes, spacing, and surface density as a function of the number n of the As reported in Figure 25b the authors quantified the size and the surface density of the Au NPs as a function of n.In particular, N versus n was analyzed by the N∝exp (E a,n /3kT) relation.Although it is difficult to obtain the absolute value of barriers due to the lack of the pre-exponential factor, the authors were able in evaluate the barrier difference between n-layer graphene by the density ratios: E a,1 − E a,2 = 3kTln(N 1 /N 2 ) = 504 ± 44 meV, and similarly, E a,2 − E a,3 = 291 ± 31 meV, E a,3 − E a,4 = 242 ± 22 meV.
Dewetting of Ag Films on Graphene
Zhou et al. [71] extended their work to the dewetting of Ag films on n-layers graphene.In this case, in addition, a detailed study of the Surface Enhanced Raman Scattering of the Ag NPs was also conducted.The authors deposited Ag films onto n-layer graphenes (supported on SiO 2 ).In this case experiments were conducted maintaining the substrate temperature at 298, 333, and 373 K during the Ag depositions and Scanning Electron Microscopy images were used to study the morphology, size, surface density of the produced Ag NPs on the graphene layers as a function of the substrate temperature.In addition, also in this case, a strict dependence of the Ag NPs morphology, size and surface density on the number of graphene layers n supporting the Ag film was found.Similarly to Au, this was attributed by the authors to the changes in the surface diffusion coefficient of Ag on n-layer graphenes at different temperatures (the substrate temperature during Ag depositions, in this case).In addition, the authors observed that Raman scattering of n-layer graphenes is greatly enhanced by the presence of the Ag NPs.In particular, they found that the enhancement factors depend on the number n of graphene layers.Monolayer graphene has the largest enhancement factors, and the enhancement factors decrease with layer number increasing.Obviously, this is due to the specific structural characteristics of the Ag NPs as determined by n.
In particular, the authors [71] thermally evaporated 2 or 5 nm Ag films onto n-layer graphenes supported on the 300 nm-thick SiO 2 layer grown on Si.During the Ag depositions, the substrate is kept at 298 K, or 333 K, or 373 K. On the basis of the substrate temperature and number of graphene layers, different shapes, sizes, and surface density are obtained for the resulting Ag NPs.As an example, Figure 26 reports Scanning Electron Microscopy images of 5 nm-thick Ag film deposited on SiO 2 , on 1-layer, and 2-layers graphene with the substrate kept at 298 K (a-b), 333 K (c-d), 373 K (e-f).The differences in the formed Ag NPs are just evident at 333 K: on one layer graphene, the density of Ag NPs larger than that on bilayer graphene, the NPs spacing is lower, but the NPs diameter are similar in the two samples.At 373 K these differences are enhanced: the Ad NPs present very different sizes, spacing, and surface density as a function of the number n of the graphene layers.For example, the NPs on monolayer graphene are much smaller than those on bilayer graphene.
Then, using Raman spectroscopy, the authors found different Surface Enhanced Raman Spectroscopy (SERS) effects of Ag on n-layer graphenes [71], as summarized in Figures 27 and 28.In Figure 27, the authors compare the enhancement effects of 2 and 5 nm Ag deposited at 298 K on the graphene samples.Raman spectra of n-layer graphenes with 5 nm are enhanced with respect to 2 nm Ag (and pristine graphene): the G and 2D bands are more intense.This can be attribute to the fact that the deposition of the 5 nm Ag leads to the formation of NPs with higher surface density and lower spacing with the result to increase the SERS hot spots number per unit area.As a consequence, the increased density of hot spots causes a higher electric filed localization and, so, higher enhancement factors.To further analyze the Raman scattering properties of the graphene supporting the Ag NPs, the authors measured the Raman spectra of n-layer graphenes supporting NPs obtained by the deposition of 5 nm-thick Ag maintaining the substrate at 298, 333, and 373 K, see Figure 28.A higher SERS enhancement factor is obtained from graphene covered by Ag NPs obtained by depositing 5 nm Ag maintaining the substrate at 333 K than at 298 K: in fact, at 333 K larger Ag NPs are obtained with the same spacing of those obtained at 298 K.However, when the 5 nm Ag film is deposited maintaining the substrate at 373 K, the particles are larger but, also, the NPs spacing increases, resulting in a decrease of the enhancement factor.
Crystals 2017, 7, 219 29 of 40 graphene layers.For example, the NPs on monolayer graphene are much smaller than those on bilayer graphene.Then, using Raman spectroscopy, the authors found different Surface Enhanced Raman Spectroscopy (SERS) effects of Ag on n-layer graphenes [71], as summarized in Figures 27 and 28.In Figure 27, the authors compare the enhancement effects of 2 and 5 nm Ag deposited at 298 K on the graphene samples.Raman spectra of n-layer graphenes with 5 nm are enhanced with respect to 2 nm Ag (and pristine graphene): the G and 2D bands are more intense.This can be attribute to the fact that the deposition of the 5 nm Ag leads to the formation of NPs with higher surface density and lower spacing with the result to increase the SERS hot spots number per unit area.As a consequence, the increased density of hot spots causes a higher electric filed localization and, so, higher enhancement factors.To further analyze the Raman scattering properties of the graphene supporting the Ag NPs, the authors measured the Raman spectra of n-layer graphenes supporting NPs obtained by the deposition of 5 nm-thick Ag maintaining the substrate at 298, 333, and 373 K, see Figure 28.A higher SERS enhancement factor is obtained from graphene covered by Ag NPs obtained by depositing 5 nm Ag maintaining the substrate at 333 K than at 298 K: in fact, at 333 K larger Ag NPs are obtained with the same spacing of those obtained at 298 K.However, when the 5 nm Ag film is deposited maintaining the substrate at 373 K, the particles are larger but, also, the NPs spacing increases, resulting in a decrease of the enhancement factor.
Some Considerations on the Electrical Behavior of Metal-Graphene Contacts
As discussed in the introductory section, metal NPs/graphene hybrid systems present properties which are exploited for applications in areas such as Surface Enhanced Raman Scattering (SERS), nanoelectronics, photovoltaics, catalysis, electrochemical sensing, hydrogen storage, etc. [17][18][19].All these applications, however, are connected to the specific interaction occurring at the metal NP/graphene interface because characteristics like metal adhesion and electrical contact properties are strongly influenced by the interface structure.In this sense, the theoretical and experimental study of the metal-graphene interface structure and how the metal contact influences the graphene electronic properties is an active field of study .From a more general point of view, any application of graphene in building electronic devices requires the graphene contacting by metal layers and it is widely recognized that the metal-graphene interaction strongly influences the graphene electrical conduction properties being, often, a limiting factor in produce high-efficiency electronic devices.For example, several theoretical and experimental analysis suggest that the difference in the work functions of the metal and graphene leads to the charge transfer and doping of the graphene layer [101][102][103][104].In general, to realize high-performance devices, it is very important to produce metallic contacts on graphene which show a very low contact resistance.In principle, an Ohmic contact is obtained without any difficulty by the contact of a metal with graphene layer due to the graphene lack of a band gap but it is concerned that a very small density of states (DOS) for graphene might suppress the current injection from the metal to graphene [78,107].In general [107],
Some Considerations on the Electrical Behavior of Metal-Graphene Contacts
As discussed in the introductory section, metal NPs/graphene hybrid systems present properties which are exploited for applications in areas such as Surface Enhanced Raman Scattering (SERS), nanoelectronics, photovoltaics, catalysis, electrochemical sensing, hydrogen storage, etc. [17][18][19].All these applications, however, are connected to the specific interaction occurring at the metal NP/graphene interface because characteristics like metal adhesion and electrical contact properties are strongly influenced by the interface structure.In this sense, the theoretical and experimental study of the metal-graphene interface structure and how the metal contact influences the graphene electronic properties is an active field of study .From a more general point of view, any application of graphene in building electronic devices requires the graphene contacting by metal layers and it is widely recognized that the metal-graphene interaction strongly influences the graphene electrical conduction properties being, often, a limiting factor in produce high-efficiency electronic devices.For example, several theoretical and experimental analysis suggest that the difference in the work functions of the metal and graphene leads to the charge transfer and doping of the graphene layer [101][102][103][104].In general, to realize high-performance devices, it is very important to produce metallic contacts on graphene which show a very low contact resistance.In principle, an Ohmic contact is obtained without any difficulty by the contact of a metal with graphene layer due to the graphene lack of a band gap but it is concerned that a very small density of states (DOS) for graphene might suppress the current injection from the metal to graphene [78,107].In general [107],
Some Considerations on the Electrical Behavior of Metal-Graphene Contacts
As discussed in the introductory section, metal NPs/graphene hybrid systems present properties which are exploited for applications in areas such as Surface Enhanced Raman Scattering (SERS), nanoelectronics, photovoltaics, catalysis, electrochemical sensing, hydrogen storage, etc. [17][18][19].All these applications, however, are connected to the specific interaction occurring at the metal NP/graphene interface because characteristics like metal adhesion and electrical contact properties are strongly influenced by the interface structure.In this sense, the theoretical and experimental study of the metal-graphene interface structure and how the metal contact influences the graphene electronic properties is an active field of study .From a more general point of view, any application of graphene in building electronic devices requires the graphene contacting by metal layers and it is widely recognized that the metal-graphene interaction strongly influences the graphene electrical conduction properties being, often, a limiting factor in produce high-efficiency electronic devices.For example, several theoretical and experimental analysis suggest that the difference in the work functions of the metal and graphene leads to the charge transfer and doping of the graphene layer [101][102][103][104].In general, to realize high-performance devices, it is very important to produce metallic contacts on graphene which show a very low contact resistance.In principle, an Ohmic contact is obtained without any difficulty by the contact of a metal with graphene layer due to the graphene lack of a band gap but it is concerned that a very small density of states (DOS) for graphene might suppress the current injection from the metal to graphene [78,107].In general [107], a metal/metal contact has no potential barrier and the carrier is transferred directly through the metal/metal interface to cancel the difference in work functions.Since graphene has not band-gap, the case of the metal/graphene contact should be similar to the metal/metal contact.However, differently from the metal/metal contact, in the metal/graphene contact the effects of the very small DOS for graphene have to be considered: in particular, the amount of charge transfer gradually decreases from the metal/graphene interface.This charge transfer forms the dipole layer at the interface and the very small DOS around the Fermi level of graphene increases produces a high screening length.As a result of the long charge transfer region, a p-n junction arises near the metal/graphene contact.On the other hand, the graphene Fermi level position with respect to the conical point is strongly influenced by the adsorption of metal atoms on the graphene surface [101][102][103][104] causing the graphene doping.As a consequence, metal/graphene contacts show different electrical behaviors depending on the specific graphene doping induced by the peculiar contacting metal.As summarized in Table 4, theoretical calculations by Giovannetti et al. [101,102], for example, show that different metals, by their specific electronic interaction with graphene, causes different shifts of the graphene Fermi level with respect to the Dirac point: those metals (Au, Pt) which interacting with graphene causes the shift the graphene Fermi level below the Dirac point, are p-type doping the graphene.These are the metals which causes an increase of the free-standing graphene work-function (4.48 eV), see Table 4.Those metals (Ni, Co, Pd, Al, Ag, Cu) which interacting with graphene causes the shift the graphene Fermi level above the Dirac point, are n-type doping the graphene.These are the metals which causes a decrease of the free-standing graphene work-function, see Table 4.
Table 4. Results of the calculations of Giovannetti et al. for the electronic characteristics of metals/graphene contacts: d eq equilibrium distance for the metal atom-graphene system, ∆E metal atom-graphene binding energy, W M metal work-function, W graphene work-function in the free-standing configuration (4.48 eV) and when in contact with the metal.Reproduced from Reference [102] with permission from the American Physical Society.So, it is clear, also from an experimental point of view, the importance to study the electrical characteristics of several metal-graphene systems.In this regard, an interesting analysis was reported by Watanabe et al. [105]: in this work the authors studied, experimentally, the contact resistance R C of several metals (Ti, Ag, Co, Cr, Fe, Ni, Pd) to graphene with the results summarized in Figure 29: it reports the contact resistance (the square marks the mean value for the specific metal) for several metal films deposited on graphene.It is interesting to note that is not strongly related to the metal work function.Instead, analyzing the microstructure of the deposited metal films, the authors conclude that the contact resistance is significantly affected by this microstructure (as determined by the deposition conditions) according to the pictorial scheme reported in Figure 30.Connecting the analysis on the contact resistance to the microstructure of the films, the authors draw the following conclusions: for the large contact resistance metals (Ag, Fe, and Cr) the films result to be formed by large grains and to present rough surfaces, while for the small contact resistance metals (Pd, Ni, Co) the films are formed by small grains and present uniform surfaces.The effects of these different situations are pictured in Figure 30: large grains and rough surface of a metal films lead to a small contact are between the metal and the graphene, resulting in high contact resistance; small grains and uniform surface of a metal film lead to a large contact are between the metal and the graphene, resulting in a low contact resistance.These results clearly indicate, as stressed throughout the entire paper, the importance of the control of the kinetics and thermodynamics nucleation and growth processes for metals deposited on graphene so to reach the optimum nano-and micro-scale structure/morphology of the growing films/NPs for specific functional applications.
Conclusions, Open Points, and Perspectives
The next developments for metal NPs/Graphene nanocomposites are conditioned to the atomic scale control of the fabrication of the metal NPs and optimization of the techniques for reaching the wide-range control of the nano-architecture.Nowadays, several properties and applications of metal Connecting the analysis on the contact resistance to the microstructure of the metal films, the authors draw the following conclusions: for the large contact resistance metals (Ag, Fe, and Cr) the films result to be formed by large grains and to present rough surfaces, while for the small contact resistance metals (Pd, Ni, Co) the films are formed by small grains and present uniform surfaces.The effects of these different situations are pictured in Figure 30: large grains and rough surface of a metal films lead to a small contact are between the metal and the graphene, resulting in high contact resistance; small grains and uniform surface of a metal film lead to a large contact are between the metal and the graphene, resulting in a low contact resistance.These results clearly indicate, as stressed throughout the entire paper, the importance of the control of the kinetics and thermodynamics nucleation and growth processes for metals deposited on graphene so to reach the optimum nano-and micro-scale structure/morphology of the growing films/NPs for specific functional applications.
Conclusions, Open Points, and Perspectives
The next developments for metal NPs/Graphene nanocomposites are conditioned to the atomic scale control of the fabrication of the metal NPs and optimization of the techniques for reaching the wide-range control of the nano-architecture.Nowadays, several properties and applications of metal Connecting the analysis on the contact resistance to the microstructure of the metal films, the authors draw the following conclusions: for the large contact resistance metals (Ag, Fe, and Cr) the films result to be formed by large grains and to present rough surfaces, while for the small contact resistance metals (Pd, Ni, Co) the films are formed by small grains and present uniform surfaces.The effects of these different situations are pictured in Figure 30: large grains and rough surface of a metal films lead to a small contact are between the metal and the graphene, resulting in high contact resistance; small grains and uniform surface of a metal film lead to a large contact are between the metal and the graphene, resulting in a low contact resistance.These results clearly indicate, as stressed throughout the entire paper, the importance of the control of the kinetics and thermodynamics nucleation and growth processes for metals deposited on graphene so to reach the optimum nano-and micro-scale structure/morphology of the growing films/NPs for specific functional applications.
Conclusions, Open Points, and Perspectives
The next developments for metal NPs/Graphene nanocomposites are conditioned to the atomic scale control of the fabrication of the metal NPs and optimization of the techniques for reaching the wide-range control of the nano-architecture.Nowadays, several properties and applications of metal NPs/Graphene nanocomposites have been explored.As a non-exhaustive synthesis, Table 5 reports some examples of the properties and technological applications for several metal NPs/graphene systems, ranging from sensing and biosensing to nanoelectronics, catalysis and solar devices [135][136][137][138][139].
Surely, new insights and perspectives are related to the nanoscale control of the spatial organization and shape of the NPs.In this sense, the use of techniques to self-assembly the metal NPs on the graphene in spatially ordered arrays will be the key approach.So, in general, the key step towards real engineering of the metal NPs/graphene nanocomposites is the development of methodologies to produce complex nanoscale architectures.Towards this end, the vapor-deposition based techniques can open new perspectives.
Fine control of the morphology of the metal NPs on graphene is also a very interesting challenge.By the possibility to grow a range of geometric shapes at the nanoscale, the production of complex-morphology metal NPs on graphene is an interesting area of research, especially with regard to the resulting plasmonic properties.
Another interesting point concerns the use of new metal NPs (with specific functionalities) in the mixing with graphene.Probably, alloys of metals and core-shell type NPs (Ag/Au, Au/Pd, Pd/Pt, Pt/Rh, Pt/Ru) could be very useful tool, particularly in information storage and biomedicine applications.
A recent field of investigation for metal NPs/graphene nanocomposites is that related to photocatalysis [140].Towards this application, however, the key requirement is the development of procedures allowing the preparation of composites which are biocompatible, biodegradable, and non-toxic and assuring, also, the control of the NPs size and shape.Notably, the long-term efficiencies of the metal NPs/graphene in real photocatalytic applications composites represents an important practical issue to be resolved.In the renewable energy production field, metal NPs-graphene composites are attracting great interest.The graphene can be used in a solar cell as a transparent conductive electrode and the metal NPs as plasmonic scattering elements [40,135,137].Significant results have been already achieved.However, in addition solar cell devices, thermoelectric devices are attracting much attention [141].
Towards these perspectives and developments, the physical vapor deposition processes-based techniques to produce the metal NPs-graphene composites will acquire, surely, more and more importance due to their simplicity, versatility, and high throughput.For these reasons such techniques are, in perspective, the main candidates to be implemented in the industry market for the large-area production and commercialization of functional devices based on the metal NPs-graphene composites.Toward this end, the present paper highlighted the key importance of the understanding and controlling the microscopic thermodynamics and kinetics mechanisms involved in the nucleation and growth processes of atoms on/in graphene.So, crossed theoretical and experimental studies characterizing these mechanisms and quantifying the involved parameters such as adsorption energies, activation energies, diffusion constants, etc. will acquire more and more importance.In fact, the fine control of these parameters will allow the superior control on the morphological/structural characteristics of the composites and so, as a consequence, the tuning of all the physico-chemical properties of the composites for high-efficiency functional applications.
Liu et al. [100] calculated several other parameters related to the atoms-graphene interactions as summarized in the other columns of as a consequence of the increase of the adsorption energy (even if some exceptions are present as in the case of Ni and Pt).(d) Liu et al.[100] calculated several other parameters related to the atoms-graphene interactions as summarized in the other columns of
Figure 1 .
Figure 1.(a) Adsorption energy (Ea) and (b) diffusion barrier (ΔE) for several adatoms on graphene as calculated by Liu et al. using density functional theory.Reproduced from Reference [100] with permission from the Royal Society of Chemistry.
Figure 1 .
Figure 1.(a) Adsorption energy (E a ) and (b) diffusion barrier (∆E) for several adatoms on graphene as calculated by Liu et al. using density functional theory.Reproduced from Reference [100] with permission from the Royal Society of Chemistry.
Figure 2 .
Figure 2. Ratio of adsorption energy to bulk cohesive energy for various materials calculated by Liu et al.Reproduced from Reference [100] with permission from the Royal Society of Chemistry.
Figure 2 .
Figure 2. Ratio of adsorption energy to bulk cohesive energy for various materials calculated by Liu et al.Reproduced from Reference [100] with permission from the Royal Society of Chemistry.
Figure 3 .
Figure 3. Stable geometries of Au clusters adsorbed on perfect graphene.Au1-Au5 and Au5(P) clusters are shown from top to bottom rows.Left and right columns show top and side views, respectively.Reproduced from Reference[92] with permission from the American Physical Society.
Figure 3 .
Figure 3. Stable geometries of Au clusters adsorbed on perfect graphene.Au 1 -Au 5 and Au 5 (P) clusters are shown from top to bottom rows.Left and right columns show top and side views, respectively.Reproduced from Reference[92] with permission from the American Physical Society.
Figure 4 .
Figure 4. Structures of the (3 × 3) surfaces used for the simulations: (a) freestanding graphene; (b) graphene on fcc Ru(0001); (c) graphene on hcp Ru(0001); and (d) graphene on ridge Ru(0001).Graphene is shown as bonds only.Top and second layer Ru atoms are shown as green and grey spheres, respectively.Reproduced from Reference[99] with permission from the American Institute of Physics.
Figure 5
Figure 5 reports, according to the calculations of Semidey-Flecha et al. [99], the potential surface energy for Au1 calculated on the same set of (3 × 3) surfaces.These potential surfaces energy furnish the preferential diffusion path for Au1 as well as the global diffusion barrier.
Figure 4 .
Figure 4. Structures of the (3 × 3) surfaces used for the simulations: (a) freestanding graphene; (b) graphene on fcc Ru(0001); (c) graphene on hcp Ru(0001); and (d) graphene on ridge Ru(0001).Graphene is shown as bonds only.Top and second layer Ru atoms are shown as green and grey spheres, respectively.Reproduced from Reference[99] with permission from the American Institute of Physics.
Figure 5 .
Figure 5. Potential energy surfaces for Au1 on the (3 × 3) surfaces: (a) freestanding graphene; (b) graphene on fcc Ru(0001); (c) graphene on hcp Ru(0001); and (d) graphene on ridge Ru(0001).The hexagon identifies the standard graphene hexagon.In each image, the dashed line signs the adatom minimum-energy diffusion path."X" marks the transition state from a local minimum energy site to another.The energy scale is in eV.Reproduced from Reference[99] with permission from the American Institute of Physics.
Figure 5 .
Figure 5. Potential energy surfaces for Au 1 on the (3 × 3) surfaces: (a) freestanding graphene; (b) graphene on fcc Ru(0001); (c) graphene on hcp Ru(0001); and (d) graphene on ridge Ru(0001).The hexagon identifies the standard graphene hexagon.In each image, the dashed line signs the adatom minimum-energy diffusion path."X" marks the transition state from a local minimum energy site to another.The energy scale is in eV.Reproduced from Reference[99] with permission from the American Institute of Physics.
Figure 5 .
Figure 5. Potential energy surfaces for Au1 on the (3 × 3) surfaces: (a) freestanding graphene; (b) graphene on fcc Ru(0001); (c) graphene on hcp Ru(0001); and (d) graphene on ridge Ru(0001).The hexagon identifies the standard graphene hexagon.In each image, the dashed line signs the adatom minimum-energy diffusion path."X" marks the transition state from a local minimum energy site to another.The energy scale is in eV.Reproduced from Reference[99] with permission from the American Institute of Physics.
Figure 6 .
Figure 6.Potential energy surfaces for Au1 sampled at the top and ring center sites in the symmetry-irreducible zone of the full graphene/Ru(0001) surface.The dashed line signs the adatom minimum-energy diffusion path The minimum energy diffusion path for the adatom is marked by a dashed line."D","E", and "F" mark the preferential adsorption sites, and "X" marks the highest-energy site.Reproduced from Reference[99] with permission from the American Institute of Physics.
Figure 6 .
Figure 6.Potential energy surfaces for Au 1 sampled at the top and ring center sites in the symmetry-irreducible zone of the full graphene/Ru(0001) surface.The dashed line signs the adatom minimum-energy diffusion path.The minimum energy diffusion path for the adatom is marked by a dashed line."D","E", and "F" mark the preferential adsorption sites, and "X" marks the highest-energy site.Reproduced from Reference[99] with permission from the American Institute of Physics.
Figure 7 .
Figure 7. Carbon vacancies formation energy in graphene (empty squares), and formation energies for Au adsorbed in graphene vacancies (full points).For each vacancy, the insets show the selected geometry for the vacancy.Reproduced from Reference[98] with permission from the American Institute of Physics.
Figure 7 .
Figure 7. Carbon vacancies formation energy in graphene (empty squares), and formation energies for Au adsorbed in graphene vacancies (full points).For each vacancy, the insets show the selected geometry for the vacancy.Reproduced from Reference[98] with permission from the American Institute of Physics.
Figure 8 .
Figure 8. Au in double vacancies in graphene: simulations of different diffusion paths (path I, II, III, IV) of the Au atom (yellow sphere), whereas the blue dots indicate the C atoms which change position as result of the Au atom jump.In addition, each path is accompanied by the estimated diffusion barrier for the Au jump.Reproduced from Reference [98] with permission from the American Institute of Physics.
Figure 8 .
Figure 8. Au in double vacancies in graphene: simulations of different diffusion paths (path I, II, III, IV) of the Au atom (yellow sphere), whereas the blue dots indicate the C atoms which change position as result of the Au atom jump.In addition, each path is accompanied by the estimated diffusion barrier for the Au jump.Reproduced from Reference [98] with permission from the American Institute of Physics.
Figure 13 .
Figure 13.Scanning Tunneling Microscopy images (70 nm × 70 nm) of (a) 0.25 ML Pt deposited on graphene/Ir(111) maintaining the substrate at 300 K.This sample was then annealed for 300 s at (b) 400 K; (c) 450 K (d) 500 K; (e) 550 K and (f) 650 K; (g) Plot of n (occupation probability of the moiré cell by a particle) versus the annealing temperature T; (h) Arrhenius plot of particle jumping rate ν(T).Lines represent fits for the hopping rate with diffusion parameters as shown in Table3.Reproduced from Reference[64] with permission from IOPscience.
Figure 13 .
Figure 13.Scanning Tunneling Microscopy images (70 nm × 70 nm) of (a) 0.25 ML Pt deposited on graphene/Ir(111) maintaining the substrate at 300 K.This sample was then annealed for 300 s at (b) 400 K; (c) 450 K (d) 500 K; (e) 550 K and (f) 650 K; (g) Plot of n (occupation probability of the moiré cell by a particle) versus the annealing temperature T; (h) Arrhenius plot of particle jumping rate ν(T).Lines represent fits for the hopping rate with diffusion parameters as shown in Table3.Reproduced from Reference[64] with permission from IOPscience.
Figure 15 .
Figure 15.(a-d) Transmission Electron Microscopy images of Au deposited on free-standing graphene increasing the amount of deposited metal; (a) Sparse coverage; (b) sparse groups of clusters at Au thickness lower than 0.1 nm; (c) Higher cluster densities at 0.12 nm of Au thickness; (d) Coalescence of clusters occurring for 2.12 nm-thick deposited Au; (e) Scanning Transmission Electron Microscopy bright-field image of 0.5 nm-thick evaporated Au.Scale bar: 10 nm in all images.Reproduced from Reference [66] with permission from Wiley.
Figure 15 .
Figure 15.(a-d) Transmission Electron Microscopy images of Au deposited on free-standing graphene increasing the amount of deposited metal; (a) Sparse coverage; (b) sparse groups of clusters at Au thickness lower than 0.1 nm; (c) Higher cluster densities at 0.12 nm of Au thickness; (d) Coalescence of clusters occurring for 2.12 nm-thick deposited Au; (e) Scanning Transmission Electron Microscopy bright-field image of 0.5 nm-thick evaporated Au.Scale bar: 10 nm in all images.Reproduced from Reference [66] with permission from Wiley.
Figure 15 .
Figure 15.(a-d) Transmission Electron Microscopy images of Au deposited on free-standing graphene increasing the amount of deposited metal; (a) Sparse coverage; (b) sparse groups of clusters at Au thickness lower than 0.1 nm; (c) Higher cluster densities at 0.12 nm of Au thickness; (d) Coalescence of clusters occurring for 2.12 nm-thick deposited Au; (e) Scanning Transmission Electron Microscopy bright-field image of 0.5 nm-thick evaporated Au.Scale bar: 10 nm in all images.Reproduced from Reference [66] with permission from Wiley.
Figure 16 .
Figure 16.Coalesced Au clusters corresponding to the deposition of 2.12 nm Au on graphene.(a) shows variations in thickness and relative crystallographic orientations and (b) planar faults such as stacking faults (white arrows) and twin boundaries (black arrow).Scale bars: 5 nm.Reproduced from Reference [66] with permission from Wiley.
Figure 17 .
Figure 17.(a,b): Transmission Electron Microscopy images of 0.2 nm Au evaporated onto hydrogenated and pristine graphene (scale bar: 20 nm).The corresponding diffraction patterns are shown as insets; (c,d) Images of Au evaporated onto hydrogenated graphene, taken in a sequence of scans, and showing the Au clusters merging by coalescence as indicated by the solid circles and dashed rectangles (scale bar: 5 nm).Reproduced from Reference [66] with permission from Wiley.
Figure 16 .
Figure 16.Coalesced Au clusters corresponding to the deposition of 2.12 nm Au on graphene.(a) shows variations in thickness and relative crystallographic orientations and (b) planar faults such as stacking faults (white arrows) and twin boundaries (black arrow).Scale bars: 5 nm.Reproduced from Reference [66] with permission from Wiley.
Figure 16 .
Figure 16.Coalesced Au clusters corresponding to the deposition of 2.12 nm Au on graphene.(a) shows variations in thickness and relative crystallographic orientations and (b) planar faults such as stacking faults (white arrows) and twin boundaries (black arrow).Scale bars: 5 nm.Reproduced from Reference [66] with permission from Wiley.
Figure 17 .
Figure 17.(a,b): Transmission Electron Microscopy images of 0.2 nm Au evaporated onto hydrogenated and pristine graphene (scale bar: 20 nm).The corresponding diffraction patterns are shown as insets; (c,d) Images of Au evaporated onto hydrogenated graphene, taken in a sequence of scans, and showing the Au clusters merging by coalescence as indicated by the solid circles and dashed rectangles (scale bar: 5 nm).Reproduced from Reference [66] with permission from Wiley.
Figure 17 .
Figure 17.(a,b): Transmission Electron Microscopy images of 0.2 nm Au evaporated onto hydrogenated and pristine graphene (scale bar: 20 nm).The corresponding diffraction patterns are shown as insets; (c,d) Images of Au evaporated onto hydrogenated graphene, taken in a sequence of scans, and showing the Au clusters merging by coalescence as indicated by the solid circles and dashed rectangles (scale bar: 5 nm).Reproduced from Reference [66] with permission from Wiley.
Figure 18 .
Figure 18.(a,b) Plan-view Transmission Electron Microscopy images of Pt atoms in a four-layer graphitic sheet held at 600 °C.The image (b) was acquired 60 s after (a).Two Pt atoms (arrowed) merge and form a cluster.The scale bar is 1 nm.Reproduced from Reference [58] with permission from Wiley.
Figure 18 .
Figure 18.(a,b) Plan-view Transmission Electron Microscopy images of Pt atoms in a four-layer graphitic sheet held at 600 • C. The image (b) was acquired 60 s after (a).Two Pt atoms (arrowed) merge and form a cluster.The scale bar is 1 nm.Reproduced from Reference [58] with permission from Wiley.
that D = ga 2 ν0exp[−Ea/kT], with g ≈ 1 a geometrical factor, a the graphene lattice constant, ν0 the attempt frequency which can be assumed to be the Debye frequency, then Ea is estimated, both for Pt and Au, in about 2.5 eV.
Figure 19 .
Figure 19.Series of Transmission Electron Microscopies showing the diffusion of Pt atoms in graphene at 600 °C as a function of time."L" marks the region in a two-three layer graphene where Pt atoms are diffusing in two dimensions."E" marks a Pt cluster located at the edge of a graphene layer and where Pt atoms are observed one-dimensionally diffuse along the edge.Reproduced from Reference [58] with permission from Wiley.
Figure 19 .
Figure 19.Series of Transmission Electron Microscopies showing the diffusion of Pt atoms in graphene at 600 C as a function of time."L" marks the region in a two-three layer graphene where Pt atoms are diffusing in two dimensions."E" marks a Pt cluster located at the edge of a graphene layer and where Pt atoms are observed one-dimensionally diffuse along the edge.Reproduced from Reference [58] with permission from Wiley.
Figure 20 .
Figure 20.Atomic Force Microscopy images (1 μm × 1 μm) of 0.1 nm Au deposited on a single-layer graphene (a) and on graphite (b).(c,d) show the same samples (Au on single-layer graphene in (c) and Au on graphite in (d)) after 2 h of thermal annealing at 350 °C.Reproduced from Reference[60] with permission from the American Chemical Society.
Figure 20 .
Figure 20.Atomic Force Microscopy images (1 µm × 1 µm) of 0.1 nm Au deposited on a single-layer graphene (a) and on graphite (b).(c,d) show the same samples (Au on single-layer graphene in (c) and Au on graphite in (d)) after 2 h of thermal annealing at 350 • C. Reproduced from Reference[60] with permission from the American Chemical Society.
Figure 22 .
Figure 22.The calculated diffusion energy, E d , and diffusion constant, D, of Au adatoms on various surfaces: graphite, hexagonal boron nitride (h-BN), single-layer graphene (SLG) on h-BN, SLG on SiO , and bilayer graphene (BLG) on SiO 2 .Calculations using different critical sizes i are given in black (i = 1) and red (i = 2) curves for comparison.For graphite, E d and D are assumed as 50 meV and 7 × 10 −6 cm 2 s −1 , independent of critical size i.Reproduced from Reference[60] with permission from the American Chemical Society.
reports Scanning Electron Microscopy images showing the dewetting of 2 nm-thick Au film into hexagonal Au NPs on graphene after thermal annealing at 700 • C for 2 h being the Au film supported directly on SiO 2 (Figure 23a left) and on monolayer graphene (Figure 23a right), supported directly on SiO 2 (Figure 23b left) and on bilayer graphene (Figure 23b right), supported directly on SiO 2 (Figure 23c right) and on trilayer graphene (Figure 23c left), supported on bilayer graphene (Figure 23d left) and on four-layer graphene (Figure right).It can be recognized that the size and density of hexagonal Au NPs is established by the number n of graphene layers.In fact, it is observed that the increase of n produces an increase of the the size of the Au NPs increases and a decrease of their surface density.Crystals 2017, 7, 219 26 of 40 n-layer graphenes are strictly dependent on the number n of graphene layers.In particular, increasing n the NPs mean size increases and the NPs surface density decreases.As an example, Figure 23 reports Scanning Electron Microscopy images showing the dewetting of 2 nm-thick Au film into hexagonal Au NPs on graphene after thermal annealing at 700 °C for 2 h being the Au film supported directly on SiO2 (Figure 23a left) and on monolayer graphene (Figure 23a right), supported directly on SiO2 (Figure 23b left) and on bilayer graphene (Figure 23b right), supported directly on SiO2 (Figure 23c right) and on trilayer graphene (Figure 23c left), supported on bilayer graphene (Figure 23d left) and on four-layer graphene (Figure 23d right).It can be recognized that the size and density of hexagonal Au NPs is established by the number n of graphene layers.In fact, it is observed that the increase of n produces an increase of the the size of the Au NPs increases and a decrease of their surface density.
Figure 24 .
Figure 24.Scanning Electron Microscopy images showing the effects of the starting thickness of the deposited Au film on the shape of the resulting NPs after the annealing process at 600 °C for 2 h.Scale bar: 200 nm.(a,b) 1.0 nm thick Au; (c,d) 1.5 nm thick Au; (e,f) 2.0 nm thick Au.It is obvious to find that with the increase of Au film thickness, the modulation becomes less effective.Reproduced from Reference [68] with permission from Elsevier.
Figure 24 .
Figure 24.Scanning Electron Microscopy images showing the effects of the starting thickness of the deposited Au film on the shape of the resulting NPs after the annealing process at 600 • C for 2 h.Scale bar: 200 nm.(a,b) 1.0 nm thick Au; (c,d) 1.5 nm thick Au; (e,f) 2.0 nm thick Au.It is obvious to find that with the increase of Au film thickness, the modulation becomes less effective.Reproduced from Reference [68] with permission from Elsevier.
Figure 25a but with a different size and surface density N of the NPs on the basis of the number n of the graphene layers.
Figure 25 .
Figure 25.Morphologies, size, and density of Au nanoparticles on n-layer graphenes after annealing at 1260 °C in vacuum for 30 s (false-color image).Note that no Au NPs are found in the substrate.(a) Au NPs on monolayer, bilayer, and trilayer graphene, respectively; (b) Statistics of the size and density of gold nanoparticles on n-layer graphenes.Reproduced from Reference [69] with permission from the American Chemical Society.
Figure 25 .
Figure 25.Morphologies, size, and density of Au nanoparticles on n-layer graphenes after annealing at 1260 • C in vacuum for 30 s (false-color image).Note that no Au NPs are found in the substrate.(a) Au NPs on monolayer, bilayer, and trilayer graphene, respectively; (b) Statistics of the size and density of gold nanoparticles on n-layer graphenes.Reproduced from Reference [69] with permission from the American Chemical Society.
Figure 26 .
Figure 26.Scanning Electron Microscopy images (1 μm scale bar) of monolayer and bilayer graphene on SiO2 after deposition of 5 nm Ag maintaining the substrate at different temperature during the deposition: (a,b) 298 K; (c,d) 333 K; (e,f) 373 K. Reproduced from Reference [71] with permission from the American Chemical Society.
Figure 26 .
Figure 26.Scanning Electron Microscopy images (1 µm scale bar) of monolayer and bilayer graphene on SiO 2 after deposition of 5 nm Ag maintaining the substrate at different temperature during the deposition: (a,b) 298 K; (c,d) 333 K; (e,f) 373 K. Reproduced from Reference [71] with permission from the American Chemical Society.
Figure 27 .
Figure 27.Raman spectra from monolayer and bilayer graphene on SiO2 having deposited on the graphene 2 or 5 nm Ag film.Reproduced from Reference[71] with permission from the American Chemical Society.
Figure 28 .
Figure 28.Raman spectra of monolayer (a) and bilayer (b) graphene covered by 5 nm Ag deposited maintaining the substrate at 298 K (black line), 333 K (red line), and 373 K (blue line).Reproduced from Reference[71] with permission from the American Chemical Society.
Figure 27 . 40 Figure 27 .
Figure 27.Raman spectra from monolayer and bilayer graphene on SiO 2 having deposited on the graphene 2 or 5 nm Ag film.Reproduced from Reference[71] with permission from the American Chemical Society.
Figure 28 .
Figure 28.Raman spectra of monolayer (a) and bilayer (b) graphene covered by 5 nm Ag deposited maintaining the substrate at 298 K (black line), 333 K (red line), and 373 K (blue line).Reproduced from Reference[71] with permission from the American Chemical Society.
Figure 28 .
Figure 28.Raman spectra of monolayer (a) and bilayer (b) graphene covered by 5 nm Ag deposited maintaining the substrate at 298 K (black line), 333 K (red line), and 373 K (blue line).Reproduced from Reference[71] with permission from the American Chemical Society.
Figure 29 .
Figure 29.Metal-graphene contact resistance versus metal work-function.The square indicates the mean value.Reproduced from Reference [105] with permission from Elsevier.
Figure 30 .
Figure 30.Schematic picture of metal contact to graphene.(a,b) indicate a schematic model of the metal/graphene junction for the large and small contact resistance values, respectively.The model shows that the contact resistance becomes smaller with increasing contact area between the metal grain and the graphene.Reproduced from Reference [105] with permission from Elsevier.
Figure 29 . 40 Figure 29 .
Figure 29.Metal-graphene contact resistance versus metal work-function.The square indicates the mean value.Reproduced from Reference [105] with permission from Elsevier.
Figure 30 .
Figure 30.Schematic picture of metal contact to graphene.(a,b) indicate a schematic model of the metal/graphene junction for the large and small contact resistance values, respectively.The model shows that the contact resistance becomes smaller with increasing contact area between the metal grain and the graphene.Reproduced from Reference [105] with permission from Elsevier.
Figure 30 .
Figure 30.Schematic picture of metal contact to graphene.(a,b) indicate a schematic model of the metal/graphene junction for the large and small contact resistance values, respectively.The model shows that the contact resistance becomes smaller with increasing contact area between the metal grain and the graphene.Reproduced from Reference [105] with permission from Elsevier.
Table
: E a /E c (metal adsorption energy on graphene to bulk metal cohesive energy and E c −E a .
Table
: Ea/Ec (metal adsorption energy on graphene to bulk metal cohesive energy and Ec−Ea.
Table 1 .
E [100]sorption energy of the metal atom on graphene, kcal/mol), ∆E (diffusion barrier of the metal adatom on graphene, kcal/mol), E a /E c (with E c the bulk metal cohesive energy), and E c −E a (kcal/mol).Reproduced from Reference[100]with permission from the Royal Society of Chemistry.
Table 5 .
Table summarizing some specific metal NPs-graphene composite systems with the corresponding exploited properties and/or applications. | 36,118.6 | 2017-07-13T00:00:00.000 | [
"Materials Science",
"Physics"
] |
Correlation length around Mars: A statistical study with MEX and MAVEN observations
Correlation lengths of ultra‐low‐frequency (ULF) waves around Mars were computed for the first time, using data from MEX (electron density from 2004 to 2015) and MAVEN (electron density and magnetic field from 2014 to 2016). Analysis of the MEX data found that, for the frequency range 8 to 50 mHz, correlation length in electron density varied between 13 and 17 seconds (temporal scale) and between 5.5 × 103 km and 6.8 × 103 km (spatial scale). For the MAVEN time interval, correlation length was found to vary between 11 and 16 seconds (temporal scale) and 2 × 103 – 4.5×10 3 km in spatial scale. In the magnetic field data, correlation lengths are observed to be between 8–15 seconds (temporal scale) and between 1 × 103 and 5 × 103 km (spatial scale) over the same frequency range. We observe that the cross sections of the plasma regions at the dayside of Mars are smaller than these correlation lengths in these regions in both analyses, where the correlation length derived from the MEX electron density data was between 5 and 25 times the size of the magnetosheath and the magnetic pile‐up region (MPR), respectively. For MAVEN these ratios are about 4 (magnetosheath) and 11 (MPR) in electron density and between 1.5 and 5.5 for magnetic field data, respectively. These results indicate that waves at the magnetosheath/MPR can be related to oscillations in the upper ionosphere. In a local region, wave trains may cause resonance effects at the planetary ionopause, which consequently contributes to the enhanced ion escape from the atmosphere.
Introduction
Mars has an induced magnetosphere caused by induction of electric fields in the upper ionosphere by the magnetized solar wind (Kivelso and Bagenal, 2007). Since the ionosphere of Mars forms a conductive layer, the solar wind magnetic field cannot easily penetrate and the deflected fields produce induced currents in the upper ionosphere. As a consequence, the magnetic field piles up in front of the planet, which causes the incident solar wind plasma to slow down and be deflected around the planet, forming a magnetosheath region similar to the magnetosphere that is created by an intrinsic magnetic field Daniell, 1973, 1979;Podgorny et al., 1980).
In the Mars orbit, the passage of interplanetary shock waves, ICMEs (Interplanetary Coronal Mass Ejections), and CIRs (Corotating Interaction Regions) perturb the solar wind; consequently, ion and energetic electron flows associated with these shocks can reach the planet. As Mars does not have an intrinsic magnetic field, the planet cannot totally deflect the solar wind particles, especially those of high energy; some of them can penetrate into the atmosphere of Mars (Luhmann et al., , 2004. Another factor that can transfer energy from solar wind to the inner magnetosphere is propagation of Ultra-Low Frequency (ULF) waves (Kivelson, 1995). Mainly generated at the bow shock upstream region by heavy ions, reflecting protons and electrons at this boundary, ULF waves are observed in the foreshock due to energized particles of the solar wind, which get their energy from multiple crossings of the bow shock and escape to the upstream region, creating instabilities in the foreshock's plasma. Those waves are also generated due to magnetosheath ions that escape across the bow shock and move in the anti-solar region (Russell et al., 1990;Delva and Dubinin, 1998;Volwerk et al., 2008). In the upstream region of Mars, ULF waves show a strong dependence on the interplanetary magnetic field (IMF) orientation. It was observed that when the IMF is more radial, the observed waves are more intense (Halekas et al., 2017). The radial geometry facilitates upstream movement of the ions when reflected from the bow shock, which contributes to the formation of upstream instabilities.
It was observed earlier that high ULF wave activity (sufficient to reach the ionospheric region and heat the plasma) is correlated with greater ionospheric ion acceleration (Lundin et al., 2011). This process can provide enough energy to planetary ions for them to escape from the planet. Consequently, ULF waves play an import-ant role in the atmospheric loss on Mars. Winningham et al. (2006) observed that ULF waves in the magnetosheath region sometimes present frequencies similar to the gyrofrequency of oxygen in the region, and these waves can be connected to waves in the ionosphere. Recent studies by Collinson et al. (2018) using MAVEN (Mars Atmosphere and Volatile EvolutioN) and MEX (Mars EXpress) data have shown that compressive ULF waves in the solar wind can drive magnetosonic ULF waves in the ionosphere of Mars and that these pulsations can heat and energize the plasma from the ionosphere.
In order to estimate the interaction region size of ULF waves in different propagation directions in the terrestrial foreshock, Archer et al. (2005) used data from the four Cluster spacecraft to compute the correlation length of ULF waves observed in the magnetic field. These authors determined that the correlation length is typically 8-18 Earth's radius in the perpendicular direction to the wave vector, and 1-3 Earth's radius along the wave vector. This study is useful for understanding the wave-particle interactions.
In order to determine whether ULF waves, when converted to compressive pulses, are capable of causing resonance effects at the ionopause of Mars, in this work we compute correlation lengths (CL) around Mars for the observation intervals of MEX (2004MEX ( -2015 and MAVEN (2014MAVEN ( -2016 and compare the values of CL in each plasma region of the dayside magnetosphere statistically with the size of the specific region.
Materials and Methods
The general definition of the correlation length is a characteristic scale over which fluctuations in a variable are correlated (Fisk and Sari, 1973). In other words, the correlation length is the distance from a given point to the most distant point beyond which there is no further correlation of a physical property associated with the given point (Mela and Louie, 2001;Wicks et al., 2010). The correlation length has many applications in different areas, such as in the study of structures in the solar wind (Fisk and Sari, 1973;Wicks et al., 2010), molecular dynamics simulation (Morales and Nuevo, 1993), scattering of cosmic rays (Parhi et al., 2002), and turbulent boundary layer flight data (Palumbo, 2012), among others.
Since our study is in the ULF range, before computing the correlation length we apply a Fourier transform to remove high frequencies present on the data. Because the highest power in foreshock ULF waves is typically between 8 and 50 mHz (Fränz et al., 2017), we define this to be the relevant frequency domain. We then use the inverse Fourier transform to transform the data back to the time domain. To compute the correlation length, we calculate the autocorrelation function (AC), lagged by a time between 0 and 60 s and sliding a window of 120 s width across the data. This restricts the possible detection of correlation lengths to the range 8-60 s.
The AC curve can be represented by an exponential of the lag (L) by the biggest lag (CL): where CL is the correlation length.
To obtain the correlation length, an exponential fit must be employed to the auto-correlation amplitude curve: After that, a linear regression ( ) has been employed to find CL from Equation (2).
The correlation length can then be found as: Here the CL are given in a temporal scale; to obtain the correlation length in a spatial dimension (CL S ), the temporal correlation length (CL T ) must be multiplied by the plasma velocity (V SW ), as Equation (4) shows.
In our analysis we used the ASPERA-3/IMA (MEX) and SWIA (MAVEN) velocity interpolated to the same timetags as those of the electron or magnetic field data.
Data
In this paper, our data come from the MEX (covering the interval 2004-2015) and MAVEN (2014-2016 spacecraft -in particular, from the ELS/ASPERA-3 (Electron Spectrometer/Analyzer of Space Plasma and Energetic Atoms Experiment) aboard MEX (Barabash et al., 2004) and from MAVEN's Solar Wind Electron Analyzer (SWEA) (Mitchell et al., 2016). Electron densities have been calculated according to the methods described in Fränz et al. (2006). As MEX does not have a magnetometer, the magnetic field correlation length has been calculated using only data from the magnetometer on board MAVEN (Connerney et al., 2015a, b). All data are downsampled to 4 s time resolution.
Results
The correlation length analysis was developed by building maps that present statistical probability, in order to observe a certain correlation length in a spatial bin around the planet. Each bin has a dimension of 0.1 × 0.1 Mars radii in cylindrical MSO (Mars Solar Orbit) coordinates. The x-axis represents the Mars-Sun line and is centered in Mars; it varies from -4R M to 3R M . The y-axis represents the y direction and varies from 0 to 4.5R M . All figures indicate the main localization of the boundaries (Bow shock and magnetic pile up boundary -MPB) of the Mars magnetosphere found by Han et al. (2014).
When the dynamic pressure of the solar wind is high, it increases wave production in the magnetosheath (Lundin et al., 2008). In order to determine whether the size of the structures around the planet change with the solar wind pressure, we performed a study of the correlation length during periods of low (between 0 nPa and 1 nPa) and high (between 1 nPa and 100 nPa) solar wind pressure values for the 2004 to 2012 time interval. It is important to mention that this analysis is based on 86 intervals selected for high pressure and 650 selected for low pressure. That difference occurs because IMA data are used for SWP analysis and those data have gaps. The solar wind pressure was determined from daily and 12 h averages of the upstream MEX/IMA ion observations. From this dataset we chose time intervals of low and high solar wind pressure.
Before presenting the statistical analyses, we provide an example of our correlation length analysis applied to the electron density (ELS/ASPERA-3/MEX) data. This example, from 08:30 UT February 01, 2012 to 10:00 UT, February 01, 2012 in temporal and spatial scale, is presented in Figure 1. Figure 1a shows the electron density time series; Figure 1b, the same time series after Fourier Transform processing; Figure 1c, the correlation length in temporal scale. Figure 1d presents IMA velocity and Figure 1e, the correlation length in spatial scale. In Figure 1c it is possible to observe that correlation lengths show peaks up to 40 seconds, but lower values are predominant (10-30 seconds). Spatial scale correlation lengths (Figure 1e) are on the order of 1 × 10 4 km. The statistical analyses of correlation length are presented for temporal and spatial scales; results will be shown in the next subsection, divided by results for each spacecraft (MEX and MAVEN).
MEX Results
As mentioned before, MEX does not have a magnetometer. Thus, the correlation lengths for its data were calculated only for electron density data.
Temporal scale
The CL T calculation results are presented as maps showing their distribution in relation to the planet and (nominal) MPB and bow shock positions. In temporal scale, CL T s are represented in color scale, which varies between 8 and 20 seconds. Dashed red bins represent regions where CL T s are higher than the maximum value of the scale, black dashed bins where they are lower than the minimum, and white bins for regions where no data were available. In our analyses we have used the highest value of CL T in each boundary/region as reference. Figure 2a shows CL T s for the entire interval covered by MEX data. Figures 2b and 2c present, respectively, CL T s during periods of low and high solar wind pressure. In Figure 2a CL T is high in the magnetotail (varing between 13 and 15 seconds). The most significant outflow of particles is observed in the region of the Mars magnetotail . High correlation length values observed in the magnetotail may be related to tail ion beams with energy levels similar to those of solar wind protons (Barabash et al., 2004;Lundin et al., 2006). It is also possible to observe high values of CL T s at the nose of the planet, from the solar wind to lower regions of the magnetosheath, which may indicate wave penetration into the upper ionosphere of Mars. Looking at the Figures 2b and 2c, it is clear that during high solar wind pressure intervals (Figure 2c), larger CL T values can be observed in all regions. But during periods of low solar wind pressure (Figure 2b), high CL T values are observed mainly in the inner regions of the magnetosphere, dayside MPR (~17-18.5 seconds), and tail (15-18 seconds). The intervals of high pressure correspond to perturbed periods near the Mars environment due to the presence of ICME and CIRS, which can increase correlation length values.
These differences between low and high solar wind pressure may indicate that either the heavy ion exosphere or reflected ions are able to destroy ULF wave trains that are transported by the solar wind during low solar wind pressure intervals. In this analysis one can also notice that the bow shock moves toward the planet during periods of high solar wind pressure (Figure 2c), as compared with periods of low solar wind pressure (Figure 2b), which agrees with the results of other studies (Trotignon et al., 1993;Schwingeschuh et al., 1992;Ruhunusiri et al., 2015b;Halekas et al., 2017;Ramstad et al., 2017). Lundin et al. (2008) have shown that the planetary ion escape rate grows with increasing solar wind pressure, and that the solar wind pressure controls the energy and momentum transfer to planetary ions. Further, ULF wave intensity is observed to be directly correlated with solar wind dynamic pressure (Lundin et al., 2011). Thus, high values of correlation length observed in the whole magnetosphere during periods of high solar wind pressure also indicate the importance of these ULF waves for the escape of atmospheric ions from Mars.
Spatial scale
In order to obtain the correlation length in spatial scale, correlation length in temporal scale was multiplied by the instantaneous plasma velocity. The maps of the correlation length in spatial scale are presented in Figure 3. The color scale here represents the correlation length in kilometers, with the scale varying from 1×10 3 to 8×10 3 km. For the whole analyzed interval (Figure 3a), CL S s are lower in terminator, in the inner region of the magnetosphere. At the nose of the planet, CL S s show higher values from the foreshock, throughout the whole magnetosheath region, down to the MPR. In spatial scale, correlation length is clearly larger in the region of the magnetosheath in general, but mainly at the nose of the planet. Espley et al. (2004) have shown that transverse waves are the dominant wave mode at the nightside of the magnetosheath, whereas compression waves dominate at the dayside. They associate these waves to Martian locally picked-up Martian ions (which are relatively cold), that by interaction with solar wind protons produce oscillations in the magnetic field. Ruhunusiri et al. (2015a) observed that the Alfven wave mode is the wave mode dominant in the Martian magnetosheath. These waves can propagate in the magnetosphere and may be converted to compressionable modes which can penetrate through the MPB (Lundin et al., 2011;Ruhunusiri et al., 2015a).
In spatial scale (Figure 3), as was observed in the temporal analysis (Figure 2), during the periods of high pressure (Figure 3c), CL S s are larger in all regions (except for the MPR), compared to values observed in periods of low pressure (Figure 3b). It is important to mention that, the spatial scale correlation length is computed using the proton plasma velocity; this can affect correlation length values during periods of high pressure intervals, since the fluctuations in this parameter increase. But it is also important to point out the fact that an increase in the CL S during high pressure intervals was observed also in the temporal analysis, which is computed without using the plasma velocity.
MAVEN Results
The analyses of the MAVEN data were performed for the interval from November 2014 to December 2016. As MAVEN has a magnetometer onboard, besides the electron density analysis we were able to calculate magnetic field correlation length. The analysis here is presented in temporal and spatial scales for the whole period. Due to MAVEN's shorter temporal coverage (2014-2016), compared with MEX data, MAVEN data were insufficient to allow analysis of the influence of solar wind pressure variation on correlation length. Figure 4 shows the correlation length in temporal scales for electron density (Figure 4a) and magnetic field (Figure 4b). The mean plasma boundaries are also shown. In the electron density map, the bow shock can be seen clearly in the CL T distribution. The dominant value of CL T in the magnetosphere of Mars is around 12 seconds, but as was seen in the MEX analysis, the region of the subsolar point is dominated by high values of CL T in the solar wind (11-15 seconds), bow shock, dayside of the magnetosheath (16 seconds), and MPR (13-15 seconds). In Figure 4b it is possible to notice that the CL T is slightly lower in the magnetic field than in the electron density data (Figure 4a). This difference may be caused by different factors: First, the SWEA density measurements depend strongly on spacecraft attitude and solar illumina- tion (via spacecraft potential), which can affect our results. Second, a physical explanation would be that there are more rotational Alfven waves in the solar wind plasma that are not visible in the total magnetic field (where only transversal Alfvenic waves can be detected), and the rotational waves may affect the elec-tron distribution. In Figure 4b, the region that has a larger CL T domain is the magnetosheath, where CL T s are about 13-15 seconds.
Temporal scale
The bow shock cannot be as clearly observed here as it was in the electron density analysis; here we calculate its average CL T as about 12 seconds. In the MPR, the CL T is around 8 seconds, the Earth and Planetary Physics doi: 10.26464/epp2019051 565 same value as observed at the tail. Taking into account that we here use 4 s time resolution data this means we cannot detect in these data a significant CL T lower than 8 seconds.
Spatial scale
The CL S in spatial scale using MAVEN data maps for electron density and magnetic field are shown in Figures 5a and 5b, respectively. Here, the color scale representing the CL S in kilometers varies from 0 to 1.0 × 10 4 km. In Figure 5a, larger CL S is observed in the solar wind. The magnetosheath shows low values of correlation length for the most part of the dayside and flank (2.5 × 10 3 km), but a correlation length of around 4.5 × 10 3 -5.0 × 10 3 km can be observed in the subsolar point.
A map similar to that of the electron density data is observed in the spatial analysis of CL S derived from the magnetic field data (Figure 5b), but again, we observe smaller scales. The characteristic CL S in solar wind here varies between 4.0 × 10 3 -5.0 × 10 3 km. Similar values are observed at the nightside of the magnetosheath and bow shock. At the dayside, the dominant CL S in the magnetosheath is around 2.0 × 10 3 km. The MPR exhibits CL S of about 1.5 × 10 3 km; in the tail, where the smallest correlation length is observed, CL S varies between 1.5 × 10 3 and 2.0 × 10 3 km.
Discussion
Comparing the values of CL T found from MEX data in temporal scale ( Figure 2a) with what was found for MAVEN data (Figure 4a), it is possible to notice that the CL T s are similar in both analyses. In the spatial analysis, CL S s are on the same scale, but the MEX data yield slightly larger values (Figure 3a). This difference is probably a consequence of the fact that the CL S s in spatial scale are computed using the solar wind velocity, a parameter whose large fluctuations can influence the results. That effect may be more prominent in the MEX results, which were based on a significantly longer interval of time (April 2004(April -2015 with more variation in the solar wind speed for that spacecraft, as compared with the MAVEN interval (November 2014-2016).
The CL S values obtained in spatial scale for electron density (MEX and MAVEN) and magnetic field (MAVEN) in the magnetosheath and MPR were compared with the mean size of these regions ( Table 1).
The size of the plasma regions was obtained from the difference between the location of the plasma boundaries; bow shock (Vignes et al., 2002); MPB (Nagy et al., 2004); and ionopause (Trotignon et al., 2006). The CL S and the ratio between them are also presented. For the MEX electron density analysis, CL S at the dayside of the magnetosheath is approximately five times the magnetosheath size, whereas CL at the MPB/MPR is 25 times larger than that region. Although the ratio between CL S and plasma region is smaller in the MAVEN analysis than the ratio obtained for MEX (explained above as probably attributable to high fluctuations in solar wind velocity), it was seen that in the MAVEN analyses CL S s are still larger than the plasma regions, even in the magnetic field data. This result can be considered as another indication that wave fluctuations at the magnetosheath and MPR are correlated with oscillations at the ionosphere, caused by ULF waves that can penetrate into the ionopause. We interpret this as oscillations from the magnetosheath causing pressure pulses at the ionopause, and as a response to these, the ionospheric plasma pushes back the boundary. Thus the energy from these waves is transferred to the ionospheric plasma, accelerating planetary ions away from the planet.
Conclusions
Correlation lengths in the plasma environments of Mars have been identified here for the first time, using data of two spacecraft, MEX (2005MEX ( -2015 and MAVEN (2014MAVEN ( -2016. The influence of solar wind pressure variation was also analyzed. In temporal scale, the correlation length in electron density data in the plasma boundaries and regions of the Martian magnetosphere varies between 13 and 17 seconds in the MEX analysis and between 11 and 16 seconds in the MAVEN analysis. In the magnetic field data (MAVEN) it varies between 8-15 seconds. In spatial scale the dominant correlation length is around 5.5 × 10 3 km for MEX electron Earth and Planetary Physics doi: 10.26464/epp2019051 567 density data. In the MAVEN analysis, correlation length of 4.5 × 10 3 km is observed at the dayside of the magnetosheath; lower values are observed in the inner magnetosphere (2 × 10 3 -3 × 10 3 km). In the magnetic field analysis, the CL S varies between 1 × 10 3 and 5 × 10 3 km. The solar wind pressure shows a significant influence on the correlation length values, which are higher during periods of high solar wind pressure.
Large correlation lengths were observed at the nose of the planet; those values can be seen throughout the magnetosheath until the inner magnetosphere. These observations indicate that waves at the magnetosheath can be related to oscillations in the ionosphere. This means that, in a local region, wave trains can cause resonance effects at the planetary ionopause, which consequently may contribute to enhanced ion escape from the Martian atmosphere. This conclusion is reaffirmed by the tabular comparison between region size and regional correlation lengths in the dayside plasma regions of Mars, where correlation lengths for both electron density data (MEX and MAVEN) and magnetic field data (MAVEN) are larger than the lengths of the regions. This indicates that wave fluctuations at the magnetosheath and MPR may be correlated with oscillations in the upper ionosphere, due to ULF waves that can cause a pressure resonance at the ionopause. This can be an important mechanism to extract ions from Mars and may have influenced the long-term evolution of its atmosphere. | 5,647.6 | 2019-11-01T00:00:00.000 | [
"Environmental Science",
"Physics"
] |
Microbial Ecology and Antibiotic Susceptibility Profile of Germs Isolated from Hospital Surfaces and Medical Devices in a Reference Hospital in Douala (Cameroon)
Background: The hospital environment is largely contaminated with pathogenic microorganisms. This colonization is a threat for hospitalized patients, especially in high-risk services. The purpose of this study was to identify the germs found on surfaces and medical devices in some departments of the General Hospital of Douala, and to establish their susceptibility profile to most commonly used antibiotics in this health facility. Results: We collected 114 surface and medical device samples, and seeded different culture media for Gram-positive and Gram-negative aerobic bacteria. Of the total samples, 108 were positive and 137 bacterial strains were isolated. The colony count revealed a high rate of contamination. Enterobacter cloacae was the most represented specie (53.3%), followed by Pseudomonas aeruginosa (22.6%) and Klebsiella pneumoniae (6.6%). Various coagulase-negative Staphylococci have been isolated in some departments, as well as Cryptococcus laurentii and molds. The isolated strains showed low susceptibility to the antibiotics tested. Enterobacter cloacae showed low susceptibility for all tested molecules, except for carbapenems with rates ranging from 82% to over 94% in Maternity, Intensive Care and Neonatology units. The strains coming vironment should be regular in critical areas in order to reinforce measures to prevent diffusion of multi-resistant bacteria.
Introduction
Microorganisms largely contaminate the hospital environment; this contamination is variable quantitatively and qualitatively from one institution to another and in a same establishment according to the services. It constitutes a risk factor for the occurrence of nosocomial infections, a real threat, both for the already precarious health of patients and that of the nursing staff and visitors. These infections increase health care costs and length of stay; and are the major cause of mortality and morbidity in hospitalized patients [1] [2]. Although it is difficult to establish a direct link between environmental contamination and the occurrence of nosocomial infections, several studies have shown that microorganisms of human and/or environmental origin contaminate hospital surfaces, and play an important role in the occurrence of these infections [3] [4]. The microorganisms involved in the hospital environment are most often multiresistant to antibiotics, and the main source of diffusion of highly pathogenic strains in services [5] [6] [7] [8]. Microbiological monitoring of the environment in health facilities is part of preventing the transmission of nosocomial infections. The microbiological controls of the environment are one of the measuring tools that make it possible to evaluate a starting situation and the effectiveness of corrective measures, they must be implemented in a relevant way and obey very precise objectives while avoiding the inflation of useless analyses, consuming time and financial means [9] [10] [11]. Efforts are being made to reduce contamination of the hospital environment by developing air and water monitoring methods, surfaces, food, medical devices, care equipment; and the strengthening of hospital hygiene measures [12]. The objective of this study was to quantify and qualify germs present on hospital surfaces and medical devices, and to study their antibiotic susceptibility profile.
Location and Type of Study
We conducted a descriptive cross-sectional study at General Hospital of Douala (GHD) from 1 st January to 30 th June 2015. This is a tertiary health facility located in the Littoral region of Cameroon. This hospital has a capacity of 320 beds and harbours all the major medical and surgical specialities. The choice of high-risk services and surfaces to be taken was made by convenience and focused on the
Sampling
The most exposed surfaces, and low-traffic areas that often escape daily cleaning have been selected, as well as some medical devices. We excluded ceilings and walls in the samples. These samples were taken between 11 AM and 01 PM using a sterile swab previously moistened with sterile saline 0.9%. The swabs were passed in parallel streaks by slightly turning them, on defined areas of 25 cm 2 .
Seeding
The swabs from the different sampling sites were eluted in the test tubes containing 2 ml of sterile physiological saline to suspend the collected elements. The tubes were then vortexed for one minute, and 40 microliters of the resulting suspension were inoculated by the rake method into the following culture media: Plate Count Agar (PCA), Eosin Methylene Blue (EMB) Agar, Mannitol-Salt Agar, The dishes were then incubated in a bacteriological oven at 37˚C for 24 hours for the bacteria, and 48 to 72 hours at 25˚C for the fungi (SC Agar).
Identification of Colonies
Observation of petri dishes after incubation allowed for colony counting and macroscopic identification (shape, size colour). The biochemical and enzymatic identification of the microorganisms was made by seeding a suspension of microorganisms on cards; Vitek2 GN TM for Gram-negative fermenting and non-fermenting bacilli, Vitek2 GP TM for Gram-positive cocci and non-spore-forming bacilli, Vi-tek2 YST TM for yeast and yeast like organisms; followed by incubation and colorimetric reading on the VITEK2 Compact TM 15, an automated microbiology system (bioMerieux SA, France).
Data Processing
The results included the identification number, the date, the time and place of isolation, the identified germs, as well as the antibiotics tested and their susceptibility profile.
The descriptive analysis of the data was made using Epi Info TM version 7.0 and Microsoft Excel 2010 software.
Results
A total of 114 samples were collected from six at-risk and high-risk services, namely: Neonatology in the incubator room, the isolation room and the cloa- Table 1).
Of these 114 sampling sites, the majority were contaminated and only six (5.26%) were uncontaminated, including the bench in the delivery room, 2 door handles and a neonatal incubator, a bubbler and equipment support in intensive care unit. In all other sectors, no uncontaminated area was noted.
The colony count gave a bacterial density ≥ 10 6 CFU/25 cm 2 , except for the six samples with a sterile culture.
From the 108 contaminated specimens, we isolated 137 microorganisms, with a clear predominance of Enterobacter cloacae ssp cloacae (53.3%), followed by Pseudomonas aeruginosa (22.6%), Negative-coagulase Staphylococcus (8.7%), and Klebsiella pneumoniae (6.6%). For yeasts, 5 strains of Cryptococcus laurentii were isolated, and molds were present in two samples ( departments, the Burn Unit and the Intensive Care Unit. As for Klebsiella pneumoniae, the strains were found in maternity, in neonatology, and in the Burn Unit ( Table 2).
The study of the biochemical and enzymatic characteristics of the most observed strains showed a homology between the strains of Enterobacter cloacae and those isolated in neonatology showed the same biochemical characteristics for Enterobacter cloacae and K. pneumonia (Table 4).
Regarding antimicrobial susceptibility, isolated strains showed low susceptibility levels. Enterobacter cloacae showed low susceptibility for all tested molecules, except for carbapenems with rates ranging from 82% to over 94% for isolated strains in Maternity, Intensive Care Unit and Neonatology. For the other services, the rates were lower than 37% for the same molecules ( Figure 1). The strains coming from the Haematology Protected Ward were practically resistant to all antibiotics, the highest susceptibility rate being towards quinolones (50% for ofloxacin) (Figure 1). The susceptibility of K. pneumoniae to the antibiotics tested is variable, ranging from 0% for amoxicillin-clavulanic acid in Maternity, to 100% for Carbapenems and Amikacin in Maternity and Neonatology ( Figure 2 for Carbapenems and Fluoroquinolones at 85% and 90%, respectively ( Figure 3). For Negative-Coagulase Staphylococcus, all the strains isolated in the Operating Room and in Neonatology were resistant to Oxacillin, and also S. carnosus and S. sciuri isolated in Maternity and Burn Unit, respectively. Concerning the susceptibility of C. laurentii to antifungal agents, the strains tested were sensitive to Fluconazole, Econazole and Ketoconazole, and resistant to Amphotericin B and Nystatin.
Discussion
The hospital environment is a real reservoir of microorganisms involved in our study, this may be due to the irregularity of the disinfection of these instruments. The swabbing method used may also play a role in the results of bacterial densities [11]. The high rate of contamination of these critical areas is paradoxical because they are protected areas, normally with low circulation of staff and visitors.
E. cloacae ssp cloacae is the most recovered species, although enterobacteria have little resistance to desiccation, hence their low presence in the environment [14]. Neonatal Intensive Care Unit in Switzerland [15]. This transmission of E cloacae through patients transferred from one hospital to another has also been proven in some France hospitals that have received patients transferred from Morocco [16]. Some strains of K. pneumoniae have been isolated in Neonatalogy, Maternity and Burn Unit. Klebsiella pneumoniae may persist in the environment alone or in combination with Pseudomonas aeruginosa in mixed biofilms [17]. The P. aeruginosa were found in the Burn and Intensive Care Units, they are microorganisms for which humidity and temperature play an important role for their survival in the environment. Some authors have shown that Pseudomonas aeruginosa can survive from few months to several years on hospital surfaces [18].
Because of this ability to grow in wetlands, it is frequently found in the services of burn patients and Intensive Care, with varying susceptibility to antibiotics [19]. Isolated Pseudomonas in health facilities typically produce biofilms, and some genotypes are more productive than others. These biofilms are the starting point of the diffusion in services in taps and bedside tables; and can infect fragile patients such as burn victims [20]. Kominas et al. has demonstrated the transmission of germs, including Pseudomonas between health care staff and patients, and patients to patients in Intensive Care and Burn units [21].
For cocci, only coagulase-negative Staphylococci have been isolated, unlike other studies where S. aureus is predominant [14]. The presence of these SCN has been demonstrated on keyboards in permanent contact with the staff's bare fingers, while the use of gloves for other activities is systematic in these services [3]. Cryptococcus laurentii is the only yeast isolated in different services. This exclusivity may be due to the use of the Vitek 2 TM automatic system for the identification of yeasts, because of the cross reactions between its capsular antigens and those of C. neoformans, identification errors are often observed as demonstrated by Xiao et al. [22]. origin, however they can survive a few days in the hospital environment and be transmitted by the hands of caregivers and surfaces [14].
Although this is only a phenotypic identification, the biochemical homology between strains isolated in some services suggests transmission by staff and patients in the mother and child sector, and between the Operating Room and the Intensive Care Unit.
The susceptibility pattern shows that isolated strains have a low susceptibility rate for antibiotics commonly prescribed in services. Apart from Carbapenemes, which have good activity, resistance levels were high with respect to other molecules, particularly in the protected hematology ward. Chapuis et al. showed the role of the environment in the diffusion of broad-spectrum betalactamase-producing E. cloacae strains in a hematology service, both in the protected area and in the unprotected area [23].
Limitations
Limited ressources, as well as local technical platform did not allow us to perform molecular tests in order to type strains circulating in the hospital. In addition, since the GHD laboratory is specialized in clinical biology, we have not yet acquired new techniques for sampling and analyzing samples taken from the environment.
Conclusion
The investigated surfaces and medical devices of the Douala General Hospital were found to be highly contaminated by pathogenic environmental bacteria and certain yeasts; this allows us confirming the existence of a microbial ecology probably implicated in the occurrence of nosocomial infections. Isolated bacteria are weakly susceptible to the most commonly used antibiotics in these at-risk services. We recommend the reinforcement of staff, spaces and reusable medical devices hygiene, throughout the hospital and particularly in the high-risk areas.
Microbiological controls of the environment should be regular in critical areas in order to reinforce measures to prevent diffusion of multi-resistant bacteria.
Author's Contribution
COE and DA drafted the manuscript; COE and HNL coordinated the study; CMN, JPNM and JB collected data and participated in its design. All the authors read and approved the final manuscript.
Funding
No funding was received in relation to this study.
Ethics Approval
This study was conducted in accordance with ethics directives related to research | 2,832.2 | 2018-02-28T00:00:00.000 | [
"Medicine",
"Biology"
] |
An Automatic Multilevel Image Thresholding Using Relative Entropy and Meta-Heuristic Algorithms
Multilevel thresholding has been long considered as one of the most popular techniques for image segmentation. Multilevel thresholding outputs a gray scale image in which more details from the original picture can be kept, while binary thresholding can only analyze the image in two colors, usually black and white. However, two major existing problems with the multilevel thresholding technique are: it is a time consuming approach, i.e., finding appropriate threshold values could take an exceptionally long computation time; and defining a proper number of thresholds or levels that will keep most of the relevant details from the original image is a difficult task. In this study a new evaluation function based on the Kullback-Leibler information distance, also known as relative entropy, is proposed. The property of this new function can help determine the number of thresholds automatically. To offset the expensive computational effort by traditional exhaustive search methods, this study establishes a procedure that combines the relative entropy and meta-heuristics. From the experiments performed in this study, the proposed procedure not only provides good segmentation results when compared with a well known technique such as Otsu’s method, but also constitutes a very efficient approach.
Introduction
Segmenting an image into its constituents is a process known as thresholding [1][2].Those constituents are usually divided into two classes: foreground (significant part of the image), and background (less significant part of the image).Several methods for thresholding an image have been developed over the last decades, some of them based on entropy, within and between group variance, difference between original and output images, clustering, etc. [3][4][5].
The process of thresholding is considered as the simplest image segmentation method, which is true when the objective is to convert a gray scale image into a binary (black and white) one (that is to say only one threshold is considered).However, in the process of segmentation, information from the original image will be lost if the threshold value is not adequate.This problem may even deteriorate as more than one threshold is considered (i.e., multilevel thresholding) since not only a proper number of thresholds is desirable, but also a fast estimation of their values is essential [1].
It has been proven over the years that as more thresholds are considered in a given image, the computational complexity of determining proper values for each threshold increases exponentially (when all possible combinations are considered).Consequently, this is a perfect scenario for implementing meta-heuristic tools [6] in order to speed up the computation and determine proper values for each threshold.
When dealing with multilevel thresholding, in addition to the fast estimation, defining an adequate number of levels (thresholds that will successfully segment the image into several regions of interest from the background), has been another problem without a satisfactory solution [7].Therefore, the purpose and main contribution of this study is to further test the approach proposed in [8] which determines the number of thresholds necessary for segmenting a gray scaled image automatically.The aforementioned is achieved by optimizing a mathematical model based on the Relative Entropy Criterion (REC).
The major differences between this work and the one presented in [8], are that a more extensive and comprehensive testing of the proposed method was carried out.To verify the feasibility of the proposed model and reduce the computational burden, when carrying out the optimization process, this study implements three meta-heuristic tools and compares the output images with that delivered by a widely known segmentation technique named Otsu's method.In addition to the aforementioned, further tests with images having low contrast and random noise are conducted; this intends to probe the robustness, effectiveness and efficiency of the proposed approach.
The following paper is organized as follows: Section 2 introduces the proposed procedure, which consists of the mathematical model based on the relative entropy and the meta-heuristics-virus optimization algorithm, genetic algorithm, and particle swarm optimization as the solution searching techniques.Section 3 illustrates the performance of the proposed method when the optimization is carried out by three different algorithms VOA, GA and PSO, where six different types of images were tested.Lastly, some concluding remarks and future directions for research are provided in Section 4.
The Proposed Multilevel Thresholding Method
A detailed explanation of the proposed method is given in this section, where the mathematical formulation of the model is presented and the optimization techniques are introduced.
Kullback-Leibler Information Distance (Relative Entropy)
The Kullback-Leibler information distance (known as Relative Entropy Criterion) [9] between the true and the fitted probabilities is implemented in [8] for estimating an appropriate model that will best represent the histogram coming from the gray level intensity of an image.According to McLachlan and Peel [10] this information distance is defined as in Equation (1).However, the gray levels (intensity) are discrete values between [0, 255]; therefore, Equation (1) can be rewritten as in Equation ( 2): where p(i) and p(i;θ d ) are the probabilities values from the image histogram and fitted model respectively.These probabilities are estimated using Equations ( 3) and ( 4), where the value of 0, 255 and represents the gray intensity of a pixel at location (x, y) on the image of size pixels; while 4) is a mixture of "d" distributions which are used to estimate the value of p(i;θ d ).Lastly, θ j is a vector containing the parameters of each distribution in the mixture: In this study Gaussian distributions are used to estimate Equation ( 4), where the central limit theorem (C.L.T.) is the motivation of using this type of distributions [11].Therefore, Equation (4) can be expressed as in Equation ( 5): where θ j contains the prior probability (or weight) w j , mean μ j , and variance σ 2 j , of the j th Gaussian distribution.The minimization of the Relative Entropy Criterion function can be interpreted as the distance reduction between the observed and estimated probabilities.This should provide a good description of the observed probabilities p(i) given by the gray level histogram of the image under study.However, finding an appropriate number of distributions, i.e., "d", is a very difficult task [12][13][14][15].Consequently, the addition of a new term in Equation ( 2), which is detailed in the following subsection helps to automatically determine a suitable amount of distributions.
Assessing the Number of Distributions in a Mixture Model
The purpose of assuming a mixture of "d" distributions in order to estimate p(i;θ d ) in the REC function, is that the number of thresholds for segmenting a given image, can be easily estimated using Equation (6).The value of each threshold is the gray level intensity "i" that minimizes Equation (7), where "i" is a discrete unit (i.e., an integer [0, 255]): Given that estimating a suitable number of distributions "d" is a very difficult task, the method proposed in [8] attempts to automatically assess an appropriate value for "d" combining Equations ( 2) and ( 8) as a single objective function.The vector w contains all the prior probabilities (weights) of the mixture model.The values max(w) and min(w) are the maximum and minimum weights in w respectively: Equation ( 8) compares each prior probability w j with respect to the largest one in the vector w.The result is normalized using the range given by [max(w)-min(w)] in order to determine how significant w j is with respect to the probability that contributes the most in the model, i.e., max(w).Therefore, Equation (8) will determine if the addition of more Gaussian distributions is required for a better estimation of p(i;θ d ).The term 1 1 will avoid Equation (8) overpowering Equation ( 2) when the mathematical model of Equation ( 9) is minimized: Therefore, by minimizing Equation ( 9), the introduced approach will not only determine an appropriate number of distributions in the mixture model, but will also find a good estimation (fitting) of the probabilities p(i) given by the image histogram.An appropriate value for "d" is determined by increasing its value by one, i.e., d l = d l−1 + 1 where "l" is the iteration number, and minimizing Equation (9) until a stopping criterion is met and the addition of more distributions to the mixture model is not necessary.Therefore, not all the possible values for "d" are used.
Mathematical Model Proposed for Segmenting (Thresholding) a Gray Level Image
The mathematical model which is used for segmenting a gray level image is presented as in Equation (10).By minimizing Equation (10) with "d" Gaussian distributions, J(d) is in charge of finding a good estimation (fitting) of the image histogram, while P(d) determines whenever the addition of more distributions to the model is necessary: w w w (10) subject to: Equation ( 11) guarantees a summation of the prior probabilities equal to 1, while Equations ( 12) and ( 13) ensure positive values to all prior probabilities and variances in the mixture model, respectively.To minimize Equation (10), a newly developed meta-heuristic named Virus Optimization Algorithm [16], the widely known Genetic Algorithm [17] and Particle Swarm Optimization algorithm [18] are implemented in this study.
The flowchart at Figure 1 details the procedure of the proposed method using VOA (the similar idea is also applied to GA and PSO).As can be observed, the optimization tool (VOA, GA, or PSO) will optimize Equation (10) with d l Gaussian distributions until the stopping criterion of the meta-heuristic is reached.Once the algorithm finishes optimizing Equation (10) with d l distributions, the proposed method decides if the addition of more components is necessary if and only if Θ(d l ) ≥ Θ(d l−1 ) is true; otherwise a suitable number of distributions (thresholds) just been found and the results coming from Θ(d l−1 ) are output.
The purpose of using three algorithmic tools, is not only to reduce the computation time when implementing the proposed approach, but also, to verify if the adequate number of thresholds suggested by optimizing Equation (10) with different optimization algorithm remains the same.The reason of the aforementioned is because different algorithms may reach different objective function values.However, if the proposed method (Figure 1) is robust enough, all algorithms are expected to stop iterating when reaching a suitable number of thresholds, and this number has to be the same for all the optimization algorithms.
Virus Optimization Algorithm (VOA)
Inspired from the behavior of a virus attacking a host cell, VOA [8,16] is a population-based method that begins the search with a small number of viruses (solutions).For continuous optimization problems, a host cell represents the entire multidimensional solution space, where the cell's nucleolus denotes the global optimum.Virus replication indicates the generation of new solutions while new viruses represent those created from the strong and common viruses.
The strong and common viruses are determined by the objective function value of each member in the population of viruses, i.e., the better the objective function value of a member the higher the chance to be considered as strong virus.The number of strong viruses is determined by the user of the algorithm, which we recommend to be a small portion of the whole population (strong and common).
To simulate the replication process when new viruses are created, the population size will grow after one complete iteration.This phenomenon is controlled by the antivirus mechanism that is responsible for protecting the host cell against the virus attack.The whole process will be terminated based on the stopping criterion: the maximum number of iterations (i.e., virus replication), or the discovery of the global optimum (i.e., cell death is achieved).
The VOA consists of three main processes: Initialization, Replication, and Updating/Maintenance.The Initialization process uses the values of each parameter (defined by the user) to create the first population of viruses.These viruses are ranked (sorted) based on the objective function evaluation Θ(d) to select strong and common members.Here the number of strong members in the population of viruses is a parameter to be defined by the user, without considering the strong members; the population of viruses is the number of common viruses.
The replication process is performed using the parameters defined by the user in the Initialization stage described above, where a temporary matrix (larger than the matrix containing the original viruses) will hold the newly-generated members.Here, Equations ( 14) and ( 15) are used to generate new members, where "vn" stands for the value of the variable in the n th dimensional space, for viruses in the previous replication."svn" stands for the value of the variable in the n th dimensional space generated from the strong viruses in the current replication, and "cvn" is the value of the variable in the n th dimensional space generated from the common viruses in the current replication: The intensity in Equation ( 14) above reduces the random perturbation that creates new viruses from the strong members.This will allow VOA to intensify exploitation in regions more likely to have a global optimum (i.e., areas where the strong viruses are located).The initial value for the intensity is set as one, which means that the random perturbation for strong and common viruses is the same in the early stages.Therefore, the exploration power of VOA is expected to be enhanced during the program's early stages.The intensity value increases by one when the average performance of the population of viruses in VOA; that is to say, the average objective function value of the whole population of viruses, did not improve after a replication.The flowchart of the proposed procedure is illustrated in Figure 1.Note that the VOA part can be easily switched to other optimization algorithms such as GA and PSO.
Genetic Algorithm (GA)
The basic concept of Genetic Algorithms or GAs [17] is to simulate processes in natural systems, necessary for evolution, especially those that follows the principles first laid down by Charles Darwin of survival of the fittest.In GA a portion of existing population (solutions) is selected to breed a new population (new solutions), individuals are selected to reproduce (crossover) through a fitness-based process (objective function).Mutation takes place when new individuals are created after crossover to maintain a diverse population through generations.The standard GA is summarized in Figure 2, for the selection of the parents the roulette wheel is used in this study, as for the population maintenance mechanism the best members in the pooled population (parents and offspring) survive.The crossover operators implemented in this paper are the geometric and arithmetic means [Equations ( 16) and ( 17)] for the creation of the first and second child respectively.Note that only the integer part is taken by the program since the chromosome contains only integers.The mutation operator in GA uses Equation (18), which is the floor function of a random number generated between [T i−1 , T i ] where T 0 = 0 and T d = 255: Figure 2. Genetic Algorithm (GA) overview.
Particle Swarm Optimization (PSO)
Particle Swarm Optimization was inspired by social behavior of bird flocking or fish schooling [18].Each candidate solution (known as particle) keeps track of its coordinates in the problem space which are associated with the best solution (fitness) it has achieved so far, also known as the particle's best (pbest).The swarm on the other hand, also keeps track of the best value, obtained until now, by any particle in the neighbor of particles.This is known as the global best (gbest).The basic concept of PSO consists of changing the velocity of each particle towards the gbest and pbest location.This velocity is weighted by a random term, with separated random numbers being generated for acceleration toward the pbest and gbest locations.The standard PSO is summarized as in Figure 3.For this study, the velocity of the particle is bounded to a V max value which is only 2% of the gray intensity range; that is to say, V i [−V max , V max ] where V max = 0.02 × (255 − 0).The stopping criterion for the VOA (GA or PSO) is when two consecutive replications (generations) did not improve the objective function value of the best virus (chromosome or particle).Once the VOA (GA or PSO) stops searching and the best value for the Θ(d l ) is determined, the proposed method will decide if the addition of more distributions is necessary when the condition Θ(d l ) < Θ(d l−1 ) is satisfied; otherwise the proposed method will automatically stop iterating.After the proposed method stops, the parameters contained inside the vector θ d l-1 that represents the set of parameters of the best result in the previous iteration are output.
In order to avoid computational effort of calculating the threshold values that minimize Equation ( 7), the VOA (GA and PSO) will code each threshold value inside each solution, i.e., each virus (chromosome or particle) will have a dimensionality equal to the number of thresholds given by Equation (6).During the optimization, when the search of the best value for Θ(d l ) is in process, each threshold will be treated as a real (not an integer) value, which can be considered as the coded solution of the VOA and PSO.
In the case of GA a chromosome containing integer values is used for encoding the solution.In order to evaluate the objective function of each virus or particle, the real values coded inside each member will be rounded to the nearest integer, whereas in GA this is not necessary since each chromosome is an array of integers.The parameters for each Gaussian distribution are computed as in Equations ( 19)-(21), which is considered as the decoding procedure of the three meta-heuristics implemented in this study: In Equations ( 19)-( 21), T j represents the j th threshold in the solution.The values for T 0 = 0 and T d = 255, which are the lower and upper limits for thresholds values.During the optimization process, special care should be taken when generating new solutions (viruses, offspring, or particles).The details are as follows: Condition 1: The threshold should be in increasing order when coded inside each solution, and two thresholds cannot have the same value, i.e., T 0 < T 1 < T 2 <...< T d .
Condition 2: The thresholds are bounded by the maximum (T d = 255) and minimum (T 0 = 0) intensity in a gray level image, i.e., 0 Equation ( 22) is checked to ensure that the first condition is satisfied, where i, j [1, d−1] and i < j.If Equation ( 22) is not satisfied then the solution (virus, chromosome, or particle) is regenerated using Equation ( 23), where • is the floor function.The second condition is also checked and whenever any threshold value is outside the boundaries, i.e., T j 0 or T j 255, the virus (chromosome or particle) is regenerated using Equation (23).( )
Experimental Results
In order to further test the method proposed in [8], five different types of images were tested.The first image, which has a known number of three thresholds as in this case is tested (Figure 4a); secondly, an image containing text on a wrinkled paper which will cause lighting variation is tested (Figure 5a).Thirdly, the Lena image (Figure 6a) [1,[12][13][14][15] is tested, which is considered as a benchmark image when a new thresholding technique is proposed.The setting of VOA, GA, and PSO was determined by using Design of Experiments (DoE) [19][20] to know which values for the parameters are suitable when optimizing Equation (10).The full factorial design, i.e., 3-levels factorial design was performed for the four parameters of the VOA; in other words, 3 4 combinations of the four parameters were tested.Table 1 shows the results after performing DoE, where the final setting of the VOA is presented in bold.Similarly, a 3 3 full factorial design was implemented in order to set the population size (ps), crossover and mutation probabilities (pc and pm) respectively for GA.Table 2 summarizes the experimental settings and the final setting (in bold) of the GA.As for PSO a 3 4 full factorial design determined the values for the swarm size, inertia weight (w), cognitive and social parameters (c1 and c2) respectively.Table 3 summarizes the experimental settings of the PSO algorithm and the final setting is also highlighted in bold.The basic idea of the DoE is to run the 3 4 , 3 3 , and 3 4 , parameters combinations for VOA, GA, and PSO respectively, to later select which level (value) yielded the best performance (lower objective function value).Once the values for each parameter which delivered the best objective function value are identified, each test image is segmented by optimizing Equation (10) with each of the algorithmic tools used in this study.
The advantage of using DoE is that it is a systematic as well as well-known approach when deciding the setting yielding the best possible performance among all the combinations used during the full factorial design.In addition to the aforementioned, it is also a testing method that has been proven to be quite useful in many different areas such as tuning algorithm parameters [20].
Segmentation Results for the Proposed Model Using Meta-Heuristics as Optimization Tools
A comprehensive study of the proposed model implementing the three meta-heuristics introduced above is detailed in this part of Section 3. Additionally, a well-known segmentation method (Otsu's) is implemented, where only the output image is observed in order to verify if the segmentation result given by the optimization algorithms used to minimize Equation ( 10) is as good as the one provided by Otsu's method.The reason of the above mentioned, is because in terms of CPU time Otsu's is a kind of exhaustive search approach; therefore, it is unfair to compare both ideas (the proposed approach and the Otsu's method) in terms of computational effort.
Tables 4-8 detail the performance of the methods used for optimizing Equation ( 10) over different images.The results (objective function, threshold values, means, variances, and weights) are averaged over 50 independent runs, where the standard deviations of those 50 runs are not shown because they are in the order of 10 −17 .
By testing the image in Figure 4a it is observed that implementing the three meta-heuristics previously introduced for the optimization of Equation (10), the correct number of thresholds needed for segmenting the image is achieved (which is three).The computational effort and parameters of each Gaussian distribution ( ) are summarized in Table 4. Here, the number of iterations for the algorithms were four, i.e., the proposed method optimized By testing the image in Figure 4a it is observed that implementing the three meta-heuristics previously introduced for the optimization of Equation ( 10), the correct number of thresholds needed for segmenting the image is achieved (which is 3). ) are summarized in Table 4. Here, the number of iterations for the algorithms were 4, i.e., the proposed method optimized Equation ( 10) for d = [1,2,3,4] before reaching the stopping criterion.
The behavior of the Relative Entropy function (Figure 7a) reveals its deficiency in detecting an appropriate number of distributions that will have a good description of the image histogram (Figure 8).The aforementioned is because as more distributions or thresholds are added into the mixture, it is impossible to identify a true minimum for the value of J(d) when implementing the three different meta-heuristic tools.
The additional function P(d) on the other hand shows a minimum value when a suitable number of distributions (which is the same as finding the number of thresholds) is found (Figure 7b), since its value shows an increasing pattern when more distributions are added to the mixture model.The combination of these two functions J(d) and P(d) shows that the optimal value for Θ(d) (Figure 7c) will be when the number of thresholds is three as P(d) suggested.Note that the purpose of J(d) is to find the best possible fitting with the suitable number of distributions (thresholds), and this is observed at Figure 8 where the fitted model (dotted line) provides a very good description of the original histogram (solid line) given by the image.The vertical dashed lines in Figure 8 are the values of the threshold found.In addition to the thresholding result, it was observed that VOA provides both, the smallest CPU time as well as the best objective function value among the three algorithms.When implementing Otsu's method, it is rather impressive to observe that the output image delivered by the algorithms when optimizing Equation ( 10) resembles the one given by Otsu's method (Figure 4e).The aforementioned, confirms the competitiveness of the proposed idea in segmenting a gray scale image given a number of distributions in the mixture model.Additionally, the main contribution is that we do not need to look at the histogram to determine how many thresholds will provide a good segmentation, and by implementing optimization tools such as the ones presented in this study, we can provide satisfactory results in a short period of time, where methods such as Otsu's would take too long.When an image containing text on a wrinkled paper (Figure 5a) is tested, two thresholds (or three Gaussian distributions) give the best objective function value for Equation (10) as observed in Figure 9c.Table 5 summarizes the thresholding results, i.e., Θ(d), computational effort and Gaussian parameters, for the three meta-heuristics implemented.As for the fitting result, Figure 10 shows that even though three Gaussian distributions do not provide an exact description of the image histogram, it is good enough to recognize all the characters on the thresholded image (Figures 5b-d).The outstanding performance of the three meta-heuristics is observed once again when comparing with the Otsu's method (Figure 5e), where the computational effort shows the feasibility of optimizing the proposed mathematical model with heuristic optimization algorithms.The thresholding results of the Lena image (Figure 6a) shows that four thresholds (five Gaussian distributions) have the best objective function value, which is detailed in Table 6.Visually, the thresholded images (Figures 6b-d) obtain most of the details from the original one, and in terms of objective function behavior (Figure 11) there is no need to add more distributions into the mixture model (i.e., more thresholds) because they do not provide a better objective function value.Once again, the fitting provided by the mixture model (Figure 12) might not be the best; however, it is good enough to provide most of the details from the original image.It is interesting to observe that all the algorithmic tools are able to find satisfactory results in no more than 1.009 seconds in the case of VOA which is the slowest one, even though the algorithmic tools had to optimize Equation ( 10 To further test the proposed method an image with low contrast is used as illustrated in Figure 13a.It is observed that all the algorithmic tools are able to segment the image providing the correct number of thresholds which is three.Additionally, when comparing the output image given by Otsu's method and the idea proposed in this study, we are able to observe that despite its novelty the proposed method provides stable and satisfactory results for a low contrast image. Three thresholds are suggested after the optimization of Equation ( 10) is performed, which is good enough for successfully segmenting the image under study (Figures 13b-d), though the fitting of the image histogram was not a perfect one (Figure 15).More importantly, the addition of more than four distributions (i.e., three thresholds) to the mathematical model Equation (10) does not achieve a better result according to Figure 14c; therefore, the power of the proposed approach is shown once again with this instance.As for the Otsu's method, even though the correct number of thresholds is provided, the low contrast causes defect in the output image (seen at the light gray region in the middle of Figure 13e.The Lena image in which a random noise is generated will be our last test instance (Figure 16a), from this it is expected to provide clear evidence concerning robustness of the proposed method, where all the parameter values and computational results are summarized on Table 8.By observing the thresholded images when implementing the proposed approach (Figures 16b-d), we are able to conclude that random noise does not represent a major issue, even though different optimization tools are used.
The objective function behavior (Figure 17c) proved once again that when a suitable number of thresholds is achieved, the addition of more distributions into the mixture model is not necessary, since it will always achieve a larger objective function value compared with the one given by having four thresholds (or five Gaussians).Additionally, the fitting of the histogram (Figure 18) given by the image, even though is not a perfect one, is proved to be good enough to keep most of the relevant details from the original test instance.
Most of the relevant details from the original instance are kept.On the other hand, Otsu's method (Figure 16e) is not able to provide an output image as clear as the ones given by the proposed approach when implementing the meta-heuristic tools.
Conclusions
In this study a new approach to automatically assess the number of components "d" in a mixture of Gaussians distributions has been introduced.The proposed method is based on the Relative Entropy Criterion (Kullback-Leibler information distance) where an additional term is added to the function and helps to determine a suitable number of distributions.Finding the appropriate number of distributions is the same as determining the number of thresholds for segmenting an image, and this study has further shown that the method proposed in [8] is powerful enough in finding a suitable number of distributions (thresholds) in a short period of time.
The novelty of the approach is that, not only an appropriate number of distributions determined by P(d) is achieved, but also a good fitting of the image histogram is obtained by the Relative Entropy function J(d).The optimization of Equation ( 10) was performed implementing the Virus Optimization Algorithm, Genetic Algorithm, Particle Swarm Optimization, and the output images are compared to that given by a well-known segmentation approach Otsu's method.The objective function behavior shows that the proposed model achieves a suitable number of thresholds when its minimum value is achieved, and the addition of more distributions (thresholds) into the model will cause an increasing trend of the model in Equation (10).
Comparing the proposed method with Otsu's method provided clear evidence of the effectiveness and efficiency of the approach where the algorithmic tools are used in order to reduce the computational effort when optimizing Equation (10).Additionally, the proposed method proved to reach the same value for the number of thresholds needed for the segmentation of the images tested in this study, even though different optimization algorithms were implemented.
It is worth mentioning that the proposed method proved to work remarkably well under test images with low contrast and random noise.A suitable number of thresholds and an outstanding result in the output thresholded images were obtained.Whereas for the Otsu's method, the output image showed some defects once the segmentation was performed.
The fitting result coming from the proposed approach might not be the best; however, when segmenting an image what matters the most is the fidelity in which most of the details are kept from the original picture.This is what makes the difference between a good and poor segmentation result.Future directions point toward testing the proposed method with more meta-heuristic algorithms, as well as a wider range of images to evaluate the robustness of the approach.
Figure 1 .
Figure 1.Flowchart of the proposed optimization procedure. 0
Figure 7 .
Figure 7. Behavior of (a) Relative Entropy function J(d), (b) P(d), and (c) Objective function Θ(d) over different numbers of thresholds with different meta-heuristics VOA, GA and PSO on test image 1.
Figure 8 .
Figure 8. Fitting of the histogram of the test image 1 implementing (a) VOA, (b) GA, and (c) PSO.
Figure 9 .
Figure 9. Behavior of (a) Relative Entropy function J(d), (b) P(d), and (c) Objective function Θ(d) over different numbers of thresholds with different meta-heuristics VOA, GA and PSO on test image 2.
Figure 10 .
Figure 10.Fitting of the histogram of the test image 2 implementing (a) VOA, (b) GA, and (c) PSO.
Figure 11 .
Figure 11.Behavior of (a) Relative Entropy function J(d), (b) P(d), and (c) Objective function Θ(d) over different numbers of thresholds with different meta-heuristics VOA, GA and PSO on test image 3.
Figure 12 .
Figure 12.Fitting of the histogram of the test image 3 implementing (a) VOA, (b) GA, and (c) PSO.
Table 1 .
Parameter values (factor levels) used during the for the VOA.
Table 2 .
Parameter values (factor levels) used during the DoE for the GA.
Table 3 .
Parameter values (factor levels) used during the DoE for the PSO.
Table 4 .
Thresholding results over 50 runs for the test image 1.
Table 5 .
Thresholding results over 50 runs for the test image 2.
Table 6 .
Thresholding results over 50 runs for the test image 3.
Table 7 .
Thresholding result over 50 runs for the test image 4.
Table 8 .
Thresholding result over 50 runs for the test image 5. | 7,677.6 | 2013-06-03T00:00:00.000 | [
"Computer Science"
] |
Detection and Measurement of Matrix Discontinuities in UHPFRC by Means of Distributed Fiber Optics Sensing
Following the significant improvement in their properties during the last decade, Distributed Fiber Optics sensing (DFOs) techniques are nowadays implemented for industrial use in the context of Structural Health Monitoring (SHM). While these techniques have formed an undeniable asset for the health monitoring of concrete structures, their performance should be validated for novel structural materials including Ultra High Performance Fiber Reinforced Cementitious composites (UHPFRC). In this study, a full scale UHPFRC beam was instrumented with DFOs, Digital Image Correlation (DIC) and extensometers. The performances of these three measurement techniques in terms of strain measurement as well as crack detection and localization are compared. A method for the measurement of opening and closing of localized fictitious cracks in UHPFRC using the Optical Backscattering Reflectometry (OBR) technique is verified. Moreover, the use of correct combination of DFO sensors allows precise detection of microcracks as well as monitoring of fictitious cracks’ opening. The recommendations regarding use of various SHM methods for UHPFRC structures are given.
Introduction
To tackle the challenges that are in front of civil engineering-such as reduction in carbon footprint with optimized design, proper allocation of scarce resources through the use of engineered structural materials or extension of service duration thanks to deeper understanding of performance of structures-up-to-date methods should be used.
From the construction material point of view, such a developing technology is the Ultra High Performance Fiber Reinforced Cementitious composite (UHPFRC). It allows for design of refined and more slender structures as well as reinforcing and upgrading existing ones. To fully master its performance on both micro-and macroscopic levels, new measurement techniques are needed.
Such a possibility is given through the development of Distributed Fiber Optics (DFO) sensing techniques. The DFOs, used mostly in the automotive and mechanical industry, have recently found place in the civil engineering field. During the last decade, Fiber Optics (FO) sensors became increasingly popular in Structural Health Monitoring (SHM), and now, they are the second most used There are numerous studies on the use of DOFs for detection of crack formation. The sensors, based on measuring losses with Optical Time Domain Reflectometry technique [3][4][5][14][15][16], were very limited in practical applications. Similarly, those based on Brillouin backscattering [6,[17][18][19][20] were limited due to their low spatial resolution, affecting their strain sensing accuracy around a crack in the concrete material [21,22]. In fact, the complicated strain distribution and its rapid variation within the spatial resolution decreases the strain measurement accuracy [23]. Later on, Optical Backscattering Reflectometry (OBR), based on the Optical Frequency Domain Reflectometry (OFDR) technique, emerged. This technique, characterized by high spatial resolution, is proven to be capable of detecting and localizing tiny microcracks in reinforced concrete structures [24]. Different methods were also proposed to quantify crack openings from the strain profiles, either based on a combination with finite element models of the structure [25,26] or on the calculation of the optical fiber elongation by summing distributed strain gradients [27,28].
Analytical Models Based on Strain Transfer Theories
A distributed optical fiber sensor is an optical fiber surrounded by various protective and adhesive layers, forming a multilayered strain transfer system. The existence of these intermediate layers leads to differences in the strain of host material and the strain measured by an optical fiber due to the shear lag effect in intermediate layers. The problem of strain transfer through an optical fiber sensor has been studied in the field of short dimensional sensors like Bragg grating or interferometric sensors [29][30][31][32][33][34][35]. Indeed, many research works focused on designing discrete sensors with improved strain transfer efficiency [36] and performing parametric studies of different mechanical and geometrical properties of multilayered sensors [37].
Since 2012, different analytical and numerical models were proposed [38] to describe the strain transfer from a discontinuous (cracked) host material. Imai et al. [6] introduced the effect of crack discontinuity in host material as a Gaussian distribution at the interface with protective coating. Later, it was assumed that the strain at the discontinuity location is equal to the crack opening over the spatial resolution of the measurement instrument [39]. Finally, the Crack Opening Displacement (COD) was introduced as an additional term provoked by the local discontinuity in the host material deformation field. Feng et al. [18] deduced a mechanical transfer equation, showing that the strain measured by the optical fiber εf(z) consists of a crack-induced strain εcrack(z) part added to the strain in host material εm(z). Recently, Bassil et al. [40,41] deduced a similar strain transfer equation for a multilayer system with imperfect bonding between layers:
Analytical Models Based on Strain Transfer Theories
A distributed optical fiber sensor is an optical fiber surrounded by various protective and adhesive layers, forming a multilayered strain transfer system. The existence of these intermediate layers leads to differences in the strain of host material and the strain measured by an optical fiber due to the shear lag effect in intermediate layers. The problem of strain transfer through an optical fiber sensor has been studied in the field of short dimensional sensors like Bragg grating or interferometric sensors [29][30][31][32][33][34][35]. Indeed, many research works focused on designing discrete sensors with improved strain transfer efficiency [36] and performing parametric studies of different mechanical and geometrical properties of multilayered sensors [37].
Since 2012, different analytical and numerical models were proposed [38] to describe the strain transfer from a discontinuous (cracked) host material. Imai et al. [6] introduced the effect of crack discontinuity in host material as a Gaussian distribution at the interface with protective coating. Later, it was assumed that the strain at the discontinuity location is equal to the crack opening over the spatial resolution of the measurement instrument [39]. Finally, the Crack Opening Displacement (COD) was introduced as an additional term provoked by the local discontinuity in the host material deformation field. Feng et al. [18] deduced a mechanical transfer equation, showing that the strain measured by the optical fiber ε f (z) consists of a crack-induced strain ε crack (z) part added to the strain in host material ε m (z). Recently, Bassil et al. [40,41] deduced a similar strain transfer equation for a multilayer system with imperfect bonding between layers: where λ is the strain lag parameter that includes mechanical (G and E, shear and Young's moduli, respectively) and geometrical properties (r) of the different i layers and z is the position of discontinuity along the optical cable. It also includes coefficients k depicting the level of interfacial adhesion between two consecutive layers.
The strain lag parameter λ is crucial for the sensing of cracks. As this value increases, the crack-induced strains ε crack (z) figure higher peaks at the crack location, and thus, the exponential part covers a narrower zone over the optical fiber length, as shown in Figure 2. Thanks to this, the capacity of detecting and localizing discontinuities increases.
Sensors 2020, 20, 3883 4 of 20 discontinuity along the optical cable. It also includes coefficients k depicting the level of interfacial adhesion between two consecutive layers.
The strain lag parameter λ is crucial for the sensing of cracks. As this value increases, the crack-induced strains εcrack(z) figure higher peaks at the crack location, and thus, the exponential part covers a narrower zone over the optical fiber length, as shown in Figure 2. Thanks to this, the capacity of detecting and localizing discontinuities increases. The authors also demonstrated the validity of the model for different types of optical cables through an experimental testing campaign on concrete specimens. The estimated CODs proved to be accurate, reaching relative errors of 1-10% for a dynamic range [CODmin, CODmax], with a strain repeatability of ±20 µm/m for the interrogator unit. In this range, the layers behave in an elastic manner and sufficient, stable bonding between them exists. CODmax varied widely from 80 to 1500 µm for different types of optical cable assemblies. On the other hand, the authors fixed the CODmin to 50 µm, below which other parameters prevail, i.e. the nature of cracking of concrete material (in the fracture process zone) or the strain accuracy and repeatability of interrogator.
In terms of crack detection, Bassil et al. [42] demonstrated that an OBR system with a strain repeatability of ± 2 µm/m and an optical cable with λ = 20 m −1 can detect concrete discontinuities of less than 1 µm.
Ultra High Performance Fiber Reinforced Cementitious Composite
UHPFRC is a composite fiber reinforced cementitious building material with a high content (>3% vol.) of short (lf < 20 mm) and slender steel fibers. Its behavior under tensile stress comprises three stages, as shown in Figure 3. The authors also demonstrated the validity of the model for different types of optical cables through an experimental testing campaign on concrete specimens. The estimated CODs proved to be accurate, reaching relative errors of 1-10% for a dynamic range [COD min , COD max ], with a strain repeatability of ±20 µm/m for the interrogator unit. In this range, the layers behave in an elastic manner and sufficient, stable bonding between them exists. COD max varied widely from 80 to 1500 µm for different types of optical cable assemblies. On the other hand, the authors fixed the COD min to 50 µm, below which other parameters prevail, i.e., the nature of cracking of concrete material (in the fracture process zone) or the strain accuracy and repeatability of interrogator.
In terms of crack detection, Bassil et al. [42] demonstrated that an OBR system with a strain repeatability of ± 2 µm/m and an optical cable with λ = 20 m −1 can detect concrete discontinuities of less than 1 µm.
Ultra High Performance Fiber Reinforced Cementitious Composite
UHPFRC is a composite fiber reinforced cementitious building material with a high content (>3% vol.) of short (l f < 20 mm) and slender steel fibers. Its behavior under tensile stress comprises three stages, as shown in Figure 3.
The first stage is an elastic stage. The cementitious matrix is continuous and the behavior of UHPFRC is simply linear. The strain of the material can be directly measured.
After the elasticity limit (f e , ε e ) is reached, discontinuities in the matrix start to appear and the material enters the strain-hardening phase. The openings of these fine, distributed microcracks (hairline cracks) are smaller than 50 µm and their spacing can vary from 2 to 30 mm [43][44][45]. They are not detrimental from a durability point of view [46,47] and are impossible to see with the naked eye. These microcracks can be, however, measured using appropriate instrumentation. From the macroscopic point of view, the material can be considered as continuous, with strain-hardening quasi-linear behavior and reduced stiffness [48]. However, after unloading, the residual strain remains in the material.
When the maximum tensile resistance f u is reached, the material enters the softening phase. One or more neighboring microcracks start rapidly growing, eventually reaching openings above 50 µm. This localized discontinuity is bridged by multiple fibers carrying the tensile stress. It is called a fictitious crack, contrary to the real crack which cannot transfer the stress [49]. Since the stress transfer capability in this critical zone is reduced, the overall stress in the area decreases. The localized fictitious crack is growing, while the strain and stress around it decrease. The location of the fictitious crack depends on the distribution of fibers [44,45,50,51]. Since this fictitious crack leads eventually to the Sensors 2020, 20, 3883 5 of 20 failure of structural elements, it is called the critical crack as well. With the gradual opening of the fictitious crack, the measured deformation increases, leading to fast growth of the apparent strain. Importantly, it is not the real strain of the material anymore due to the fictitious crack localized between the reference measurement points. The first stage is an elastic stage. The cementitious matrix is continuous and the behavior of UHPFRC is simply linear. The strain of the material can be directly measured.
After the elasticity limit (fe, εe) is reached, discontinuities in the matrix start to appear and the material enters the strain-hardening phase. The openings of these fine, distributed microcracks (hairline cracks) are smaller than 50 µm and their spacing can vary from 2 to 30 mm [43][44][45]. They are not detrimental from a durability point of view [46,47] and are impossible to see with the naked eye. These microcracks can be, however, measured using appropriate instrumentation. From the macroscopic point of view, the material can be considered as continuous, with strain-hardening quasi-linear behavior and reduced stiffness [48]. However, after unloading, the residual strain remains in the material.
When the maximum tensile resistance fu is reached, the material enters the softening phase. One or more neighboring microcracks start rapidly growing, eventually reaching openings above 50 µm. This localized discontinuity is bridged by multiple fibers carrying the tensile stress. It is called a fictitious crack, contrary to the real crack which cannot transfer the stress [49]. Since the stress transfer capability in this critical zone is reduced, the overall stress in the area decreases. The localized fictitious crack is growing, while the strain and stress around it decrease. The location of the fictitious crack depends on the distribution of fibers [44,45,50,51]. Since this fictitious crack leads eventually to the failure of structural elements, it is called the critical crack as well. With the gradual opening of the fictitious crack, the measured deformation increases, leading to fast growth of the apparent strain. Importantly, it is not the real strain of the material anymore due to the fictitious crack localized between the reference measurement points.
The fictitious crack grows until opening of half of the steel fiber length, in the present case lf/2 = 6.5 mm [44] and the resistance of the material decreases. After the fibers are pulled out, no more stress transfer is possible and the real crack is formed.
In the case of a structural R-UHPFRC (Reinforced UHPFRC) element under bending action, the tensile behavior of UHPFRC has important influence on the overall response. Each of the three stages are present under the maximum bending moment in the critical section, where the fictitious crack forms. Under the assumption that the cross-sections remain plain, the distribution of stress along the height of the beam is nonlinear due to nonlinearity of the constitutive law of UHPFRC, as presented schematically in Figure 4. The proportion between parts in elastic, strain-hardening and softening regimes depends on geometry of the element [44]. The fictitious crack grows until opening of half of the steel fiber length, in the present case l f /2 = 6.5 mm [44] and the resistance of the material decreases. After the fibers are pulled out, no more stress transfer is possible and the real crack is formed.
In the case of a structural R-UHPFRC (Reinforced UHPFRC) element under bending action, the tensile behavior of UHPFRC has important influence on the overall response. Each of the three stages are present under the maximum bending moment in the critical section, where the fictitious crack forms. Under the assumption that the cross-sections remain plain, the distribution of stress along the height of the beam is nonlinear due to nonlinearity of the constitutive law of UHPFRC, as presented schematically in Figure 4. The proportion between parts in elastic, strain-hardening and softening regimes depends on geometry of the element [44].
Test Set-Up and Specimen
The tested beam has a T-shaped cross-section and dimensions according to Figure 5. This kind of design refers to the use of UHPFRC for waffle deck or unidirectional ribbed slab designs. An
Test Set-Up and Specimen
The tested beam has a T-shaped cross-section and dimensions according to Figure 5. This kind of design refers to the use of UHPFRC for waffle deck or unidirectional ribbed slab designs. An example of such a structure is the railway bridge in Switzerland described in reference [52].
Test Set-Up and Specimen
The tested beam has a T-shaped cross-section and dimensions according to Figure 5. This kind of design refers to the use of UHPFRC for waffle deck or unidirectional ribbed slab designs. An example of such a structure is the railway bridge in Switzerland described in reference [52]. Commercially available UHPFRC premix Holcim710 ® was used, with 3.8% vol. of 13 mm long straight steel fibers with an aspect ratio of 65. Its mechanical properties as obtained by material testing were compressive strength f c = 149 MPa; elastic limit stress f e = 6.3 MPa; tensile strength f u = 12.0 MPa; strain at f u − ε u = 3.5% ; modulus of elasticity E = 41.9 GPa. Steel reinforcement bars B500B (with f sk = 500 MPa) were used for both stirrups and longitudinal rebars.
To observe the behavior of UHPFRC at the three stages of its performance, the beam was designed with a reinforcement bar of 34 mm diameter at a height of 187 mm from the bottom, thus, the distance between the bottom face of the beam and bottom of the reinforcement was 170 mm at midspan ( Figure 5), allowing for observation of unreinforced UHPFRC. To impose bending failure rather than shear failure under four-point bending, Ω shaped stirrups, Ø 6 mm, were placed outside the constant bending moment zone. Additionally, L-shaped Ø 34 mm reinforcement bars were used on the bottom of the beam, outside of the constant bending zone, to increase the lever arm of longitudinal reinforcement in shear.
The beam of 2 m span was tested in displacement-controlled four point bending. The displacement of the servo-hydraulic actuator was transmitted with the use of hinges and a steel beam. The application points were symmetrically positioned at ±0.25 m from the midspan of the R-UHPFRC beam. The course of the actuator was done with velocity of 0.01 mm/s during the first loading, and 0.02 mm/s in unloading and re-loading phases. Several unloadings were performed to obtain the residual deflection of beams at each loading stage.
The beam was instrumented with extensometers; photogrammetry DIC by means of two 20 MP cameras; DFO sensors ( Figure 5). The fiber optics sensors for distributed strain sensing were installed in three lines at each face of the beam-40, 90 and 190 mm from the bottom of the beam. As shown in Figure 6, the DFO sensors were glued in a 2 × 2 mm groove on the UHPFRC surface using a bicomponent epoxy adhesive (Araldite 2014-2). On the front side of the beam, the SMF-28 Thorlabs ® fiber was glued, with an external diameter of Ø 900 µm and elastomer tubing. On the back side of the beam, the Luna ® High-Definition Polyimide fiber was used, with an external diameter of Ø 155 µm. The DIC measurement zone spanned 35 cm from the midspan symmetrically, and over the whole height of the beam on the front side. The extensometers of 100 mm measurement base were glued on the back side of the beam, at the level of each DFO measurement line. Additionally, three LVDTs with the common measurement base were vertically installed on the back side of the beam, at midspan and over the supports. The mean vertical displacement over the supports is subtracted from the vertical displacement at midspan to obtain the deflection of the beam. The resistance force was measured by the load cell of the actuator.
longitudinal reinforcement in shear.
The beam of 2 m span was tested in displacement-controlled four point bending. The displacement of the servo-hydraulic actuator was transmitted with the use of hinges and a steel beam. The application points were symmetrically positioned at ±0.25 m from the midspan of the R-UHPFRC beam. The course of the actuator was done with velocity of 0.01 mm/s during the first loading, and 0.02 mm/s in unloading and re-loading phases. Several unloadings were performed to obtain the residual deflection of beams at each loading stage.
The beam was instrumented with extensometers; photogrammetry DIC by means of two 20 MP cameras; DFO sensors ( Figure 5). The fiber optics sensors for distributed strain sensing were installed in three lines at each face of the beam-40, 90 and 190 mm from the bottom of the beam. As shown in Figure 6, the DFO sensors were glued in a 2 × 2 mm groove on the UHPFRC surface using a bicomponent epoxy adhesive (Araldite 2014-2). On the front side of the beam, the SMF-28 Thorlabs® fiber was glued, with an external diameter of Ø 900 µm and elastomer tubing. On the back side of the beam, the Luna® High-Definition Polyimide fiber was used, with an external diameter of Ø 155 µm. The DIC measurement zone spanned 35 cm from the midspan symmetrically, and over the whole height of the beam on the front side. The extensometers of 100 mm measurement base were glued on the back side of the beam, at the level of each DFO measurement line. Additionally, three LVDTs with the common measurement base were vertically installed on the back side of the beam, at midspan and over the supports. The mean vertical displacement over the supports is subtracted from the vertical displacement at midspan to obtain the deflection of the beam. The resistance force was measured by the load cell of the actuator.
Global Response of the Beam
The force-midspan deflection curve is presented in Figure 7. Several loading-unloading cycles were executed at different stages of the test. The goal was to visualize the influence of residual strain of the UHPFRC in the strain-hardening domain after unloading on the global response of the beam. Thanks to this, a gradual degradation of material can easily be observed. The load steps (LS) were chosen arbitrarily to discuss the state of material in detail.
The first linear part of the curve is very short. This is due to the material at the bottom of the beam entering the strain-hardening regime relatively soon. As the zone where UHPFRC is in the strain-hardening regime is growing, gradual reduction in material stiffness, and thus, beam rigidity occurs, effecting nonlinearity of the force-deflection curve. The residual deflection in the unloading cycle comes from the fact that this part of cross-section contains discontinuities (microcracks < 50 µm) or, in the further stages, the fictitious crack (> 50 µm) is present. Both types of discontinuities transmit the tensile stresses thanks to fibers, but do not close completely while unloaded. Finally, when the beam resistance is maximum with the force of 313 kN, gradual degradation with a rise in deflection continues as the localized fictitious cracks propagate and the longitudinal rebar is yielding.
The force-midspan deflection curve is presented in Figure 7. Several loading-unloading cycles were executed at different stages of the test. The goal was to visualize the influence of residual strain of the UHPFRC in the strain-hardening domain after unloading on the global response of the beam. Thanks to this, a gradual degradation of material can easily be observed. The load steps (LS) were chosen arbitrarily to discuss the state of material in detail. The first linear part of the curve is very short. This is due to the material at the bottom of the beam entering the strain-hardening regime relatively soon. As the zone where UHPFRC is in the strain-hardening regime is growing, gradual reduction in material stiffness, and thus, beam rigidity occurs, effecting nonlinearity of the force-deflection curve. The residual deflection in the unloading cycle comes from the fact that this part of cross-section contains discontinuities (microcracks < 50 µm) or, in the further stages, the fictitious crack (> 50 µm) is present. Both types of discontinuities transmit the tensile stresses thanks to fibers, but do not close completely while unloaded. Finally, when the beam resistance is maximum with the force of 313 kN, gradual degradation with a rise in deflection continues as the localized fictitious cracks propagate and the longitudinal rebar is yielding.
Detailed Examination: DIC
The unloaded state of the beam is presented in Figure 8. The measurement noise for DIC is mostly at the level of ±100 µε, with local peaks of −300 µε. The strain noise is not only due to the quality of the cameras and nonuniformity of light, but mostly from the variation of size and distribution of speckles.
Detailed Examination: DIC
The unloaded state of the beam is presented in Figure 8. The measurement noise for DIC is mostly at the level of ±100 µε, with local peaks of −300 µε. The strain noise is not only due to the quality of the cameras and nonuniformity of light, but mostly from the variation of size and distribution of speckles. Figure 7. The color scale is the same as presented in Figure 8. LS 1 is not shown since mostly the noise is registered. At load step 2, the uniform elastic strains are registered. At LS 3, strain peaks are observed due to the distributed microcracking of UHPFRC in strain-hardening. They are more pronounced in two weak spots at around −0.25 m and +0.25 m (Figure 9b). While the microcracks keep growing and propagating, two of them grow faster than others, leading to localization of fictitious cracks (Figure 9c). At LS 5, fictitious Crack 1 develops a second, left branch. This could be due to the first branch reaching a stronger area with higher concentration of steel fibers (Figure 9d). Simultaneously, fictitious Crack No. 2 keeps propagating on the right side. At LS 6, the (Figure 9b). While the microcracks keep growing and propagating, two of them grow faster than others, leading to localization of fictitious cracks (Figure 9c). At LS 5, fictitious Crack 1 develops a second, left branch. This could be due to the first branch reaching a stronger area with higher concentration of steel fibers (Figure 9d). Simultaneously, fictitious Crack No. 2 keeps propagating on the right side. At LS 6, the fictitious cracks are clearly visible to the naked eye ( Figure 9e). As the fibers bridge these macrocracks, the overall response of the beam remains in the hardening domain. When the beam reaches the peak resistance with a force load of 313 kN, the fictitious cracks reach the level of the reinforcement bar (see Figure 9f). In their bottom part, they transmit hardly any stress due to the large opening and advanced fiber pullout. This is why the bottom part of the beam between the fictitious cracks is almost unloaded. The highest strains are present at the level of the reinforcement bar. After this stage, due to transformation of the fictitious cracks into real cracks with no stress transfer and reinforcement yielding, the resistance of the beam started to decrease and the test was stopped.
Detailed Examination: Strain Measurements
The strain is directly obtained from DFOs and extensometers. For DIC, the virtual measurement
Detailed Examination: Strain Measurements
The strain is directly obtained from DFOs and extensometers. For DIC, the virtual measurement lines (Figure 8), positioned at the same height as the DFOs and extensometers ( Figure 5), were prepared in the post-processing software VIC 3D ® .
The measurements taken along each measurement Line 1, 2 and 3 are presented below from the top to the bottom, respectively, in coherence with their position over the height of the beam (Figure 5).
At load step 1 (LS 1), all systems, except DIC, show good agreement ( Figure 10). The strain spatial distribution can be considered as uniform in the constant bending moment zone, between ±0.25 m from the midspan. The material remains elastic and the structural response is linear. In the bottom line At LS 2 (Figure 11), as UHPFRC enters into the hardening stage at Lines 2 and 3, clear peaks from microcracks are visible over the Polyimide lines, while Thorlabs do not present any local strain variations. The microcracked zones can be identified with extensometers as well, which show higher strains than in the neighboring zones. It is important to mention that at this stage, propagating microcracks are identifiable by the naked eye when the surface is wetted with alcohol. The difference between the measurements of systems deployed on the back (Polyimide, extensometers) and the front (Thorlabs, DIC) sides of the beam may come from non-horizontal loading of the beam, despite the hinge between the actuator and redistribution beam, or to locally weaker material close to the surface. In perfect conditions, the total elongation obtained with extensometers and DFOs, thus, 'smeared' strain, are equal [39]. These incoherencies are not observed for Line 1, which remains in the elastic stage. At LS 2 (Figure 11), as UHPFRC enters into the hardening stage at Lines 2 and 3, clear peaks from microcracks are visible over the Polyimide lines, while Thorlabs do not present any local strain variations. The microcracked zones can be identified with extensometers as well, which show higher strains than in the neighboring zones. It is important to mention that at this stage, propagating microcracks are identifiable by the naked eye when the surface is wetted with alcohol. The difference between the measurements of systems deployed on the back (Polyimide, extensometers) and the front (Thorlabs, DIC) sides of the beam may come from non-horizontal loading of the beam, despite the hinge between the actuator and redistribution beam, or to locally weaker material close to the surface. In perfect conditions, the total elongation obtained with extensometers and DFOs, thus, 'smeared' strain, are equal [39]. These incoherencies are not observed for Line 1, which remains in the elastic stage. Under the force of 90 kN (LS 3, Figure 12), more microcracks are visible over Line 3. Most of these cracks are localized around positions −0.2 m and +0.25 m. Line 2 presents more uniform microcracking behavior. The origin of this nonuniformity in the bottom of the beam is discontinuity of the L-shaped rebars (see Figure 5) causing disturbance of fiber orientation and concentration of stresses. Zones where the fictitious crack will further develop are now clearly visible with DIC and Thorlabs fiber (Crack 1 and 2 line 3, Crack 1 line 2), as well as extensometers (both fictitious cracks, Lines 2 and 3). For zones where the fictitious cracks are developed, the apparent strain measured with extensometers cannot be considered as material strain anymore (see Figure 3). Clear microcracks start to appear at Line 1. Under the force of 90 kN (LS 3, Figure 12), more microcracks are visible over Line 3. Most of these cracks are localized around positions −0.2 m and +0.25 m. Line 2 presents more uniform microcracking behavior. The origin of this nonuniformity in the bottom of the beam is discontinuity of the L-shaped rebars (see Figure 5) causing disturbance of fiber orientation and concentration of stresses. Zones where the fictitious crack will further develop are now clearly visible with DIC and Thorlabs fiber (Crack 1 and 2 line 3, Crack 1 line 2), as well as extensometers (both fictitious cracks, Lines 2 and 3). For zones where the fictitious cracks are developed, the apparent strain measured with extensometers cannot be considered as material strain anymore (see Figure 3). Clear microcracks start to appear at Line 1. Under the force of 90 kN (LS 3, Figure 12), more microcracks are visible over Line 3. Most of these cracks are localized around positions −0.2 m and +0.25 m. Line 2 presents more uniform microcracking behavior. The origin of this nonuniformity in the bottom of the beam is discontinuity of the L-shaped rebars (see Figure 5) causing disturbance of fiber orientation and concentration of stresses. Zones where the fictitious crack will further develop are now clearly visible with DIC and Thorlabs fiber (Crack 1 and 2 line 3, Crack 1 line 2), as well as extensometers (both fictitious cracks, Lines 2 and 3). For zones where the fictitious cracks are developed, the apparent strain measured with extensometers cannot be considered as material strain anymore (see Figure 3). Clear microcracks start to appear at Line 1. At LS4 (Figure 13), dropout points start to appear at crack locations in Lines 2 and 3 in the DFOs results. These points are dropped out by the spectral shift calculation algorithm due to low Sensors 2020, 20, 3883 12 of 20 correlation with the reference spectrum. This phenomenon of miscalculated points increases due to rapid variation of strain over the spatial resolution length. For fictitious Crack 1, Line 3, DIC shows three fictitious crack fronts forming at positions: −0.25, −0.2 and −0.17 m. They all lay within the same extensometer measurement base, and thus, cannot be distinguished with this technique. Additionally, the Thorlabs fiber is arguably not sensitive enough to clearly separate these fronts due to low shear lag parameter λ (Equation (1)). For fictitious Crack 2, Line 3, the apparent strain reaches ε u , exponential shape is being formed in Thorlabs, and UHPFRC enters softening stage. Two other fictitious crack fronts can be noticed with DIC but hardly with Thorlabs. Extensometer of location [0.05; 0.15 m] does not show fictitious crack formation, while it is visible in the same position with DIC and Thorlabs fiber. This comes from the nonorthogonality of the crack regarding the beam axis and is confirmed by Polyimide fiber recording only microcracks in the discussed location. On Line 2, localization of fictitious Crack 2 starts being detectable by Thorlabs fiber and DIC. At LS4 (Figure 13), dropout points start to appear at crack locations in Lines 2 and 3 in the DFOs results. These points are dropped out by the spectral shift calculation algorithm due to low correlation with the reference spectrum. This phenomenon of miscalculated points increases due to rapid variation of strain over the spatial resolution length. For fictitious Crack 1, Line 3, DIC shows three fictitious crack fronts forming at positions: −0.25, −0.2 and −0.17 m. They all lay within the same extensometer measurement base, and thus, cannot be distinguished with this technique. Additionally, the Thorlabs fiber is arguably not sensitive enough to clearly separate these fronts due to low shear lag parameter λ (Equation (1)). For fictitious Crack 2, Line 3, the apparent strain reaches εu, exponential shape is being formed in Thorlabs, and UHPFRC enters softening stage. Two other fictitious crack fronts can be noticed with DIC but hardly with Thorlabs. Extensometer of location [0.05; 0.15 m] does not show fictitious crack formation, while it is visible in the same position with DIC and Thorlabs fiber. This comes from the nonorthogonality of the crack regarding the beam axis and is confirmed by Polyimide fiber recording only microcracks in the discussed location. On Line 2, localization of fictitious Crack 2 starts being detectable by Thorlabs fiber and DIC. At LS 5 (Figure 14), both fictitious cracks are clearly formed in Line 3, and UHPFRC is in the softening stage. The DFOs do not work properly in their vicinity anymore. The transversal skewness of fictitious Crack No. 1 can be seen, since the peak of DIC is shifted with respect to the extensometers. Interestingly, it is positioned some 7 cm towards the left regarding the previously observed strain concentration. For both Lines 2 and 3, the clear exponential shapes can be noticed in Thorlabs fiber measurements, but with multiple dropouts. While comparing the measurement Line 1 at the current load step with Line 2 and Line 3 at LS 3, it can be concluded that microcracking is more uniformly spaced for the lines positioned higher on the beam. The reasons might be the nonuniformity of fiber dispersion and discontinuity of strains, both due to the rebar alignment. At this load step, the fictitious cracks are clearly visible to the naked eye, and UHPFRC is in the softening stage (see Figure 9d). The stress transferred by bridging fibers is lower than fu (see Figure 4), and stress in the neighboring material decreases. Thus, the strain measured at midspan is similar for all the measurement lines. At LS 5 (Figure 14), both fictitious cracks are clearly formed in Line 3, and UHPFRC is in the softening stage. The DFOs do not work properly in their vicinity anymore. The transversal skewness of fictitious Crack No. 1 can be seen, since the peak of DIC is shifted with respect to the extensometers. Interestingly, it is positioned some 7 cm towards the left regarding the previously observed strain concentration. For both Lines 2 and 3, the clear exponential shapes can be noticed in Thorlabs fiber measurements, but with multiple dropouts. While comparing the measurement Line 1 at the current load step with Line 2 and Line 3 at LS 3, it can be concluded that microcracking is more uniformly spaced for the lines positioned higher on the beam. The reasons might be the nonuniformity of fiber dispersion and discontinuity of strains, both due to the rebar alignment. At this load step, the fictitious cracks are clearly visible to the naked eye, and UHPFRC is in the softening stage (see Figure 9d). The stress transferred by bridging fibers is lower than f u (see Figure 4), and stress in the neighboring material decreases. Thus, the strain measured at midspan is similar for all the measurement lines. Due to multiple dropouts, DFOs are not useful anymore. The DIC measurements were presented before and, as mentioned above, the results obtained with extensometers crossed by fictitious cracks are not useful. Thus, the detailed analysis of strains ends here.
Monitoring of Fictitious Crack Opening
After examining the DFOs, discontinuity detection performance, it is interesting from both a structural and material point of view to follow the material discontinuities that evolve to discrete fictitious cracks in order to assess their implication on the safety of the UHPFRC structure. Thus, in this section, the strain transfer model is applied to Thorlabs fiber measurements. The Polyimide fiber was not examined because of its limited dynamic range that does not exceeded 80µm in ordinary concrete [41], preventing fictitious COD monitoring.
The notation of COD is continued here in view of previously discussed state of the art for crack measurement in concrete. As explained before, UHPFRC has more complex response under tensile action. Conveniently, the term COD refers to opening of the matrix discontinuity, be it a microcrack in strain-hardening stage, a fictitious crack bridged by fibers or a real crack with no stress transfer.
The mechanical strain transfer equation for the multiple cracks case is fitted to the strain profiles using the robust least square method: where CODi is the opening displacement of each discontinuity i, and λ is the strain lag parameter. Each CODi and λ are selected as variable parameters. Similar to [42], a trapezoidal approximation of material strain ε_m (z) is adapted based on the measurements outside the constant bending moment zone; zi corresponds to the position of the 20 most important strain peaks in the strain profiles. Figures 15 and 16 present fitted strain profiles to those measured over Line 2 and Line 3 respectively, together with the corresponding residuals for different load levels. A discontinuity propagates in the UHPFRC material through searching the lowest energy path depending on the local fiber content and orientation [51]. Despite the host material's complex microcracking nature, the proposed mechanical model fits clearly the distributed strain profiles measured by the DFOs system Due to multiple dropouts, DFOs are not useful anymore. The DIC measurements were presented before and, as mentioned above, the results obtained with extensometers crossed by fictitious cracks are not useful. Thus, the detailed analysis of strains ends here.
Monitoring of Fictitious Crack Opening
After examining the DFOs, discontinuity detection performance, it is interesting from both a structural and material point of view to follow the material discontinuities that evolve to discrete fictitious cracks in order to assess their implication on the safety of the UHPFRC structure. Thus, in this section, the strain transfer model is applied to Thorlabs fiber measurements. The Polyimide fiber was not examined because of its limited dynamic range that does not exceeded 80µm in ordinary concrete [41], preventing fictitious COD monitoring.
The notation of COD is continued here in view of previously discussed state of the art for crack measurement in concrete. As explained before, UHPFRC has more complex response under tensile action. Conveniently, the term COD refers to opening of the matrix discontinuity, be it a microcrack in strain-hardening stage, a fictitious crack bridged by fibers or a real crack with no stress transfer.
The mechanical strain transfer equation for the multiple cracks case is fitted to the strain profiles using the robust least square method: where COD i is the opening displacement of each discontinuity i, and λ is the strain lag parameter. Each COD i and λ are selected as variable parameters. Similar to [42], a trapezoidal approximation of material strain ε_m (z) is adapted based on the measurements outside the constant bending moment zone; z i corresponds to the position of the 20 most important strain peaks in the strain profiles. Figures 15 and 16 present fitted strain profiles to those measured over Line 2 and Line 3 respectively, together with the corresponding residuals for different load levels. A discontinuity propagates in the UHPFRC material through searching the lowest energy path depending on the local fiber content and orientation [51]. Despite the host material's complex microcracking nature, the proposed mechanical model fits clearly the distributed strain profiles measured by the DFOs system at different levels. Low residual levels are randomly scattered around zero all over the length of FO Line 2 and 3. On the left beam part, two microcracks are developing to form fictitious cracks. Unlike in concrete, there is no immediate unloading around these discontinuities. Thus, when the fictitious crack localizes and the stress transferred by bridging fibers reaches the value fu, another fictitious crack can appear nearby. This phenomenon is observed with fictitious Crack 1, where the propagation of one branch stops (Crack 1-Right) and a second one develops (Crack 1-Left). On the other hand, fictitious Crack 2 goes through a more localized propagation. When the force reaches 170 kN for Line 3 and 200 kN for Line 2, an increase in strain residuals is observed around Crack 2. On the left beam part, two microcracks are developing to form fictitious cracks. Unlike in concrete, there is no immediate unloading around these discontinuities. Thus, when the fictitious crack localizes and the stress transferred by bridging fibers reaches the value fu, another fictitious crack can appear nearby. This phenomenon is observed with fictitious Crack 1, where the propagation of one branch stops (Crack 1-Right) and a second one develops (Crack 1-Left). On the other hand, fictitious Crack 2 goes through a more localized propagation. When the force reaches 170 kN for Line 3 and 200 kN for Line 2, an increase in strain residuals is observed around Crack 2. On the left beam part, two microcracks are developing to form fictitious cracks. Unlike in concrete, there is no immediate unloading around these discontinuities. Thus, when the fictitious crack localizes and the stress transferred by bridging fibers reaches the value f u , another fictitious crack can appear nearby. This phenomenon is observed with fictitious Crack 1, where the propagation of one branch stops (Crack 1-Right) and a second one develops (Crack 1-Left). On the other hand, fictitious Crack 2 goes through a more localized propagation. When the force reaches 170 kN for Line 3 and 200 kN for Line 2, an increase in strain residuals is observed around Crack 2. As discussed in reference [41], this could be attributed to the optical cable/host material mechanical system entering a post-elastic phase. Figure 17 shows the estimated strain lag parameter λ as well as the discontinuity openings COD i of fictitious Cracks 1 and 2, under loading and unloading cycles. For both Line 2 and 3, the estimated strain lag parameter λ varies around 35 m −1 in a ± 10% interval (Figure 17a,c). Higher λ values can be observed at early stages of the tests. Similar to previous findings on concrete structures [42,53], this variation can be associated with the first stages of UHPFRC cracking behavior, where discontinuities in the cementitious matrix are starting to develop in the so-called fracture process zone, and end up leading to the creation of a microcrack. When most of the matrix discontinuities exceed an estimated opening COD min of 50 µm, the strain lag estimations become stable and consistent around λ ≈ 35 m −1 . This confirms the assumption of one global strain lag parameter characterizing the Thorlabs fiber/epoxy glue/UHPFRC mechanical response in the presence of a fictitious crack. Lower λ (compared to concrete's surface-mounted fibers (50 m −1 )) can be attributed to a lower stiffness level at the Epoxy/UHPFRC interface, possibly due to much smaller porosity.
Sensors 2020, 20, 3883 16 of 21 As discussed in reference [41], this could be attributed to the optical cable/host material mechanical system entering a post-elastic phase. Figure 17 shows the estimated strain lag parameter λ as well as the discontinuity openings CODi of fictitious Cracks 1 and 2, under loading and unloading cycles. For both Line 2 and 3, the estimated strain lag parameter λ varies around 35 m -1 in a ± 10% interval (Figure 17a, c). Higher λ values can be observed at early stages of the tests. Similar to previous findings on concrete structures [42,53], this variation can be associated with the first stages of UHPFRC cracking behavior, where discontinuities in the cementitious matrix are starting to develop in the so-called fracture process zone, and end up leading to the creation of a microcrack. When most of the matrix discontinuities exceed an estimated opening CODmin of 50 µm, the strain lag estimations become stable and consistent around λ ≈ 35 m −1 . This confirms the assumption of one global strain lag parameter characterizing the Thorlabs fiber/epoxy glue/UHPFRC mechanical response in the presence of a fictitious crack. Lower λ (compared to concrete's surface-mounted fibers (50 m -1 )) can be attributed to a lower stiffness level at the Epoxy/UHPFRC interface, possibly due to much smaller porosity. The estimated CODs for discontinuities Cracks 1 and 2 are shown in Figure 17 c and d. At the level of Line 3, the discontinuities Crack 1-right and Crack 2 are formed as microcracks (<50 µm) and propagate steadily until a force of around 80kN, where they grow rapidly to form fictitious cracks. At F = 120 kN, another microcrack grows rapidly to form the fictitious Crack 1-left. This growth leads to a decrease in the growth rate of fictitious Crack 1-right.
Similar development of COD for the three discontinuities can be observed for Line 2, with a delay regarding Line 3 due to its closer position to the neutral beam axis. Akin two-phased growth of COD is observed: stable during microcracking and fast once the fictitious crack is formed in the softening phase.
The growth of COD of fictitious Crack 2 is faster than Crack 1, where the damage development is shared by the two branches. Once it reaches a CODmax of 400 µm, unstable growth in estimated COD is observed in both measurement lines. This threshold marks the validity limit of the strain transfer model, where all the layers behave in an elastic manner with no progressive debonding occurring at successive layer interfaces. This phenomenon, equally observed in concrete [41], is pronounced by a change in the exponential form of the strain profiles initiated near the strain peak, and thus, leading to an increase in strain residuals ( Figure 15 and Figure 16). Consequently, this leads to a change in the tendency of λ and COD variations due to increased estimation errors. The estimated CODs for discontinuities Cracks 1 and 2 are shown in Figure 17 c and d. At the level of Line 3, the discontinuities Crack 1-right and Crack 2 are formed as microcracks (<50 µm) and propagate steadily until a force of around 80kN, where they grow rapidly to form fictitious cracks. At F = 120 kN, another microcrack grows rapidly to form the fictitious Crack 1-left. This growth leads to a decrease in the growth rate of fictitious Crack 1-right.
Similar development of COD for the three discontinuities can be observed for Line 2, with a delay regarding Line 3 due to its closer position to the neutral beam axis. Akin two-phased growth of COD is observed: stable during microcracking and fast once the fictitious crack is formed in the softening phase.
The growth of COD of fictitious Crack 2 is faster than Crack 1, where the damage development is shared by the two branches. Once it reaches a COD max of 400 µm, unstable growth in estimated COD is observed in both measurement lines. This threshold marks the validity limit of the strain transfer model, where all the layers behave in an elastic manner with no progressive debonding occurring at successive layer interfaces. This phenomenon, equally observed in concrete [41], is pronounced by a change in the exponential form of the strain profiles initiated near the strain peak, and thus, leading to an increase in strain residuals (Figures 15 and 16). Consequently, this leads to a change in the tendency of λ and COD variations due to increased estimation errors. Importantly, the COD and λ estimations show proper agreement for the loading-unloading cycles. In other words, the UHPFRC as well as the optical fibers attached to it deform in the same manner, even under multiple crack opening and closing over an important area of the beam. It also shows the great potential of the DFOS techniques to monitor residual and periodical openings of discontinuities, which is an important feature for long-term structural health monitoring and studying of the fatigue of the structural elements.
In this experiment, the large noise level of DIC measurement prevented accurate microcrack and early fictitious crack opening measurements. The COD values obtained using DIC were outside of applicability of the DFOs measurement method. Thus, the results cannot be validated using both methods.
Discussion
The detailed analysis of results revealing the differences in performance of discussed measurement techniques is presented and summed up in Table 1.
The extensometers allow for measurement of strains in the elastic and strain-hardening phases, which is important from a practical 'smeared' approach point of view. They allow for early detection of microcrack propagation with faster rise of strains in the given area in the strain-hardening phase of the UHPFRC response. However, it is impossible to distinguish between accumulation of distributed microcracks and the onset of the fictitious crack formation. Thus, the determination whether the material is in the hardening or softening phase cannot be directly achieved. Additionally, the strain resolution and the localization of discontinuities is limited to the measurement base length of the extensometer. Furthermore, they do not allow for measurements of the fictitious crack opening. Still, they remain the measurement technique that is the easiest in installation and provide results that can be analyzed straightforwardly.
Due to the large measurement noise, the DIC technique did not allow in this experiment for observation of strain variations during the elastic stage of the structural response. However, it allows for tracking the localized fictitious cracks, particularly their length and their opening, at the macro-level. The large measurement noise is due to the relatively large measurement field (0.7 × 0.4 m) and nonuniformity of speckles. It was proven that this technique allows for tracking of microcracks for smaller observation fields [45]. This method remains highly complex and sensitive in practical application for Structural Health Monitoring.
The results obtained using the DFOs technique depend on the sensitivity of the used optical cable or fiber, with regard to discontinuities in the host material. The fiber with Polyimide coating features high sensitivity, allowing early and accurate detection and localization of microcracks. Through computation of the total elongation of segment of fiber, the strain of UHPFRC in the strain-hardening domain can be obtained [28]. Therefore, both the practical 'smeared' as well as 'discrete' approach to distributed microcracking can be used. This is relevant for Structural Health Monitoring, as structural UHPFRC remains in the elastic or strain-hardening state during normal service life.
On the other hand, the Thorlabs fiber with Acrylate and Hytrel double coatings features lower crack sensitivity than Polyimide fiber. This allows for strain measurement during elastic and strain-hardening stages. The detection, localization and measurement of microcracks is limited due to its sensitivity. It is however capable of detecting and localizing fictitious cracks, as well measuring their opening since their formation and up to 400 µm. More importantly, in this range, the optical fiber sensors maintain their elastic behavior allowing accurate estimation of cracks widths during closing-opening cycles. From a practical point of view, formation of fictitious cracks can indicate problems in the UHPFRC structure, for example, due to overloading. Thus, this kind of DFOs can play an important role in SHM and verification of structural safety.
In order to take full advantage of the DFOs technique, both types of optical fibers with their different crack sensitivity could be used to monitor the behavior of UHPFRC in the elastic, strain-hardening and softening domains.
In recent years, rapid development in the field of DFOs interrogation units enabled accurate, continuous, dynamic and simultaneous strain sensing along different types of optical fibers. With a better understanding of the sensor properties (like crack and temperature sensitivity) and durability (long-term fatigue and aging), DFOs technique can perform global and local strain measurements to provide information on the overall UHPFRC behavior in a holistic manner. Thus, DFOs can form an undeniable asset for long-term continuous health monitoring of this type of new structures.
Conclusions
In this work, the DFOs technique based on the Rayleigh backscattering phenomenon is used to follow the behavior of the R-UHPFRC beam tested under four-point bending. The capacity to measure strains and monitor matrix discontinuities with two types of optical fiber sensors was evaluated. The comparison with DIC and extensometers revealed application ranges of each method.
The usefulness of extensometers is limited to the elastic and strain-hardening phases. They can measure strains in the UHPFRC and detect microcrack accumulation. It is impossible to distinguish between advanced microcracking and nucleation of fictitious cracks.
The DIC is highly dependent on size of the measurement field. In this research, it allowed for detection and tracking of fictitious cracks. The complexity regarding the measurement area preparation and data processing makes this technique too complex to be used in situ for now.
The DFOs technique is able to precisely monitor the elastic, strain-hardening and softening stages of UHPFRC. While using a high spatial resolution OBR measurement technique, its performance depends on the type of fiber used for sensing. While strain measurement in the elastic phase or detection and localization of microcracks is of interest, Polyimide coated optical fiber should be used. If the strain measurement in both elastic and strain-hardening phases or fictitious crack detection and localization is to be observed, the Thorlabs fiber with thicker coating prevails.
It was confirmed that the COD of fictitious cracks can be successfully estimated using the proposed analytical model with proper choice of sensing optical fiber. Importantly, the coherent estimation of opening-closing fictitious crack width shows the potential of this method for SHM under repeated loading and real-time SHM of UHPFRC structures. However, testing of the optical fiber sensors under high numbers of crack closing/opening cycles should be considered. | 12,873 | 2020-07-01T00:00:00.000 | [
"Engineering",
"Materials Science"
] |
Supercover Semantics for Deontic Action Logic
The semantics for a deontic action logic based on Boolean algebra is extended with an interpretation of action expressions in terms of sets of alternative actions, intended as a way to model choice. This results in a non-classical interpretation of action expressions, while sentences not in the scope of deontic operators are kept classical. A deontic structure based on Simons’ supercover semantics is used to interpret permission and obligation. It is argued that these constructions provide ways to handle various problems related to free choice permission. The main result is a sound and complete axiomatization of the semantics.
Introduction
The standard approach to deontic logic, represented by standard deontic logic (SDL), suffers from a large number of so-called paradoxes, where the paradox of free choice permission is perhaps the most discussed in the literature.These are not paradoxes in any strict sense, but rather clashes between inferences valid in formal deontic logics, and intuitively valid and non-valid inferences as they occur in informal deontic reasoning.
SDL is the normal modal logic KD.Models are of the form W , R, V , where W is a non-empty set of possible worlds, R is a binary relation on W , and V is a valuation function for the propositional variables of the language.The relation R has the intended meaning that (w, v) ∈ R if and only if v is ideal from the point of view of w.The set I w = {v ∈ W : (w, v) ∈ R} is the set of ideal worlds from the point of view of w.The relation R is assumed to be serial, i.e. for each w ∈ W , there is some v ∈ W such that (w, v) ∈ R. A sentence P(ϕ)-where the intended reading of P is 'it is permitted that…'-is then true at a world w if ϕ is true in some world that is ideal from the point of view of w, and a sentence O(ϕ)-where O has the intended reading 'it is obligatory that…'-is true at a world w if ϕ is true in all worlds that are ideal from the point of view of w.
The problems of free choice permissions stem from the intuition that the sentences "Jane may go by bus or go by train" and "Jane may go by bus and Jane may go by train" seem to amount to more or less the same thing.One would then expect the following principle of free choice to be valid: P(ϕ ∨ ψ) ↔ P(ϕ) ∧ P(ψ). (1) In the standard semantics for the modal operator P outlined above with ∨ interpreted as Boolean disjunction, (1) is not valid.Rather, the following principle holds: P(ϕ ∨ ψ) ↔ P(ϕ) ∨ P(ψ). (2) Of course, (1) cannot just be added to the standard system (say as an axiom), since the right-to-left direction of (2), together with the left-to-right direction of (1) results in P(ϕ) ↔ P(ψ) being valid; if something is permitted, then everything is permitted.One solution is to introduce an operator for which (1), but not (2), is stipulated to hold (Asher and Bonevac 2005;Kamp 1973).However, if the underlying non-modal logic is classical, and the P operator is extensional with respect to classical logical equivalences, this has the unwanted consequence that the left-to-right direction of (1) gives (Hilpinen 1982, pp. 176-177): (3) This problem may be illustrated with the vegetarian free lunch example (Hansson 2013).If it is permitted to order a vegetarian meal, then, by (3), it is permitted to order a vegetarian meal and not pay for it.Even very weak assumptions allow the inference of (3) from (1), which shows that the problem of free choice is not that easy to avoid.According to Hansson, this "indicates that the free choice postulate may be faulty in itself, even if not combined with other deontic principles such as those of SDL." (2013, p. 208).
Since the seminal work of von Wright (1951), deontic logics where the deontic operators attach to action expressions (names of actions) have been studied in different forms, for example in deontic variants of propositional dynamic logic (PDL) (e.g., Castro and Maibaum 2009;Meyer 1988;van der Meyden 1996), as well as in static deontic action logics (Bentzen 2014;Segerberg 1982;Trypuz andKulicki 2009, 2015).The basic idea behind the semantics to be developed is that a disjunctive action expression such as 'go by bus or go by train' expresses a choice between different courses of action corresponding to each disjunct.As an example, consider the sentence "Jane may go by bus or by train".This sentence can be taken to express a permission to choose between two different courses of action: the action of going by bus, and the action of going by train: Jane may choose an action from the set {[go by bus], [go by train]}, where [go by bus] and [go by train] are the actions described by the expressions 'go by bus' and 'go by train', respectively.In general, a sentence of the form 'Permitted α or β' can be analyzed as saying: Permitted to choose an action from the set {[α], [β]}.
Given certain natural assumptions, an analysis along these lines will produce the desired properties of free choice permissions.If it is permitted to choose between having pasta and having pizza, then it is also permitted to have pasta and permitted to have pizza.In general, if every action in a set of actions are permitted, then any (non-empty) subset of that set will contain permitted actions only.This idea is not new; according to Hansson, …free choice permission should be represented as a property of the set of actiondescribing sentences ({a, b} respectively {a, b, c}) rather than a property of the disjunction of these sentences (a ∨ b respectively a ∨ b ∨ c).(2013, p. 218) Hansson does not develop the idea further.In the context of natural language semantics, the alternative semantics approach interprets disjunction as introducing sets of alternatives (see e.g., Alonso-Ovalle 2006;Ciardelli and Roelofsen 2011;Ciardelli et al. 2009;Groenendijk and Roelofsen 2009;Roelofsen 2013;Simons 2005a, b).The idea is, essentially, that a disjunctive statement tells you that at least one proposition from a larger set of propositions is true.One of the motivations for this kind of interpretation of disjunction is to account for free choice phenomena.The alternative analysis of disjunction allows interpreting permission modals as operating over sets of alternatives.A permitted disjunction, then, tells you that each proposition from the set of alternatives introduced by the disjunctive statement is permitted.Simons (2005a, b) develops this idea in more detail, introducing a precise notion of how deontic modals interact with a set of alternatives in terms of supercovers.However, her account makes certain counterintuitive predictions with regards to disjunctive statements not in the scope of deontic operators.In addition, Simons does not develop a full formal semantics suitable for a deontic logic.
In this paper, I will combine Simons' alternative semantics approach to disjunction and deontic modals with a static deontic action logic based on Boolean algebra.Specifically, I will be concerned with logics in the style of Segerberg (1982) and Trypuz andKulicki (2009, 2015), and the action-theoretic layer of the logic of Castro and Maibaum (2009).In these logics, the arguments of deontic operators are names of actions, rather than propositional statements.Action expressions are given a semantics based on an underlying Boolean algebra, and permission is interpreted as an ideal on this algebra.This construction validates the free choice principle; however, substitution of Boolean algebra identities within the scope of the permission operator is a valid rule of inference, so the vegetarian free lunch problem arises.In addition, the distinction between action expressions and propositions is syntactically sharp, but semantically less so-the logical behavior of both types of expressions is essentially classical.When the semantics is extended with an interpretation of action expressions in terms of sets of action types, the logic of action expressions will deviate from the Boolean algebra interpretation, resulting in a system where propositional formulas behave classically, while action expressions do not.I will argue that this move indeed offers ways to avoid the problems of free choice permission.
The structure of the paper is as follows.Section 2 introduces Simons' supercover semantics and highlights some problems.In Sect.3.1, basic action theoretic and deontic structures are defined; these structures are then used to construct a formal semantics in Sect.3.2.I discuss the concepts of permission and obligation in Sect. 4. In Sect.5, an axiomatization of the semantics is defined, and soundness and completeness results are obtained.In Sect.6, I discuss certain aspects of the logic in more detail and compare the semantics to related work.Section 7 concludes the paper and discusses ideas for further research.
Supercover Semantics
Simons' supercover semantics is an attempt to deal with free choice phenomena in the context of natural language semantics (Simons 2005a, b). 1 Simons suggests supplementing the standard semantics for disjunction in the scope of deontic modals with a distribution requirement.This distribution requirement guarantees that P(ϕ or ψ) is true only if there are ideal worlds in both the proposition expressed by ϕ and the proposition expressed by ψ, and that O(ϕ or ψ) is true only if there are ideal worlds in both disjunct propositions, and the sum of the proposition expressed by ϕ and the proposition expressed by ψ contains all ideal worlds.
Formally, this is accomplished in two stages.First, 'or' is treated as a set-formation operator, introducing sets containing propositions corresponding to the disjuncts.Second, Simons introduces the notion of a supercover.Let U be some background set.A non-empty S ⊆ P(U ) is a supercover of A ⊆ U if and only if (i) every member of S contains some member of A, and (ii) every member of A belongs to some member of S (Simons 2005a, p. 276).In other words, S is a supercover of A if the union of S is a superset of A, and every element of S has a non-empty intersection with A.
Denote the set of possible worlds where ϕ is true by ϕ .Simons' proposal for the interpretation of 'or'-sentences is obtained by the clause (Simons 2005a, p. 292) This clause expresses the idea that each disjunct in an 'or'-sentence is non-vacuous: each disjunct contributes to the truth of the whole sentence in which it occurs (Simons 2005b, p. 212).Turning to deontic sentences, Simons suggests defining truth conditions for sentences of the form P(ϕ or ψ) and O(ϕ or ψ) as follows. - I w is the set of ideal worlds form the point of view of w.Given non-disjunctive and nondeontic ϕ and ψ, the first clause gives the free choice equivalence between P(ϕ or ψ) and P(ϕ)∧ P(ψ).In addition, Ross' paradox (Ross 1941), which consists in the inference of O(ϕ or ψ) from O(ϕ), is blocked by the supercover condition in the second clause.On the other hand, the interpretation of 'or'-sentences not embedded under deontic operators fails to account for classical disjunctions.Suppose that (ϕ or ψ) is true at w under the supercover semantics.This implies that w is in either ϕ or ψ (or both).The supercover semantics essentially agrees with Boolean disjunction in this aspect.As noted by Simons (2005a, p. 293, n. 33), the other direction-from ϕ infer (ϕ or ψ)-is much more problematic.The principle of disjunction introduction may be explicated as follows: If ϕ is true at w, then (ϕ or ψ) is true at w.
In the usual Boolean semantics, disjunction introduction is a valid principle, since ϕ or ψ = ϕ ∨ ψ = ϕ ∪ ψ .In supercover semantics, on the other hand, disjunction introduction is not valid.Consider the following example sentence given by Simons (2005a, p. 293, n. 33): "Jane dances or 2 + 2 = 5".Under the supercover semantics (provided that "2 + 2 = 5" is false at every possible world), this sentence will turn out false at all worlds, since a supercover cannot contain the empty set.Nevertheless, there is a strong intuition that if "Jane dances" is true, then "Jane dances or 2 + 2 = 5" is true as well.In general, any disjunction with a logically impossible disjunct will inevitably be false under the supercover semantics.This constitutes a counter-example to the Boolean principle of disjunction introduction.
It is an open question whether it is possible to tinker with the supercover semantics in such a way as to make it agree with Boolean disjunction outside the scope of deontic modals.In this paper, I will take a different approach to this problem.With a careful distinction between action expressions and propositional statements, the usual Boolean story may be told for propositional statements, while a supercover semantics may be developed for action expressions.This makes it possible to deal with free choice phenomena while keeping classical disjunction in purely factual contexts outside the scope of deontic modals.
Are there independent reasons for giving up disjunction introduction for action expressions?Anglberger et al. (2014) argue that there are.One can for example appeal to normality, in the sense that action expressions are taken to refer to normal instances of actions (Pelletier and Asher 1997), or one may argue that action expressions are resource sensitive in the sense of Linear Logic (Girard 1987).Anglberger, Dong, and Roy give an example where action expressions display a kind of resource sensitivity (2014, pp. 24-25).Suppose that you are at a restaurant and are offered to order sushi.This does not imply that you are offered to choose between ordering sushi or pasta.The chef at the restaurant might not know how to cook pasta, or the restaurant might not have the right ingredients for making pasta, etc.In many cases, it seems that choosing between different alternatives is only possible if all the alternatives are live options.
A Deontic Logic Based on Supercover Semantics
In Segerberg's seminal paper (1982), and in the subsequent extensions and variants (Castro and Maibaum 2009;Trypuz andKulicki 2009, 2015), actions are interpreted as elements of a Boolean algebra, with permission and prohibition interpreted as (disjoint) ideals on this algebra.This means that these logics take notions of strong permission and prohibition as primitive.The model theoretic characterization of these logics interprets elements of the Boolean algebra of actions as sets of action tokens.The semantics to be developed in this paper extends this theory of action by introducing sets of sets of action tokens, and replaces the interpretation of permission by a deontic structure based on Simons' supercover semantics.The supercover semantics is here developed in a different way compared to the presentation in the previous section.In particular, legal and required sets of sets of action tokens are collected in two sets satisfying certain conditions, similar to neighborhood semantics for modal logics (see e.g.Chellas 1980, Chapter 7).
Action, Choice and Deontic Status
Assume that a single agent in a single situation has available a (non-empty) set H = {h 1 , h 2 , . ..} of action tokens.Action tokens can instantiate action types.Formally, an action type is a subset of H . Let A = P(H ) be the set of action types.Symbols s, t, . . .will be used as variables ranging over action types from A .I will also introduce the notion of a choice set.Formally, a choice set is a set of action types.While the impossible action type is represented by the empty set, choice sets are always required to be non-empty.Let C = P(A )\{∅} be the set of choice sets available to the agent in the situation.Symbols S, T , . . .are used as variables ranging over choice sets from C .Informally, a choice set represents choosing between the action types in the choice set.As an example, suppose that s 1 and s 2 are the action types denoted by the expressions 'go by bus' and 'go by train', respectively.The expression 'go by bus or go by train' can then be interpreted as denoting the choice set {s 1 , s 2 }.The idea, then, is that the expression 'go by bus or go by train' has a reading on which it describes a choice between the action denoted by 'go by bus' and the action denoted by 'go by train'.
Let G ⊆ H be a non-empty subset of the set of action tokens.G is supposed to represent the set of legal (right, good, deontically ideal, etc.) action tokens in the situation.This set is used to determine the deontic status of action types and choice sets. 3An action type is said to be legal if it contains some legal action token, i.e. if there is some legal way to perform the action type.A choice set is said to be legal if all the action types in it are legal-the agent is permitted to choose between different action types only if each one of them is legal.Formally, the set of legal choice sets is defined as4 LEG def = {S ∈ C : for all s ∈ S, s ∩ G = ∅} .
As an example, take the sentence "Jane may go by bus or go by train".The idea here is that this sentence has a reading on which it says that both the action type denoted by 'go by bus' and the action type denoted by 'go by train' are permitted.Again, let s 1 be the action type denoted by 'go by bus' and s 2 the action type denoted by 'go by train'.The proposal, then, is that the sentence 'Jane may go by bus or go by train' is interpreted as saying that {s 1 , s 2 } ∈ LEG.This, in turn, is true if and only if {s 1 } ∈ LEG and {s 2 } ∈ LEG.This property of LEG generalizes: if a choice set S is legal, then every non-empty subset of S is legal, and if two choice sets S, T are legal, the union S ∪ T is also legal.In this sense, the just introduced semantic constructs can be used to model free choice permission.
I will also define the set of required choice sets, which will be used to interpret a concept of obligation.To do this, a slightly different construction is needed.A choice set is legal if it contains legal action types only.On the other hand, a choice set may be required even if it contains non-required action types.The following example given by Alchourrón and Bulygin illustrates this point: There is e.g. the well known case of Sempronius who has an obligation to give a cow or a horse to Ticius, but he has not the obligation to give Ticius a cow nor has he the obligation to give him a horse.He can fulfill his obligation by giving either of the two things, since he must give one of the two, but he is not obliged to give either in particular.(1971, p. 157) Thus, Sempronius is obliged to give a cow or a horse, but neither obliged to give a cow, nor obliged to give a horse.On the other hand, it may be said that Sempronius is obliged to choose one of the alternatives.I will interpret this as meaning that the sum of the action types in a required choice set contains all legal action tokens, and that each action type in a required choice set is legal.The last assumption seems quite natural, since if Sempronius can "fulfill his obligation by giving either of the two things", it can hardly be the case that he is not permitted to, for example, give a cow.Formally, let While the above example gives some intuitions regarding the particular modelling choices when it comes to obligation, the primary reason for introducing the REQ set is that it reflects Simons' truth conditions for obligation in terms of supercovers.Indeed, the sets LEG and REQ can be formulated equivalently using the supercover notion.
First, every element of S has a non-empty intersection with X .Second, it holds that X ⊆ S; hence, S is a supercover of X .(⇐) Suppose that S is a supercover of some X ⊆ G.Then, for every s ∈ S, s ∩ X = ∅, and so s ∩ G = ∅.It follows that S ∈ LEG. 2. (⇒) Suppose that S ∈ REQ.By definition, G ⊆ S and S ∈ LEG, so every element of S has a non-empty intersection with G.It follows that S is a supercover of G. (⇐) Suppose that S is a supercover of G.It follows that G ⊆ S. By the rightto-left direction of the first item of the theorem, it holds that S ∈ LEG.Hence, S ∈ REQ.
Language
The language for the deontic action/choice logic (DACL) to be developed is similar to the language used for the deontic logics based on Boolean algebra (Castro and Maibaum 2009;Segerberg 1982;Trypuz andKulicki 2009, 2015).It is characteristically two-sorted, with a clear distinction between action expressions and propositional formulas.The language is given by the following recursive syntax rules: where a i belongs to a finite set Act 0 = {a 1 , a 2 , . . ., a n } of generators.Let Act be the set of terms defined by (5) for fixed Act 0 .The missing operators of propositional logic ∨, →, and ↔ are defined as usual.The term connectives −, , and will be referred to as action-negation, action-disjunction, and action-conjunction, respectively, or when there is no risk of confusion with the corresponding propositional connectives, they will be referred to simply as negation, disjunction, and conjunction.The designated term 0 represents the impossible (empty) action, while the designated term 1 represents the universal (necessary) action.
The language has three types of atomic formulas.First, formulas of the form α .= β are used to express type-identity, with the intended meaning that α and β refer to the same action type.Second, formulas of the form α β are used to express choice-identity, meaning that α and β describe the same choices.Third comes deontic formulas of the form P(α), intended to express that α is permitted.The operators of propositional logic are then used to form complex statements about equivalence and deontic status of actions and choices.
Algebra of Actions
In the deontic action logics based on Boolean algebra (Castro and Maibaum 2009;Segerberg 1982;Trypuz andKulicki 2009, 2015), the action-theoretic layer is described by an underlying Boolean algebra of terms from Act.A standard set of axioms for Boolean algebra is given below.
In Boolean algebras, a partial order ≤ is induced by definition: α ≤ β if and only if α = α β.
Since fields of sets are Boolean algebras (Monk 1976, pp. 150-151), there is a straightforward way to construct a semantics based on the theory of action described in Sect.3.1.Every term from Act is mapped to an element of the set of action types A such that the designated terms 1 and 0 are mapped to H and ∅, respectively, and complex terms involving term operations correspond to the set-theoretical operations of union, intersection and complement in the obvious way.
Recall that the set of generators Act 0 defined in the previous section is assumed to be finite.As is well-known, a Boolean algebra generated by a finite set of generators is atomic.If there are n generators in Act 0 , every atom in the Boolean algebra generated by Act 0 is equal to an element of the form where each δ i is one of the generators from Act 0 or its negation.It should be pointed out that not every element that is equal to an element of this form is an atom, since it might be equal to the bottom element 0. Every element not equal to 0 of an atomic Boolean algebra is equal to a sum of atoms (Monk 1976).In particular, note that the top element 1 is equal to the sum of all atoms, while the bottom element 0 contains no atoms.Assuming that the set of generators is finite is integral to the proof of completeness, and it will be possible to make use of results obtained by Castro and Maibaum (2009) and Trypuz and Kulicki (2009).In particular, atoms are used to construct canonical models.
Deontic Action Models and Semantics
In this section, the basic action theoretic and deontic structures defined in Sect.3.1 will be used to construct a formal semantics.
A deontic action model M is a structure H , G, V , where H is a non-empty set representing the available action tokens, G ⊆ H is a non-empty subset of H representing the legal action tokens, and V : Act 0 → P(H ) is a valuation function assigning an action type V (a i ) ⊆ H to every generator a i ∈ Act 0 .To get models for a Boolean algebra of terms from Act, the function V is recursively extended to Act using the usual set-theoretical operations: These models are similar to the models defined by Trypuz andKulicki (2009, 2015).In their models, however, atoms of the underlying algebra of action are interpreted as singleton sets.This assumption makes it possible to consider legal closure principles at the semantic level.For my purposes here, this assumption is not necessary.
Every term α is also associated with a choice set.To interpret and −, I will introduce two special operations on choice sets.For S, T ∈ C , define S ⊗ T = {s ∩ t : s ∈ S and t ∈ T } , and where the operator Alt, originally introduced by Groenendijk and Roelofsen (2009), is defined as follows: for X a set of sets, AltX = {x ∈ X : for no y ∈ X , x ⊂ y}.The Alt operator picks out the maximal elements of a set X in the sense that it removes all elements that are proper subsets of some other element in X .
The choice set associated with a term α ∈ Act in a model M, denoted α M , is recursively defined as follows5 : The following result follows directly from the definition of choice sets.
In light of this result, one can think of V (α) as the range of α: the set of action tokens which are live options in the choice described by α.
A choice set α should be thought of as the choices described by the term α.A term whose choice set is a singleton describes a trivial choice; a choice with only one alternative.A term describes a genuine choice if its choice set consists of more than one alternative.It is clear that the only way to describe a genuine choice is by means of the operator.
The clause for conjunctive terms interprets α β as the pairwise intersection of the choices described by α and the choices described by β.The intuition behind this interpretation can be illustrated with an example.Suppose that you are at a restaurant and you are told that "You may order wine or beer and pasta or sushi".This sentence can be taken to introduce four permitted courses of action: the action of ordering wine and pasta, the action of ordering wine and sushi, the action of ordering beer and pasta, and the action of ordering beer and sushi.The choice set interpretation of conjunctive terms reflects this: simultaneously choose between ordering wine or beer and ordering pasta or sushi, then perform the two chosen actions together.
Following Ju and van Eijck (2016), I use a notion of 'to do something else' in the motivation for the choice set interpretation of α.To do something else than α is to do an action type that is different from the action types introduced by α.Say that two action types are different if their intersection is empty.For a given choice set S of action types, the set {s ∈ A : s ∩ t = ∅ for all t ∈ S} contains all action types that are different from the ones in S.However, 'doing something else than α' should not be understood as describing a choice between every possible action type different from the ones described by α.Take a sentence such as "Jane may do something else than going to the movies".What kind of things are Jane permitted to do? Combining the free choice interpretation of permission with the idea that 'doing something else than going to the movies' denotes a choice between every possible action type that is different from going to the movies has counterintuitive consequences.For example, among the action types different from that of going to the movies is the action type of robbing a bank (at least assume so for the sake of the argument).But it seems perfectly consistent that Jane is permitted to do something else than going to the movies, while not being permitted to rob a bank.For a given α, there may be many action types that are different from the ones denoted by α.In order to arrive at a precise interpretation of the choice set α , the set operator Alt is applied, picking out action types that are maximal in the sense that they are not properly included in any other action type in the set.It is readily verified that the set {s ∈ A : s ∩ t = ∅ for all t ∈ S} contains a unique maximal action type which is equal to H \ α .By Theorem 2, it follows that α = {V (α)}.Basically, then, negation collapses choice sets into singleton sets.
A formula ϕ being true in a deontic action model M (denoted M ϕ) is defined as follows, where LEG is defined based on the particular elements H , G in M as in Sect.3.1: A formula is said to be satisfiable if it is true in some model.A formula ϕ is valid (denoted ϕ) if it is true in all models.A set of formulas Σ is true in a model (denoted M Σ) if M ϕ for all ϕ ∈ Σ, and satisfiable if Σ is true in some model.A formula ϕ is a logical consequence of a set of formulas Σ (denoted Σ ϕ) if, for any M, if M Σ, then M ϕ.
Some Properties and Abbreviations
The following properties are easily verified: In principle, then, the operator .= could be introduced by definition: α .= β def = α β.It will also be convenient to introduce a couple of abbreviations: It can be verified that The abbreviation α ≤ β corresponds to the standard partial order induced by a Boolean algebra of Act.A sentence of the form α β expresses that the choices described by α are included in the choices described by β, i.e. that the actions included in the choice set α are included in the choice set β .
A deontic operator for expressing obligation in accordance with the deontic structure defined in Sect.3.1 can be introduced as an abbreviation: It is readily verified that formulas of the form O(α) have the following satisfiability condition: where REQ is defined based on the particular elements H , G in M as in Sect.3.1.On the intended reading of the operators, α is obligatory if and only if α is permitted and doing something else than α is not permitted.
A deontic operator for prohibition can be introduced as the negation of a permission.Such a concept says that a choice is prohibited when there is an illegal action type among the alternatives.One can also define a stronger concept of prohibition using a combination of external (propositional) negation and negation of terms: Recall that negation collapses choice sets into singleton sets.Thus, a sentence F(α) is true if and only if α = {V (α)} = {V (α)} does not belong to LEG, i.e. precisely when there are no legal action tokens in V (α).It is easily verified that In this sense, the stronger prohibition concept says that a choice is prohibited when there is no legal alternative: it is forbidden (in the strong sense) to choose between going by bus and going by train if the action of going by bus and the action of going by train are both illegal.
Permission and Obligation
In this section, I will argue that the semantics just outlined deals quite naturally with the problems connected with free choice permissions, and then discuss the defined concept of obligation.
Permission in DACL
Suppose that Jane may go by bus or by train.Intuitively, it follows that Jane may go by bus, and that Jane may go by train; Jane is permitted to choose one of the options.In everyday discourse, it seems that the permission to do one thing or another is equivalent to both disjuncts being permitted.In the present semantics, the principle of free choice is valid.
Proposition 1
The following is a validity: Proof For the left-to-right direction, let M = H , G, V be a deontic action model and suppose that M P(α β), i.e. α β M ∈ LEG.By the clause defining the choice sets of disjunctive terms and properties of LEG, it follows that α M ∈ LEG and β M ∈ LEG, which implies that M P(α) ∧ P(β).The right-to-left direction follows directly from the fact that S, T ∈ LEG implies that S ∪ T ∈ LEG.
The reason for this is that these logics take the principle of free choice as an axiom, and allow for substitutions of Boolean algebra identities within the scope of the permission operator.In the semantics in this paper, substitution of Boolean equivalents is in general not a valid rule of inference.This means that, for example, even though the classically valid equation a a .= b b is valid in the semantics, one can find models such that M P(a a) ↔ P(b b).Given the free choice reading this is desirable since one may be permitted to choose between going by train or not going by train, while not being permitted to choose between robbing a bank or not robbing a bank.As another example, take the classically valid equation a .
= (a b) (a b).Since a and (a b) (a b) are extensionally equivalent, i.e. denote the same action type, the equation is valid in the semantics.However, the two expressions may describe different choices.Indeed, a may not describe a genuine choice at all, while (a b) (a b) describes a choice between doing a b and doing a b.In terms of vegetarian lunches, one may take a to describe the action of ordering a vegetarian meal, a b to describe the action of ordering a vegetarian meal and pay for it, and a b to describe the action of ordering a vegetarian meal and not pay for it.
Proposition 2 The vegetarian free lunch problem is avoided, that is Thus, DACL keeps the free choice postulate but avoids the vegetarian free lunch problems.Even though intuitively deeply problematic, one may argue that there is nothing wrong with vegetarian free lunches per se: one just needs to give permission operators for which the schema P(ϕ) → P(ϕ ∧ ψ) are valid the right kind of informal reading.For example, one can interpret the permission operator in the strong or open sense (henceforth, I will refer to this interpretation as strong permission, and use P s to refer to a strong permission operator).According to the strong permission account, P s (ϕ) means that every way to perform the action denoted by ϕ is legal (Anglberger et al. 2014;Broersen 2004;Segerberg 1982;Trypuz andKulicki 2009, 2015).This account should be contrasted with the weak reading of permission, where an action being weakly permitted means that at least some way of performing it is legal. 6he strong permission account seems to offer an explanation of the problem of vegetarian free lunches: if every way to perform the action of ordering a vegetarian meal is legal, then it follows that ordering a vegetarian meal and not paying for it, which is indeed a way to order a vegetarian meal, must be legal as well.Given this interpretation, one can argue that the clash with intuition arises because of the incompleteness of informal normative discourse (Broersen 2004, pp. 163-164).When I permit you to order a vegetarian meal, I usually implicitly assume that further properties of the permitted action must be taken into account (e.g. that ordering a vegetarian meal requires paying for it).What was actually permitted in the first place, then, was the action of ordering a vegetarian meal and paying for it.Dignum et al. (1996) offer a formalization of this idea by introducing an operator on action expressions that allows referring to actions performed in isolation, and special action expressions that, apart from naming actions, also refer to contexts in which the actions can be performed.A contextual action expression α C means a performance of the action named α, possibly in combination with actions in the context C. The contextual action expressions are used to refer to a restricted set of all possible ways to perform an action.A permission P s (α C ), then, means that every way to perform the action α in combination with actions in the context C is legal.In the system of Dignum et al. (1996), it is possible to have P s (α C ) without having P s (α).The correct way of translating the sentence "It is permitted to order a vegetarian meal" into formal language, they argue, is to translate it into P s (a C ), where a denotes the action of ordering a vegetarian meal and C is some context specifying actions that are 'safe' to perform in combination with the action of ordering a vegetarian meal.In this way, one need not say that every possible way to order a vegetarian meal must be legal, but only those ways which are expressed explicitly using some appropriate context.
Even though I agree that vegetarian free lunches are less problematic under the strong reading of permission, I do not think that this account necessarily is the most natural one or the only account worth investigating when it comes to interpreting free choice permissions.For example, Jane may very well choose freely between driving her Volvo to work and driving her BMW to work.The fact that Jane ought to be sober while driving does not cancel her free choice permission: it seems strange to say that the only free choice Jane is permitted to make is that between driving her Volvo sober and driving her BMW sober.Giordani and Canavotto (2016) make a similar point, arguing that "ordinary choices can be risky: we are ordinarily allowed to choose between alternative actions even if there are ways of performing such actions that lead to a violation of the law."(2016, p. 89).To capture this property, strong permission is too strong, and weak permission is too weak (cf.van der Meyden 1996, p. 470).Even the contextual permission approach of Dignum et al. (1996) fails to account for permissions of risky choices.The present approach, on the other hand, offers a way to account for free choice permissions without resorting to strong permission.The operator P is a kind of mix between the strong and weak reading of permission: P(α) means that every alternative action in the choice described by α is weakly permitted.Thus, I accept the idea of a free choice permission being a permission in which every alternative action to choose from is legal, but I reject the idea that an action is legal only if every way to perform it is acceptable.Free choice permission is permission applied to choices, rather than directly to actions.
That being said, the present framework provides a straightforward way to combine two kinds of deontic operators: one referring to action types and the other referring to choice sets.For example, the P and O operators refer to choices, while the F operator is technically equivalent to an operator applying directly to action types.It is not possible to introduce strong permission in DACL as a syntactic abbreviation, but it is straightforward to introduce it as a primitive notion.Adding strong permission to DACL results in an extension of Segerberg's B.C.D. system (1982).
Turning back to the free choice principle itself, it can be noted that the right-toleft direction of it is also valid in any deontic logic where the permission operator is analyzed as a normal modal diamond, that is, as a weak permission operator.However, such logics also validate a stronger principle: P(ϕ) → P(ϕ ∨ψ).This can be seen as a permission variant of Ross' paradox, admitting the following counterintuitive instance: "If you may post the letter, then you may post the letter or burn it".This time, the culprit is closure of permission under logical consequence: from the tautology ϕ → ϕ ∨ ψ, apply closure of permission under logical consequence to obtain P(ϕ) → P(ϕ ∨ ψ).In the present framework, permission is not even closed under logical equivalence (valid equations of Boolean algebra), and P(α) → P(α β) is not valid.
Proposition 3
The following properties hold: Proof For a proof of ( 8), let M = H , G, V be a model and assume that M P(α β), i.e. α β M ∈ LEG.It follows that t ∩ G = ∅ for each t ∈ α M = {s ∩ s : s ∈ α M and s ∈ β M }, which implies that s ∩ G = ∅ and s ∩ G = ∅ for every s ∈ α M and s ∈ β M .This, in turn, implies that α M ∈ LEG and β M ∈ LEG, i.e.M P(α) ∧ P(β).For a proof of ( 9), let M = H , G, V be a model such that By properties of LEG, it follows that α β M ∈ LEG and α δ M ∈ LEG, i.e.M P(α β) ∧ P(α δ).For ( 11), consider a model These properties nicely illustrate the double nature of permission in DACL: (8) says that permitted conjunctions can be weakened, which is a characteristic property of weak permission.Another characteristic property of weak permission is closure: for every action, either it or its negation is permitted.This property fails for the operator P as shown by ( 11).
I will close this discussion with some remarks regarding (9).In everyday discourse, it seems that free choice phenomena are preserved when 'or' is embedded under 'and'.Suppose that a 1 means 'sit on the sofa', a 2 means 'read a book', and a 3 means 'watch TV'.Then, the term a 1 (a 2 a 3 ) means 'sit on the sofa and read a book or watch TV'.Now, consider the following informal inference: Jane may sit on the sofa and read a book or watch TV.Therefore, Jane may sit on the sofa and read a book and Jane may sit on the sofa and watch TV.
The inference seems intuitively valid, and illustrates that free choice effects are not canceled when 'or' is embedded under 'and'.This property is reflected in the validity (9) of Proposition 3.
Obligation in DACL
Regarding the interaction of permission and obligation, it can be noted that the O and P operators satisfy the following principle, which follows directly from the fact that REQ ⊆ LEG.
Proposition 4 'Ought implies may', that is, Note that a consequence of the above principle is that O(α β) → P(α) ∧ P(β) is valid.This is in accordance with the justification for the REQ set given in Sect.3.1.
Proposition 5 Ross' paradox is avoided, that is, The semantics also validates the well-known principles of obligation aggregation, obligation weakening, the impossibility of conflicting obligations and a principle saying that choosing to do an impossible action is never obligatory.
Proposition 6
The following validities hold: Proof The proof of ( 14) is left to the reader.Here is a proof of ( 15 That O(α) and O(α) are not jointly satisfiable guarantees what is known as deontic consistency: one and the same choice can never be both obligatory and prohibited.In fact, Theorem 2 together with the definition of REQ shows that conflicting obligations require accepting models where G = ∅, i.e. models where there are no legal action tokens available.
Regarding the interaction of obligation and prohibition, the following validities are shown to hold.
Proposition 7
The following validities hold: Proof ( 18) is immediate from the syntactic definition of O and F. For ( 19), let M = H , G, V be a deontic action model and assume that M F(α).Then G ⊆ V (α).Since α M = {V (β)}, it immediately follows that α M ∈ REQ. ( 20) is a consequence of ( 19) and ( 14).Trypuz andKulicki (2015, p. 1254) take the principles of obligation economy (18) and obligation trimming (20) together with ( 17) as axioms characterizing a minimal concept of obligation.The O operator is stronger than this; for example, obligations can be weakened according to (15).In the basic system of Trypuz and Kulicki (2015) where obligation is axiomatized by ( 17), ( 18), and (20), it is not possible to derive (15).Castro and Maibaum (2009) introduce an obligation operator in terms of strong permission and prohibition, which in the present framework corresponds to the abbreviation O P F (α) def = P s (α) ∧ F(α) (where P s is strong permission with truth conditions M P s (α) iff V (α) ⊆ G).A consequence of this definition is that there is only one obligatory action type: = β is valid.As observed by Trypuz andKulicki (2015, p. 1253), this property makes many of the intuitively desirable properties of obligation trivially valid.The O operator of DACL is introduced using the P operator instead of P s , which guarantees that there may be several different obligations.Consider, for example, a model
Axiomatization
In this section, the logic DACL is presented axiomatically.The axiom system is shown to be sound and complete with respect to the semantics defined in previous sections.
For the rest of what follows, assume a fixed set Act 0 of generators.DACL is axiomatized by the following axioms and rules.
-A complete set of axioms for Propositional Logic (PL).Σ ϕ means that ϕ is derivable (in the axiom system) from Σ; this notion is defined as usual.
Some Theorems
The following theorems provide a syntactic characterization of the concept of prohibition, as well as the interaction between prohibitions and permissions.
Lemma 1
The following are theorems of DACL.
Proof These theorems are straightforward consequences of the deontic axioms and the definition of F.Here is a proof of Theorem ( 27).
1 The following theorems give a flavor of the logical behavior of choices.
Lemma 2
The following are theorems of DACL.
The proofs of these are straightforward.Below I provide proofs of theorem ( 29) and (33).
Soundness
Theorem 3 (Soundness theorem) The axiom system is sound with respect to the semantics, that is, if Σ ϕ, then Σ ϕ.
Proof It must be shown that each axiom is valid, and that the rules of inference preserve validity.I prove some representative cases below.Axiom (A14).Let M = H , G, V be a deontic action model such that M α β δ.This means that α This, in turn, shows that α M ∈ LEG or β M ∈ LEG, i.e.M P(α) ∨ P(β).The other direction is similar.
Disjunctive Negative Translation
The completeness proof utilizes the fact that every term has a certain normal form.First, I will define the disjunctive negative translation of a term α, denoted Dnt(α).This translation is similar to the one defined by Ciardelli and Roelofsen (2011, p. 69) Proof The proof is by induction over α.For the induction base, note that for α = a i , α = 1, and α = 0, axioms (A11), (A12), and (A13) give that α Dnt(α).For the induction step, that the statement holds true for terms α , α .There are three cases to consider.
Completeness
The completeness proof follows the same structure as the corresponding proofs given by Castro and Maibaum (2009) and Trypuz and Kulicki (2009).Completeness is proved by proving the equivalent result that each consistent set of formulas has a model.
Definition 2 (Canonical model) Let Φ be a maximally consistent set of formulas with respect to the axiomatization of DACL, and let [α] .= be the equivalence class of The following two lemmas are proved along the same lines as done by Castro and Maibaum (2009, p. 448) (the proofs are stated here for completeness of presentation).
Lemma 3 For any atom
Proof The proof is by induction over α.First, for α = a i , the claim is true by definition of V Φ .For α = 0, the claim holds since V Φ (0) = ∅ and γ ≤ 0 / ∈ Φ for every atom γ .For the induction step, there are three cases to consider.
The two lemmas above show that the interpretation function V Φ has the right behavior, and so: Proof First, note that G Φ ⊆ H Φ .It is shown that G Φ is non-empty.Suppose that there are n atoms of Act.Suppose, for a proof by contradiction, that for every atom 26).This is, however, a contradiction since it holds that ¬F(1) ∈ Φ by (23).
Proof
The proof is inductive.For the PL operators, the proof is standard.All the remaining cases follow from Lemmas 4, 8, and 10.
Lemma 11 shows that the canonical model has the desired behavior, and completeness is then proved by a routine argument.
Theorem 6 (Completeness theorem) For each consistent set Σ of formulas of DACL, there is a model which satisfies it.
Proof If Σ is consistent, then there exists a maximally consistent set Σ which is an extension of Σ.By the definition of the canonical model and Lemma 11, it follows that M Σ Σ, so Σ has a model which satisfies it.This concludes the proof.
Discussion
In this section, I will discuss some aspects of the approach in this paper that deserve further attention.First, I will briefly compare choice sets with the interpretation of propositions in inquisitive semantics.Second follows a discussion of the algebraic properties of choice sets, and finally, I will make a comparison with the conceptually similar Action Type Deontic Logic of Bentzen (2014).
Alternativeness in Inquisitive Semantics
It should be stressed that arbitrary sets of action types count as choice sets under the present action theory.One may reasonably think that the notion of a choice set should be much more restricted.For example, a standard assumption in decision theoretic settings is that alternative actions are mutually exclusive.
In the literature on inquisitive semantics (Ciardelli and Roelofsen 2011;Ciardelli et al. 2009;Groenendijk and Roelofsen 2009;Roelofsen 2013), propositions are interpreted as sets of possibilities, where possibilities, in turn, are sets of possible worlds.
Weak forms of inquisitive semantics (for example the system Inq∅; Ciardelli et al. do not put any restrictions on propositions (conceived of as sets of possibilities), and the resulting semantics comes very close to how choice sets are characterized in this paper.In stronger forms of inquisitive semantics (for example the system InqB; Ciardelli and Roelofsen 2011), two possibilities are said to be alternatives if neither of them is a proper subset of the other.In a similar spirit, why not restrict the notion of choice set so as they contain alternative (in the sense used above for possibilities) action types only?In the present action theoretic context, a restricted version of the concept of a choice set may be defined as follows: a choice set S is restricted if for all s ∈ S, there is no s ∈ S such that s ⊂ s .In other words, the interpretation of terms as restricted choice sets is obtained by applying the operator Alt, defined in Sect.3.2.3, to the unrestricted choice sets of terms of any form, not only those of the form α.
The reason for not making this move is the use of Simons' supercover semantics.By using supercover semantics for permission and obligation in terms of the sets LEG and REQ, information will be lost by moving to restricted choice sets.For example, if S = {s}, T = {t} and t ⊂ s, it follows that Alt(S ∪ T ) = {s}.If s ∩ G = ∅ and t ∩ G = ∅, it follows that Alt(S ∪ T ) ∈ LEG, even though AltT / ∈ LEG.In order to keep the free choice principle, there is a point in allowing a more liberal definition of choice sets, even though this makes the algebraic properties of choice sets more complex.7
Algebraic Considerations
The behavior of choices in DACL deviates from the Boolean interpretation of actions.Indeed, the algebraic structure defined on choice sets does not even form a lattice, since absorption is missing.On the other hand, a straightforward extension of DACL turns out to have an underlying semiring structure.
As developed in this paper, DACL is only concerned with non-empty choice sets.This is in part motivated by its relation to Simons' supercover semantics.One may wish to extend the semantics with an empty choice set.This extension is straightforward, but interesting for technical reasons since it gives a semiring structure with ∅ as the identity element of the union of choice sets.The structure is a special kind of commutative idempotent semiring: -P(P(H )), ∪, ∅ is a join-semilattice; -P(P(H )), ⊗, {H } is a commutative monoid; -⊗ distributes over ∪ and ∅ is an annihilator for ⊗; -B, ⊗, ∼, {∅}, {H } is a Boolean algebra, where B is the set of singleton choice sets; -∼ is an operation mapping every choice set to the set containing complement of its union.
The language and axiomatics of DACL must be modified slightly to account for the addition of the empty choice set.A new designated term, say f, whose action type interpretation and choice set interpretation both equals the empty set, should be added. 8dding axioms to the non-deontic axioms of DACL and replacing axiom (A15) by result in a complete axiom system for the extended version of the non-deontic fragment of DACL.The proof of this claim is similar to the completeness proof in Sects.5.3 and 5.4.Note that adding (38) allows inferring Algebraic considerations suggest that any finite idempotent commutative semiring with an additional Boolean algebra structure on its join-irreducible elements and a suitable 'negation' operation satisfying axioms corresponding to (A10), (A14), ( 39) and ( 40) is isomorphic to a semiring P(P(H )) for H some finite set, with operations ⊗, set union ∪ and ∼.The argument for this claim is similar to corresponding proofs of representation theorems for finite distributive lattices and Boolean algebras (see e.g.Davey and Priestley 2002, Chapter 5).In the infinite case, things are less clear.Note, however, that the syntactic restriction on the set of generators Act 0 already presupposes finiteness, and that the construction of the canonical models in the completeness proof shows that any satisfiable DACL formula is satisfiable in a model with a finite domain.However, this is not the place to discuss this in detail, and I will leave the issue for further research.
Bentzen's Action Type Deontic Logic
A deontic action logic that is conceptually related to the present approach is presented by Bentzen (2014).Bentzen uses a distinction between action expressions (terms) and propositional statements, and introduces a kind of distribution requirement in the interpretation of disjunctive action expressions.The semantics is intended to solve many of the problems with the standard approach to deontic logic.
In order to account for the special interaction between deontic operators and disjunction, Bentzen introduces a disjunctive term operator which is interpreted so as to be non-empty: the action type denoted by the disjunctive (α or β) is instantiated by an action token h if and only if h instantiates the action type denoted by α or h instantiates the action type denoted by β and there are action tokens instantiating the action type denoted by α and action tokens instantiating the action type denoted by β. 9 Bentzen interprets this non-emptiness condition as a "a criterion of relevance or availability" (2014, p. 405).
The models of the semantics are structures M = G, V 10 : G is a non-empty set representing the legal action tokens available to an agent in a situation, and V is function assigning subsets of G to every term.Formally, the relevance criterion is captured by interpreting disjunctive terms α β as follows: otherwise.
The satisfiability conditions for permission and obligation sentences are defined as Conceptually, the approach in this paper is closely related to Bentzen's, even though the formal implementation is quite different.Bentzen motivates his semantics by considering several benchmark cases.These consist of principles that in some way or another indicate problems with other deontic logics, and are divided into principles that should be valid and principles that should not be valid.Interestingly, DACL agrees with Bentzen's semantics on all of these principles except for two.In Bentzen's semantics, permission and obligation are duals, and a closure property of permission, stating that for every action either it or its negation is permitted, is valid.As is clear from the syntactic definition of O, the duality property does not hold in DACL.Item (11) of Proposition 3 shows that there is no closure of permission in DACL.However, note that DACL preserves free choice effects when disjunction is embedded under conjunction [item (9) of Proposition 3].This property fails for Bentzen's semantics.An interesting difference between DACL and Bentzen's semantics is that the latter only model ideal behavior in the sense that only legal action tokens are included in the domains of the models: "it is presupposed that the agent chooses an acceptable action."(Bentzen 2014, p. 406).This assumption is a limitation of Bentzen's approach.The concept of norm-violation is often seen as an integral part of deontic logic, for example when modeling contrary-to-duties or in applications to agent-regulation.Some even claim that the possibility of norm-violations is inherent to the definition of a normative system.I interpret Carmo and Jones (2002) as holding this view.They argue that if it can be assumed that agents always behave as they should, 9 Bentzen uses symbols S, T , . . .as variables ranging over terms, and lower case Greek letters as ranging over action tokens.To avoid confusion, I have changed Bentzen's notation here. 10I have omitted the interpretation function for propositional constants originally used by Bentzen.…the normative dimension ceases to be of interest: the actual does not depart from the ideal, so nothing is by merely describing what agents in fact do.(Carmo and Jones 2002, p. 265) In the semantics presented in this paper, the possibility of agents having illegal action tokens available is included.Whether it is possible to extend Bentzen's semantics in order to account for norm-violations is a question that will be left open here: suffice it to note that the approach in the present paper represents an alternative formal implementation of the ideas underlying Bentzen's semantics.
Conclusion
I have presented an approach to deontic action logic where action expressions have two kinds of formal interpretations: as action types, and as choice sets.This distinction is then utilized when interpreting deontic concepts.A formal deontic logic based on the logics of Trypuz andKulicki (2009, 2015) was developed.In this logic, permissions are sensitive to the choice meaning of action expressions, and substitution of logical equivalents within the scope of the permission operator is not in general a valid rule of inference.The main result is the completeness of an axiomatization of the logic.
The logic is intended to capture properties of informal deontic reasoning, and in particular provide ways to handle the various problems related to the interaction of permission and disjunction.The present approach is conceptually similar to Bentzen's Action Type Deontic Logic (2014), but the formal implementation is different.Unlike Bentzen's approach, it allows for the modeling of non-ideal actions.This opens up possibilities for modeling norm-violations, for example contrary-to-duty obligations (Carmo and Jones 2002).This is an interesting topic for further research.
There are additional requirements one may put on choice sets.For example, the notion of alternative could be made more restrictive as done in inquisitive semantics and in decision theory in general.What kind of logic such different restrictions give rise to is a topic for further research.In the approach taken here, the interpretation of action-negation essentially collapses the choice sets of negated terms into singleton choice sets.This makes it possible to utilize the disjunctive negative translation in the completeness proof.On the other hand, one might think that this interpretation lacks sufficient philosophical motivation.
At present, the logic is quite limited in its scope.It cannot be used to talk about performances and consequence of actions and choices.It would be interesting to consider the approach developed here in a dynamic setting (see e.g.Castro and Maibaum 2009;Meyer 1988), thus arriving at a considerably more expressive theory.Neither are there any resources for reasoning about sequential composition of actions, and I did not consider contrary-to-duty normative reasoning.These are all topics for further inquiry.
Finally, the algebraic foundations of DACL deserve closer attention.I argued in Sect.6.2 that a straightforward extension gives rise to a special kind of semiring structure.Because of the close connection with inquisitive semantics, research in this direction may provide results not only on the algebraic properties of choice sets, but ).Let M = H , G, V be a model and assume that M O(α β), i.e. α β M ∈ REQ.By (12) of Proposition 4, it holds that M P(α β), so by (8) of Proposition 3 M P(α), i.e. α M ∈ LEG.By the definition of REQ and properties of choice sets, it holds that G ⊆ α β M ⊆ α M .Taken together, this implies that α M ∈ REQ, i.e.M O(α).(16) follows from (18) of Proposition 7 below.(17) follows from the syntactic definition of O and the fact that ¬P(0), the latter being valid because {∅} / ∈ LEG. | 14,330.4 | 2019-01-04T00:00:00.000 | [
"Philosophy",
"Computer Science"
] |
Highly birefringent do-octagonal photonic crystal fibers with ultra flattened zero dispersion for supercontinuum generation
Brazilian Microwave and Optoelectronics Society-SBMO received 8 Sept 2018; for review 10 Oct 2018; accepted 21 Dec 2018 Brazilian Society of Electromagnetism-SBMag © 2019 SBMO/SBMag ISSN 2179-1074 Abstract— Photonic crystal fiber (PCF) structures with do-octagonal geometry have been studied. These do-octagonal PCF structure have smaller circular holes arranged in rhombic fashion at its centre. Moreover, these small holes are doped with materials like butanol, ethanol, methanol and propanol. Do-octagonal PCF structures doped with methanol and air filled structure report very high birefringence. Ultra flattened zero dispersion has been achieved by all the simulated structures. Besides, low confinement loss and large nonlinearity have also been reported. Numerical simulation for supercontinuum generation has been performed. Supercontinuum spectra obtained for peak power 1 kW, 2 kW, 5 kW and 10 kW are 650 nm, 950 nm, 1450 nm and 2050 nm respectively.
I. INTRODUCTION
Optical properties in PCF can be easily tailored to obtain desire results.It can be achieved by designing a particular pattern or arrangement of holes and also by changing the dimension of the hole.Moreover pitch factor of hole and the number of hole in the cladding region can also result desired changes.Photonic crystal fiber due to their extraordinary properties compared to standard optical fibers has drawn the attention of many researchers [1]- [4].These properties include chromatic dispersion [5], birefringence [6], ultra low loss [7], endless single mode propagation [8], large nonlinear co-efficient [9] and effective mode area [10].In conventional fiber, achieved birefringences are very low due to very low refractive index contrast.Different to this, PCF are having large index contrast and design flexibility as well.Hence very high value of birefringence can be easily achieved in PCF [11].
Researchers have reported high birefringence by using squeezed crystal lattice.In this structure number of holes are different along two orthogonal axes [12].Researchers have also used elliptical holes to obtain high birefringence [13].Lyngso et al [14] reported polarization maintaining index guiding PCF.
Cho et al shown large birefringence in plastic PCF [15].Highly birefringent PCFs can be obtained by adopting two ways.First way is to break the symmetry in the cladding region.And other way is to introduce asymmetry in a porous core.Highly birefringent PCFs have wide application in optic sensor, Précised optical instruments, and high transmission speed, optical communication system.Control over chromatic dispersion in PCF is vital for their partial application.Again there is a tradeoff between high birefringence and dispersion with low losses.Large index contrast sometimes result excessive chromatic dispersion.Hence to make a control over dispersion with high birefringence has always been a challenge for the researchers.Several PCF structures with zero dispersion and high birefringence have been achieved by the researchers [16]- [18].To achieve more significant result PCF with arrangement like square [19], rectangular [20], octagonal [21], decagonal [22], and do-decagonal [23] have been investigated.Moreover, various PCF structures with nanometric holes have been reported [24]- [28].
PCF structures with such holes have been selectively filled or fully filled with liquids, gases and other materials [29]- [32].Very tight confinement of optical mode in core results large non linearity.It can be achieved by reducing the core area.It can also be obtained by increasing the index contrast between core and cladding .The contrast can be increased by use of soft glass material.Supercontinuum generation is an inherent property of nonlinear optics.It has wide application in pulse compression, coherence tomography and spectroscopy meteorology [33]- [34].Basically, supercontinuum generation, in nonlinear process produces broadband light.Interaction of short and intense pulses data output of nano band sources 81elps in achieving this.Zero ultra flattened dispersion is the primary need of achieving a broadband supercontinuum generation .Ranka et al was the first to demonstrated supercontinuum generation [35].Supercontinuum spectrum are generated by pumping ultra short pulses in fiber whose wavelength lie in dispersion regime close to zero dispersion wavelength.Razak et al achieved large nonlinearity with octagonal PCF [36].Moreover Camerlengo et al introduced a W-type index profile PCF with nonlinearity 0.82 W -1 m -1 at zero dispersion wavelengths [37].
In this work, do-octagonal PCF structures doped with material of alcoholic group have been studied.
Initially, a hexagonal PCF has been designed.Later a do-octagonal shaped core has been made by introducing defects at the centre.This defect is made by removing holes at the centre of fiber.After that new holes, smaller in dimension has been arranged in a rhombic fashion.The structure has a rhombic arrangement of holes fill with materials of alcoholic group and air.Alcoholic material like butanol, ethanol, methanol and propanol has been used.The structure report ultra flattened zero dispersion at visible range and at infrared region.Birefringence shown by the structure is much higher and is of the order of 10 -1 .PCF structure doped with methanol reported highest birefringence .Moreover this structure reported ultra low confinement loss and very large nonlinear coefficient.Supercontinuum generation has also been generated at a wavelength of 1250 nm.Full vector finite element method (FEM) numerical technique have been adopted to analyse the different propagation characteristics of PCF.First FEM processes complex structured PCFs into homogeneous subspaces.Secondly, it is computed with Maxwell's vector equation as given by equation ( 1) [38].
Where [s] is perfectly matched layer matrix of dimension 3X3.It includes even parameters Sx and Sy.
Electric vector is denoted by 'E'.Wave number in vacuum is obtained as: A circularly perfectly matched layer, boundary condition having thickness 10% of the fiber radius have been used to absorb the scattered light towards the surface of the fiber.Propagation constant ( ) and effective refractive index at different wavelength ( ) are provided by the simulating software COMSOL Multiphysics 5.2.These are represented as Modal birefringence defined as the difference between two polarized modes, is considered to play important role in determining PCFs to work as sensors.Mathmatically, it can be expressed as [30]: The cross sectional area of mode field, over which the field gets confined along the fiber during its propagation is termed as effective area ( eff ).High optical intensities are the results of smaller effective area.Hence, PCF with small effective area results large nonlinear coefficient ( ) [40].
Where E is the transverse electric field.
Where A (Z, T) represents slow varying envelope of the electric field of the optical pulse.The pulses move in a frame of reference along the z-direction at the pump frequency of the group velocity.α represent the attenuation constant of the fiber.βn is the n th order propagation constant at the center frequency ωo .R (T) shows the nonlinear response function .It includes Raman contribution.It is defined as fr represent fractional contribution of the delay Raman response .Its value is taken to be 0.18.hr represent form of Raman response function and it is calculated as Where τ1=12.2fs and τ2=32 fs use for silica .Possibility of cross phase modulation between pulses of two different polarizations are minimized as the assume input pulse with either posses vertical or horizontal polarization during launching into the fiber.
III. SIMULATION AND RESULTS
Simulated PCF structures have circular holes arranged in rhombic fashion.External six rings are arranged in hexagonal arrangements.Dimension of six rings with hexagonal arrangements have diameter d1, where d1=0.6*˄.Here ˄ is the pitch factor and its value taken is 1.0 µm.However holels arranged in rohmbic fashion have smaller diameter d2, where d2=0.2*˄.Designed PCFs have been simulated by finite element method (FEM) method of COMSOL Multiphysics 5.2 software.
Investigated PCF structures report highly birefringent behavior.Do-octagonal structure with air hole and do-octagonal PCF structure dopped with methanol report highest birefringence in comparison to other PCF structures studied in this work.Achieved birefringence for these two PCF structure is of the order of 10 -1 .Microstructured core are feasible to obtain enhanced birefringence.Further increasing or decreasing the diameter of air hole in the microstructure core and reducing the size of spacing between two consecutive holes (pitch factor) results much higher birefringence.Methanol is an active , volatile , toxic and flammable raw material for the production of synthetic resin and plastic.Advantage of photonic crystal slabs doped with methanol solve the problem of accuracy, sensitivity and security [44], [45].Moreover researchers have reported a highly birefringence spiral photonic crystal fiber for gas sensing application [46] and Shengsi et al have reported a new two dimensional photonic slab with methanol doped photonic crystal slab [47].Fig. 2 shows birefringence behavior at diffrent wavelengths.Fig. 3 shows linearily polarized mode of the simulated structure.Due to rhombic arrangement of smaller holes, achieved birefringence at higher wavelengths is much higher.standard fiber is dominated by the dispersion of bulk silica.However in photonic crystal fiber design parameters like hole diameter, center to center spacing and geometry of holes enable flexibility in designing PCF to control over dispersion [48], [49].Zero dispersion photonic crystal fiber with very small core and efficient at generating supercontinuum light have been reported [50], [51].By optimizing d and Ʌ it become possible to obtain zero dispersion with 1 / ( . ) ps nm km center approximately around 1.52 μm, (d=0.73 μm and Ʌ=3.02 μm) [17].
Similarly, a dispersion of 0.5 / ( . ) D ps nm km = is achieved with d=0.63 μm and Ʌ=2.64 μm [52].This makes the fiber applicable for high data transmission.Also such fibers can be used supercontinuum generations.Dispersion behavior of the studied structures is shown in Fig. 4. Confinement loss at different wavelength have been plotted in Fig. 5. Do-octagonal structure with air hole has shown the highest loss in comparison to the doped do-octagonal PCF structure .However it is to be noted that the loss observed for all the structure is ultra low.The confinement loss obtained is of the order of 10 -14 .Ultra short laser pulses with hyperbolic secant shape are introduced as the input to the PCF.These pulses equation can be characterize as: (0, ) sech( ) Where T0 represents the temporal width of input pulse.
Higher order soliton become a dominant phenomena in the case of ultra short pulses pumped into zero dispersion regime.Soliton number determines these high order soliton.It can be calculated as: is the group velocity dispersion coefficient.
In Fig. 8, soliton numbers for the generation of supercontinuum are calculated against the variation of input pulse duration .It reveal that decrease in the duration of the input pulse leads to the generation of more number of high order soliton.Calculated soliton number are very large at the given peak power.Optical pulse of duration 50 fs at 1250 nm has been used in pumping pulse for supercontinuum generation.Numerical simulation for supercontinuum generation has been done at four different peak power levels 1 kW, 2 kW, 5 kW and 10 kW for air filled PCF structure.However , it can also be done for the liquid filled fibres, as also done previously by many researchers [55]- [58].Liquid evaporation is an important limiting issue which prevents the realization of fiber for long term application in practical.Many application have been enabled by the feasibility of inserting gas, liquids, polymers, and colloids into the microstructure core fully or partially.It result and efficient interaction of the guided light and thus modifies the waveguide characteristics [59], [60].However in some cases contact of the liquid with the external environment may degrade its properties.It is expected that very low fiber loss will not affect supercontinuum generation.First of all a numerical simulation for supercontinuum generation for fiber having different length have been perform by using pulse of 1kW power.Fig. 10 (a Results obtained in this paper are compared with the previously reported results of PCF structures at the wavelength 1.33 µm.This comparison is tabulated in Table II. II. DESIGN OF DO-OCTAGONAL PCF STRUCTURE Six ring hexagonal PCF structures have been studied.The PCF structure has holes doped with different material and air arranged in a rhombic fashion at the centre.These holes have much smaller dimension than the holes arranged in the external six rings.Material used for doping are butanol, ethanol, methanol and propanol.The schematic diagram of the investigated structure is shown in Fig. 1(a).Fig. 1(b) shows the three dimensional view of the same investigated structure.Table I shows the description of all five PCF structure simulated in this work.
Silica_Methanol
This structure has six rings of holes of circular dimension filled with air.At centre it has smaller circular holes arranged in rhombic fashion filled with methanol.Smaller circular holes have diameter of d2=0.2*˄,where ˄=1µm.External six rings have air holes of diameter d1=0.6*˄.Silica_Propanol This structure has six rings of holes of circular dimension filled with air.At centre it has smaller circular holes arranged in rhombic fashion filled with propanol.Smaller circular holes have diameter of d2=0.2*˄,where ˄=1µm.External six rings have air holes of diameter d1=0.6*˄.
effective refractive indices of x polarized and y polarized mode respectively.Again, obtained effective refractive index of the guided fundamental modes at different wavelengths helps in calculating chromatic dispersion parameters of PCF by using the following mathematical expressions [
2 n
decides the degree to which non linear effects occur when light with high intensity propagate into the fiber.Modes having leaky nature, together with non-perfect structure of PCFs result confinement loss.It is an extra form of loss which occurs in PCFs, usually made up of silica.These modes get leaky due to the finite lattice structure of PCFs.Confinement loss is calculated by considering imaginary part of the refractive index.It is calculated using formula[40]: of supercontinuum generation in the design fiber has been made.Modified nonlinear Schrodinger equation describes the mathematical model of supercontinuum generation.Schrodinger equation has different linear and nonlinear effects.This equation is solved using Split step Fourier method[41][42][43].
Fig. 2 .
Fig. 2. Birefringence behavior.Do-octagonal PCF structure has shown ultra flattened zero dispersion.From visible range to far infrared region, all the five PCF structure have shown flattened zero dispersion.Group velocity dispersion in
Fig. 5 .
Fig. 5. Confinement loss obtained at different wavelength.Do-octagonal PCF structure doped with methanol has the highest effective mode area in comparison to the other structures .Ethanol doped do-octagonal has the lowest effective mod e area in comparison to other structures .Figure 6 shows the effective mode area at different wavelength .Nonlinearity of a fiber is inversely proportional to the effective mode area.Nonlinearity of designed fiber is plotted in Fig. 7.
L
is the nonlinear length .0 P is the peak power used.2
Fig. 8 ..
Fig. 8. Number of solitons generated at different input pulses.Such a large generation of soliton may cause intra soliton interaction[53],[54]. Again dispersion length calculated is found to be 55 cm .It shows much larger fiber than the actual fiber length of 15 cm.Dispersion effect degrade in comparison to the nonlinear terms.Nonlinear effect determine the pulse evolution and result spectral broadening of these pulses.Effect of pulse compression are affected by soliton fission length .These length are calculated using / fiss D L L N = .The calculated value have been plotted in Fig. 9. Small duration of pulses cause in early pulse compression.It results smaller fission length and hence result wide spectrum.
) represent the spectral and temporal evolution of the input pulse of five different length of fiber respectively.A density plot has been used for getting more information about spectra broadening dynamic.Both spectral and temporal intensity have been plot using logarithmic density scale shorter at -40 dB relative to maximum value.Fig. 10 (b) displays density plot.This plot is utilized for studying the low amplitude spectral and temporal components.
Fig. 10 .
Fig. 10.Density plot of spectral and temporal profiles Fig. 10 (a) and Spectral profile and temporal profile Fig. 10 (b) of supercontinuum generation of a 15 cm long silica PCF at peak power of 1kW with pulses of 50 fs duration.
11 .Fig. 12 .
Fig. 12. Density plot of spectral and temporal profiles Fig. 12 (a) and Spectral profile and temporal profile Fig. 12 (b) of supercontinuum generation of a 15 cm long silica PCF at peak power of 5 kW with pulses of 50 fs duration.
PCF structure with holes arranged in rhombic fashion is investigated.These holes of circular dimension have been doped with different materials of alcoholic groups (-OH group).In one of the investigated structure holes are filled with air.Results of doped PCF structures are compared with PCF structure having air holes.Ultra flattened zero dispersion with much high birefringence has
TABLE I . DESCRIPTION OF SIMULATED PCF STRUCTURES PCF Structures Descriptions Silica_Air This structure has six rings of holes of circular dimension filled with air. At centre it has smaller circular holes arranged in rhombic fashion filled with air. Smaller circular holes have diameter
of d2=0.2*˄,where ˄=1µm.External six rings have air holes of diameter d1=0.6*˄.
Silica_ButanolThis structure has six rings of holes of circular dimension filled with air.At centre it has smaller circular holes arranged in rhombic fashion filled with butanol.Smaller circular holes have diameter of d2=0.2*˄,where ˄=1µm.External six rings have air holes of diameter d1=0.6*˄.Silica_Ethanol This structure has six rings of holes of circular dimension filled with air.At centre it has smaller circular holes arranged in rhombic fashion filled with ethanol.Smaller circular holes have diameter of d2=0.2*˄,where ˄=1µm.External six rings have air holes of diameter d1=0.6*˄..
TABLE II .
COMPARISON OF OBTAINED RESULTS WITH PREVIOUSLY REPORTED PCF STRUCTURES AT 1.33 µm WAVELENGTH. | 3,960.6 | 2019-03-01T00:00:00.000 | [
"Physics"
] |
Bias-variance decomposition in Genetic Programming
Abstract We study properties of Linear Genetic Programming (LGP) through several regression and classification benchmarks. In each problem, we decompose the results into bias and variance components, and explore the effect of varying certain key parameters on the overall error and its decomposed contributions. These parameters are the maximum program size, the initial population, and the function set used. We confirm and quantify several insights into the practical usage of GP, most notably that (a) the variance between runs is primarily due to initialization rather than the selection of training samples, (b) parameters can be reasonably optimized to obtain gains in efficacy, and (c) functions detrimental to evolvability are easily eliminated, while functions well-suited to the problem can greatly improve performance—therefore, larger and more diverse function sets are always preferable.
Introduction
Bias-variance decomposition is a fundamental method in machine learning. It allows for the decomposition of the error rate of a predictor into two components: the bias, representing the systematic error made by a model, and the variance, representing the error associated with the particularities of a training set. There are many "non-parametric" estimators characterized by a learning error that always tends to zero as the number of samples becomes large. Unfortunately, these learners become computationally expensive to deal with as the number of training samples increases, especially when problem dimensionality is high. Given a fixed number of training samples, non-parametric estimators typically encounter the "bias-variance trade-off", where greater complexity is required to exclude model bias but too much complexity will cause over-specialization to the training data. In light of this trade-off, several authors suggest that the "hard" part of solving a complex problem is precisely finding a proper model with a bias suited for the domain at hand [10,11], for instance, via the inclusion of appropriate heuristics.
Genetic Programming (GP) refers to the use of evolutionary computation to generate computer programs or mathematical expressions. The most typical form of GP is the tree-based version pioneered by Koza [17]. There are many other types, however, including a family easily expressed as graph-based networks, which include Cartesian Genetic Programming [24], Parallel Distributed Genetic Programming [27], Linear Genetic Programming (LGP) [3], and others [26]. These forms of GP are often static-length, while the complexity of the program is derived from the ratio of neutral to active code in the representation. In this work, we concentrate on LGP, an attractive choice for applications due to its tendency to produce parsimonious solutions [3] and its capacity to be converted directly to machine code [28]. We use a variable-length version, in which the effective length of a program will be less than some varying maximum value.
Our goal in this study is to explore the application of LGP to several benchmark problems under the lens of bias-variance decomposition. Some analysis of this form has already been conducted for tree-based GP, where it was shown that GP is generally a low-bias approach for regression problems. Some authors have used variance adjustment [1,13] or other strategies [8] to improve generalization of discovered solutions. In particular, Fitzgerald and Ryan hypothesize that low operator complexity (a smaller or simpler function set) corresponds to lower variance [7]. In this study, we find some evidence to the contrary.
Here we investigate more deeply this breakdown for several problems, both regression and classification, by considering the effect of various key parameters on this decomposition. First, we look at program length, a key parameter for the complexity of GP programs and the variable leading to the classic bias-variance trade-off. Next, we examine more closely choices involving initialization and function sets as potential means of reducing either the bias or the variance portions of the decomposition. In these latter cases, we do not attempt to produce yet other versions of the usual bias-variance trade-off, but rather explore means toward the amelioration of either component of error given realistic constraints. We believe this analysis will help guide practitioners in their choice of models and parameter setting.
Bias-variance decomposition
Let x 2 R p be a real-valued input vector, and y 2 R be an output value, with joint probability distribution P .x; y/. Let our loss function in output space be L.y; y 0 /, some measure of similarity between y and y 0 in R. We seek a function f which, when provided with an input x, will predict an "appropriate" output value f .x/, i.e., one that tends to minimize the average loss at that point: R L.y; f .x//P .yjx/dy.
Regression problems
For regression problems, the most common loss function is L.y; f .x// D .y f .x// 2 . The best choice of predictor, in this case, is the simple conditional expectation, f .x/ D EOEyjx D R yP .yjx/dy, also known as the regression function.
Assume that we have some predictor f , generated through the use of a data sample T , and tuned by a set of parameter values . In the case of a stochastic system, it also takes an initial seed I . For a given , we will write the output of f at x as f .xI T; I / to recall the other two dependencies. Then, the mean square error (MSE) of f at point x 0 can be expressed as the expected loss between f .x 0 / and f .x 0 / over various instances of T and I : in which we impose fixed-size training sets T . Note here that mse.x 0 / refers to the error of the expected predictor in x 0 , and as such, is a measure of the efficacy of the technique (and parameters) which spawned the predictor. Via algebraic manipulation, and making the assumption that our problem is deterministic, we can break the MSE into two components: var.
where O f .x 0 / D E T;I OEf .x 0 I T; I / denotes the average response of the predictor over T and I . The bias-variance dilemma refers to the trade-off between the two components of error: whereas the bias should be reduced, to prevent var.
Note that P OEY D yjx will be 1 or 0, due to the determinism of the problem. The term P T;I OEY f D yjx is the probability of guessing value y via the learning algorithm over all possible training samples T and initial seeds I . As with previous expectations, we estimate this probability via 50 runs of the system.
Integrated statistics
Finally, we will report the integrated forms of the MSE, MMR, bias and variance, respectively denoted b mse, b mmr, b bias and c var, to compare predictors on the basis of a single global measure in each category. For regression problems, integrals are computed numerically over a large set of uniformly distributed samples Q D fx j 0 g as follows: where jQj D 360;000. Note that since our numerical integration uses independently chosen samples, it can also be considered as an independent test set, and hence would detect any overfitting. For classification problems, we can similarly approximate the integrated mean misclassification rate, denoted b mmr, over the test problem instances.
Linear Genetic Programming
We follow Brameier and Banzhaf's definitions of LGP closely [3], with some minor modifications. An LGP individual consists of a collection of registers, n reg , equal to the number of inputs, n in , plus a number of additional registers initially filled with genetically defined constant values, n const . Thus n reg D n in C n const . Following this is a list of n program statements, with n ranging from 1 to a maximum program length, n prog . A program is executed by loading the input values into the initial registers, executing the program statements, then reading the output from the 0-th register. Figure 1 shows an example program. LGP program, instantiating the 2D Euclidean distance function, written in pseudo-Java notation. Note the existence of ineffective ("neutral") code, commented out in light gray. LGP individual is initialized by generating a sufficient number of constants to fill the additional registers, then generating a series of program statements. The constants are chosen uniformly and randomly from [0,1]. The number of program statements is selected randomly and uniformly between 1 and a maximum initialization length n init Ä n prog . The statements are generated by selecting three registers r a , r b and r c uniformly and randomly from all the value registers n reg , and then selecting a function g from the function set to generate the statement r c D g.r a ; r b /, or r c D g.r a / if g takes only one variable. Finally, any output from the LGP individual is constrained within a certain range, where outlying values are rounded to the closest extreme bound. These problem-specific output bounds were added to prevent undue influence of singularities on statistical analysis. The global output function produced by the LGP individual is denoted f as before: it is equal to some (more or less complicated) composition of a certain number of functions g. We use two function sets to explore our problems: one short list, G short , and one long list, G long . In some experiments, we utilize arbitrary subsets of G long . All possible functions are listed in Table 1. Generally, in this article, we will write our LGP individuals as mathematical expressions. The reader should be aware that: (1) they are an expanded view of the program, since modules are written out explicitly, and (2) while we remove unused code, we do not remove any redundancy (i.e., a statement such as a a is not replaced by 0), in order to give a realistic view of the raw evolutionary outputs.
Evolutionary algorithm
For all problems, we use a steady-state evolutionary algorithm. In the beginning, a population of N pop randomly initialized individuals f is created and each of them is evaluated by calculating its fitness F .f / (see below). The population is maintained at a constant size N pop throughout the evolutionary search by performing one-to-one replacements of individuals. During the search, an additional N new evaluations are performed as follows: for each evaluation, a deterministic tournament is held between two randomly chosen individuals of the current population. The worse of the two is replaced by either a cross between the winner and a second tournament-selected individual (with probability p cross ), or a mutation of the winner (individual elements are mutated with probability p mut and equal chances of macro-or micro-mutation). We also sometimes include a "parsimony pressure": if the difference between the fitness of the two individuals selected for tournament is less than F pars , then we select the individual with the smaller number of program statements. In sum, while the population's size remains N pop , the total number of evaluations is N eval D N pop C N new and the total number of individuals that are effectively replaced is comprised between 0 and N new .
Four benchmarks
We perform our investigations on several benchmark problems. For each benchmark, we execute approximately 500 runs with randomly chosen parameter values similar to the original source. From these runs, we estimate the combination leading to the lowest test fitness (since the "fitness" represents an error or a mismatch to be minimized). The problems and their associated search parameters are summarized in Table 2.
MexHat
The first problem is the "Mexican hat" (MexHat), borrowed from [3] and so named after the shape of its 2D manifold in 3D space. The MexHat function is reduced here to its 2D expression, denoting x D .a; b/: Note that Euler's number e is not included in the function set, and hence must be approximated genetically. For this regression problem, the fitness value F of an LGP individual f is defined as the sum of squared errors (SSE), with respect to the target f Mex , approximated over the training samples T D fx i g:
DistND
Next, we evaluate several "distance" problems (Dist1D, Dist2D, ..., DistND). These are a series of regression problems based on Euclidean distance in any even number of dimensions: Note that, since x D .a 1 ; :::; a N ; b 1 ; :::; b N /, the dimensionality of the problem is actually 2N . The distance functions are useful for investigating a related series of problems in increasing dimensionality. The fitness function F SSE is calculated as in Eq. (10), with target f Dist .
Spiral
We also include two classification problems. The first one is the artificial "spiral" problem, as described by Lang and Witbrock [19]. Here, the target f Spir is a binary function whose domains are intertwined in a double spiral pattern ( Figure 2). There has been significant research on this problem, including in the GP community, due to both its difficulty and its capacity to be easily visualized [5]. For this classification problem, the fitness function is an approximation of the misclassification rate (MR), i.e., the average of all binary mismatches:
Cenparmi
The second classification problem is the Cenparmi database of hand-written characters, collected by the CENPARMI lab at Concordia University ( Figure 3). This real-world supervised learning challenge consists of 6000 image samples of hand-written digits, and constitutes a high-dimensional problem with tightly correlated features. We scaled the images to a size of 12 12 D 144 integer inputs between 0 and 255 representing gray-level pixels. Our treatment made the classification problem binary by distinguishing between a selected class and the remainder of the set (e.g., between "4" and "not-4" instances). At the start of each run, we randomly selected the particular class, involving jT j D 300 training samples from the training pool, and jV j D 600 test samples from the test pool. Note that our approach to the database remained "naive" on purpose, i.e., we did not include geometric information about the relative location of the pixels. Our goal here was to test the bias-variance limits of genetic programming, not achieve competitive performance. The fitness function F MR was calculated as in Eq. (12), with target f Cenp representing the correct binary answer for the chosen class. Note that the state-of-the-art MR, across all learning techniques and available information, is approximately 0.02 [20].
Initial exploration
As expected, LGP was generally successful at evolving good regression functions and classifiers. Some examples of outputs for the Spiral problem are shown in Figure 2, and for the MexHat problem in Table 3. In further sections we will look closely at the variance associated with the individual runs of the evolutionary algorithm. Recall that we are discussing the variation of the solutions in terms of their behaviour in input, i.e., "phenotypic", space. While this is typically the object of interest during the use of genetic programming-as practitioners care how well they achieve some objective or fit some data-it should be noted that this is not the same as variance in genotypic space. In other words, two largely different mathematical expressions (genotypes) might have nearly identical performance (phenotypes), while, conversely, two genetic programs differing by a single instruction might produce dramatically different output functions.
The question here is about genetic convergence, that is, the propensity of evolutionary methods to find the same or equivalent mathematical expressions for the same problem on different runs. Indeed, this is a difficult concept to evaluate, since while there are ways to detect when some related programs are similar, there is no way, in general, to determine if two arbitrary programs are equivalent. There exist several measures of genotypic dissimilarity (termed "diversity", after their typical usage 2 ) for GP. For instance, edit distance (a measure of the number of steps required to transform one program into another, adapted for LGP in [3]), entropy, and behavioural diversity (comparing distributions of program outputs) are known to correlate well with expected fitness for some problem domains [4,12]. Unfortunately, in the case of edit distance and entropy, typical applications of these measures to GP tend to make the assumption that individuals are genetically related, hence are not useful for programs generated via independent means. Furthermore, some identities, such as the capacity to construct one primitive function from combinations of other functions, are not detectable. Informally speaking, in most cases that we examined, some form of genetic convergence was the norm. For instance, consider the solutions evolved from the Dist2D problem using the G short function set (see Table 2). We show below the two functions of x D .a 1 ; a 2 ; b 1 ; b 2 / that had the best fitness values among 33 inexact solutions: In these cases, the evolved solutions strikingly "resemble" the target function f Dist .x/ D ..a 1 b 1 / 2 C .a 2 b 2 / 2 / 1=2 , genetically speaking. To obtain exactly f Dist , all that would be required is minor tweaks and some elimination of redundancy. One could reasonably expect that additional computational effort would achieve at least the former, and under parsimony pressure, possibly the latter.
In the case of the Spiral classification problem, we also observed convergence to a similar form of solution, even if there were differences between the individual runs. For instance, using the G long function set, 5 out of 50 runs found zero-fitness solutions to the problem. Each of the 5 runs admits a similar structure of concentric rings (Figure 2), in which some additional singular boundary, like a flaw in a crystal, separates regions of rings to compensate for the ascending radius of the spirals. All five solutions make prodigious use of the div, mag2, and thresh functions, and one of either sin or cos. While this strategy is relatively consistent for the best of the LGP runs, it is by no means the only solution to the problem generally. For instance, techniques using constructive neural networks generate quite different output patterns, including true spirals [6].
On the other hand, consider the best solutions to the MexHat problem using its G long function set. The three best solutions are shown in Table 3. Notice how all three individuals depend on a 2 C b 2 , i.e., they discovered the radial symmetry of the MexHat target. Otherwise, these solutions display much more genetic variance than in the previously discussed problems. The edit distance between these statements is evidently quite high, as both the statement structure and the functions used differ wildly. Regardless, the outputs of these functions in the 2D plane are quite similar, and do not significantly overfit. Hence, despite great genotypic variation, they are all highly successful examples of regression solutions.
While our description is rather informal (the development of a more rigorous measure of genetic convergence lying beyond the scope of this study), we believe that it highlights the possibility of phenotypic convergence in the absence of genotypic convergence.
Typical bias-variance numbers
The bias-variance decomposition of each of our benchmark problems, including five different instances of DistND, is shown in Table 4. Parameters were set as indicated in Table 2. As proceeding sections will show, the listed values are typical. Nearly everywhere, the variance portion of the error dominates the bias component, often by several multiples. This is generally consistent with a view of GP as a low-bias/high-variance approach, which suggests that overfitting should be of concern for GP practitioners. In all cases, the use of G long also outperforms G short , especially Table 3. The three best solutions on a run of the MexHat problem using the G long function set.
Detailed analysis
In this section, we examine the effects of varying one of four control parameters separately from the others. First, we look at a key parameter of GP complexity, the maximum program length n prog . It is here that we expect to see the classic bias-variance trade-off, and the existence of a range corresponding to the optimal point in that trade-off. Next, we examine parameters related to the genetic initialization I , population size N pop , and choice of function set G. Our goal here is to explore the potential for reducing the error due to variance and bias, respectively, in a manner achievable by a GP practitioner. As such, in these latter experiments we aim not to generate new forms of the bias-variance trade-off, but instead, to study the error components under computationally constrained experimentation.
Varying maximum LGP length
First, a series of experiments were undertaken in which the maximum length of the LGP expressions was varied. The n init value (the maximum initial number of program statements) was chosen randomly and uniformly from the range OE1; 150, and the maximum LGP program length was set to n prog D 2n init . Over 200 values of n prog (including repeats) were explored, and b mse (or b mmr), b bias and c var were computed for each value. The G short function set was used throughout. Table 4. Integrated error and bias-variance decomposition on the target benchmarks. "Exact" solutions, for the regression problems DistND, refer to individuals whose symbolic expression reduces exactly to the target function f (impossible for MexHat, in the absence of Euler's number e) and, for the classification problems Spiral and Cenparmi, to those achieving a zero fitness. Our first question dealt with the best choice of model for the integrated error quantities over an independent parameter (such as n prog here). Based on experimentation with several curve types, we elected to fit b mse (or b mmr) and b bias to a four-parameter model err 4 . / D˛eˇ C 2 C , and c var to either the same curve, or to a straight line. Our choices are motivated in Annex B. Figure 4 shows the results. The data fits closely to the expected view of the bias-variance decomposition of a non-parametric learner over a complexity measure 3 . Indeed, as the maximum complexity of the evolved solutions increases, the bias term quickly drops to a level close to zero. Simultaneously, however, the variance term rises, showing an increased propensity to overfit. Clearly, selecting a maximum length too low will significantly sabotage results. An important question is, on the contrary, whether a practitioner could plausibly be expected to choose higher or intermediate values so as to favor good results. To verify this, we broke our independent variable n prog into a series of equally sized bands of length 50.
We report the mean b mse (or b mmr) over the best band, as opposed to over all runs, including the improvement and the certainty (according to a two-sample t -test): Hence, we conclude that some reasonable amount of one-dimensional experimentation with n prog could be expected to lead to improvements.
Variance due to genetic initialization
Here, we confirm our intuition regarding the role of choice of random seed for the efficacy of the evolutionary algorithm. Our goal is to estimate the proportion of variance resulting from the training samples T versus the random seed I . For our regression problems, MexHat and DistND, using the G short function set, we computed b mse, b bias and c var as described in Section 2. Note that the Spiral classification problem uses a static set of samples, hence could not be analyzed in this fashion. For the other classification problem, Cenparmi, we calculated b mmr. First, we used different random seeds I .k/ with the same training sample set T ("same T "); then, we used different seeds I .k/ paired with different sample sets T .k/ ("normal"). In both cases, the size of the sample set jT j was fixed, as indicated in Table 2. Finally, we computed a third experiment in which the training sets were larger ("large jT j"), with jT .k/ j D 6400 for the regression benchmarks and jT .k/ j D 600 for the Cenparmi benchmark. The results over approximately 50 runs for each trial are shown in Figure 5 Comparing the "normal" runs against the "same T " runs, we see statistically significant gains in performance for the latter in the case of the Cenparmi benchmark only, although the absolute difference is small. This implies a smaller role for the particularities of training set selection in the generation of variance, relative to the role of the initialization seed. Similarily, comparing the "normal" runs against the "large jT j" runs shows statistically significant gains for the latter in the MexHat benchmark only. This time, the reduction in variance due to the increased training set size is approximately 40% of total variance, leaving 60% due to initialization seed. For the other two benchmarks, there is negligible difference in c var. Again, we see that the selection of the initialization seed has more influence on the variance than the size of the training set, even when increased by a factor 16.
Therefore, it is clear that in these examples the majority of the variance associated with the error rates stems from the initial sample of genetic space. We would expect this to be reflected in the final genetic outputs. var on three benchmarks. Plots are "Tukey-style" boxplots: dark lines are median values, boxes are based on quintiles, whiskers represent the 95% confidence interval, circles are outliers.
Varying the population size
In this third series of experiments, we elected to explore the effect of the population size N pop (the steady number of evolved individuals f ) on the performance of the algorithm, given a constant number of evaluations N eval . This parameter plays here the role of a trade-off, which involves the amount of initial exploration taken by the EA (in a larger population), as opposed to the exploitation of the better individuals (in a smaller population). In order to avoid greater amounts of computation, we maintain the number of evaluations N eval D N pop C N new constant, i.e., diminish the number of individuals created via genetic operators, N new , as N pop grows.
We computed over 200 samples for each problem, with ranges of OE1; 4000. Due to the different role of parameter N pop , i.e., that of a trade-off rather than a measure of model complexity like n prog , we re-evaluated our choice of fitting curves to model the data and decided to use err 4 for all three error measures. These results are shown in Figure 6.
In two cases, we observe that the variance component of error drops to some minimal level, and then plateaus. This suggests that following some critical population size, an adequate sample of genotypic space is found. The bias component of error also drops initially, and then gradually begins to climb. This is likely due to a decrease in evolutionary evaluations, where unnecessarily large initial population sizes encroach on the time devoted to exploitation in the algorithm. (It is unlikely that the bias is caused by the discovery of difficult-to-find local minima via larger samples, since these would not only increase bias but also lower variance.) In the other two cases, no significant effect on variance was observed, suggesting that small populations sample the genetic space sufficiently well.
A key point here is that the lowest values of variance for all these problems is still significantly higher than the variance we associate with the selection of the training set (see Section 4.1). That is, we cannot reasonably expect larger initial samples of the genomic space to eliminate the variance due to initialization.
An interesting effect can be seen with the Dist3D benchmark: namely, the best results were observed with a very small population, followed by an increase in error rates, and finally a decrease. Indeed, the error scores seen at the larger population sizes are significantly better than the middle range. This difference is driven largely by bias, not variance. We are at a loss to explain this behaviour.
Again, we asked whether or not a practitioner could hope to select optimal values of N pop in order to increase success. We broke the possible values into bands of size 500. We summarize our results below (noting that no significant changes were observed with the Cenparmi runs): The conclusion here is that, in some cases, modest but significant improvements can be made by adjusting N pop .
Varying the function set
In a final series of experiments, we elected to vary the size of the function set, jGj, and its membership. Here, each run uses a random subset of G long as a selection of available choices for the evolutionary algorithm. In each subset G, the basic functions fplus, minus, times, divg were included by default. Next, an integer was chosen randomly and uniformly in OE0; 14 and that many additional functions were drawn from G long (see Table 1) to form the pool available to the evolutionary algorithm. Each function was equally likely to be chosen by genetic initialization or mutation. Results are shown in Figure 7. For all benchmarks save Cenparmi, there is a sharp increase in performance with the number of functions included (in the case of Cenparmi, the performance is unchanged at all sizes). It is immediately evident that the expected performance, in terms of b mse or b mmr, improves rapidly with more functions. Although there is some drop in variance, too, especially with values near four functions, the primary gains are made via reduction in b bias, until the value drops nearly to zero. The c var score, on the other hand, appears to plateau before this. The fact that c var does not begin to increase with more functions is interesting. It suggests that the addition of new choices to the function set is not an increase in model complexity, i.e., that it does not generally enable the production of things previously impossible. Instead, we should view it as a means of skewing the distribution of solutions so as to make relevant solutions more probable. Thus, we propose that the function set can be used to control the bias of the system, that is, introduce heuristics that may (or may not) be appropriate to a given problem.
If the above hypothesis is correct, we should be able to see changes to output associated with the addition of particular functions while the set size is held constant. To test this, we generated over 50 runs of the system where the function set was selected as above, but the size was fixed to 11 (the necessarily included functions fplus, minus, times, divg along with 7 additional randomly chosen functions from G long ). For each function, we compared the mean of b mse in those runs which included the function versus those runs which did not. Indeed, we discovered several important results. Below we list all those functions with significant certainty (p < 0:05) for the MexHat problem, noting that the mean b mse score over all runs is 0.0082 (see Figure 8 for a graphic comparison): The majority of the functions had an adverse effect (8 out of 14 increased b mse), implying that either they tended towards overfitting or that evolutionary effort was wasted on removing them from the potential solutions. The most significant single function, mag2, had a highly beneficial effect, decreasing the expected b mse score by about 67%.
Most of the improvement in efficacy when augmenting the function set can probably be ascribed to this single function. The most useful function, mag2, accounts for all gains when increasing the function set. This is not surprising, as mag2 is a repeated element in the target solution f Dist3D . Again, the majority of additional functions (10 of 13) have an adverse effect on the problem (increasing the fitness), but a very useful function can compensate this, and provide large gains to overall performance, primarily through elimination of bias. For the Cenparmi problem, there are several moderately significant functions, but none whose effect increased or decreased error by more than 0.005.
Conclusions
Our study has generally confirmed the view of GP as a low-bias and high-variance approach to regression and classification problems. Furthermore, our analysis of variation on the maximum program length n prog has shown results consistent with the bias-variance decomposition of a non-parametric learning technique.
We have reached several key conclusions from this study. While these results have been seen in particular contexts in the literature, here we contrast their effects between benchmarks, and quantify the expected effect. The conclusions are: -Initialization creates the most variance: The variance associated with GP runs is largely due to the initialization seed, and secondarily to the selection of training samples. Further, increasing the sample of the genomic space taken in the population cannot be realistically expected to reduce this variance. -Parameters can be optimized: For all three parameters that we examined (maximum program length n prog , population size N pop , and function set G), one-dimensional selection of a reasonably sized band of values usually led to significant improvements in overall results. Of the three parameters, the largest gains were obtained by making minor changes to the function sets: indeed, in three of four benchmarks, the inclusion of one appropriately chosen function affected performance more than the best expected gains from tuning the other two parameters. In none of the benchmarks was the inclusion of all functions detrimental. The consistency of these results between benchmarks suggests that this conclusion can be generalized. -Population size effects are unclear: The choice of population size, N pop , led to largely inconsistent results.
For two benchmarks, variance could be decreased with larger initial populations. Along with this decrease was an increase in bias, due to the lessened efforts devoted to genetic optimization. For the other two benchmarks, significant changes in variance were not seen. -Larger function sets are better: Regarding the choice of function set G for inclusion in the genetic search space, the widest possible space was consistently preferred by evolution, reflected in a steady decrease of regression or classifier bias to near-zero levels. This was true despite the fact that the majority of functions were demonstrably detrimental to the evolvability of the problem. Thus it appears easier for evolution to eliminate ill-suited heuristics than to construct well-suited heuristics from more primitive operators. In particular, when increasing the function set size, we found no increase in either the average error or the variance of the results, thus providing evidence against the hypothesis of Fitzgerald and Ryan [7]. -Well-chosen functions are best: In most cases we explored here, there existed some non-standard functions in the larger function set very well suited to the problem at hand. It is these functions which accounted for the majority of gain in efficacy.
Future directions
Today, GP is increasingly being applied to knowledge extraction, where a symbolic description of a given database is desired. For instance, GP serves to extract scientific hypothesis from selected databases [2,30,33]; extract symbolic features from image databases [15,16,25,34]; explore the space of network generators to create predictive descriptions of agent behaviours or complex networks [22,23]; and other engineering-related applications [18]. In all these tasks, the genetic component of the evolved solution has definite meaning, possibly independently of the evaluation of the solution.
The most popular philosophy of science generally admits any model which makes useful and testable (falsifiable) predictions, and is parsimonious [21]. These conditions, however, are the product of an age in which the general assumption was made that only a few competing hypothesis would be available at any time, and hence, that determination of the most accurate or parsimonious solution would be simple. In the case of automated knowledge extraction, the possibility exists that indefinitely many models can be posited without any clear means of determining a best one: generalization becomes a multi-dimensional question, and parsimony, if at all definable, is potentially subject to the non-computability of minimal program length.
While in some cases human-understandable (or even elegant) solutions are discovered [2,30], generally speaking, little attention has been paid to the matter. This study has shown that these issues are problem-dependent: in cases where a clear solution existed in the space (such as the DistND regression problems) genotypic convergence was possible, while in other cases (such as the MexHat regression problem) many competing genotypically distinct solutions existed. The consequences of consistent genetic diversity on the capacity to extract knowledge automatically remains to be investigated.
A A note on several other UCI databases
In the course of conducting this research, we also experimented with several popular data sets from the University of California, Irvine (UCI) [9]. They were explored in some detail, but ultimately rejected as inappropriate for this style of research. Specifically, we worked with the Breast Cancer Wisconsin (Diagnostic) data set [32], the Pima Indians Diabetes data set [31] (both original and corrected versions), and the Statlog (Australian Credit Approval) data set [29]. Performance was systematically tested by measuring MR for different program lengths: n prog 2 f1; 2; 20; 50; 100g. We discovered that in all three cases the naive application of GP was incapable of improvement when given additional complexity (i.e., increasing n prog ), relative to the natural stochasticity due to the selection of training and test sets. For all data sets, the difference in MR on randomly chosen test samples was not significantly different between n prog D 2 and n prog D 100 (over 30 runs, a textbook t-test did not discover any trends with p < 0:1). This implied that a simple threshold on one or two input variables was the best discoverable performance by a naive technique. Lest our results be interpreted as a failure of our particular approach to GP, we re-ran the same experiments using another non-parametric learner, a neural network. Specifically, neural networks with a varying number of hidden nodes were trained and tested on the above databases, and trained via backpropagation (using a sigmoid activation function .v/ D 1:7159 tanh.2v=3/, and 50 epochs of training). The number of hidden neurons used varied over the set f1; 2; 5; 10; 50; 100g and 30 runs. In all cases, the test error did not change significantly, save for the Diabetes database, where in fact the test error worsened significantly. An illustration of these results is shown in Figure 9. In conclusion of these findings, we deemed the above three databases too noisy for non-parametric learning, and recommend future researchers to proceed with caution.
B Curve selection
Selection of a model (curve) for data fitting was carried out using the MexHat domain, using the G short function set, and over 100 runs. All curves were fit using the Gauss-Newton method of non-linear regression. Goodness-offit error was the residual standard error. All polynomials up to degree seven were fit. We also tested three curves designed to resemble expected curve shape (from previous experiments with MSE): err 5 . / D˛eˇ C 2 C ı C err 4 . / D˛eˇ C 2 C err 4 0 . / D˛eˇ C ı C The best error rate for fitting the mse data was achieved by the err 4 curve (0.00809), slightly outperforming the other two exp curves, and even outperforming the more complex 7-term polynomial (0.00865). Further simplifications to the exp curves rapidly increased the error rate. Hence, we elected to use err 4 as a default guess for all curves, with other err curves substituted in the case of an improvement of error greater than 0.001. The var curves were typically modelled via straight lines, unless a curve improved error by more than 0.001. | 9,247 | 2016-01-01T00:00:00.000 | [
"Computer Science",
"Mathematics"
] |
SHAPER: A General Architecture for Privacy-Preserving Primitives in Secure Machine Learning
. Secure multi-party computation and homomorphic encryption are two primary security primitives in privacy-preserving machine learning, whose wide adoption is, nevertheless, constrained by the computation and network communication overheads. This paper proposes a hybrid Secret-sharing and Homomorphic encryption Architecture for Privacy-pERsevering machine learning ( SHAPER ). SHAPER protects sensitive data in encrypted or randomly shared domains instead of relying on a trusted third party. The proposed algorithm-protocol-hardware co-design methodology explores techniques such as plaintext Single Instruction Multiple Data (SIMD) and fine-grained scheduling, to minimize end-to-end latency in various network settings. SHAPER also supports secure domain computing acceleration and the conversion between mainstream privacy-preserving primitives, making it ready for general and distinctive data characteristics. SHAPER is evaluated by FPGA prototyping with a comprehensive hyper-parameter exploration, demonstrating a 94 × speed-up over CPU clusters on large-scale logistic regression training tasks.
Introduction
Cross-agency data collaboration maximizes the accuracy of Machine learning (ML) models.Nonetheless, from the perspective of user privacy and business interests, concerns about data privacy and security arise [ARC19].In practice, ML cannot be applied directly to health or financial data for competitive and regulatory reasons.These sensitive data sets are isolated by different parties, which is also known as the "isolated data island" problem.To solve this problem, privacy-preserving machine learning (PPML) [XBJ21] allows participants to collaborate on training and inference procedures by applying privacy-preserving computing techniques, e.g.multi-party computation (MPC) [Yao82], homomorphic encryption (HE) [FV12], and trusted execution environment (TEE) [CD16].These security primitives prevent the raw data, model weights, and gradient values from being revealed to any other participants.Since the algorithms and protocols of PPML heavily depend on the data characteristics, scale, ownership, and security model, debates on technical roadmap never stop.Fig. 1 shows an example of PPML in a healthcare scenario.A hospital and a pharmaceutical company collaborate to develop a predictive model for personalized medicine while protecting patient data.The parties have access to different sensitive patient records (labels and features).The parties use privacy-computing techniques to jointly train the model.The computational load is divided between the two parties, with each party performing local calculations and exchanging encrypted updates.The PPML scheme can prevent data security from being compromised beyond the trust barriers.On the one hand, the semi-honest parties act curiously and try to extract data privacy from each other.On the other hand, third-party adversaries can monitor the communication in the insecure network.The goal is to create an accurate model while preserving the privacy of individual patient data.
MPC covers a series of privacy-preserving techniques that support secure computation protocols on mathematically masked data.Garbled circuit (GC) is a secure two-party logical computation protocol, where the evaluation of each gate requires the transmission of a ciphertext look-up table.Secret sharing (SS) guarantees information-theoretic security by randomly sharing the raw data.However, arithmetic on the SS domain relies on intensive in-order data interaction.Even though MPC is versatile to different PPML scenarios, the network overhead always hinders the further development of MPC-based PPML with complex models in real-time applications.
HE-based schemes support multiple operators on encrypted data.Fully HE (FHE) schemes can ideally support any multiplication level by refreshing its noise budget with bootstrapping.Nevertheless, ciphertext evaluation and bootstrapping always require complex modular operations, which introduce tremendous computational overhead.Existing academic FHE accelerators are still expensive and only feasible on small-scale training and inference scenes [SFK + 22].On the other hand, additive HE (AHE) provides partial linear operators except for ciphertext-to-ciphertext multiplication with affordable overhead.However, purely AHE-based two-party schemes require a trusted party to generate and manage the secret key [HHIL + 17].
There are gaps between research and practice when it comes to PPML applications in the real world.In the real world, three or more parties usually involve more commercial interests and regulations, so two-party PPML is the most common use case.In addition, the features are usually sparse in practice, such as intelligent risk control or wire fraud detection, because of the feature engineering such as one-hot [CZW + 21].And the performance of PPML must also be considered.A task that takes a few minutes in non-private ML takes several hours when converted to PPML.Recent works show that hybrid SS-AHE solutions achieve 130× speedup with practical dataset and network bandwidth [CZW + 21, FZT + 21], compared with fully MPC-based PPML schemes.The key insight is to prevent the characteristics of the training set, e.g.sparsity, from being masked in the SS domain or encrypted in the AHE domain.This is achieved by keeping the samples as plaintext within their owner and only transferring small-size intermediate values in the HE domain.Participants can evaluate the layer functions with sparse operations and share the result in the SS domain other than revealing any sensitive values to one participant or a third party.
However, no existing hybrid PPML work tackles the challenges of co-designing implementations and optimizations of PPML protocols.New architectural considerations and methodologies are required when the complex HE algorithm combines SS protocol in the end-to-end PPML solutions.We observe that the computation and communication complexity, which are the bottlenecks of the two primitives, can complement each other.The standalone SS and HE approaches present a highly polarized communication-computation ratio, for which latency hiding between the data transfer and execution units provides little return.We optimize the hybrid approach based on the intuition that a well-balanced and parallel communication-computation flow can ideally reduce latency by 50%.This observation can also make the architecture less sensitive to network bandwidth, which typically dominates MPC performance.At the algorithmic level, it is helpful to tune hyperparameters, such as an overflow-free pack level, to mitigate ciphertext explosion.Since practical computational settings are also critical for PPML, a ready-to-use architecture should be suitable for Field Programmable Gate Array (FPGA) platforms.
This paper presents a general architecture that can efficiently execute the SS-AHE hybrid PPML protocols on the large industrial-level training dataset.The architecture can generally handle different PPML tasks using hybrid primitives.The proposed design preserves privacy in either the SS domain or the AHE domain without relying on trusted hardware manufacturers.Compared with existing software-only hybrid PPML schemes [CZW + 21, FZT + 21], the co-designed architecture takes advantage of hardware units, and has more potential for optimization and acceleration.In summary, this paper makes the following contributions: • A hybrid Secret-sharing and Homomorphic encryption Architecture for Privacy-pERsevering ML (SHAPER) with algorithm-protocol-hardware co-optimization between CPU, hardware accelerators, and network collaboration.SHAPER's hardware design improves throughput, and its software design optimizes data flow through system scheduling for latency overlap and parallelization.
• Vectorized high-performance modular multiplication (MM) engines to improve the efficiency of encryption, decryption, and ciphertext domain evaluation.We present new algorithmic and hardware optimizations for these operations of Paillier, including new MM algorithm, new hardware engine, pipelined execution, etc.
• SHAPER shows universal performance improvement on micro-operations and reduces the end-to-end latency by 94× on large-scale logistic regression training tasks, compared with the software-only benchmarks.
Background
Descriptions of backgrounds, threat model, and primitives are discussed in this section before introducing our SHAPER architecture.
Related Work
Various PPML schemes have been proposed to ensure the security of data and models with different cryptographic primitives.Actually, MPC-based PPML schemes [KVH + 21, Kel20, ZXWG22] divide ML models into fragments of circuits, and then engage multiple parties to cooperatively perform circuit computations, including arithmetic and binary circuits, without additional privacy leakage.Afterwards, the results of these fragments of circuits are collected by the parties to construct the complete result of complex computational tasks.Historically, MPC was proposed in [Yao82], which solved the "Millionaire Problem" with GC. 20] provides the capability to perform operations on encrypted data to protect privacy.Unlike public-key cryptography, AHE supports not only key generation, encryption, and decryption, but also addition/multiplication over ciphertexts without private keys, thus revealing no information about the corresponding plaintexts.Due to the additions and multiplications that one can perform on the ciphertexts, HE-based PPML requires less communication than MPC-based PPML, but requires more computation for expensive HE encryption/decryption.Fig. 2 describes a typical linear function in PPML, the sparse matrix is kept by its owner, Alice, and the result is shared between the participants Alice and Bob.Since AHE protects the confidentiality of the vector y, Alice cannot recover the plaintext from the ciphertext [y] b .On the other hand, Alice shares [z] b in line 5, which guarantees that Bob can only learn a masked result z b .Recent works on the hybrid SS-AHE PPML [CZW + 21,FZT + 21] framework achieve 130× speedup over MPC-based schemes.AHE supports additions between ciphertexts and multiplications between ciphertexts and plaintexts.However, most of the existing AHE algorithms, such as Paillier [Pai99], DGK [DGK07], OU [OU98], depend on large integer modular operations, especially modular multiplications (MM) and exponentiation (ME), which incur large computational overheads.Therefore, the overall performance of SS-AHE hybrid PPML is strongly dominated by the efficiency of the basic modular multiplications.Montgomery modular multiplication [Mon85] is the most classical method, while new modular algorithms have also been proposed recently [LC21].
Paillier Cryptosystem
We choose Paillier as the AHE example in our architecture.The Paillier cryptosystem consists of the following interfaces.
As suggested in [DJ01, CGHGN01], we choose primes (p, q) which satisfy p = q = 3 mod 4 and gcd(p − 1, q − 1) = 2 and set g = n + 1, so that g m can be simplified as: And we have µ = λ −1 .The key generation randomly selects x ← Z * n , and adds h s = −x 2n mod n 2 into the public key.Then the encryption is modified as c = (mn + 1)h a s mod n 2 , where a is randomly chosen in Z . The optimization has two advantages.First, the exponentiation g m is simplified as a multiplication mn.Second, since a is much shorter than n, it is easier to compute hs a than r n .
Additive Secret Sharing
A value additively shared by two parties refers to [[x]] = (x 1 , x 2 ), where x i = x over field F, and (x 1 , x 2 ) are random.The addition over additive shares is almost free, as [[x + y]] = (x 1 + y 1 , x 2 + y 2 ).The multiplication over shares is more tricky.A common approach is to use Beaver triples [Bea92].The Beaver triple is three shared random values
Host
On-Chip [
SS-AHE Library
MPC-based PPML schemes require a large number of beaver triples because each multiplication consumes a triple.Beaver triples can be generated in batch using Paillier [DSZ15, P + 13].
Threat Model
As a co-designed architecture, the threat model of SHAPER takes into account cross-layer assumptions.
At the protocol level, the adversary model follows the semi-honest assumption in a 2-party setting, as SHAPER mainly focuses on implementing and accelerating existing semi-honest schemes [FZT + 21, CZW + 21].In the semi-honest model, a probabilistic polynomial-time adversary with semi-honest behaviors controls one of the parties and the adversary can corrupt and control one party, and try to learn more information about the other honest party's input, such as recovering the secret messages sealed in the ciphertexts or shares.Meanwhile, the adversary is required to follow the protocol specification honestly.The semi-honest setting is adopted by most existing PPML models, such as [MZ17,MR18].
At the algorithm level, including SS and AHE, the security is given as a security parameter, which defines the hardness of the algorithm the adversary attempts to break.The parameter is positively related to the key lengths.A 2048/3072-bit Paillier cryptosystem corresponds to a 112/128-bit computational security parameter.
Architecture Design
To accelerate the hybrid SS-AHE framework, SHAPER proposes an instruction set and explores efficient design methodologies of AHE, SS, and conversion functions.
Architecture overview
An overview of our proposed SHAPER architecture is shown in Fig. 3, which includes both software and hardware implementations.The host application controls the start and convergence conditions of the training tasks, and also consults the hyper-parameters between the participants, such as the optimal plaintext packing level, the pre-computation window size, etc.The on-chip hardware modules aim at fast computation on basic primitives, mainly including AHE and SS function units.Since AHE computation is still a performance bottleneck of hybrid PPML schemes [CZW + 21], we design new MM algorithms and hardware engines in the AHE units, implement algorithmic optimizations in hardware, and improve the scheduling modules to achieve better acceleration.
SHAPER focuses on 2-party PPML, which is the most common case in industrial applications.The application calls the SS-AHE library, which supports execution flows encapsulated as kernel functions.The kernel functions update algorithm parameters and architecture flags by setting control and status registers (CSRs), and implement the security primitives with customized instructions summarized in Table 1.SHAPER analyzes the control flow dependencies and packs the instructions in VLIW style, ensuring that the packed instructions in a VLIW instruction can be executed in parallel.SHAPER adopts the static scheduling scheme.Each VLIW instruction packs RISC instructions which decode and issue synchronously.Since the instructions are executed sequentially and deterministically, memory allocation is scheduled in a static manner.To communicate with other participants, all network interaction is handled by a network interface card (NIC).The host application always waits for the NIC and SHAPER to interrupt.Since the runtime and driver layers are common components in HW/SW co-design, we omit them in Table 1 for brevity.
On the SHAPER hardware, the parser unpacks the instructions and dispatches them to the appropriate function units.AHE.init reloads data from device memory during the offline phase when the host updates its key pair.Other AHE instructions consist of a series of MM operations handled by the AHE controller.SS.gen returns a vector of random shares sampled from the cryptographic-secure pseudorandom number generator (CSPRNG).Int.add and Int.mul perform a series of integer arithmetic operations in a continuous address space.The memory hierarchy consists of the on-board device memory and the on-chip scratchpad managed by DM.ld/st and SPM.ld/st.
Algorithm-Protocol Co-Optimization
Fig. 4 describes the methodology for analyzing and exploring the PPML solutions.We map a task to the coordinate point according to the computational and communication overhead.The network bandwidth is represented as a dotted guideline, points on which have the same communication and computation latency.The schemes above the guideline (e.g.SecureML [MZ17]) are communication dominated.On the other hand, the communication-less FHE solutions (e.g.CraterLake [SFK + 22]) cost most of the time for ciphertext evaluation.The position of SS-AHE-based solutions depends on computational power, especially the performance of cryptographic engines.In our work, the following optimizations are applied to explore an optimal solution.
Data Characteristic
In real-world scenes, the training dataset is sparse due to incomplete user information and one-hot encoding [CZW + 21].Since SS-AHE schemes preserve the data sparsity, the number of instructions is significantly reduced.
Plaintext Packing
Packing multiple ciphertexts of short plaintexts into one ciphertext greatly reduces the number of ciphertexts and allows SIMD-style computation [P + 13], as explained in Sec.3.5.The packing strategy reduces the communication overhead for transmission and the computational overhead for decryption at the expense of additional homomorphic computation over ciphertexts. .
Latency Hiding
Since the SS-AHE schemes have balanced overhead, overlapping computation and communication brings more benefits.Fig. 5 shows the pipeline execution process of SHAPER, corresponding to line 1 to 3 in Fig. 2. The AHE encryption is the most time-consuming operation in the example, and can hide other delays.Once the first encryption is complete, the second encryption and the transmission of the first ciphertext are performed in parallel in a pipelined flow.In this case, the computation instructions overlap the communication delay.SHAPER consumes the data as soon as the source data is created with multi-buffer transfer.
Efficient AHE Function Units
The AHE unit of SHAPER consists of a Paillier controller and several MM engines.The controller manipulates MM engines to compute the functions of the Paillier cryptosystem with key length |n| = 3072 in parallel.Each MM engine implements our proposed fast MM algorithm, which supports a 5-stage pipeline.To accelerate the modular exponentiation (ME) in the Paillier encryption, a set of Ultra-RAMs (URAMs) and Block-RAMs (BRAMs) are deployed to store the public/private keys of the device, as well as some pre-computed values.
When executing an AHE instruction, the controller divides it into multiple multiplications and exponentiations based on DJN optimizations of Paillier [CGHGN01].Several optimizations suggested in [DSZ15] are considered, including Chinese-Remainder-Theorem (CRT) optimization and fixed-base pre-computation (see Appendix B), which scales down both the base size and the exponent size of the ME.The call to a single ME is divided into multiple multiplications in SHAPER, and the controller then schedules the datapath between different MM engines to compute the ME collaboratively.
The performance of MM engines has a large impact on the efficiency of various AHE interfaces and higher-level applications.Therefore, we propose an efficient MM construction with optimizations in both algorithm and hardware implementation.
The MM Algorithm
Our proposed MM algorithm is inspired by the shift-sub algorithm in [LC21] (see Appendix A), which has the advantage of dealing with large integers.The algorithm requires multiple serial full adders, one for each bit of b, which results in long data paths.To avoid multiple serial additions of large integers, we propose a high-radix shift-sub MM algorithm as described in Alg. 1.Our high-radix shift-sub deals with k bits of b in a single iteration, rather than a single bit, where k is the radix width.Single-bit shift sub in [LC21] deals with a single bit of b in each iteration.Therefore, the strategy does not work well in hardware design as k grows, since it leads to too many cycles when dealing with significantly large a and b.A more efficient MM algorithm is needed to speed up Paillier in hardware.
Our high-radix MM algorithm processes k bits of b in each round, and has τ rounds in total.Each round consists of a Multiply-Accumulate phase (Phase_c) and a Shift-Reduce phase (Phase_a).In the i-th round, Phase_c multiplies the i-th piece of b by the current round's a and adds the product to the accumulation of previous rounds.In the first τ − 1 rounds, Phase_a updates the next round's a with the current round's a. a is modulo reduced after shifting k bits to the left.In the final round, Phase_a modulo reduces the accumulation of Phase_c to get the final result.The correctness of the algorithm is guaranteed: Note that except for the final round, there is no data dependency between Phase_c and Phase_a.Therefore, Phase_c and Phase_a can be executed in parallel to reduce latency.After the latencies of multiplication and addition in Phase_c are hidden by parallelization, the total execution time of one MM is reduced by more than 30%.
Since the modular reductions of Phase_a have additional length constraints, we propose a quick modular reduction algorithm QR in Alg. 2. We note that the inputs of the modular reduction have upper bounds.Each round's a k is less than m k, and the final round's c is less than τ m k.Therefore, the QR algorithm limits the length of the dividend to no more than (l + ∆), where l is the length of the modulus m.The ∆ is set to k in the first τ − 1 rounds and to k + log τ in the final round.The radix k has a large impact on the total number of rounds, as well as the efficiency and consumption of hardware implementations in SHAPER.Different choices of k are discussed in the next subsection about hardware implementation.
We propose and adopt a new strategy using the Most Significant Bits (MSB) approximation to simplify the reduction.Unlike the remainder (i.e., the output of the modular reduction), the quotient in a division is mainly determined by the MSBs of the dividend and divisor, while the lower bits contribute little to the quotient.Therefore, the algorithm approximates a quotient γ with the MSBs of a and m, and then computes an approximate remainder with a − γm, which is then modified to the result with a conditional subtraction.The error between the approximated and the precise quotients is proven to be within 1 if we use the most significant ∆ + 2 bits of m for the approximation, as in Eq.(4,5).(Note that ∀x, y ∈ R, if |x − y| ≤ 1, then | x − y | ≤ 1. ) Furthermore, the existing Barrett approximation [Bar86], which converts the division of a by m + 1 into the product of a and m , is further used to simplify the quotient computation, which involves a deviation of no more than 1, as Eq.(6,7) shows.Therefore, at most two conditional subtractions are needed in the algorithm.
In fact, QR computes b = a − (γ + 1)m instead of b = a − γm.A small change is made to accommodate the hardware implementation.Additions over large integers are not cheap in hardware.Direct computation of b = a − γm results in two additions in the worst case.But when switching to (γ + 1)m, the hardware engine determines whether to compute b − m or b + m based on the sign bit of b.Computing γ + 1 is cheap because γ is short, and this small cost reduces the additions of large integers here from 2 to 1.The optimization effectively reduces the consumption of on-board resources in the hardware implementation.
The MM Engine
The MM engine (shown in Fig. 6) is the fundamental processing element that supports our MM algorithm.It can be divided into two modules: one for Phase_c and one for quick reduction in Phase_a respectively.Phase_c contains a block multiplication (BM) module and an adder module for accumulation, consisting of a carry-save adder and a ripple-carry adder.Phase_a contains a multiplier to compute γ, a BM module for −(γ + 1)m, an adder for a − (γ + 1)m, and a Conditional Subtraction (CS) module for correction.A CS module contains an adder that performs either −m or +m.Note that the subtraction −m is replaced by +m_n, where m_n is the complement of m.Phase_a and Phase_c are updated in parallel to compress the total number of clock cycles.Two phases need no data exchange except for Phase_c fetching a at the beginning of each round.Also, to run an integrated MM, a controller is needed to schedule the input/output of the MM engine in each round.
We implement the BM modules with multiple multipliers on a smaller scale.Specifically, a k × 3072 multiplication is divided into k × k parts, whose subproducts are combined into two large integers.The k × k multipliers are implemented using on-board digital signal processing (DSP) units.
When exploring the design space of on-board resources and hardware clock cycles, we choose radix k = 72.A single piece of DSP supports 27 × 18 multiplication.For example, implementing 64 × 64 multiplication requires 12 DSP units, but the DSP utilization rate is only about 70%, since 12 DSP units theoretically allow 81 × 72 multiplication.The utilization rate peaks at 100% when the multiplier width equals 54 or 108.At 54, a multiplier needs only 6 DSPs, but the round number τ rises to 57 with a 3072×3072 multiplication, leading to more clock cycles of the MM engine.In contrast, in the case of 108, there are only 29 rounds, but one multiplier requires 24 DSPs, making the MM engine too large.A larger MM engine consumes more resources (especially DSP).Therefore, fewer MM engines can be placed in the FPGA implementations, which reduces the overall hardware parallelism.In addition, a larger engine has longer data paths, further reducing the frequency of the hardware implementation.
Considering the trade-off between time and space, we choose the case of the 78-bit multiplier, which requires 40 rounds of multiplication and 12-DSP multipliers.Although the DSP utilization rate cannot reach 100%, it is still higher than 90%.For hardware compatibility of the final round, the hardware implementation should support k + log τ bit quick reduction, as shown in Fig. 6.Therefore, the radix k is finally fixed to 72.
Another bottleneck in the design of an MM engine is the 3072-bit addition, because it introduces large logic delays that limit the hardware frequency.In our design, however, we optimize serial adders with a prediction strategy, along with splitting two addends into multiple 128-bit chunks.Each such chunk (x, y) uses two 128-bit ripple-carry adders to compute two potential sums, x + y and x + y + 1.Using the carry bit propagated from the lower chunk, a multiplexer selects one of the summations and propagates the corresponding carry bit to the higher chunk.Since x + y + 1 ≤ 2 × (2 128 − 1) + 1 = 2 129 − 1, the propagation will not lead to the growth of the carry bit, and there is at most one carry bit during the propagation, which guarantees the correctness of the strategy.
We set the chunk size to 128, taking into account resource consumption and maximum frequency.When the chunks are large, the logic delay within each chunk is still large, and the frequency cannot be improved efficiently.However, when the chunks are particularly small, although the resource consumption for each chunk is reduced, the logic delay outside the chunks to merge the subsums into the final output increases.And this also leads to a decrease in frequency.Therefore, we set the chunk size to 128 to get the peak frequency.
The acceleration of the MM engine over the MM implementation on a standard CPU is discussed in section 5.3.
Paillier Controller
A 3072-bit Paillier cryptosystem has a 3072-bit message space (|n| = 3072) and a 6144bit ciphertext space (|n 2 | = 6144).Making the hardware compatible with the 6144-bit modulo operation is a waste of on-board resources.And our Paillier controller uses Chinese Remainder Theory to convert 6144-bit modulo operations in encryption and decryption to 3072-bit modulo operations.We follow the dataflow of open-sourced Paillier implementation of [DSZ15], and transform it into a micro-instruction control flow that takes more advantage of the MM engines.CRT gives a unique solution to simultaneous linear congruences with coprime moduli.Since n 2 = p 2 q 2 , CRT transforms modulo operations over n 2 into modulo operations over p 2 and q 2 .The prerequisite for CRT optimization is obtaining the private key, since the private key λ can be computed as λ = (p − 1)(q − 1)/2.In public key cryptosystems, it is assumed that the encryptor does not have the private key.However, in HE (including AHE) scenarios, the encrypting party usually has the private key.HE scenarios in hybrid PPML schemes are analogous to proxy execution, such as the matrix multiplication in Fig. 2. Both encryption and decryption are handled locally by the client, and the server only handles execution over ciphertexts.Therefore, it makes sense to optimize Paillier encryption on the client side with CRT.Encryption.Eq.8 shows the DJN-Paillier encryption.
To optimize hardware computation with CRT, the controller first computes the projections of c over the modulo field p 2 and q 2 .c p = c mod p 2 = [(mn mod p 2 ) + 1] × ((hs mod p 2 ) a mod p 2 ) mod p 2 c q = c mod q 2 = [(mn mod q 2 ) + 1] × ((hs mod q 2 ) a mod q 2 ) mod q 2 (9) (hs mod p 2 ) a mod p 2 and (hs mod q 2 ) a mod q 2 are under fixed bases depending on the public keys, and can be computed with precomputed tables.The details of computing ME under fixed bases with precomputation are explained in Sec.4.2.After computing c p and c q , the ciphertext c can be recovered.
(p −2 mod q 2 ) mod q 2 also depends on the keys, and will be precomputed during key generation.The control flow of Paillier encryption at the micro-instruction level is listed as follows.ME_P refers to modular exponentiation with precomputation.Note that the final step of encryption, c p + t c × p 2 , necessarily requires 6144-bit computations, so the hardware sends back c p and t c to the host to obtain the ciphertext.
The controller follows the same CRT strategy to calculate the intermediate To continue the decryption, a naive approach is to send d p and t d back to the host, which recovers d, calculates d−1 n , and returns it to the hardware.However, this approach obviously lacks efficiency, since it involves a round of communication for each decryption.Therefore, we expect the controller to compute m directly using d p and t d .
For any legal plaintext-ciphertext pair (m, c), the correctness of Paillier holds as c λ − 1 = λmn(modn 2 ).Since n = pq, we have d − 1 | p, and of course d p = d mod p 2 > 0. Suppose p is the smaller prime between (p, q), then d p < p 2 < n.Therefore eq.14 holds.
The control flow of the Paillier decryption at the micro-instruction level is listed as follows.RED modulo reduces a 6144-bit input with a 3072-bit modulus, and MDIV returns the quotient of the three inputs x × y/z.Both RED and MDIV can be supported by a slightly modified MM engine.Specifically, Phase_a can independently handle RED in τ rounds, and MDIV can be implemented by collecting the corrected γ in each round of Phase_a and merging them into the final quotient.
Secret Sharing Function Units
Although computation is not the critical overhead in SS-based schemes compared to communication, we design a dedicated SS unit in SHAPER due to the following latencyrelated concern: In hybrid PPML schemes such as [CZW + 21, FZT + 21], the computation of AHE and SS is interleaved, which means that the data must be transmitted frequently between the host and the hardware if the hardware is not capable of computing SS functions locally.Therefore, each transfer requires reading/writing from device memory, and introduces non-negligible redundant latency.
The SS unit consists of multiple integer processing engines and a CSPRNG.The CSPRNG generates the random numbers used in SS schemes.And the integer processing engines support computation over 64-bit integers, which is a common choice in SS-based schemes.
For higher random number generation throughput, we have optimized the CSPRNG in the SS unit with several improvements.Actually, existing CSPRNG constructions in PPML usually use ECB-mode AES encryption, which benefits a lot from AES-NI hardware extensions.However, recent works [XHY + 20] pointed out that SHA3-based CSPRNG would outperform AES hardware implementations because SHA-3 takes advantage of its 1600-bit Keccak structure and fast binary executions, resulting in higher throughput during each iteration.In addition to the SHA-3 Keccak engine, we also use a first-in-firstout (FIFO) buffer to cache the generated random numbers.The SHA-3 Keccak engine dynamically generates random numbers and pushes them into the buffer when it is not full.And SS units pop random numbers from the buffer as needed.The strategy packs different ciphertexts into one.For example, if the server normally computes x 1 y 1 and x 2 y 2 over ciphertexts, two ciphertexts c x1y1 and c x2y2 are sent back to the client.And the client decrypts them to get the plaintexts.However, when using the packing strategy, the server computes the ciphertext of x 1 y 1 + x 2 y 2 × 2 i .Then the client decrypts the ciphertext and truncates the plaintext to get x 1 y 1 and x 2 y 2 .This reduces the number of decryptions from 2 to 1.The packing strategy works if x 1 y 1 < 2 i , otherwise an overflow occurs and the MSBs of x 1 y 1 get mixed with the LSBs of x 2 y 2 .Also, x 1 y 1 + x 2 y 2 × 2 i should stay within the message space.
Conversions between Primitives with Packing
The Paillier message space (3072 bits) is too large for the values in the models (within 64 bits), and decryption in Paillier costs much more than encryption.Therefore, the space can be divided into smaller buckets, with a smaller value in each bucket.The computation results in each bucket will not interfere with others if the bucket size is large enough to ensure that there is no overflow in the subsequent computation.Since there are fewer ciphertexts to send and decrypt, both communication and computation are greatly reduced.
The optimal bucket size depends on the computation under encrypted values in different protocols.In hybrid schemes, the optimal bucket size is roughly (m + 1)l + log(a + 1) + σ to ensure that there is no overflow in each bucket [P + 13], where l is the share length, usually equal to 64. m and a are the numbers of multiplication with plaintext shares and addition with other shares.σ is the statistical security parameter of the scheme, which is 40 by default.For example, AHE handles matrix multiplication in [CZW + 21], where one multiplication and multiple additions are processed with each ciphertext.And the bucket size can be set to 180 by default, where each ciphertext contains about 17 buckets.The 180-bit bucket size remains valid unless the number of additions in the matrix multiplication exceeds 2 12 .Then the decryption overhead can be reduced at the expense of more ciphertext additions and plaintext multiplications for packing.
Performance Optimizations and Security Enhancement
Several optimizations are applied to our implementation to improve performance and FPGA resource efficiency.
Parallel Modular Operations
We observe that there are a large number of matrix computations in real-world PPML scenarios [CZW + 21, FZT + 21], consisting of multiple AHE operations without data dependency.Meanwhile, a single Paillier encryption can also benefit from parallelization, since fixed-base pre-computation is involved to improve efficiency.Therefore, we provide support for vectorized modular operations in our design.
The pipeline implementation of the MM engine has five stages for each iteration, as shown in Fig. 7.Each stage takes 4 execution cycles.Since Phase_a has a longer datapath than Phase_c, we divide the datapath into five.The division (Div) stage computes the Barrett division in Alg. 2 to obtain γ.The Reduction Computation (RC) stage multiplies γ + 1 by −m.The CSA stage includes the carry-save adders to merge c + b i a − km into a single addition, and the Add stage includes an optimized ripple-carry adder.The CS stage performs the conditional subtraction of a.The pipelined datapath of Phase_c consists of 3 stages, BM, CSA, and Add.The block multiplication (BM) stage computes b i a in Alg. 1, and the hardware implementation of the BM stage is identical to the RC stage in Phase_a.Phase_c and Phase_a in the same round can be executed in parallel, so the latency of Phase_c can be overlapped by Phase_a except for the final round.Therefore, pipelining brings almost 5× performance improvement to the MM engine.Besides pipelining, we also use multiple MM engines on FPGA to improve parallelism.
Optimal Pre-computation Window
The ME in Paillier encryption is under fixed bases depending on the public keys.An optimization using this insight is to store all ME of short powers (e.g.window) in the offline phase.Large integer ME are converted to multiple MM operations in the online phase [BGMW92].Enlarging the precomputation window can reduce ME latency.However, the maximum window size is limited by the on-chip memory size, since a larger window has a larger enumeration space.The size of the pre-computed table S pre for encryption depends on the window size w and the key length |n|.Eq.16 shows the theoretical estimation of S pre based on w and n.
The precomputed table sizes for different window sizes in a 3072-bit Paillier cryptosystem are shown in Table 2.The number of MM operations in a precomputed ME also depends on the window size.When the window size is 4, the required memory size for the precomputed table is about 34 MB.If the window size increases to 8, the size increases to about 287 MB.However, the number of windows is only reduced from 384 to 192, and the cost-effectiveness of the increased storage and reduced multiplication is significantly lower.Considering the URAM size of the hardware implementation, SHAPER provides the interface AHE.init to reload the precomputed table with the default window size of 4.
Implementation and Evaluation
We implement the prototype of SHAPER on a Xilinx 16nm VU13P FPGA using the Xilinx Vivado toolchain.MM engine is important in the hardware implementation of SHAPER, and its throughput significantly influences the performance of high-level functions and applications.We evaluate the throughput of the MM engine in Table 4, compared with state-of-art MM designs in [BJ20, YHC20, XYCL22].Since it is unfair to discuss throughput without considering resources, these designs are evaluated based on the average throughput generated by each piece of DSP.In specific, the throughput is measured as the operations or output bits executed by the MM engine.Existing MM implementations usually focus on 1024 or 2048-bit MM operations, while the MM in SHAPER needs to fit in the 3072-bit Paillier cryptosystem.It makes SHAPER handle fewer MM instructions than [XYCL22, YHC20], as their benchmarks are tested with 1024-bit MM.However, considering the output length, our MM engine shows advantages compared with other proposals.
MM Throughput Comparisons
It is notable that our MM engine requires more DSP units than other designs.Because of the pipelining optimization, the DSP units cannot be reused across different stages.So our design assigns different DSPs for each stage, leading to more DSP utilization.
Function-Level Comparisons
We evaluate the latency of general functions, including modular operations, Paillier functions, and several MPC-level functions.The latencies of these micro-benchmarks are shown in Table 5.The inputs of the MM and ME benchmarks are as long as the key length, and the length of plaintexts in Paillier is set to 64 bits.We test the performance of SHAPER with different settings.To fairly compare the latency of our MM engine in SHAPER with the cryptography processor (CP) in [BJ20], we implement a single MM adopted as the performance baseline, whose latencies are taken from [CZW + 21].SHAPER performs 94× faster than CAESAR executed on the CPU when both using 2048-bit Paillier (112-bit security).The acceleration is mainly due to the fast Paillier encryption and pipeline execution.Even when the key is lengthened for 128-bit security (3072-bit key), SHAPER still performs 7.2× better than OU-based CAESAR with 112-bit security.In addition, most solutions of hybrid schemes show significant efficiency gains compared with SS or HE-based solutions, confirming the performance advantage of hybrid PPML schemes.SecureML performs the worst among the solutions since SS-based solutions mask sparse features to dense data shares.
Conclusion
In this paper, we propose SHAPER to accelerate hybrid SS-AHE PPML protocols.The algorithm-protocol-hardware co-design methodology explores the full-stack techniques to minimize the end-to-end latency in various network settings.SHAPER further supports secure domain computing acceleration and the conversion between mainstream privacypreserving primitives, making it ready for general and distinctive data characteristics.We provide a prototype of SHAPER on an off-the-shelf FPGA with several hardware optimizations.Our evaluation shows that SHAPER provides significant speedup over CPU clusters on a large-scale logistic regression training task.
Figure 1 :
Figure 1: PPML allows two parties to securely train ML models on sensitive data.
Figure 3 :
Figure 3: SHAPER Architecture Overview -The grey and blue boxes represent software and hardware components, respectively.
Figure 4 :
Figure 4: Exploring optimization space on data characteristics and algorithms.The example network bandwidth is 50Mbps.Applying the optimizations reduces the encryption overhead for the 40Mbps and 160Mbps throughput configurations.
Figure 5 :
Figure 5: The pipeline execution process of SHAPER, corresponding to line 1 to 3 in Fig. 2. Two successive executions overlap their latency.
Algorithm 1
High-radix Shift-sub Modular Multiplication.MM(a, b, m) Require: Radix width k Require: a
Figure 6 :
Figure 6: The architecture of a single MM engine based on the MM Algorithm.
SHAPER supports an efficient SIMD-style conversion between SS and AHE.We adopt and improve the conversion protocols in [FZT+ 21].Details are shown in Appendix C. The conversions can be optimized with the packing strategy proposed in [P + 13].
Figure 7 :
Figure 7: Pipelined modular multiplication engine.Each round of MM in Alg. 1 is divided into five stages.In the first τ -1 rounds, the accumulation phase (c) and the QR phase (a) are executed in parallel, and in the final round the phases run in serial.
Table 1 :
The instruction set supported by SHAPER.
* The argument len is the length of input or output data.The arguments _ptr is the physical base address of a specific data structure.
Table 2 :
Pre-computed table sizes under different window sizes when |n| = 3072.
Table 3
shows the resource usage of SHAPER.The maximum clock frequency is 285 MHz by default.As the most expensive module, 14 MM engines are used considering performance and LUT consumption.32 integer engines are used to support vectorized SS operations, contributing little to the overall consumption.Only one CSPRNG is used because its throughput is over 2.6 Gbps, which is sufficient for existing hybrid schemes.The resource consumption, excluding the controllers, is about 40% LUT/FF and 75% DSP in terms of the total FPGA resource.75% of URAM is used for the precomputed table, which is a good balance between performance and area.
Table 3 :
Resource utilization on the Xilinx FPGA.
* Measured by percentage in terms of Xilinx VU13P FPGA.
Table 4 :
Comparison between the Hardware Performance of MM implementation. | 9,518.6 | 2024-03-12T00:00:00.000 | [
"Computer Science"
] |
Wolbachia Utilize Host Actin for Efficient Maternal Transmission in Drosophila melanogaster
Wolbachia pipientis is a ubiquitous, maternally transmitted bacterium that infects the germline of insect hosts. Estimates are that Wolbachia infect nearly 40% of insect species on the planet, making it the most prevalent infection on Earth. The bacterium, infamous for the reproductive phenotypes it induces in arthropod hosts, has risen to recent prominence due to its use in vector control. Wolbachia infection prevents the colonization of vectors by RNA viruses, including Drosophila C virus and important human pathogens such as Dengue and Chikungunya. Here we present data indicating that Wolbachia utilize the host actin cytoskeleton during oogenesis for persistence within and transmission between Drosophila melanogaster generations. We show that phenotypically wild type flies heterozygous for cytoskeletal mutations in Drosophila profilin (chic221/+ and chic1320/+) or villin (qua6-396/+) either clear a Wolbachia infection, or result in significantly reduced infection levels. This reduction of Wolbachia is supported by PCR evidence, Western blot results and cytological examination. This phenotype is unlikely to be the result of maternal loading defects, defects in oocyte polarization, or germline stem cell proliferation, as the flies are phenotypically wild type in egg size, shape, and number. Importantly, however, heterozygous mutant flies exhibit decreased total G-actin in the ovary, compared to control flies and chic221 heterozygous mutants exhibit decreased expression of profilin. Additionally, RNAi knockdown of profilin during development decreases Wolbachia titers. We analyze evidence in support of alternative theories to explain this Wolbachia phenotype and conclude that our results support the hypothesis that Wolbachia utilize the actin skeleton for efficient transmission and maintenance within Drosophila.
generations. We show that after only two generations in a phenotypically wild type, heterozygous mutant fly, Wolbachia infections are cleared or reduced in titer. Characterization of the mutants suggests that Wolbachia is sensitive to the regulation of actin in the ovary and that actin may be used by Wolbachia to both target and proliferate within host tissues and to be faithfully, maternally transmitted.
Here we present data showing that Wolbachia persistence and transmission within Drosophila melanogaster is sensitive to mutations affecting the actin cytoskeleton. The importance of actin during Wolbachia infection was investigated by acquiring Drosophila mutants in actin binding proteins, both involved in the regulation of F-actin filaments: the homologs of profilin (chickadee), which regulates the formation of filamentous actin, and villin (quail), which bundles actin filaments. We show that flies heterozygous for mutations in profilin (chic 221 /+ and chic 1320 /+) or villin (qua 6-396 /+) lose Wolbachia infection after only a few generations. Importantly, the effect is due to both an inability of Wolbachia to efficiently colonize germaria in heterozygous mutant hosts and by a reduction in titer when the host is infected. Importantly, both the less severe chic allele (chic 1320 ), known to decrease an oocyte specific isoform of Drosophila profilin chickadee [22], as well as the null chic allele (chic 221 ) produced a Wolbachia titer phenotype. We identified two different actin binding proteins (profilin and villin) that affect Wolbachia transmission and maintenance, supporting the conclusion that Wolbachia persistence within the host is sensitive to actin.
Drosophila stocks
Standard methods were used for all crosses and culturing. The following stocks were obtained from the Bloomington Drosophila Stock Center (BDSC) at Indiana University (http://flystocks. bio.indiana.edu/): stock number 145, which carries w 1 was used as the Wolbachia infected control line. Two chickadee mutant fly stocks were used in this study. The chic 221 cn 1 /CyO; ry 506 flies carry a null recessive allele resulting from the deletion of 5' non-coding and some chic-coding sequences [22]. The P{PZ}chic 01320 cn 1 /CyO; ry 506 flies carry a strong homozygous infertile loss-of-function allele in chickadee, generated by P-element insertion [23]. The quail mutant flies, qua 6-396 /SM1, carry a female sterile, recessive mutation induced by ethyl methanesulfonate [24]. We also utilized two chromosomal deficiency stocks: #9507, w 1118 ; Df(2L)BSC148/CyO, is a chromosomal deletion of segments 36C8-36E3, covering the region containing the quail locus. The second of these stocks #24377, w 1118 ; Df(2L)BSC353/CyO, covers segments 26A3-26B3, the region containing the chic locus. Both of these chromosomal deletions are part of the aberration stock collection and were created by FLP-mediated recombination between FRT-bearing transposon insertions [25]. Wolbachia were introduced into the heterozygous mutant backgrounds through crosses between w 1 infected females (stock 145) and uninfected heterozygous males (mutant/CyO). In order to control for genetic background, we also created isogenized lines by backcrossing stock 145 and each mutant line to an uninfected w; Sco/Cyo stock for three generations (as per [26], S1 Fig). We used sibling controls to identify Wolbachia titer differences related to genotype.
In addition to these isogenized lines, and to examine the effect on Wolbachia titer of profilin knockdown during development, we utilized a fly stock carrying a UAS inducible profilin-specific short hairpin silencing trigger (RNAi; stock #34523, genotype y 1 sc à v 1 ; P{TRiP. HMS00550}attP2) [27]. In order to test the effect of induction on fly development (to recapitulate the developmental lethality of the profilin null) we crossed homozygous females from this line to w; P{w+, Act GAL4} /TM3 males. In order to knock down profilin, we then crossed homozygous females from this line to a homozygous Hsp70:Gal4 driver (a generous gift from Brian Calvi). An additional control for expression from the Hsp70:Gal4 driver included a UAS: GFP stock (also a gift from Brian Calvi). Flies were shocked at 37C for 10 minutes to induce the short hairpin. Wobachia infection status for stocks acquired from the BDSC was determined via PCR and Western blot targeting the gene wsp or its product (see methods below). All flies examined for Wolbachia infection in the experiments below were age matched in order to avoid confounding correlations between fly age and Wolbachia titer.
Western blots
Flies were ground in 1.5ml centrifuge tubes using an electric hand drill and disposable pestle in lysis buffer: 150mM NaCl, 1% Triton X-100, 50mM TrisHCl (pH8) containing HALT protease inhibitor cocktail (Thermo Scientific) and 5 mM EDTA. The lysates were centrifuged for 1 minute at 8000 X g to pellet debris. Samples were heated for 5 minutes at 95°C in Laemmli sample buffer containing 5% β-mercaptoethanol (Bio-Rad) prior to SDS-PAGE electrophoresis. Proteins were separated on 4-20% Tris-Glycine NB precast gels (NuSep) in 1X Tris/Glycine/SDS running buffer (Bio-Rad) and transferred to PVDF membrane in Tris-Glycine transfer buffer with 15% methanol at 40v on ice for 3-4 hours. The membrane was blocked for 5 minutes in Starting Block T20 (TBS) Blocking Buffer (Thermo Scientific), followed by incubation in primary antibody (for 1 hour at RT or O/N at 4°C) according to standard protocols. SuperSignal West Pico Chemiluminescent Substrate (Thermo Scientific) was used according to the manufacturer's instructions to detect HRP (after incubation with secondary antibodies) on the immunoblots. Blots were re-probed after stripping in 100mM Glycine, 0.15 ND-40, 1% SDS, pH 2 for 1 hour at RT, then overnight at 4°C. PageRuler prestained protein ladder (Thermo Scientific) was used as a molecular mass marker. The following antibody was obtained through BEI Resources, NIAID, NIH: Monoclonal Anti-Wolbachia Surface Protein (WSP), NR-31029, and used at a dilution of 1:1000. Additionally, we used anti-actin monoclonal at 1:10,000 (Seven Hills Bioreagents) as a loading control as well as secondary antibodies: HRP enzyme conjugates (Invitrogen) at 1:5000. Densitometry measures were made in ImageJ using scanned film with same exposure times across multiple experiments. Control and experimental flies were included on the same blot in order to ensure consistencies in measured ratios.
Immunohistochemistry, fluorescence in situ hybridization, and microscopy
Immunohistochemistry was performed as follows: ovaries for immunolocalization were dissected in Ringer's solution 3-5 days after fly eclosion, then fixed as previously described [28] with following modification: 6% formaldehyde devitellinizing buffer was replaced with 5.3% paraformaldehyde in same (Electron Microscopy Sciences). After a series of washes in PBS buffer, ovaries were blocked with 0.5% BSA in PBST for 10 min. The monoclonal anti-Heat Shock Protein 60 (HSP60), clone LK2, H 3524 (Sigma) was diluted 1:150 in PBST with 1% BSA or a custom antibody created against full length Wolbachia FtsZ was diluted 1:150 in PBST with 1% BSA. Cy3 conjugated to goat anti-mouse secondary antibody (Jackson Immunoresearch) or rabbit secondary antibody (Jackson Immunoresearch) diluted 1:250 in PBST + BSA was used to detect the primary antibody. For F-actin detection we used Acti-stain 488 Fluorescent Phalloidin (Cytoskeleton, Inc). Tissues were mounted in Slow Fade "Gold" antifade reagent (Invitrogen) and stored at 4°C.
To confirm staining by immunohistochemistry, we also used fluorescent in situ hybridization, following published protocols [18] with the following modifications: post-fixation in 4% paraformaldehyde in DEPC treated PBS, ovaries were dehydrated in methanol and stored overnight at -20°C. In the morning, washes in DEPC-PBST preceded a 5 minute proteinase K treatment (0.05 mg/mL) at 37C before prehybridization in hyb buffer (50% formamide, 5X SSC, 250 mg/L SS DNA, 0.5x Denhardts, 20 mM Tris-HCl and 0.1% SDS). Universal bacterial probe EUB338 conjugated to Alexa488 (Molecular Probes) was used to detect Wolbachia in the ovarioles. Hybridized ovaries were mounted in Slow Fade "Gold" antifade reagent (Invitrogen).
Images were taken as Z-series stacks at 1.5 um intervals using a Nikon E800 fluorescent microscope with 40x oil objective and processed using Metamorph imaging software (Molecular Devices). Care was taken such that exposure times were normalized across all experiments. For quantification of Wolbachia and F-actin within the germarium z-sections maximum projections were used and regions of the germarium demarcated using masks (S2 Fig). We were careful to exclude the peritoneal sheath for F-actin quantification and for Z-stacks where the sheath was difficult to exclude (due to placement of the sections), the images were not included in the F-actin quantification. Germaria showing aggregates of Wolbachia were scored based on a striking pixel intensity in the presumed somatic stem cell niche.
DNA and RNA extractions and polymerase chain reactions DNA was extracted from flies utilizing the Qiagen DNeasy Blood and Tissue Kit (Qiagen) according to directions with the following modification. Flies were ground in a 1.5ml centrifuge tube using a disposable pestle and an electric hand drill in 180 ul PBS, 200 ul ALT buffer, and 20 ul Proteinase K solution. The samples were incubated at 56°C for 10 minutes with vigorous shaking and then centrifuged briefly to pellet debris before continuing with the ethanol precipitation in the kit protocol. DNAs were quantified by measuring absorbance at 260nm using an Epoch spectrophotometer (Biotek). Semi-quantitative PCR was performed by standardizing the amount of DNA in each reaction. We utilized Phusion High Fidelity PCR Master Mix with HF buffer (New England Biolabs). The protocol for amplification was: 98°C for 3 minutes, followed by 25 cycles of 98°C for 10 seconds, 56°C for 45 seconds, 72°C for 1 minute 30 seconds with a final 10 minute extension at 72°C. Primers were as follows: wsp F1 5'-GTC CAA TAR STG ATG ARG AAA C-3' and wsp R1 5'-CYG CAC CAA YAG YRC TRT AAA -3' [29]. RNA and DNA were extracted from individual flies or pupae using a modified Trizol extraction protocol. Briefly, 500 uL of Trizol was added to flies and samples homogenized using a pestle. After a 5 minute incubation at room temperature, a 12,000 rcf centrifugation (at 4C for 10 min) was followed by a chloroform extraction. Aqueous phase containing RNA was extracted a second time with phenol:chloroform before isopropanol precipitation of RNA. This RNA pellet was washed and resuspended in The RNA Storage Solution (Ambion). DNA extraction from the same flies or pupae was performed using ethanol precipitation of the organic phase during the first chloroform extraction. Quantitative PCR was performed on the DNA to detect the Wolbachia titer (with reference to the host) using an Applied Biosystems StepOne Real-time PCR system and SybrGreen chemistry (Applied Biosystems). We used wsp primers for Wolbachia (Forward: CATTGGTGTTGGTGTTGGTG; Reverse: ACCGAAATAACGAGCTCCAG) and Rpl32 primers for the host (Forward: CCGCTTCAAGGGACAGTATC; Reverse: CAATCTCCTTGCGCTTCTTG) at the following temperatures: 95°C for 10 min, then 40 cycles of 95°C for 15 seconds and 60°C for 1 minute. To detect number of profilin transcripts we utilized the RNA extracted from these flies and the SensiFAST SYBER Hi-ROX One-step RT mix (Bioline) and the following primer set: chicF: TGCACTGCATGAAGACAACA, chicR: GTTTCTCTACCACGGAAGCG (FlyPrimerBank, DRSC). Reactions were performed in a 96-well plate and calibration standards were used in every run to calculate primer efficiencies. These efficiencies, along with the CT values generated by the machine, were used to calculate the relative amounts of Wolbachia using the ΔΔ Ct (Livak) and Pfaffl methods [30].
F and G-actin quantification
In order to identify the ratio of filamentous to globular actin in ovaries from age matched flies, we used ultracentrifugation coupled to SDS-PAGE and Western blots using an in vivo F/G actin assay kit (Cytoskeleton, Inc). Age-matched, virgin female flies from chic 221 /Cyo or control (stock #145) were dissected in LAS2 buffer at 37°C and incubated for 10 minutes at 37°C. A brief 300 g centrifugation step (5 minutes) was followed by a 1 hour ultracentrifugation at 100,000 g at 37°C. Supernatants containing globular actin were removed and pellets resuspended in actin depolymerization buffer on ice, by pipetting up and down every 15 minutes for 1 hour. Pellets containing F-actin fractions and supernatants containing G-actin fractions were run on an SDS-PAGE gel and Western blots performed (as above) using a primary mouse monoclonal anti-actin antibody. Bands were quantified using densitometric analysis in ImageJ (as above).
Results
Wolbachia infection is lost or reduced in fly mutants heterozygous for actin binding proteins chickadee and quail All three actin binding protein mutant fly stocks used in this study were uninfected with Wolbachia upon receipt from the Bloomington Drosophila Stock Center. In order to establish an infection in the flies, infected control females were crossed with mutant uninfected males to generate F1 progeny, half of which carried the mutation, and half of which carried the Cyo balancer (a second chromosome containing inversion breakpoints and a dominant visible mutation of curly wings). F1 heterozygous mutants for the actin binding protein alleles were then back-crossed to the paternal mutant line (mutant/Cyo) and F2 progeny from that cross, carrying the mutation and harboring straight wings, were collected. We screened both the F1 and F2 progeny for Wolbachia infection using PCR against the Wolbachia surface protein gene (wsp) (Fig 1A). We observed a trend where Wolbachia transmission was not complete in these crosses. For example, the bacterium could be introduced into some heterozygous mutant backgrounds; F1 progeny were infected if they resulted from crosses between control females and chic 1320 /CyO as well as qua 6-396 /CyO fathers, but the bacterium failed to colonize chic 221 /+ F1 progeny efficiently. We were unable to detect Wolbachia in many of the F2 progeny ( Fig 1A). In order to quantify this reduction in titer, we performed qPCR on DNA extracts from F1 progeny from each of five individuals from the heterozygous mutants and compared these results to the quantified Wolbachia loads found in control flies ( Fig 1B). Progeny from each F1 cross have a statistically significant reduction in Wolbachia titer (as quantified through qPCR) compared to the control lines (p < 0.01 for all pairwise comparisons, using a Bonferroni correction for df = 8). As additional support for the importance of the chic and qua loci in the Wolbachia titer defects we observed, we also quantified the amount of Wolbachia within two chromosomal deficiency stocks (deletions in the same region as either chic or qua in isogenic backgrounds) [25]. These deficiencies showed the same phenotype as our chic and qua mutants, supporting our observation that these genomic loci are responsible for the Wolbachia titer defect ( Fig 1B). In addition to reductions in the F1 progeny, we also quantified a reduction in F2 progeny for the three actin mutant lines. For flies in which we can detect Wolbachia, the F2 progeny are further reduced in titer compared to the F1 lines (ratio of expression F1 versus F2: min = 0.56, max = 0.78).
In order to control for effects of host genetic background on Wolbachia titer, we created isogenized lines from the control stock (145) and each of the mutant stocks by backcrossing to an uninfected w; Sco/Cyo line for three generations. We then crossed these Wolbachia infected F3 females (w; Sco/Cyo) to Wolbachia uninfected w; mutant/Cyo males (S1 Fig). In the F5 generation, we observed a significant effect of genotype on Wolbachia titer. Specifically, and regardless of mutant allele, mutant/Cyo progeny were reduced in Wolbachia titer by 1/3 compared to their w; Sco/Cyo siblings (mean relative ratio wsp/rpl32; t = -4.514; df = 9; p = 0.001). This result suggested to us that the reduction in titer was at least partially due to a result of a developmental defect in Wolbachia maintenance and persistence within the heterozygous mutant hosts.
As an additional control for host genetic background and to explore direct effects on profilin knockdown during development, we took advantage of an infected fly stock carrying a UAS inducible profilin-specific short hairpin silencing trigger (RNAi; stock #34523, genotype y 1 sc à v 1 ; P{TRiP.HMS00550}attP2) [27]. In order to test the effect of induction on fly development (to recapitulate the developmental lethality of the profilin null) we crossed homozygous females from this line to w; P{w+, Act GAL4} /TM3 males. From this cross we only recovered stubble progeny, suggesting that this particular RNAi line, which hadn't previously been utilized in a publication to knock down profilin expression, is effective. In order to test the effect of induction on fly development we crossed homozygous females (y 1 sc à v 1 ; P{TRiP.HMS00550}attP2) to a homozygous Hsp70:Gal4 driver [2][3][4][5]. Third instar larvae were shocked at 37C for 10 minutes to induce the short hairpin and late pupae collected for RNA and DNA extraction (N = 8 for each treatment and genotype; y 1 sc à v 1 ; P{TRiP.HMS00550}attP2 with or without Hsp70: Gal4 and with or without heat shock). In the maternal y 1 sc à v 1 ; P{TRiP.HMS00550}attP2 background, heat shock did not affect either Wolbachia titers (t = 1.207, df = 2, p = 0.351) nor profilin expression (t = -1.144, df = 2, p = 0.371). In contrast, profilin expression was statistically significantly reduced in flies expressing the RNAi construct compared to non-heat shocked siblings (the mean expression ratio chic/rpl32 = 0.57; t = -6.240; df = 2; p = 0.025). In addition, knockdown of profilin did have a significant and measurable effect on Wolbachia titers in these same flies; the fly Wolbachia titers were reduced by 1/3 compared to their non-heat shocked siblings (mean relative ratio wsp/rpl32 = 0.66, t = -8.593; df = 2; p = 0.013).
To provide additional support for the reduction in titer observed via PCR, we probed Western blots of pooled or individual fly lysates produced from the F1 and F2 progeny and their parents for Wsp (Fig 1C, 1D and 1E). Results corroborated our previous finding that Wolbachia transmission was imperfect in the mutant flies (Fig 1A and 1B). Specifically, infected F1 progeny, especially in the chic mutant backgrounds, appeared to carry a reduced titer of Wolbachia when compared to the maternal, infected line (Fig 1). Indeed, flies from control crosses are consistently higher titer in Wolbachia, as based on densitometric quantitation of Western blot bands (Average +/-STERR over 5 experiments for Control = 13,106 +/-3,294; chic 1320 /+ = 6,418 +/-4,890; chic 221 /+ = 6,545 +/-1,576; qua 6-396 /+ = 6,179 +/-645; t-test; p = 0.036, 0.001, 0.002 for each heterozygous mutant compared to control). Additionally, we could detect a statistically significant reduction between the F1 and F2 heterozygous mutant flies (p = 0.012). As observed in our results based on PCR, Wolbachia titer (based on quantity of protein on a Western blot) is also reduced, with some variability, in the F2 progeny ( Fig 1D). We hypothesized that the loss of Wolbachia in some F2 progeny was a result of a reduction in Wolbachia titer in F1 females during oogenesis. We therefore visualized the Wolbachia infection in the germarium in F1 females (mutant/+; below).
Wolbachia is reduced in the germarium and early egg chamber when hosts are heterozygous mutants in chickadee or quail To colonize the oocyte, and therefore complete maternal transmission, Wolbachia occupy the germline and somatic stem cell niches (SSCN) in their hosts [18,26,31]. Wolbachia can achieve this localization after injection into the fly abdomen, suggesting that the stem cell niche targets are essential for Wolbachia infection [31]. The Drosophila ovariole provides an opportunity to view oocyte development and Wolbachia localization within each progressive stage. Wolbachia concentrate preferentially in the somatic stem cell niche, which is thought to serve as a source of infection for the germline. As germline development progresses from regions 2a to 2b, Wolbachia are thought to infect via the somatic stem cell niche, increasing the numbers of bacteria found within the germline after association with the SSCN [31]. We utilized immunohistochemistry to detect Wolbachia in the germarium of our flies, producing localizations expected based on previous publications [15,18,26,31](S1 Table and control and chic 1320 /+ or qua 6-396 /+ heterozygous mutants, respectively; Fig 3). Additionally, Wolbachia infection within early egg chambers (stage 1) is significantly reduced in all heterozygous mutant flies (when comparing the amount of fluorescence observed in control flies to that found in either chic 221 /+, chic 1320 /+ or qua 6-396 /+, respectively; Mann-Whitney U = 74, Z = -5.74, p < 0.001; Mann-Whitney U = 58, Z = -5.872, p < 0.001; Mann-Whitney U = 39, Z = -5.767, p < 0.001; Figs 2 and 3). In order to quantify this reduction, for each germarium, we calculated the ratio of fluorescence intensity in the earliest egg chamber over that found in region 2 (as quantified by anti-Hsp60 staining). Each of the three mutant lines showed a statistically significant reduction in this ratio when compared to control germaria (average ratios for control flies: 1.72; chic 221 /+: 0.52; chic 1320 /+: 0.64; qua 6-396 /+: 0.80, t-test; p < 0.0001). The reductions in infection in the germaria suggest two things: (1) that Wolbachia has difficulties in transiting or maintenance in a population within the germarium during development in the heterozygous mutant flies and (2) even when region two, the location of the SSCN, is occupied by Wolbachia, the bacteria are deficient in colonization of the early egg chamber in the heterozygous mutant flies (Fig 3). We did not quantify differences in staining of the presumed germline stem cell niche due to variability in staining in this region within the control flies.
Within heterozygous mutant flies, we observed that the Wolbachia that successfully manage to colonize the germarium do so with a distinctive localization; these Wolbachia appear as aggregates, in sharp contrast to the more even distribution of Wolbachia within control germaria (Table 1 and Fig 2). Under high magnification (100x), the Wolbachia aggregates within the heterozygous mutant flies appear to be multiple Wolbachia forming micro-colonies within the tissue, based on shape and size and consistent localization within the genotypes.
Characterization of F/G-actin and profilin expression within heterozygous mutant flies
Both Drosophila profilin (chickadee) and villin (quail) are important in the regulation of Factin during oogenesis. Because profilin promotes the polymerization of F-actin filaments and villin stabilizes these filaments through bundling, we were curious to know whether or not the heterozygous mutant flies differed in the quantity of F-actin found in the germarium, when compared to control flies. In addition, visualization of the F-actin cytoskeleton allowed us to examine the actin ring canals in the heterozygous mutant flies at all stages of oocyte development. At no point were ring canals occluded by nuclei, supporting our finding that cytoplasmic streaming and maternal dumping are unaffected in heterozygous mutant flies (N = 300, scored by eye). Using quantified fluorescence of F-actin in the images we were unable to detect a statistically significant difference between median levels of phalloidin staining in control flies compared to the heterozygous mutants (Kruskal Wallis test: χ2 = 4.005, df = 3, p = 0.261; S4A Fig). Because F-actin levels in the germarium (observed through phalloidin staining) did not correlate with Wolbachia intensity (as quantified by anti-Hsp60 staining), the Wolbachia titer phenotype observed in these flies may not be directly related to the F-actin network in the germarium. We therefore examined the in vivo amounts of filamentous and globular actin in ovaries from control flies and compared this to that seen in heterozygous mutant chic 221 flies. Using ultracentrifugation coupled to Western blot, we found that we could consistently detect globular actin in the ovaries of control flies. In contrast, we found a statistically significant decrease in total amount of globular actin detected in the heterozygous mutant lines (Kruskal Wallis: χ 2 = 4.192, df = 1, p = 0.041; S4B Fig).
The difference in G actin between control and heterozygous chic 221 flies prompted us to investigate expression of profilin in the chic 221 /+ F1 mutants and control flies. The rationale was that although these flies are phenotypically wild type, the dosage effect of a single, wild type chromosome in the chic 221 /+ F1 mutants might be significant and correlate with Wolbachia absence. We extracted both RNA and DNA from individual F1 chic 221 /+ female flies as well as age-matched control flies and used quantitative RT-PCR to detect profilin transcript levels (in total RNA) and Wolbachia surface protein (in total DNA) relative to Rpl32. Control flies express, on average, 2x as much profilin as heterozygous mutant F1 progeny (means control μ = 4.03; mutant μ = 2.28; t = 2.590, df = 11.31, p = 0.025). Additionally, although we could detect Wolbachia in each of the wild type flies included (N = 10), we were only able to detect a Wolbachia infection in three of the heterozygous mutant F1 flies (S4C Fig). Wolbachia may have been present in these flies, but at titers below the limit of detection for this method. Heterozygous mutants in chickadee and quail produce the same number of progeny as control flies and lay eggs of normal size and shape Because Wolbachia target the germline, and within the germarium, the stem cell niche [18,31], the number of egg chambers produced by the host may affect Wolbachia's ability to be transmitted between generations. Flies that are homozygous mutants in chickadee show defects in germline stem cell proliferation as well as enclosure by somatic cyst cells [32,33] so it was therefore important to confirm that the heterozygous mutant flies do not display similar defects. We counted the number of viable progeny resulting from individual crosses within mutant fly lines and compared the number of resulting offspring to those from control crosses. Heterozygous villin or profilin mutant flies do not show a defect in fertility when compared to control flies (S5 Fig). Additionally, we observed over 300 eggs for each of the fly mutant stocks and did not see any morphological abnormalities when compared to the control stock (N = 300, scored by eye).
Discussion
Wolbachia maternal transmission in Drosophila melanogaster is normally extremely effective, with perfect transmission observed in laboratory populations and near perfect transmission in the wild [10][11][12]. Wolbachia are thought to localize in the germarium, and ultimately in the oocyte, in order to accomplish this maternal transmission. Previous work has shown that Wolbachia use host microtubules to localize preferentially to the oocyte during development [15][16][17]. The striking anterior localization of Wolbachia during oogenesis can be perturbed by feeding Drosophila microtubule inhibitors such as colchicine, or by mutations that perturb the microtubule cytoskeleton [15]. In contrast, direct treatment of dissected ovaries with actin disrupting drugs (such as cytochalasin-D) does not alter this localization [15]. However, other pieces of evidence suggest that Wolbachia manipulate the host actin cytoskeleton. For example, Wolbachia injected into the abdominal cavity of Drosophila migrate to the germline stem cell niche, a feat that requires traversing several host tissues and cell types [31]. Also, Wolbachia in the terrestrial isopod Armadillidium vulgare are not found in all primary oocytes and instead, enrichment of Wolbachia is seen during the course of development [34]. Finally, Wolbachia are associated with areas of weak cortical actin staining in filarial nematodes, suggestive of a mechanism for entry into the germline from somatic cells [17,19]. Therefore, it is likely that Wolbachia use both microtubules and actin for persistence in the host and maintenance across host generations. Oogenesis in Drosophila relies on rearrangements of both the actin and microtubule networks [35]. We were therefore careful in our analysis to separate direct effects of actin modulation from indirect effects resulting from perturbations of the reproductive biology of the fly. Products of both the quail and chickadee loci are necessary for fly reproduction [22,[36][37][38]; homozygous or hemizygous mutants in either gene result in fertility defects or are lethal. Importantly, in this study we followed Wolbachia infections in phenotypically wild type flies harboring a functional copy of the actin binding protein in question. These heterozygous mutant flies produce the same number of offspring as the control flies and produce eggs with the same morphology as controls, however the flies do not faithfully maintain a Wolbachia infection. Several hypotheses partially explain our data, and below we delineate our hypothesis and alternative hypotheses and summarize our evidence to support or refute them.
Heterozygous mutant flies are phenotypically wild type with respect to oocyte polarization and number of progeny
The developing oocyte is loaded with maternal determinants (e.g. mRNA and protein), a process which begins early (stage 1), and continues until about stage 10 when maternal nurse cells dump their remaining cytoplasmic contents into the oocyte [35]. The actin cytoskeleton is critical to this process, as mutations in actin binding proteins have been known to cause severe defects. Specifically, cytoplasmic actin bundles are required to restrain the nurse cell nuclei during transport; mutations in quail, which regulates bundling of cytoplasmic actin, cause a dumpless phenotype [39,40]. In quail mutant flies, nurse cell nuclei can be observed extending through the actin ring canals [39]. We reasoned that although heterozygous mutant flies (chic 221 /+, chic 1320 /+ and qua 6-396 /+) produce viable progeny, and we found no occluded ring canals in any of these backgrounds, a subtle defect in maternal cytoplasmic dumping could alter the ability of Wolbachia to be transmitted faithfully to the oocyte. Wolbachia has been suggested to utilize cytoplasmic dumping to increase titer in the oocyte (as compared to the nurse cells) [15]. In addition to regulating the bundling of microtubules and therefore cytoplasmic streaming, profilin is also required for posterior patterning in the oocyte as chic mutants fail to localize STAUFEN and oskar mRNA [41]. Wolbachia utilizes these posterior determinants to localize in the oocyte, as disruption of osk and stau results in mislocalization of Wolbachia in D. melanogaster [16]. If heterozygous mutant flies are defective in cytoplasmic dumping or polarization, we should observe both egg size and morphology defects. Over 300 eggs were scored for each of the mutant lines, as well as control flies, without any phenotypic differences detected. Importantly, however, the primary loss of Wolbachia in these heterozygous mutants occurs in the germarium, before defects would begin to affect Wolbachia titers. Therefore, although our fly mutants could conceivably exhibit subtle polarization defects, these defects alone would not entirely explain the observed phenotype.
In addition to serving important roles during maternal loading in the late stage oocyte, profilin functions in germline stem cell (GSC) maintenance and germ cell enclosure by somatic cyst cells [32,33]-homozygous chickadee mutants fail to maintain germline stem cell number. However, chic 221 /+ flies are equivalent to wild type [32]; that is to say, heterozygous mutant flies do not have a GSC deficiency. Importantly, although Wolbachia are known to alter germline stem cell proliferation [26] and some Wolbachia colonize the germline stem cell niche [18], wMel colonizes the somatic stem cell niche in Drosophila melanogaster (Fig 2). Regardless, a defect in fertility, resulting from defects in GSC maintenance might affect Wolbachia proliferation in these mutant flies. We therefore counted the number of viable progeny (a measure of fertility) for each of the mutant lines. No statistically significant difference was observed for any of the heterozygous, mutant flies, when compared to the control (S5 Fig). We therefore did not find support for this hypothesis to explain the Wolbachia clearing phenotype of profilin and villin heterozygous mutants.
Wolbachia localization during development impacts maternal transmission
There is significant evidence that Wolbachia colonize the primordial germ cells and the posterior pole of developing embryos in numerous insect hosts. In D. melanogaster, for example, strain wMel concentrates at the posterior pole in a poleplasm dependent fashion [16,42,43]. However, this posterior concentration of Wolbachia is not universal in insects nor in Drosophila. Wolbachia strain wRi infects the entire embryo uniformly while B group Wolbachia actually show exhibit anterior localization [14]. Similarly, in other Drosophila species there are different patterns of Wolbachia colonization: although wWil infects primordial germ cells, wAu infects the entire embryo [44]. This posterior localization is clearly important-the extent of CI is correlated with the number of Wolbachia in the posterior of the embryo [14]. However, this posterior localization is not necessarily correlated with maternal transmission, which is near 100% for some Drosophila species and quite low for others [45][46][47]. This result suggests that high titer localization to primordial germ cells and the posterior pole does not guarantee maternal transmission. However, if our heterozygous mutant flies induce defects in these early localization patterns (to the posterior pole or to the developing germ line), we might expect the inefficient transmission phenotype observed.
What other ways might Wolbachia use to eventually colonize the germline? Wolbachia colonization of somatic tissues has been known for some time [48] but recently, it has been suggested that Wolbachia infection of the soma may serve as a reservoir for germline infection. In the terrestrial isopod, Armadillidium vulgare, Wolbachia is absent from many early oocytes and infects the older oocytes late in development, an enrichment that is thought to come from a somatic reservoir (the follicle cells) [34]. In nematodes, Wolbachia initially are concentrated in the posterior of the P 2 blastomere, the precursor of the adult germ line. However, Wolbachia are subsequently excluded from the germ line in the next cell division and instead, invade the germ cells later, from the surrounding somatic gonadal cells [19]. This soma to germ cell invasion in Brugia is correlated with a disruption in polymerized actin at those foci [19]. Because we observed a reduction in anti-Hsp60 staining in stage 1 egg chambers of heterozygous mutant flies as well as transmission defects, one interpretation of our data is that Wolbachia require actin for soma to germline transmission. Importantly, however, we did not observe actin disruptions (similar to those seen in Brugia) within Drosophila germaria.
Actin regulation impacts Wolbachia titers during development, affecting transmission efficiency
Our data suggest that Wolbachia rely on the actin cytoskeleton to achieve adequate titer in the Drosophila host during development. First, we observe reductions in titer of Wolbachia in heterozygous mutants compared to both their non-mutant sibling controls as well as parental controls (Fig 1). Second, knockdown of profilin in third instar larvae reduces Wolbachia titer in pupae, suggesting that the regulation of actin is important to the maintenance of a Wolbachia infection during development. Additionally, passage of Wolbachia through heterozygous mutant lines for multiple generations results in the enrichment for mutant Wolbachia; the heterozygous mutant flies bottleneck the Wolbachia infection, increasing the stochastic segregation of variants [49]. This decrease in titer may explain the inefficient transmission of Wolbachia observed in the mutant flies. Actin may be used by Wolbachia to properly localize during development, or may support the infection via other unknown mechanisms.
Potential mechanisms to explain the Wolbachia phenotype in mutant flies
Both of the proteins investigated here (profilin and villin), are known to increase the amount and stability of F-actin in the Drosophila egg chamber. Profilin promotes F-actin in the follicular epithelium while villin bundles and binds to filamentous actin [37,50]. One potential cause of the Wolbachia phenotype in these backgrounds is a mis-regulation in F-actin content. Interestingly, chic mutants have been previously observed to exhibit decreased F-actin levels in the follicle cells [50]. Both the somatic stem cell niche and the follicular epithelium have been suggested to be a source of Wolbachia during oogenesis [18,34]. Because Wolbachia densely colonize the follicular epithelium tissue, and because it surrounds the oocyte throughout development, this tissue may be a candidate for the source of the infection. We detected a significant reduction in the amount of actin in heterozygous mutant chic 221 flies compared to controls, which corresponded to a decrease in profilin transcripts and a decrease in detected Wolbachia (S4 Fig). These data are suggestive of a role for actin in Wolbachia maintenance and transmission but do not elucidate an exact mechanism.
We have shown that the host actin cytoskeleton is clearly important for the maintenance of a Wolbachia infection. Perhaps this reproductive parasite secretes proteins that interact directly with eukaryotic actin or host actin binding proteins. Indeed, other members of the Rickettsiales are known for their striking coopting of host actin in the production of comet tails [51]. However, when intracellular, Wolbachia persist within membrane-bound compartments and no such comet-like structures have been observed to be associated with the vacuole [21]. That said, our results here and the work of others strongly suggest that Wolbachia is able to enter and exit eukaryotic cells; Wolbachia transit to the germline from the fly abdomen and are loaded into the germ cells from surrounding somatic cells [18,26,31]. Wolbachia's success likely depends upon an ability to secrete proteins that modify host actin to promote internalization by non-phagocytic cells. Recently, in vitro biochemical associations between the filarial nematode Wolbachia (wBm) PAL-like protein wBm0152 and actin have been observed, although results do not conclusively implicate this particular protein in interactions with host actin during infection [20]. Regardless, as is clear from our work, a Wolbachia infection depends on the actin cytoskeleton. Therefore, future work to identify and characterize Wolbachia proteins that bind to or alter host actin dynamics will be important for understanding the molecular basis of the interaction between the host and the symbiont.
Summary
In order for intracellular, maternally transmitted symbionts to successfully infect the next generation, the bacteria must target the oocyte. Wolbachia achieves this through a specific infection of the somatic stem cell niche in the germarium of Drosophila melanogaster [18]. Here we show that Wolbachia is extraordinarily sensitive to the regulation of actin, such that phenotypically wild type heterozygous mutant flies cannot faithfully transmit the bacterium to their progeny. Our results, particularly that titer is significantly reduced in the germaria of chic 221 /+, chic 1320 /+, and qua 6-396 /+ flies, suggest that Wolbachia utilize host actin to enter and persist within host tissues during Drosophila development. Additionally, our finding that these heterozygous mutant flies cannot transmit the infection suggests that Wolbachia titers within a host are reduced when actin regulation is disrupted, impacting transmission efficiency.
Supporting Information S1 Table. Total number of flies and germaria fixed, stained, and imaged for anti-Hsp60 intensity quantification as proxy for Wolbachia titer. Fig. (A) Quantification of amount of F-actin in Drosophila melanogaster germaria during oogenesis, within the entire germarium. Maximum projections, generated from z-stacks, were utilized to compare between control flies and qua 6-396 /+, chic 1320 /+, and chic 221 /+ F1 Wolbachia infected progeny with regards to amount of F-actin staining (using Acti-stain 488 phalloidin). Bars = minimum and maximum values. Box = first and third quartiles while the median is shown as a band through the box. Although the 95% confidence intervals overlap for all genetic backgrounds, the distributions of values for the mutants are much more variable than found in the control flies (Standard deviations = control = 1.7e6, qua 6-396 /+ = 2.4e6, chic 1320 /+ = 2.2e6, and chic 221 /+ = 2.1.e6). (B) Quantification of G-actin in the ovaries of control and chic 221 /Cyo female flies. Densitometry measures using western blots (a-actin) showed statistically significant reductions in actin in heterozygous mutant female flies (χ2 = 4.192; df = 1; p = 0.041) (C) Relative quantification of profilin transcripts within individual chic 221 /+ F1 female flies as well as wild type, control flies (stock #145). A statistically significant decrease in profliin expression was observed in the heterozygous mutant flies compared to controls (means control μ = 4.03; mutant μ = 2.28; t = 2.590; df = 11.31; p = 0.025). Importantly, Wolbachia was only detected in three of the twenty heterozygous mutant flies but consistently found in all of the wild type flies (using qPCR on wsp). | 9,500.4 | 2015-04-01T00:00:00.000 | [
"Biology"
] |
Research on the Method of Detecting the Spreading Rate of the Simultaneous Crushed Stone Sealing Layer Based on Machine Vision
Synchronous chip seal is an advanced road constructing technology, and the gravel coverage rate is an important indicator of the construction quality. The traditional method to measure the gravel coverage rate usually depends on observation by human eyes, which is rough and inefficient. In this paper, a detection method of gravel coverage based on improved wavelet algorithm is proposed. By decomposing the image with two-dimensional discrete wavelet, the high-frequency and low-frequency coefficients are extracted. The noise of the high-frequency coefficients in the image is removed by improving the threshold function, and the contrast of the gravel target in the low-frequency coefficients is improved by the multiscale Retinex algorithm, and then two-dimensional wavelet reconstruction is carried out. Finally, the gravel target is segmented by the block threshold method, and the pixel ratio of the gravel is calculated to complete the detection of the gravel coverage. The experimental results show that the proposed method can effectively segment the gravel target and reduce the influence of environmental factors on the detection accuracy. The detection accuracy error is within ± 2%, which can meet the detection requirements. The improved wavelet algorithm improves the signal-to-noise ratio of the denoised image, reduces the mean square error, and achieves a relatively good denoising effect.
Introduction
Synchronous gravel seal construction is an advanced asphalt pavement construction method in recent years. e basic method is as follows: during construction, the synchronous gravel seal vehicles drive over the construction road surface, synchronously spread asphalt, and gravel on the ground. e asphalt and gravel are bonded on the ground and rolled by tires or steel wheel rollers to form a single layer of asphalt and gravel wear layer. Compared with other methods, this construction method has extremely high construction eciency, and it can reduce the tra c control of the construction section and complete the construction on the road where vehicles pass. e gravel coverage is the percentage of the projected area covered by the gravel to the entire pavement and is an important construction index in the construction of the synchronous gravel seal. In the synchronous gravel seal construction, improper gravel spreading rate or uneven gravel spreading will cause disease (too many gravels will cause threshing, and insu cient gravel will cause oil panning). Generally speaking, the upper seal layer of crushed stones should be in the size of 9.5-13.2 mm, the distribution rate of crushed stones should be 80%∼90%, the lower seal layer should be in the size of 9.5 mm-16 mm (highway) or 4.75-9.5 mm (other Grade), the distribution rate of crushed stone should be 60%∼80%, the stress absorbing layer should use 9.5 mm∼16 mm gauge, and the distribution rate of crushed stone should be 60%∼80% [1]. At present, in the actual construction process, only the construction personnel can use the method of visual inspection to estimate the rubble distribution rate, which is subjective and arbitrary. erefore, it has a great significance for the machine vision-based method for detecting the distribution rate of the crushed stone in the synchronous gravel seal.
Many scholars have conducted research on the use of machine vision to solve problems in production and life. Chowdhury et al. of Texas A&M University in the United States used Hough transform and other image analysis methods to quantify the angularity of fine aggregate particles and distinguish the quality of the aggregate in the hot-mix asphalt mixture [2]. Song et al. used digital image processing to evaluate the uniformity of the asphalt pavement surface texture structure distribution [3]. Song and Wang studied the application of nuclear-free densitometer and digital image segregation evaluation method in asphalt pavement construction quality monitoring and conducted correlation analysis of the two methods [4]. Wang et al. studied the detection method of the coverage of the rubble spreading of the synchronous gravel seal layer. First, the Retinex algorithm was used to restore the image, remove the shadows, and enhance the image, and then the image binarization method was used to obtain the rough spreading coverage. e method fails to treat particulate matter as an independent object, so it is difficult to obtain accurate results [5]. Pan and Tutumluer and others in the United States proposed a three-view-based method for measuring the surface area of irregular aggregate particles and compared the results of the method with the results of the three-dimensional laser scanner to verify the accuracy of the method. e method can also be used for the calculation of asphalt film thickness [6]. Browne et al. designed and realized the ability to dynamically collect images of aggregate particles scattered in a light-assisted background environment and analyze the size characteristics of the particles [7]. Abdullah et al. of Jordan University of Science and Technology used digital image analysis method to quantify the porosity of mineral material in asphalt mixture and compared it with traditional detection methods [8]. In addition, AMIS developed by Texas A&M University, UIAIA developed by the University of Illinois at Urbana-Champaign, and WipShape developed by the University of Missouri all use image analysis technology to achieve automated grading analysis [9,10]. Tajeripour and Fekri-Ershad proposed detecting abnormalities in stone textures based on one-dimensional local binary patterns, and the proposed approach is fully automatic and all of the necessary parameters can be tuned [11]. Al-Utaibi et al. and Basheera M. Mahmmod used Krawtchouk and Hahn polynomials to reconstruct images and analyzed the influence of different parameters on the quality of reconstructed images to complete the detection of the targets [12,13]. Currently, widely used image segmentation algorithms include threshold segmentation, watershed algorithm, cluster segmentation, genetic algorithm, and so on. ese algorithms can measure the target and background segmentation well. However, after studying the impact on the accuracy of rubble spreading detection, it is found that environmental factors such as light and noise in actual construction often cause the final treatment result to fail to meet the requirements.
Aiming at the abovementioned problems, this paper proposes a detection method of gravel coverage based on improved wavelet algorithm. By decomposing the image with two-dimensional discrete wavelet, the high-frequency and low-frequency coefficients are extracted, the high-frequency coefficients are removed by improving the threshold function, and the low-frequency coefficients are improved by the multiscale Retinex algorithm to improve the contrast of the gravel target, and then the two-dimensional wavelet reconstruction is carried out. Finally, the crushed stone target is segmented by the block threshold method, the pixel proportion of the crushed stone is calculated, the detection of the crushed stone coverage is completed, and the relationship between the spreading rate and the spreading amount is established. In the laboratory, the spreading conditions of 2.36-4.75 mm, 9.5-13.2 mm, and 16-19 mm crushed stones under different spreading rates were tested and verified in actual road engineering.
Image Segmentation Based on Machine Vision.
In this study, an industrial camera was used to capture images of scattered gravel. e picture is processed by MATLAB software. According to the result of segmentation, the distribution rate of crushed stone of the synchronous gravel sealer can be obtained, and then the relationship between the distribution rate and the amount of distribution can be established, so as to adjust the subsequent distribution section to ensure the quality of the distribution. First, the impact of crushed stone specifications on the accuracy of spreading rate detection was tested in the laboratory, and secondly, the relationship between the spreading rate of different specifications of crushed stone and the amount of spreading was established. e laboratory test equipment used for testing is shown in Figure 1. In this experiment, the crushed stone type used is AC-16, and the asphalt type is SBS emulsified asphalt. e flow chart of the laboratory test is shown in Figure 2.
In the process of detecting the distribution rate of the synchronous gravel seal layer, after preprocessing operations such as distortion correction and image enhancement, the coverage of the gravel on the scattered road section can be detected.
is paper adopts the method of image binary segmentation to detect the spreading rate of the spreading road. However, in the process of image acquisition, the target and the background cannot be completely separated due to environmental factors such as light and noise, resulting in wrong segmentation, and the results cannot meet the requirements. erefore, in response to this problem, this paper uses discrete wavelet to extract the highfrequency and low-frequency coefficients of the image for processing to eliminate the influence of environmental factors such as light and noise, and then perform the binary segmentation processing on the wavelet-reconstructed image. Carry out the detection of the rubble spreading rate and 2 Advances in Civil Engineering Step 2 Step 1 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 11 Step 12 Step 3 Advances in Civil Engineering establish the relationship between the spreading rate and the amount of spreading. Take the method of image binary segmentation to calculate the spreading rate. Since the stones and the uncovered asphalt have significant color differences, the original image can be segmented using a certain segmentation algorithm to segment the gravel from the background (asphalt) [14], which is as follows: en, the spread rate can be calculated: It can be seen from the above two formulas that the accuracy of the detection method is determined by the accuracy of image segmentation. e specific steps are as follows: Step 1. Select the right industrial camera and lens so that the picture accuracy can reach 0.1 mm, that is, the 1.18 mm size gravel can occupy at least 10 pixels. After comparison, the CCD camera model MV-EM200 M and the lens of BT-23C1214MP5 were finally selected.
Step 2. Adjust the camera distance according to the camera focus position. LED lights should be installed in front of the test equipment to reduce the impact of uneven natural light on shooting. In this experiment, the focal length of the camera is 1.4 mm to 16 mm, the frame rate is 20 fps, the area of the imaging part is 1/1.8 '' , and the number of effective pixels is 1920000.
Step 3. Simulate the spreading process of the synchronous gravel sealer in the laboratory. Simulate the spreading scenes of gravel in different specifications and spreading rates. e camera can sample the road surface after spreading. e picture can be processed by MATLAB software.
(1) Use the imread function to read the selected picture. Step 4. Calculate the actual distribution rate of gravel using existing methods [15].
(1) Sprinkle a layer of 1∼2 mm thick cementing material evenly on the enamel plate or oil felt with a known area, and weigh the combined weight of the oil felt and the cement m 1 . (2) Heat the clean aggregate (single particle size) to be spread to 120-140°C. (3) Spread the heated aggregate on an enamel pan or linoleum felt. (4) After the aggregate and cement are cooled to room temperature, weigh the total weight of the enamel pan or felt, cement, and aggregate m 2 . (5) Calculate the spreading rate of full-paved aggregate and design aggregate spreading rate.
where P m is the spreading amount of aggregate in full spread, kg/m 2 ; P d is the designed amount of aggregate, kg/m 2 ; m 1 is the combined weight of enamel plate or oil felt and cementing material, kg; m 2 is the combined weight of enamel plate or linoleum felt, cement, and aggregate, kg; r is the aggregate design coverage rate, %; and S 1 is the enamel plate or oil felt area, m 2 .
Compare the actual spread rate with the detected spread rate, analyze the error rate of the algorithm and the cause of the error, and make improvements.
Step 5. Calculate the actual amount of spreading using existing methods.
(1) Place the enamel tray or felt with area S 1 on the place where the distributor passes.
(2) Take out the enamel tray or linoleum felt immediately after the car with distributor passes through. (3) Shovel off the aggregate and part of the cement with a scraper, and it is better to shovel off all the aggregates on the porcelain plate or linoleum. (4) e weight of aggregate m 1 is obtained by extraction method or trichloroethylene soaking and washing method. (5) Calculate the aggregate spreading amount: where P s is the amount of aggregate spreading, kg/m 2 ; and m 1 is the weight of aggregate, kg.
Compare the detected value with the actual value, analyze the algorithm error rate and the cause of the error, and make improvements.
Step 6. Repeat steps 3-8 to obtain the detected and actual values of the spreading rate and spreading amount of crushed stones of different specifications.
Step 7. After the detection algorithm is corrected, the actual gravel seal pavement is tested.
For laboratory tests, according to actual working conditions, aggregates of 2.36-4.75 mm, 9.5-13.2 mm, and 16-19 mm are divided. e 0-1.18 mm aggregate has a small particle size, and a camera with a higher resolution should be used to shoot clearly. erefore, the sieving of the 0-1.18 mm aggregate is not considered in this study.
Wavelet Decomposition and Reconstruction.
e wavelet decomposition method is used to obtain low-frequency coefficients and high-frequency coefficients. e low-frequency coefficients mainly include the global information of the image, including the contour information of the image, and the high-frequency coefficients mainly include the local information of the image, including the edges, details, and noise of the image. e expression of two-dimensional discrete wavelet decomposition is as follows [16]: where W φ (j 0, m, n) is the low-frequency coefficient after decomposition; W i ψ (j, m, n) is the high-frequency coefficient after decomposition, means H, V, and D; j 0 is any starting scale, usually let it be 0; f(x,y) is the discrete function, x and y represent discrete variables; m and n are expressed as relative offsets; M × N represents the image is composed of pixels; φ j 0 ,m,n (x, y) is a two-dimensional scaling function, and H,V,D is the wavelet function corresponding to i in the horizontal, vertical, and diagonal directions.
Process the low-frequency coefficient W φ (j 0, m, n) and high-frequency coefficient W i ψ (j, m, n) obtained after decomposition. e reconstructed image is obtained through the inverse discrete wavelet transform, and the wavelet reconstruction expression is as follows. e schematic diagram of the two-layer wavelet decomposition is shown in Figure 3 [17].
where S represents the decomposed image, cA1 and cA2, respectively, represent the low-frequency components of the two-layer wavelet decomposition, that is, low-frequency images, and cD1 and cD2 represent the high-frequency components of the two-level wavelet decomposition, that is, the horizontal (H), the vertical (V), and the diagonal (D) components of each layer. e core processing flow is as follows: (1) Image wavelet decomposition: including selecting a certain wavelet base function and determining the optimal wavelet decomposition level N, perform N-layer wavelet decomposition on the noisy image f(x, y) to obtain high-frequency wavelet coefficients ω j,k and low-frequency wavelet image S(x, y). (2) reshold quantization of high-frequency coefficients of wavelet decomposition: according to a threshold quantization criterion, an appropriate threshold is determined for each high-frequency coefficient of the first to Nth layers. By thresholding ω j,k , the estimated wavelet coefficients ω ∧ j,k are obtained, and ‖ω ∧ j,k − ω j,k ‖ is as small as possible.
(3) Retinex enhancement of the low-frequency coefficients of wavelet decomposition: according to the principle of the Retinex algorithm, the low-frequency image is converted to the logarithmic domain to obtain the reflection image, and an illumination adjustment parameter k is added in the process of eliminating the illumination image, so that the obtained reflection image is more natural. After Gaussian filtering, the filtering results on different scales are averagely weighted to obtain the estimated illuminance image. (4) Wavelet reconstruction: inverse wavelet transform is performed on the high-frequency coefficients ω j,k of the 1st to Nth layers after threshold quantization and the low-frequency wavelet coefficients of the Nth layer to obtain the estimated image.
Improved reshold Function Wavelet Denoising Method
(1) Selection of Wavelet reshold. An improved threshold function method is used to denoise the high-frequency coefficients after wavelet decomposition. In order to effectively separate the noise components in the high-frequency coefficients, the function threshold must first be determined. When the threshold function is too small, the denoising effect of the image is not obvious, and the denoising result image is not much different from the original image, which loses the meaning of threshold denoising. When the threshold function is too large, the degree of image noise removal is too large. Although the noise is removed more thoroughly, the image is too smooth and the image is blurred, which cannot reflect the essential information of the image. erefore, choosing a Advances in Civil Engineering suitable threshold is of great significance to the results of threshold denoising [18]. e fixed threshold estimation method has a more thorough denoising effect when the noise is more distributed at high-frequency coefficients. erefore, the fixed threshold estimation method is used to estimate the function threshold, and the expression is as follows [19]: where λ is the determined fixed threshold; and σ m is the standard deviation of noise.
(2) Selection of reshold Function. e traditional soft threshold (ST) and hard threshold (HT) function methods are less computationally intensive and easy to implement, but the method will produce constant errors when the highfrequency coefficient is greater than the fixed threshold, resulting in blurred edge details. rough the analysis of ST function in Figure 4, we can see that the continuity of ST function at ± λ is better, but when |ω j,k | > λ, the estimated wavelet coefficient ω ∧ j,k obtained by the ST function has a constant deviation λ from the original threshold coefficient ω j,k . e constant deviation will cause the loss of highfrequency information and cause distortion. From the analysis of the HT function in Figure 5, it can be seen that the HT method solves the constant error problem of the ST method, but there is a discontinuity point ± λ. e HT function is not continuous at the discontinuity point ± λ, and it is easy to cause oscillation when reconstructing the image.
(1) Soft threshold function is as follows: (2) Hard threshold function is as follows: (3) is paper improves the threshold function: From the analysis of equation (13), we can see that in terms of function continuity, when the wavelet coefficients tend to a fixed threshold, the estimated wavelet coefficient limit is 0, so the function value is continuous at the fixed threshold, avoiding the shock phenomenon when the hard threshold function has a discontinuity point. In terms of function asymptoticity, when the wavelet coefficients tend to positive or negative infinity, the limit of the ratio of the estimated wavelet coefficients to the original wavelet coefficients is 1, which proves that the improved threshold function takes ω ∧ j,k � ω j,k as the asymptote; thus, eliminating the constant error of the ST function problem. In terms of function deviation, the difference between the estimated wavelet coefficient and the original wavelet coefficient is calculated with the wavelet coefficient tending to plus or minus infinity as the limit, and the difference is 0, so when the wavelet coefficient tends to infinity, the estimated new wavelet coefficient is infinite closed to the original wavelet coefficients to avoid the problem of deviation.
Image Enhancement Algorithm Based on Improved
Retinex. An improved Retinex image enhancement algorithm is used to estimate the illumination image of the lowfrequency coefficients after wavelet decomposition, and the reflection image is obtained through logarithmic domain conversion. e improved Retinex algorithm in this paper adds a light adjustment parameter based on the single-scale filter Retinex (SSR) algorithm, which makes the reflected image more natural, avoids the halo phenomenon in effect, and has a better edge retention effect.
(1) Illumination Image Estimation. According to the principle of Retinex algorithm, the illumination image is the convolution of the original image and the Gaussian kernel function. In order to obtain the reflection image and eliminate the influence of the illumination on the image, the function is converted to the logarithmic domain, and then the reflection image after the logarithmic domain conversion is obtained. e number field conversion expression is as follows [20]: However, through experiments on the SSR algorithm, it is found that if the illumination estimation part in the original image is completely eliminated, the image will often be unnatural. erefore, an illumination adjustment parameter is added in the process of eliminating the illumination image to make the reflected image more natural. e expression of the reflection image after introducing the adjustment factor is as follows: R(x, y) � log a S(x, y) − k log a S(x, y) * F(x, y), (12) where k is the light adjustment parameter; F(x,y) is the Gaussian kernel function; R(x, i) is the illumination image; and a is the number of image channels, usually 3. 6 Advances in Civil Engineering After Gaussian filtering is performed, the filtering results on different scales are averagely weighted to obtain the estimated illuminance image.
where ω k is the weight coefficient.
Reflection Image Stretch.
e reflection image obtained after the image is transformed in the logarithmic domain often cannot reach the range of 0∼255 in the image value domain, which may cause the image to be gray and white, which affects the visual effect and subsequent processing. erefore, the reflection image needs to be stretched. Firstly, by traversing the pixel values, find the maximum and minimum pixel values in the reflection image, and then stretch the image by the following formula to stretch the reflection image to the range of [0,255] [21].
where d(x,y) represents the reflected image after stretching; R(x,y) represents the reflected image before stretching; and R max and R min represent the maximum and minimum gray values of the reflected image before stretching, respectively.
Piecewise Linear Transformation.
Aiming at the pangray phenomenon in the reconstructed image, this paper uses a three-segment piecewise linear transformation method to improve the image contrast. e three-stage piecewise linear transformation expression is as follows: where f(i,j) is the output image after contrast enhancement; d(i,j) is the input image; and k 1 , k 2 , and k 3 represent the slope of the three-stage transformation. and the expression is as follows [22]: where (a,b) and (c,d) indicate the point where the slope of the piecewise function changes. e segmentation function can set different segmentation points according to the image characteristics, enhance the details of the region of interest, and can also suppress the region of interest.
Detection of Spreading Rate and Spreading Amount
Based on Segmentation reshold Segmentation Method. By dividing the image into several blocks and performing threshold segmentation, the uneven effect caused by illumination or reflection can be solved to a certain extent. e blocks are chosen to be small enough so that the lighting of each block is approximately uniform, so that when auto-thresholding, high-threshold segmentation is used in high-gray areas and low-threshold segmentation is used in low-gray areas. Since the size of a single aggregate is too small, if a single aggregate is divided into blocks, the amount of calculation will be greatly increased. erefore, in this paper, the size of 5 aggregates is selected to be divided into n × n small images of equal length and width. After the blocks are divided, the global threshold method is performed according to the block, and the threshold T of each image block is calculated. By calculating the average gray difference Δd between classes of each image block, the interference of pure background or pure object is excluded, and combined with Otsu algorithm, the image block is binarized based on this condition. en, the binarized images of each image block are stitched together to form a complete crushed stone binarized image.
Advances in Civil Engineering
Δd � m 1 (k) − m 2 (k) , where C 1 is the pixels whose gray level is [1,2, · · ·, k]; C 2 is the pixels whose gray level is [k+1, k+2, · · ·, L]; P(i) is the frequency distribution of gray levels; m(k) is the average gray value of gray levels from 1 to k; and Δd is the average grayscale difference between classes. e average grayscale difference Δd between classes calculated according to the formula is combined with the threshold value T of each image block to realize the binarization operation on each image block. When the interclass grayscale difference Δd of the image block is less than the set value d 0 , it is determined that the pixels in the image block are of the same class, and the image block is not binarized; otherwise, the image block is binarized. e detection method in this paper divides the image into 4 × 4 image blocks (i.e., n � 4), the accuracy of the detection result is 98.1%, and the average processing speed of a single image is less than 85 ms. In this paper, comparisons of single aggregate, 5 aggregates, and 10 aggregates as a block size are listed in Table 1.
It can be seen from Table 1 that when a single aggregate and 5 aggregates are selected as the size of the block, the recognition accuracy is basically the same, but the operation speed of a single aggregate is much slower than that of 5 aggregates. Too many blocks will slow down the recognition speed; the operation speed of 5 aggregates and 10 aggregates is roughly the same, but the accuracy of 5 aggregates is better than 10 aggregates, which is because the block is too large, the thresholds of the targets in the block are sometimes quite different, and the entire target cannot be accurately and completely segmented, resulting in a decrease in the accuracy rate. erefore, 5 aggregates are selected as one block in this paper.
Under a fixed shooting area, after obtaining a certain specification of the crushed stone distribution rate and the weight of the used crushed stone, the crushed stone weight and distribution amount of a certain specification of crushed stone in this area can be obtained under the condition of spreading. Furthermore, it is possible to detect the weight and the amount of crushed stones of different specifications of crushed stones under different spreading rates.
where r i-1 , r i , and r i+1 are the known distributing rates of crushed stones at different moments; m i-1 , m i , and m i+1 are the known crushed rock weights at different distributing rates of crushed stones; r i+2 is the distributing rate of crushed stones at any time ( ≤ 100%); m i+2 is the weight of the gravel at the spreading rate r i+2 ; and s is the shooting area.
Processing Result of a Single Image.
In this study, using 9.5 mm-13.2 mm gravel particles as an example, a picture is randomly selected for segmentation, as shown in Figure 6. e processing of each phase is showed in Figures 7-10. e test value of the spreading rate of the scattered rubble is 54.11%, the actual value is 54.18%, and the difference is 0.07%, within the error range ± 2%, indicating that this algorithm can meet the detection requirements.
As shown in Table 2, comparing the proposed method with hard threshold, soft threshold, and multiscale Retinex, it can be found that the peak signal-to-noise ratio and mean square error of the proposed method are better than other single methods, and the detection speed is basically the same.
e proposed method is compared with the image reconstructed by Krawtchouk and Hahn polynomials. As shown in Table 3, when the mean square error is smaller than the original image, the orders of these two polynomials are 10 and 14, respectively, but the peak signal-to-noise ratio and the mean square error are still inferior to the proposed method. Also, the calculation speed is much lower than that of the proposed method. If the orders of Krawtchouk and Hahn polynomials continue to increase, the detection accuracy can be better than the proposed method, but the calculation speed is too slow which cannot meet the realtime requirements.
Different Specifications of Crushed Stone and Testing
Test of Spreading Rate. Using the proposed method, a series of experiments have been carried out on the spreading conditions of different specifications of crushed stones under different spreading rates and have been tested. Figure 11 is an indoor weighing picture of indoor gravel.
is paper carries out testing tests for different specifications of crushed stones and spreading rates. Compared with the existing method, the average value of the difference in the detection accuracy of the three types of gravel is 0.6%, 0.7%, and 0.4% respectively. From the detection results, it can be seen that the proposed method can meet the requirements of detection accuracy.
Calculation of Spreading Amount and Full Spreading
Amount of Different Specifications of Gravel. According to (18) and (19), the weight of each kind of crushed stone 8 Advances in Civil Engineering can be calculated under the full spread, and then the scattering quality and amount of each kind of stone can be calculated under different spreading rates, as shown in Table 8.
Calculation Result Verification.
e spreading pictures of two kinds of stone materials randomly collected are shown in Figures 15-16. espreading rates detected by the proposed method are 19.5% and 33.1%, respectively, and the weights of crushed stones are calculated to be 63.18 g and 342.15 g, respectively. e actual weighed weight is 60.3 g and 340.6 g, and the difference is 2.88 g and 1.55 g, respectively. It is within the allowable range of error, indicating that the proposed method can basically meet the requirements of the rubble spreading detection.
Actual Engineering Verification
is paper collects images of the road surface after the synchronous gravel sealer has been spread in actual engineering to verify the effectiveness of the algorithm. e collection location was a high-speed construction bid section in Inner Mongolia, and the road surface after the synchronous gravel seal truck was spread. e working process of the synchronous gravel sealing truck is shown in Figure 17. e collected pictures are shown in Figure 18. e pictures collected this time are the spreading construction pictures of the lower seal layer, and the spreading gravel specification is 9.5-13.2 mm. According to the processing results of the algorithm, the processing results of the three collected images were 71.08%, 71.69%, and 68.95%, respectively, with an average value of 70.57%. e average of the actual spreading rate test result is 69.81%, and the difference is 0.76%. Furthermore, the amount of spreading can be calculated to be 1.52 kg/m 2 . e test results of spreading rate and spreading amount are both within the allowable range of error. Advances in Civil Engineering 13
Conclusions
For the pavement spread by the synchronous gravel sealer, environmental factors such as light and noise, as well as gravel of different specifications and spreading rates, have an impact on the detection accuracy. is paper processes the high-frequency and low-frequency coefficients of the image after two-dimensional wavelet decomposition and then reconstructs the image to eliminate the influence of environmental factors such as lighting. Next, the segmented Otsu threshold method is used to separate the asphalt and gravel to detect the spreading rate of gravel and to further establish the relationship between the spreading amount and the spreading rate.
(i) After extracting the high-frequency and low-frequency coefficients of the image by using two-dimensional wavelet decomposition, the highfrequency coefficients are processed by the improved threshold method, the low-frequency coefficients are processed by the improved Retinex method, and then the image is reconstructed, which can quickly, accurately, and effectively detect the spreading rate of gravel. (ii) rough the segmented Otsu threshold processing of the image, the regional threshold can be set in each block, which can further eliminate the influence of environmental factors such as light, so as to accurately segment the asphalt and gravel, detect the rubble spread rate, and establish the relationship between the rubble spread rate and the amount of spread. (iii) By collecting and testing crushed stones of different specifications and spreading rates, and comparing them with actual testing results, it can be found that the proposed method can meet the requirements of actual construction testing and has good reproducibility. (iv) rough the proposed method, the poor quality of the spreading part can be found in time in the spreading process, so as to make real-time adjustments to ensure the quality of road construction.
Data Availability
e data used to support the findings of this study are included within the article.
Conflicts of Interest
e authors declare that they have no conflicts of interest. | 7,681.8 | 2022-10-19T00:00:00.000 | [
"Engineering",
"Computer Science"
] |
The deep OB star population in Carina from the VST Photometric H$\alpha$ Survey (VPHAS+)
Massive OB stars are critical to the ecology of galaxies, and yet our knowledge of OB stars in the Milky Way, fainter than $V \sim 12$, remains patchy. Data from the VST Photometric H$\alpha$ Survey (VPHAS+) permit the construction of the first deep catalogues of blue excess-selected OB stars, without neglecting the stellar field. A total of 14900 candidates with 2MASS cross-matches are blue-selected from a 42 square-degree region in the Galactic Plane, capturing the Carina Arm over the Galactic longitude range $282^{\circ} \lesssim \ell \lesssim 293^{\circ}$. Spectral energy distribution fitting is performed on these candidates' combined VPHAS+ $u,g,r,i$ and 2MASS $J,H,K$ magnitudes. This delivers: effective temperature constraints, statistically separating O from early-B stars; high-quality extinction parameters, $A_0$ and $R_V$ (random errors typically $<0.1$). The high-confidence O-B2 candidates number 5915 and a further 5170 fit to later B spectral type. Spectroscopy of 276 of the former confirms 97% of them. The fraction of emission line stars among all candidate B stars is 7--8% . Greyer ($R_V>3.5$) extinction laws are ubiquitous in the region, over the distance range 2.5--3 kpc to $\sim$10~kpc. Near prominent massive clusters, $R_V$ tends to rise, with particularly large and chaotic excursions to $R_V \sim 5$ seen in the Carina Nebula. The data reveal a hitherto unnoticed association of 108 O-B2 stars around the O5If$+$ star LSS 2063 ($\ell = 289.77^{\circ}$, $b = -1.22^{\circ}$). Treating the OB star scale-height as a constant within the thin disk, we find an orderly mean relation between extinction ($A_0$) and distance in the Galactic longitude range, $287.6^{\circ}<\ell<293.5^{\circ}$, and infer the subtle onset of thin-disk warping. A halo around NGC 3603, roughly a degree in diameter, of $\sim$500 O-B2 stars with $4
INTRODUCTION
Massive OB stars are critically important objects in shaping the evolution of galactic environments. But because of their relative rarity due to the initial mass function (IMF) and their short lives, they have proved to be difficult to nail down in terms of their evolution before and after the main sequence: their formation is still subject to debate (Tan et al. 2014) and we cannot say with any certainty what exact fate awaits which type of massive object (Langer 2012). It has long been recognised that the UV radiation and supernovae they produce are huge factors in shaping the interstellar medium (ISM).
As things stand, the best-studied resolved massive star population can be claimed to be located in the Magellanic Clouds, thanks to the VLT-FLAMES Tarantula Survey (Evans et al. 2011, and subsequent papers) that has produced a coherent spectroscopic dataset on over 800 massive stars. This has captured well the properties of a population of massive stars at reduced metallicity ([Fe/H] −0.3). In contrast, the impact of varying levels of significant extinction has rendered the higher metallicity disk of our own galaxy more of a challenge. Existing catalogues of the O and early-B stars are confined to objects brighter than ∼12th magnitude (complete only to ∼ 2 kpc, see e.g. Garmany et al. 1982) and are heterogeneous (e.g. Reed 2003). An effort is under way to collect complete spectroscopy of the known bright Galactic O-star population (GOSSS by Maíz Apellániz et al. 2011, and subsequent papers) but, limited by the source material it presently rests on, only a few tens of objects have yet been covered over the range 12 < B < 16 (Maíz Apellániz et al. 2016). So far the known fainter reddened OB stars are mostly located in massive clusters, that are more easily noticed against the Galactic background.
There is thus a gap in our knowledge of the wider field population: this presents a problem to the debate over the significance of the runaway phenomenon (Portegies Zwart et al. 2010) and how this should be tensioned against the possibility of forming massive stars outside densely clustered environments (de Wit et al. 2005;Bressert et al. 2012). Furthermore, as we await the arrival of advanced astrometry from ESA's Gaia mission, it is the perfect time to trace how OB stars fit into the structure of the star-forming Galactic thin disk, reaching well beyond the solar neighbourhood. Mapping these intrinsically luminous objects is important for another reason: they have long been valued as distant and bright back-lighters of the ISM -much of what is known about interstellar extinction has been deduced from fitting the SEDs of OB stars (e.g. Cardelli et al. 1989;Fitzpatrick & Massa 2007;Maíz Apellániz et al. 2014). A new deep census of OB stars has much to offer.
The cheapest method of astronomical census is provided by photometry. At the time Johnson & Morgan (1953a) introduced the U BV photometric system they also described the concept of exploiting the (U − B,B − V ) colour-colour (CC) diagram to construct reddening-free parameters labelling reddening lines for distinct stellar spectral sub-types. This introduced a method of analysing stellar photometry that can now be applied with greatly increased power to very large, homogeneous data sets in this new era of survey photometry. It works especially well as a tool to select hot massive OB stars: the aim of this paper is to apply a cus-tomised version of it to newly-minted data from the VST 1 Photometric Hα Survey of the Southern Galactic Plane and Bulge (VPHAS+, Drew et al. 2014). The target region for this work, intended both as an up-scaling of our already validated method and as an exploration of a part of the Milky Way particularly rich in massive OB stars, is the Carina region of the Galactic plane.
In a previous paper (Mohr-Smith et al. 2015), we presented a first blue selection from VPHAS+ data that focused on a region spanning just 2 square degrees, around the massive O-star-rich cluster, Westerlund 2. This adapted the method of reddening-free parameters to the Sloan filter system in use at the VST and performed a validation test on a catalogue of objects, that had been selected from the (u − g,g − r) diagram, and further winnowed through fitting u,g,r,i and published J,H,K magnitudes to progressivelyreddened synthetic stellar photometry. The haul from this was a list of 489 objects with spectral types of B2 or earlier -most of them were new discoveries, representing an order of magnitude increase on the total known from previous catalogues.
It became clear in this first pilot that the characterisation of extinction is particularly high in quality: the typical precisions achieved are 0.1 or better in each of A0, the monochromatic extinction in magnitudes at 4595Å, and RV , the ratio of total to selective extinction. The new, expanded catalogue of candidate OB stars included both discoveries within Westerlund 2 itself and a handful of similarly reddened O stars scattered around it at offsets of between 10 and 40 arcminutes. The latter may have been ejected from the cluster or they may be evidence of a wider star-forming event within which Westerlund 2 is the most prominent feature. To settle this, spectroscopic follow up is required. The new work here expands the sky area from 2 square degrees up to 42 and the number of high-confidence candidate O to B2 stars from 489 to 5915.
The total footprint spanning the Carina Nebula and environs is shown in Fig. 1: it runs from close to the arm's tangent direction, at ∼ 282 • (Dame 2007;Vallée 2014), through Westerlund 2, and on through the Carina Nebula, to beyond the brilliant massive open cluster, NGC 3603, ending at 293 • . The irregular footprint outline, with reduced latitude coverage at lower longitudes, reflects the processed data available at the outset of this work. The longitude range examined is much the same as that investigated by Graham (1970) who used Walraven photometry to map 436 bright (8.5 V < 11.5) OB stars. Indeed, the work we present amounts to an update, almost 50 years on, that reaches from 10 to more than 1000 times fainter.
On the map of Galactic spiral arm structure presented by Russeil (2003) the Carina Arm is the single most compelling and coherent feature. In CO maps (Grabelsky et al. 1987;Dame et al. 2001) the arm is traceable as a somewhat broken ridge of emission that has a near side about 2 kpc away, running from higher Galactic longitude to the tangent point 4-6 kpc distant (see the discussion by Dame 2007): it connects to the far side beyond the tangent as it (Mohr-Smith et al. 2015) and the circle shows the area studied with spectroscopy in Section 4. The two large bright smudges in the far right, and that on the far left of the footprint are due to scattered light in the constituent images that are not pipeline corrected for illumination effects (which are included in the photometric catalogue generation).
carries on unwinding out beyond the Solar Circle: Grabelsky et al. (1987) suggested heliocentric distances of the order 10-12 kpc for the arm at ∼ 293 • . The famous Carina Nebula is generally regarded as being embedded in the near portion of the arm, 2.5-3 kpc away (Tapia et al. 2003;Hur et al. 2012;Kumar et al. 2014), while NGC 3603 is associated with the far arm, ∼7 kpc away (Sung & Bessell 2004). It aids visualisation of the arm to notice that 11 degrees of longitude corresponds to roughly 1.1 kpc at ∼5 kpc distance -not much of a bend over the potential heliocentric distance range to ∼10 kpc. Nevertheless, a little curvature, turbulent motions and recent star formation create complexity in the dust distribution that demands high density sightline sampling.
This paper is organised as follows: the first major section, section 2, presents the photometry and how it is exploited to select and characterise the optically-fainter Carina OB-star population; the results of the selection are presented in section 3 along with exercises aiming to distinguish the minority of non main sequence objects included in it; the quality of the selection is then examined more closely in section 4 by analysing follow-up spectroscopy of a subset of candidates located within a single 2 degree field as marked on Fig. 1. The outcome is that almost all the high confidence candidates are confirmed. Finally in section 5, the new catalogue of 5915 candidate OB stars is put to use in an appraisal of the trends in extinction (A0) and extinction law (RV )across the studied region. We then experiment with adopting the OB-star scale height within the thin disk as a standard ruler in order to set a scale to the rise in extinction with heliocentric distance. This works over the longitude range 287.6 • < < 293.5 • and leads in turn to measures of the onset of the warp of the Galactic thin disk. The paper ends with some discussion and the main conclusions in section 6.
METHOD: THE OPTICAL PHOTOMETRY;
OB-STAR SELECTION AND SED FITTING
VPHAS+ optical photometry
The optical photometry we exploit is from the VPHAS+ survey (described in full by Drew et al. 2014). This survey of the southern Galactic Plane began at the end of 2011 and, at the time of writing, continues to execute on the VST at the Paranal site in Chile. The VST camera, OmegaCam, delivers 1 × 1 square-degree images of the sky at a typical seeing of 0.8-0.9 arcsec in the Sloan gri and narrowband Hα filters, rising to 1.0-1.1 arcsec in Sloan u. In all bands, the limiting (Vega) magnitude is typically greater than 20th, reaching as faint as 22nd in g. All data from the survey are pipelinereduced to source lists, calibrated against nightly standards, by the Cambridge Astronomical Survey Unit (CASU). These are used in this study in the form of band-merged ugr and riHα contemporaneous catalogues. We note that the blue and the red filters are usually observed months apart -the repeated r band observations are in place to serve as basic checks on variability. The raw materials for this study, are (Fig. 1).
A new feature of expanding to the larger set of fields is that it is even more important to impose a uniform photometric calibration across all the data. To achieve this, we have made comparisons on a field by field basis with g, r and i-band stellar photometry from The AAVSO Photometric All-Sky Survey (APASS) and have then used the main stellar locus in the (u − g, g − r) colour-colour (CC) diagram to determine the u band shifts required. The Hα band data are tied to the r band calibration simply by requiring the Hα photometric zeropoint to be offset from the r zero-point by 3.08. The details of this alignment process will be presented in a forthcoming presentation of VPHAS+ data products (Drew et al, in prep). The mean photometric adjustments made to the broadband data, as a result of these comparisons, are given in Table 1. The sense of all the tabulated shifts is such that the revised magnitude scale is brighter than the unrevised. In this paper, we express all magnitudes in the Vega system.
We have exploited the field overlaps provided by the tiling pattern of VPHAS+ (see Drew et al. 2014) in order to check the final uniformity of the recalibration. Within the overlap regions, it is possible for a star to have up to four independently recalibrated detections in each band. Using these, we can evaluate the convergence to a common scale by comparing the standard deviation of multiple measurements before and after the calibration adjustments. These are set out, for the broad bands, in Table 1: there is noticeable improvement in all of them and especially in g.
As final confirmation of the improved uniformity of the data, after correction, we show in Fig. 2 before and after source density plots of the (u − g, g − r) and (r − i, g − r) CC diagrams for the region studied here. We can see that the diagrams have much tighter distributions with less scatter after correcting the individual field calibrations. The mainstellar locus (highest density of sources) is also placed in the correct position with respect to the synthetic tracks. The data in Table 1, alongside Fig. 2, show that the main consequence of the u re-calibration is to bring this band into better (astrophysical) alignment with the longer-wavelength bands, rather than to reduce scatter. For the successful selection of candidate OB stars, this is critical.
OB-star selection and SED fitting
The methods for the selection of candidate OB stars and spectral energy distribution (SED) fitting are the same as those used and described in full by Mohr-Smith et al. (2015). Below, we summarise the main features.
Photometric Selection and Cross Matching
First, a (u − g, g − r) CC diagram is constructed that includes all catalogued objects with g 20, a u detection and random photometric magnitude errors below 0.1 in g, r and i. OB stars in this diagram are offset above the main stellar locus and can be selected using a method related to the well-established Q method of Johnson & Morgan (1953b). We select targets blue-ward of the B3V reddening vector, i.e. above it, as drawn in the (u − g, g − r) CC diagram in Fig. 2 (see also Fig. 3 in Mohr-Smith et al. 2015). This aims at picking out all objects earlier than B3 (our target group). The number of objects in this initial selection was 37971.
All candidates are then cross-matched against the Two Micron All Sky Survey (2MASS), the only available nIR survey covering the whole region. The maximum cross match distance was set to 1 arsec in forming optical near-infrared (OnIR) SEDs. As long as the nIR magnitudes of the the initially selected objects are within the 2MASS range, the crossmatching is very successful since the VPHAS+ survey astrometry is calculated with reference to 2MASS. The 90 th percentile cross match separation is 0.3 arcseconds and the median is 0.073 arcseconds. Only objects with catalogued magnitudes in all seven bands (u, g, r, i, J, H, Ks) are retained for input into the SED fitting procedure.
SED fitting
We compare the empirical SEDs to a parametrized model in a simple Bayesian scheme using Markov Chain Monte Carlo (MCMC) sampling. The model consists of four parameters log(T eff ), A0, RV and µ, the distance modulus. The intrinsic SEDs are taken from the Padova isochrone database (CMD v2.2 2 ; Bressan et al. 2012;Bertelli et al. 1994). As the OnIR colours of OB stars do not vary significantly with luminosity class or metallicity (Martins & Plez 2006), only main-sequence, solar-metallicity models have been considered (log(g) ∼ 4, Z = 0.019). The models are then reddened using a set of Fitzpatrick & Massa (2007) reddening laws and shifted according to distance modulus. As the apparent OnIR SEDs of OB stars change only subtly as a function of effective temperature (Martins & Plez 2006) the shape of their SEDs is controlled mainly by extinction. This means that log(T eff ) is relatively weakly constrained, whilst permitting reasonable O/B separation (see Section 4). The extinction parameters, on the other hand, are well constrained. As there is no luminosity class discrimination, µ acts primarily as a normalization factor and is highly correlated with effective temperature (see Fig. 6 of Mohr-Smith et al. 2015).
The likelihood function used in the Bayesian scheme is a multivariate Gaussian that embeds the assumption that the uncertainties on all measurements/parameters are uncorrelated 3 . This reduces to the familiar sum for χ 2 : where P (SED obs | θ) is the probability of obtaining the observed SED (SED obs ) given a set of parameters θ, and where m(obs)i and m(mod)i are the observed and model magnitudes in each band i. In this equation only, i is just a summation index We have adopted uniform priors on each parameter which are as follows: The lower limit on log(T eff ) is chosen to be below the temperature of a B3V star (cf. table 3 in Nieva 2013) and the upper limit is the maximum temperature of a MS star in the Padova isochrones. The latter corresponds to earlier than O3V (see e.g. Martins et al. 2005). The upper limit on A0 is chosen to comfortably enclose the likely extinction range among the selected OB stars, given the g = 20 limiting magnitude, assuming a typical rate of rise in A0 of ∼ 1.5 mag kpc −1 . The limits on RV cover what we expect to find in the Galaxy (Fitzpatrick & Massa 2007) and the upper limit on µ amounts to leaving it unbound. The MCMC fitting procedure was performed using the python package emcee (Foreman-Mackey et al. 2013).
As in Mohr-Smith et al. (2015), SED fits with χ 2 < 7.82 are taken to be acceptable: the probability of achieving this value in the case of the null hypothesis is 0.05 for the 3 degrees of freedom involved in this fitting process. Table 2 shows the breakdown of the number of OB candidates according to effective temperature and fit quality. In total 14900 OB stars were selected for SED fitting. Around a quarter of the candidates where found to have poor, χ 2 > 7.82, SED fits. This leaves a clear majority of object with acceptable SED fits. Just under half of these are probable B3 and later type stars with log(T eff ) < 4.30. So finally, there are 5915 objects in our target effective temperature range, log(T eff ) 4.30 with χ 2 < 7.82. Of these, 905 are probable O stars with log(T eff ) 4.477. There are thus around five times as many B2-B0 star candidates as O star candidates -a ratio that exceeds the IMF ratio of ∼3, thanks in part to the bright magnitude limit set by the survey data.
Overview
All candidates were cross matched with SIMBAD to within an acceptance radius of 1 arcsec in order to check if any objects with already known spectral type are in the photometric selection. Table 3 shows a numerical breakdown, according to derived effective temperature and fit quality, of the subset of OB candidates with spectroscopically confirmed types according to SIMBAD. These are supplemented with the spectroscopically confirmed types from our AAOmega spectroscopy to be presented in Section 4. The majority of objects with known spectral type from SIM-BAD were found to be OB stars as expected, with some WR stars appearing in the χ 2 > 7.82 groupings. There is also contamination from a handful of M giant stars and one carbon star (C*) among the poor fits. These objects have mimicked very highly reddened OB stars in the (u − g, g − r) diagram but nevertheless they are easily distinguished in the selection both via SED fit quality and via r − i colour as discussed in Section 3.2.2. A very positive feature of tables 2 and 3, in combination, is the high success rate in placing stars correctly into the O and B spectral types. Inevitably the application of a cut in χ 2 will exclude some genuine O and early B stars, either randomly or because of source blending and/or the presence of circumstellar emission. Fig. 3 shows the distributions of parameters for all objects with acceptable (χ 2 < 7.82) SED fits. Objects with log(T eff ) 4.30 that are our main focus are coloured grey. As was found for the test case by Mohr-Smith et al. (2015), the entire region requires extinction laws with enhanced values of RV with a median value of 3.74. The majority of the candidates have best-fit extinctions in the range (3 < A0 < 6) at likely distances of 3 -10 kpc. The Galactic longitude and latitude distributions of the accepted OB stars are shown in Fig. 4. There is evidently a broad peak in the latitude distribution between the Galactic equator and b −1.5 • . The logitude distribution, on the other hand, shows a gradual rise with increasing separation from the tangent direction. The sharp O star peak in the latter, sitting close to = 292 • is associated with NGC 3603.
The restrictions on the magnitude range of the photometry sourced from VPHAS+, in combination with photometry from 2MASS, inevitably carry through to some constraint on the properties of the candidates uncovered by the selection and SED-fitting process. This is illustrated in Fig. 5, showing the distribution of g band magnitudes and g − K colours of all candidates with acceptable B3 or earlier-type SED fits. The fact that the magnitude ranges of the VPHAS+ g and 2MASS K band only overlap between 13 m 15 prevents us from detecting a greater number of . Distribution of the best fit parameters for the selection of objects with χ 2 < 7.82. Objects with log(T eff ) > 4.30 are coloured in grey. The remaining cooler objects are coloured red. The turn over in the log(T eff ) distribution at ∼ 4.26 is a product of the initial photometric selection seeking to exclude cooler B3 and later type stars. intrinsically fainter and less reddened hot stars with lower g − K. As we are targeting intrinsically-bright massive OB stars, rather than sdO and sdB stars, this is not detrimental to our intended goal. A notable feature of the g distribution is the sharp upturn in the number of candidates as the g = 20 faint limit is approached. This effect can be attributed to the growing number of sub-luminous objects at these faint magnitudes as discussed in detail in Section 3.2.1. At g > 19, we are seeing the mixing of two separate distributions; one for the massive OB stars and another for the sdO and sdB stars. If the faint g-band limit on the selection had been raised from 20 to 21st magnitude, it is likely that some more highly-reddened OB stars would have been found, along with a higher proportion of sub-dwarfs. Nevertheless, the main motive behind setting the selection limit at g = 20 was to avoid growing incompleteness due to the increasing incidence at high extinction of u non-detections (the typical VPHAS+ 5σ faint limit is between 21 and 21.5 in g, in the Vega system).
A database containing information on all 14900 candidate objects is provided as supplementary material suitable for sorting by e.g. χ 2 . An explanation of the database content is set out in the Appendix A1. The adopted naming convention is of the form 'VPHAS OB1 NNNNN', where 'NNNNN' is the identification number for individual objects ordered by Galactic Longitude.
The identification of non-MS OB stars and emission line objects
The SED fitting performed on our blue photometric selection could not distinguish luminosity class, nor did it make practical sense to take into consideration the possibility of line emission. So now we use evidence from the distributions of SED fit parameters to relax the MS assumption of the SED fits, and then bring in narrow-band Hα photometry to distinguish the emission line stars.
Sub-and Over-luminous Stars
Due to the large numbers of objects included in this selection it becomes more difficult to separate the sub-luminous and over-luminous stars in the same manner as in Mohr-Smith et al. (2015). This is because the different luminosity groups drawn from a much wider sky area start to mix in the µ vs A0 and µ vs log(T eff ) diagrams used in the selection.
Here, a different technique is necessary. We can separate sub-luminous and over-luminous stars from our MS OB star targets primarily by using the colourmagnitude diagram (CMD). In the (g, u − g) CMD the subluminous and over-luminous stars will, for a given temperature and distance, form separate sequences below and above the main sequence. As we are looking at a range of distances these sequences become somewhat blended. Hence we aim to make a crude cut that errs on the conservative side.
First, we take all objects with acceptable χ 2 < 7.82 fits and bin the data into deciles in effective temperature. For each decile, we then take the lowest effective temperature and the reddening vector corresponding to it, and place that vector at the 95 th percentile in distance modulus (based on all temperatures in the decile) on the (g, u − g) CMD. All stars fainter than this plausible lower-limit line are selected as sub-luminous (see Fig. 6): they are statistically fainter than the coolest and most distant MS stars in their temperature bin. We also take the highest temperature in each bin and place it at the 5 th percentile in distance modulus on the (g, u − g) CMD. All stars brighter than this line are selected as over-luminous: they are statistically brighter than the hottest and closest MS stars in their temperature bin. Figure 6 shows the CMD, (log(T eff ) vs µ) and (A0 vs µ) with likely MS stars in grey and the selected sub-luminous and over-luminous stars in red and green respectively. These distributions are compared with the positioning of examples confirmed as either sub-or over-luminous relative to the MS assumption. In all three diagrams the known evolved OB stars reassuringly tend to co-locate in the diagram with the over-luminous candidates, whilst the one confirmed lower luminosity object also falls in the right zone.
The impact of the MS assumption in SED fits to the under-luminous objects is to make them appear as very distant objects with relatively low reddening. The absolute magnitudes of sdO stars range from MV = 3 − 6 (Stark & Wade 2003) -some ∼ 6 mag fainter than MS OB stars for a given temperature. If this adjustment is made, their inferred distance moduli reduce to ∼ 10 − 12 from ∼ 16 − 18. Viewed in these terms, these objects would most likely be significantly reddened sub-dwarfs to the foreground of the main massive OB population. This is tenable for the less reddened sub-luminous candidates, but especially where A0 is 4 or more (a typical value for the MS OB stars) it becomes more likely that any downward correction of distance modulus needs to be more modest -which in turn hints at classification as e.g. post-AGB, rather than lower mass blue horizontaal branch. We remind there is a bias to select more highly reddened subdwarf stars due to the 2MASS faint limit (see Section 3.1).
Conversely, in Fig. 6, the over-luminous objects appear erroneously as close-by with higher-than-average reddening. If these objects are, for example, blue supergiants their absolute visual magnitudes would be around ∼ −6.5 (Crowther et al. 2006). If these are adopted in place of MS values, their derived distance moduli, µ, would rise from ∼ 10 to ∼ 14, placing them in the midst of the general near-MS massive OB population. From our own spectroscopy (Sec. 4) and also from the literature, we have 8 objects plotted in Fig. 6 that illustrate this behaviour.
There will be some over-and under-luminous objects which we cannot distinguish clearly from the MS population and indeed objects falsely labelled as probably underor over-luminous objects. For example, in the middle panel of Fig. 6, the distance moduli of the coolest candidate subdwarfs seemingly entirely overlaps the upper end of the main stellar locus. In total 299 objects are tagged as likely to be under-luminous while 344 are tagged over-luminous. This equates to around 5% of the whole sample going into each category -a proportion that is a direct consequence of the distance modulus percentile cuts chosen (95 th for overluminous and 5 th for the sub-luminous). This cut was chosen by visual inspection of the CMD, noting where the sequences show signs of separating.
Meylan & Maeder (1983) estimated a surface density of 10 -20 blue supergiants (BSGs) per kpc 2 in the Galactic Plane. Taking our distance range as 3 -10 kpc we are sampling a projected disk surface area of a little over 9 kpc 2 . This suggests that our selection of 344 over-luminous stars is too generous by a factor of two or more. Turning to the faint end of the range, we note that Han et al. (2003) proposed a space density of sdB stars of 2 − 4 × 10 −6 pc −3 . Assuming that we are detecting sdB stars at distances between 1 to 2.5 kpc then we are sampling a volume of around ∼ 0.06 kpc 3 which predicts around ∼180 sdB stars. Again this suggests a somewhat over-enthusiastic selection of 344 possible sub-luminous stars. The fact that these selections 'over-shoot', suggests that the remaining 90% is likely to be a relatively clean selection of near main-sequence OB stars.
The candidate stars selected as candidate over-and under-luminous stars are marked as such in the supplementary table (see Table A1 in the appendix). Figure 6. Objects coloured in red are likely to be sub-luminous compared to the rest of the population. Objects coloured in green are probable over-luminous objects. The black diamond is the candidate sdO object with a spectrum presented in Sec. 4. The cyan pentagons pick out known WR stars and the black star symbols represent known/confirmed luminosity class I and II OB stars.
Emission line stars
We now use the VPHAS+ Hα measurements to pick out any emission line stars in our basic blue selection. Following Mohr-Smith et al. (2015) we use the (r − i, r − Hα) diagram to select all objects that lie more than 0.1 mag in r − Hα above the O9V reddening vector (equating to ∼ 10Å in emission line equivalent width). This secondary selection misses out 152 stars (∼ 1%) that are presently without recorded Hα magnitudes for quality reasons. Figure 7 shows this selection for objects with log(T eff ) 4.30 in the accepted fit group (top panel) and the poor fit group (χ 2 > 7.82, bottom panel). The black crosses show objects selected as emission line stars, while the various coloured symbols show stars with known spectral type from the SIMBAD cross match and those with AAOmega spectra from Section 4. Here we can see that the emission line objects co-locate in the diagram with classical Be (CBe) stars and WR stars while the non-emission line objects co-locate in the diagram with the known dwarf and giant OB stars. Previous experience with the same selection method in the Northern Hemisphere has shown that most candidate emission line stars are CBe stars, at least at brighter magnitudes (Raddi et al. 2015). As discussed in Section 4.2 the majority of WR and CBe stars produce poor χ 2 values when fit to MS OB star SEDs.
The bottom panel of Fig. 7 shows in addition a group of poor χ 2 objects with r − i > 2 that co-locate with a group of known M giant stars. These very red contaminant objects showing extreme r − i values, are found in the bottom right corner of the (u − g, g − r) CC diagram, permitting them to enter into the original selection as candidate highly reddened OB stars. It is likely that the measured u band magnitudes for these intrinsically red objects is affected by red leak discussed by Drew et al. (2014), pushing them apparently blue-ward into the OB-star area of the diagram. The fact that none of these objects yields a fit with χ 2 < 7.82 is further illustration of how the SED-fitting is critical in enhancing the overall blue-selection quality.
How the candidate emission line stars are distributed in terms of χ 2 and broad spectral type is illustrated in Fig.8. The growth in the fraction of emission line candidates with declining fit quality stands out. The numbers provided in the diagram also show that it is the later B group that presents the highest fractions as well as the highest absolute num-bers. Taking all the B stars together with good fits from the first two χ 2 ranges in Fig. 8, the computed fraction of emission line stars is 7.0%. This rises to 8.0%, if χ 2 up to 12 is accepted also. Given that LBV and B[e] stars are rolled in, these overall fractions certainly appear consistent with the findings of McSwain & Gies (2005), as summarised in Fig.5 of their paper. Our estimates cannot support the 10-20% range that emerged from the study by Zorec & Briot (1997). The differences here may well reflect the way in which CBe stars are distinguished from normal B stars. We place a clear threshold in requiring evidence of an Hα colour excess equivalent to at least 10Å emission equivalent width across an observed population -an approach that is similar to that of McSwain & Gies (2005) who studied southern clusters. In older works, quantitative thresholds of this kind were less commonly applied.
Objects with Hα excess are marked as such in the database provided in the supplementary materials. Objects with Hα emission are removed from the later discussion in section 5 regarding extinction as the derived extinction parameters may be affected by the presence of a circumstellar disk.
DIRECT SPECTROSCOPIC VALIDATION OF THE PHOTOMETRIC SELECTION AND SED FITS
We now present the new spectroscopy, already used to supplement the known SIMBAD-listed objects in Table 3, in order to appraise the quality of outcome from our photometric selection and SED fitting procedures.
Spectroscopic observations
Low resolution spectra of 323 OB candidates (13 < g < 19) from our selection were taken using the multi-fibre spectrograph, AAOmega, at the Anglo-Australian Telescope, in service mode during June and July 2014. The targets observed were drawn at random from across the χ 2 and effective temperature range (i.e. some poor fits were included). The large white circle in Fig. 1 shows the AAOmega two-degree field of view centred on RA 10 28 45.25 DEC -58 25 56.12 (J2000) containing all observed targets. The 580V grating was used, covering the wavelength range ∼ 3000 − 6000Å at a resolution of R=1300 in order to capture the critical blue hydrogen and helium photospheric lines needed for reliable classification. The 'red' arm grating, chosen mainly for a different programme, was the 1700D: this captured the calcium triplet region which provided some further classification evidence. We used dedicated sky fibres to support pipeline sky subtraction. The data were extracted and reduced to one-dimensional form using the 2dfdr soft- B2 and later B0-B2 O9 and earlier Figure 8. The fraction of emission line stars relative to the total number of objects selected in 3 different spectral type groups, as a function of SED fit quality (χ 2 ). The numbers of objects contributing to each ratio are provided above the coloured bar representing the fraction. As noted in text, the presence of circumstellar emission in an OB stellar SED unavoidably reduces the quality of fit to a pure photospheric SED. Hence the fraction of emission line stars rises as χ 2 rises, in all three groups, although the absolute numbers of objects fall. CBe stars and some B[e] and LBV objects most likely dominate the B spectral type range, while WR stars will be most frequent in the O range.
ware package with default settings; the wavelength calibration was obtained using a third order polynomial fit. Due to the large magnitude range of the candidates the observations were split into two configurations; a faint set-up and a bright set-up. The faint set-up included objects in the magnitude range 16 g < 19 and was exposed for a total of 140 minutes. The bright set-up included objects in the magnitude range 13 g < 16 and needed only 40 minutes exposure. Some of the spectra had to be discarded due to inadequate counts for classification purposes. The 276 spectra retained span a range in signal-to-noise ratio from 20 to 50 with a median value of 35 as measured in the wavelength range 4560 − 4650Å.
Each spectrum was continuum fitted and normalized using a spline fit in the pyraf package onedspec. Before further analysis, the prominent diffuse interstellar bands (DIBs) at λ 4430, 4892, 4748 and 5362Å were cut out.
Broad classification of the spectra
The 'blue' and 'red' wavelength range of each stellar spectrum was visually inspected in order to place the objects into broad spectral types. Of the 276 candidates observed, using the spectral features listed below, we found that the spectral classes break down as follows: Including the more exotic CBe and WR stars among the desired massive star selection, we find the remaining contamination comes from just a handful of lower mass A, F and G type stars. Subsequent close inspection of the original VPHAS+ data revealed that all of the A/F/G stars had photometry that was compromised either by source deblending failures, or by poor background subtraction due to a very bright neighbouring star, or by falling close to the edge of a CCD (corrupting the photometry in one or more bands). Fig. 9 shows the distribution of spectral classes for the selection. The distribution in red is for those objects that have unacceptable χ 2 > 7.82 photometric SED fits. Here we can see that the majority of A/F/G star contaminants have emerged with poor fits to main-sequence OB star SEDs thanks to the contaminated photometry. For studies focused on small numbers of objects, it is quite easy to limit contamination of the selection by visually inspecting thumbnails of every star in the sample. However, when the numbers grow this becomes increasingly less practical and the benefit becomes less obvious given the small percentage of contaminants likely. The SED fitting procedure usefully reduces the contamination rate from 8% to just 3% when making a cut at χ 2 < 7.82.
We also note that around 70% of the CBe stars are found to have poor χ 2 values. Although the OnIR SEDs of classical Be stars are not greatly different from normal B stars of similar effective temperature, the presence of a warm circumstellar disk can affect the NIR colours. It is in fact easy to separate CBe stars from the rest of the population through detection of line emission via the VPHAS+ narrow band Hα filter (see Section 3.2.2). Both of the previously known WR stars have similar colours to MS OB stars in the optical and are hence in our selection, but they do not fit well to MS OB star OnIR SEDs, again because of NIR excess -this time due to their dense stellar winds (Faherty et al. 2014). Inspection of the SED fit residuals for spectroscopically-confirmed OB stars with χ 2 > 7.82 reveals that most of them have been affected by blending in the NIR photometry. At these longer wavelengths, blending will be more common due to the combination of higher prevailing stellar densities and the lower angular resolution of 2MASS.
Model atmosphere fitting
Each OB-star spectrum covering the wavelength range ∼ 3000 − 6000Å (225 stars in total) was fitted to a grid of model spectra in order to derive effective temperatures for comparison to our photometric estimates. The method used for the O stars had to differ from that applied to the B stars in order to adapt to different model grids, supplied in different forms. For the B stars the TLUSTY NLTE grid (Lanz & Hubeny 2007) the entire spectrum was used in the fitting procedure. The FASTWIND grid treats individual line profiles, including the hydrogen and helium lines needed to determine effective temperature and surface gravity -just these (stronger) lines were input to the fitting procedure. Solar metallicity was adopted in both cases. Since this sight line samples only a limited range of Galactocentric radii (RG ∼ 7 − 10 kpc) this should be a reasonable approximation.
B star model fitting
We begin with a set of TLUSTY model spectra which are parametrised in terms of just effective temperate and surface gravity. Each spectrum in the grid was rotationally broadened to a range of output projected rotation velocities (v sin i) and convolved to match the resolution of the instrument using the python package PyAstronomy. The grid was then linearly interpolated to form a continuous set of models for MCMC sampling, growing the parameter set to three: The best fit parameters were derived using MCMC sampling with a χ 2 likelihood function akin to that used in the photometric fits: is the probability of obtaining the observed spectrum (SP EC obs ) given a set of parameters θ and f (obs)i and f (mod)i as the observed and model normalized flux at each wavelength i.
We compare the observed spectra to a grid of parametrised TLUSTY models using uniform priors: The boundaries of the priors match the limits of the model grid.
The models are parametrised by the following: -T eff : effective temperature -log(g): surface gravity -n(He): helium abundance, by number -ξt: micro turbulence -Q: wind strength parameter,Ṁ (R v∞) −1.5 -β: exponent of the wind velocity law -v sin i: rotational velocity -RV: heliocentric radial velocity In this case each line profile was fit independently using the same style of likelihood function as Eqn. 4. The overall function is the product of probabilities for all line profiles: where P (SP EC obs | θ) is the probability of obtaining the observed spectrum (SP EC obs ), given a set of parameters θ, and where P (LP obs(j) | θ) is the probability of obtaining the observed line profile, LP obs(j) , again given a set of parameters θ. The parameters ξt and β were fixed at typical values, 5 kms −1 and 0.8 respectively, as our spectra are too low resolution to detect any tangible change in them. As for the B stars, each spectrum in the grid was rotationally broadened to deliver a set of v sin i templates, which were all subsequently convolved with a Gaussian to match the resolution of the instrument. Again, because of the limited resolution of the spectra, the contribution to line profiles from macroturbulent broadening, known to affect O stars (Simón-Díaz & Herrero 2014; Markova et al. 2014), can be regarded as subsumed within the typically more prominent rotational broadening. This leaves 6 free parameters: θ = {T eff , log(g), vsini, RV, log(Q), n(He)} The uniform grid of templates was linearly interpolated to form a continuous grid for MCMC sampling. The following uniform priors for each parameter were adopted and are defined by the limits of the model grid: The key constraint expected from these fits is on effective temperature. There is also useful information contained in the derived surface gravities and rotational velocities. Given the low resolution nature of the spectra we treat all the other parameters as 'nuisance parameters' since the derived values will carry large uncertainties and are not relevant to this discussion. However, their influence on the other parameters is, by default, taken into account when using the marginalised posterior probability distributions. We also tried fitting the O stars to O star NLTE TLUSTY models (Lanz & Hubeny 2003) using the same method as for the B stars and found little difference in the average derived temperatures and surface gravities compared with the FASTWIND results: we note there is a tendency for the TLUSTY models to offer combinations of slightly higher surface gravities and effective temperatures relative to FAST-WIND, especially in the hottest cases (see the example discussed below in the next section).
Results of the spectroscopic fitting
The median of the posterior probability distributions for each parameter is taken as the best fit value. The 16 th and 84 th percentiles are taken as the upper and lower uncertainty on each parameter. The best-fit spectroscopic parameters for all the OB stars observed with AAOmega are added to the database provided as supplementary material. Fig. 10 shows example spectra, after normalisation and excision of DIBs present, over-plotted on the best fit model. The top panel presents an O star spectrum compared with FASTWIND best-fit line profiles, while the bottom panel presents a comparison between an observed B-star spectrum with an NLTE TLUSTY fit. Fig. 11 shows the distribution in T eff , log(g) and v sin i for the spectroscopic fits of OB stars. The distribution in T eff peaks at around 20kK and falls off at higher temperatures. This is very similar to the distribution in the photometric temperature estimates shown in Mohr-Smith et al. (2015). As expected the majority of stars show MS surface gravities with a median value a little less than 4 (more precisely, 3.92). The three lowest surface gravity objects log(g) 3.2 are likely to be evolved B stars. Their relatively cool temperatures (19kK < T eff < 24kK) and lower surface gravities would be consistent with luminosity class II bright giants (Schmidt-Kaler 1982). Their over-luminous position in the (g, u − g) CMD also supports the notion that these are evolved objects (see Section 3.2.1: these are 3 of the objects emphasised in black in Fig. 6).
One very hot O star whose spectrum has been compared with model atmospheres, has also been selected as a subd- Figure 10. Example of spectra and best fit models. Top: ID #1374, g = 15.5 mag, A 0 = 5.6, T eff = 38600 K and log(g) = 4.19, with the FASTWIND fit to the hydrogen and helium lines superimposed in red. Bottom: ID #2593 g = 17.2 mag, A 0 = 4.5, T eff = 23100 K and log(g) = 4.32, with the TLUSTY NLTE full spectrum fit superimposed. The signal to noise ratios of the two spectra are ∼ 25 (top) and ∼ 31 (bottom).
warf (ID 1558) using the technique outlined in Section 3.2.1. We found that the fits both to the FASTWIND grid and to the TLUSTY (OSTAR) grid struggled with the upper limits on log g (respectively 4.3 and 4.75: the fits returned gave log g = 4.2 and 4.7). To overcome this problem, we carried out a fit against a grid of hydrogen and helium NLTE model atmospheres used by Napiwotzki (1999) for the analysis of central stars of planetary nebulae (CSPN). The fit results are T ef f = 55 ± 2 kK, log g = 4.4 ± 0.2 and n(He) = 0.23 ± 0.05. Whilst the neglect of metals in this third model grid might cause a modest systematic shift, a gravity well below what is typical for most hot sdO stars (5.5 log g 6.0 Green et al. 2008) is supported. This, and the presence of weak, spatially-unresolved [OIII] λλ4959,5007 in emission in this object's spectrum suggests post-AGB status for this star. Interestingly, in addition, the sdO atmosphere exhibits helium enrichment n(He) = 0.23 and 0.15, respectively, from the CSPN and FASTWIND grids). The history of this object could be similar to that of the unusual PN central star, K648 in M15 (Rauch et al. 2002), which shows signs of material being mixed into the atmosphere during a final helium flash. For now we acknowledge that our one 'sub-luminous' spectroscopic target is potentially not so sub-luminous and that higher quality data are required to conclude on its nature. Nevertheless, the placement of this star in the non-massive "subluminous" group is sound.
The distribution in projected rotational velocities (v sin i) for the entire sample of OB stars is broadly consistent with the distributions presented by Huang et al. (2010), for B stars, and by Simón-Díaz & Herrero (2014), describing O stars in the Milky Way. The values returned for this parameter are provided in the database for individual objects for completeness. But we caution that as individual measures they will be appreciably more uncertain than the quoted MCMC-derived random errors might suggest. This is due to limited spectral resolution (corresponding to a ve- locity resolution of ∼230 km s −1 , and the moderate S/N of the data (most often, 30 − 40)-which have both a direct impact through e.g. uncertainties in continuum placement, and more indirectly through the lack of capacity to distinguish binarity (SB2 component blending).
Comparison of the spectroscopic and
photometric best-fit effective temperatures Figure 12 shows the effective temperatures determined from the photometric SED fits compared to those determined by spectroscopy. The red circles show objects with χ 2 > 7.82 in the SED fitting routine. We find that, despite the necessary reservations about determining effective temperatures through photometry alone, there is a good correlation between the two methods. We do however see a systematic tendency in the photometric method to under-estimate the temperature of O stars and over-estimate those of the B stars, when compared to the spectroscopy. As the photometric calibration appears to be well behaved, this is most likely to be due to differences between the photometric effective temperature scales in the Padova isochrones (based on LTE model atmospheres, Bressan et al 2012) and those relevant to the TLUSTY and FASTWIND NLTE models used to fit the spectra. Another factor that affects the extreme cases is photometric blending or contamination. For example the poor χ 2 object with the largest disagreement is close to a very red object which is very likely to have affected the measured magnitudes, particularly 2MASS J to K.
With the extra information on temperature provided by the spectroscopic fits, we can check what effect the systematic offset in the photometrically derived log(T eff ) has on the derived reddening parameters. To do this we re-calculated the SED fits using a much narrower uniform prior on temperature, based on the 16th and 84th percentiles of the marginalized posterior distribution of spectroscopic temperature for each star (as indicated by the horizontal error bars in Fig. 12 & Fig. 13). Fig. 13 shows the impact on the derived values of A0 and RV when the more precise 'restricted' temperature prior is used in place of almost no constraint in the SED fitting. Here we can see that for both reddening parameters that restricting log(T eff ) has a greater effect on stars below ∼25kK. This is due to the higher sensitivity of the shape of the SED as a function of temperature for the cooler stars. At effective temperatures above ∼ 25kK, the SEDs approach the Rayleigh-Jeans limit more closely, lowering the sensitivity to temperature: in this regime, the shape of the SED is almost entirely dominated by extinction. It is important to notice that these systematic effects are very small; for stars with T eff 25kK the median difference in A0 and RV ('free' -'restricted') is respectively -0.025 and 0.026, and for those with T eff < 25kK the median differences rise to 0.09 and -0.07. In the worst cases these systematic uncertainties are comparable to the random uncertainties on the parameters due to the photometric errors. However, whilst there is indeed a modest disagreement between the photometric and spectroscopic effective temperature scales, it would amount to forcing photometric fits to systematically 'incorrect' SED models if the temperature prior were restricted to suit the spectroscopic results. This idea is supported by systematically poorer fits in the 'restricted' case where the median χ 2 = 2.99, in contrast to χ 2 = 1.58 in the 'free' case. Accordingly it does not make sense to regard the trends seen in Fig. 13 as providing a systematic correction to the parameter estimates based on photometry. What it does all point to is the issue of fit degeneracy between effective temperature and extinction: this begins to acquire some significance towards the Figure 13. Change in derived reddening parameters when using a temperature prior defined by the spectroscopic fits (free -fixed).
cool end of the OB range where we find the larger discrepancies. But the magnitude of this effect is very much smaller than that affecting fits to broad-band photometry of A to K type stars (see Bailer-Jones, 2011), underlining the longrecognised value of OB stars in tracing Galactic extinction.
EXTINCTION PROPERTIES AND SPATIAL DISTRIBUTION
It was demonstrated by Mohr-Smith et al. (2015) and also in preceding sections that the SED-fitting process places strongest constraints on the reddening parameters, A0 and RV , achieving typical precisions in the region of ±0.1. These are now put to use to better understand the full pencil beam, passing through the Carina Arm to distances at least as great as ∼7 kpc, the distance to NGC 3603. We begin with an overview of extinction across the region, before extracting more detail.
In this analysis and discussion, we remove from consideration the objects tagged as either emission line stars or as potentially sub-luminous (reducing 5915 objects to 4770).
Overview of extinction in the region
It is already well known, going back in the literature to before Cardelli et al (1989), that the Carina region is associated with flatter extinction laws, charaacterised by higher RV (> 3.5). Fitzpatrick & Massa (2007) and Hur et al. (2012) found this near the open clusters Trumpler 16 (Tr 16) and NGC 3293, whilst normal values of RV ∼ 3.1 still seem to apply to less-reddened stars with A0 2 magnitudes. In a Chandra X-ray study of the wider Carina Nebula, spanning a sky area of 1.49 sq.deg., Povich et al (2011) confirmed this general pattern and recommended RV = 4 as representative of higher extinctions (from AV 1.8 to AV ∼ 4, based on an X-ray selected sample of 94 OB candidates).
First, we need to identify the spatial and extinction parameter domain open to examination. To this end, we . An increase in extinction of 0.8 mag/kpc is adopted in the modelling of the contours -the implied heliocentric distance scale is marked across the top. The offset between the range of maximum detectability and the measured extinctions is to be expected without the incorporation of a Galactic model and IMF weighting: the drop off in detections beyond A 0 ∼ 7 is attributable to the overall downward trend in stellar density. The pencil beam studied exits the Solar Circle at a distance of ∼6 kpc, while at a distance of 10 kpc, the Galactocentric radius is 10-11 kpc.
. consider the constraints set by the sample magnitude limits using some straightforward modelling: we take all of the photometric OB main sequence star models in the grid used in SED fitting (log(T eff ) 4.30) and redden them, assuming a rise in A0 of 0.8 mag/kpc (retrospectively a plausible growth rate for the region, see Section 5.3) for all values of RV . This permits us to see which combinations of A0 and RV produce an SED falling within the survey-imposed lim- Figure 15. The distributions of A 0 , top panel, and R V lower panel, as functions of Galactic longitude. The plot is restricted to non-emission χ 2 < 7.82 candidate OB stars in the Galactic latitude range 0.0 • > b > −1.5 • (4770 stars). The blue line, in both panels, is the running mean of the distribution sampled every 0.25 degrees. The standard deviation about the mean is also shown shaded in light blue. The typical random error on each data point is ¡0.1 (magnitudes, in the case of A 0 ). . its: 12 < u < 21, 12 < i < 21, 12 < r < 21 and 13 < g < 20.
We collect the fraction of simulated SEDs meeting requirement for each combination of A0 and RV and (by implication of the adopted A0 rise rate) distance. This model of detectability does not reveal how many stars we expect to find in the selection given A0 and RV , as this would require taking into account IMF weighting, the growth in the volume captured with increasing distance, and a Galactic stellar density model. Instead, our present purpose is restricted to establishing limits on the detectable (RV , A0) parameter space.
Fig. 14 answers this question: it turns out that the amount of extinction, A0, places the stronger constraints, in that the detectability at A0 < 2 and A0 > 10 of OB stars is low. Note that only B stars are intrinsically faint enough at the low end of this range to be picked up, while only O stars are luminous enough at the other. The constraints on RV within the open A0 window are much weaker: there is little/no constraint on RV until, at A0 > 9, SEDs present-ing RV 2.5 become increasingly difficult to capture. This reflects the link between falling RV and a steepening extinction law (at higher A0), such that the u magnitude will be more readily pushed beyond the faint limit as RV drops.
The observed distribution in RV as a function of A0, superimposed in Fig. 14, reveals a striking absence of correlation between these parameters, except that only below A0 2 is RV < 3.5 relatively common. From A0 3 to A0 ∼ 8, where the distribution begins to peter out, the trend is flat and broad. Relatively few objects are picked up at distances below 2.5-3 kpc, indicating this new sample misses out the foreground to the Carina Arm. The apparent offset between the peak detectability range defined by the contours in the figure (4 A0 10), and main concentration of the measurements (3 A0 7) has two different origins dependent on Galactic longitude: near the Carina Arm tangent 0.8 mag/kpc is too low a growth rate in extinction, while at greater longitudes where this rate is better matched there is a strong decline in stellar density beyond both the Solar Circle (crossed at a heliocentric distance of 5.5 kpc) and the outer Carina Arm (crossed at 7-10 kpc, depending in detail on longitude). We now turn to considering the pattern of extinction variation on the plane of the sky to explain why this is so. Fig. 15 shows how A0 and RV vary across the region as a function of Galactic longitude. The 4770 stars plotted are limited to the latitude range −1.5 • < b < 0.0 • , the most completely and densely sampled part of the region (see Fig. 4). In the upper panel it is unsurprising to see the wide spread in A0 at all longitudes, but there is nevertheless the appearance of a broad dip such that the median extinction is 4-5 in the range 285 • < < 289 • , as compared with 5-6 to either side. This broad minimum is where the relatively nearby Carina Nebula is located.
At the lower longitudes closest to the tangent region, the A0 distribution is most disorderly and the highest measures are found. The Planck XI dust map (Abergel et al 2013) indicates that the total dust optical depth at these longitudes is strongly variable and typically ∼ twice as high as at > 285 • , implying total visual extinctions of around 15-20 magnitudes. This is consistent with what is known of the CO distribution (Grabelsky et al. 1987). In contrast, at > 289 • , the pattern is at its most regular: indeed, there are signs of a gradual rise in extinction with increasing longitude, passing through the location of NGC 3603. As shall become evident in section 5.3, this trend translates into a broadly regular increase in distance sampled with increasing A0. The OB stars found in this region mainly belong to the receding outer Carina Arm and more nearly sample the total dust column (τ353 ∼ 2 × 10 −4 corresponding to a maximum visual extinction of 8-10, see Abergel et al 2013).
Variations in A0 and RV near massive clusters, and a newly-identified OB association
The most striking feature in the RV variation with Galactic longitude (lower panel in Fig. 15) is the explosion of high values in the mid-longitude range (286.5 to 288, roughly) occupied by the Carina Nebula: any value from ∼ 3.5 up to more than 5 is apparently possible. Elsewhere excursions beyond ∼4 are relatively infrequent. Interestingly, echoes of this behaviour are also apparent at the longitudes of West- erlund 2 and NGC 3603. The relatively sharp spikes associated with these two clusters follow from their greater distances and correspondingly reduced angular sizes. Indeed this result suggests that systematically higher RV and flatter optical extinction laws -implying larger typical dust grain sizes -is a persistent property of the environments around young massive (O-star rich) clusters. This may betray greater columns of dust grain populations biased to larger typical grain sizes in the surrounding molecular gas, unused in the star formation event, or the origin may be more dynamic and arise as a consequence of star formation feedback (see e.g Draine 2011; Allen et al. 2014;Ochsendorf & Tielens 2015): further detailed investigation is needed.
In general terms, 3.5 < RV < 3.8 appears typical of the Carina Arm field, while near the prominent clusters, average values of 3.7 < RV < 4.2 are much more frequently encountered -with the Carina Nebula presenting as an extreme case.
On collapsing the Galactic latitude distribution, as in Fig. 15 (and also in the lower panel of Fig. 4), it becomes easy to pick out the well-known massive clusters -showing up as dense concentrations, linking to localised peaks in RV and A0. In addition, the eye is drawn in both figures to an OB clustering near ∼ 290 • that has no clear literature counterpart, so far. A close-up of the on-sky distribution of the χ 2 < 7.82 objects in this region, pinpointing the main clustering at = 289.77 • , b = −1.22 • , is provided as Fig. 16, with WISE 8µm (warm dust) emission added as background.
Visual extinctions 4.5-5 magnitudes are typical. The total number of objects falling in the red box, of rough dimension 9 × 10 sq.arcmin, superimposed on Fig. 16 is 103, of which 32 are candidate O stars.
The most dense sub-clustering, of 42 objects spread across ∼2 arcmin (coloured cyan in Fig. 16), coincides with LSS 2063, an 11 th magnitude star, classified by Walborn & Fitzpatrick (2000) as O5If+. These same authors give B − V = 1, which we interpret as a likely visual extinction of about 5 (adopting an intrinsic colour of -0.28 from Martins & Plez 2006, and RV ∼ 3.8, on the basis of Fig. 15). This fits in well with the newly-revealed clustering. In the first edition of their Galactic O-Star Catalogue, Maíz- Apellániz et al. (2004) cautiously described LSS 2063 as a 'field' object, there being no clear reports of an associated cluster at the time. Nevertheless, Dutra et al. (2003) did catalogue a nearinfrared cluster essentially co-incident with LSS 2063, and more recently Majaess (2013) has noted this location as a plausible YSO clustering based on raised mid-infrared emission (Majaess 133, in the associated catalogue). Georgelin et al. (2000) noted the HII emission here, in Gum 35 (also known as RWC 54a), and cited the Caswell & Haynes (1987) HI recombination line measurement that places the region at the same kinematic distance as NGC 3603 (∼7 kpc away). Avedisova (2002) in her list of star forming regions also notes a coincidence between radio emission in this location and RAFGL 4120 (an earlier mid-IR detection effectively). So here, finally, the optical has caught up and the very much larger group of ionizing stars, helping LSS 2063 shape this environment, has emerged.
At a distance of about 7 kpc, the over-density's full angular extent of 9-10 arcmin corresponds to a linear size of ∼20 pc, allowing this clustering to be viewed as an OB association. The count of 103 OB stars misses LSS 2063 itself and 4 more that are also above the VPHAS+ bright limit (an O9.5 Iab star classified by Sota et al 2014, and 3 candidate O stars from Wramdemark (1976). If the 108 stars found conform to a Kroupa (2001) IMF, and a mainsequence mass of 7 M may be associated with an effective temperature of 20000 K, the implied mass of stars in the association, is at least ∼ 8 × 10 3 M . On the same basis, the predicted number of O stars (> 15 M ) is 39 -to be compared with our estimate of 37.
5.3
The changing on-sky OB star distribution with increasing extinction Fig. 17 shows the selected and accepted OB star candidates divided up between three different extinction windows (A0 4, 4 < A0 < 6 and A0 6). What stands out the most in this figure is that the distribution in Galactic latitude narrows as A0 increases, revealing the receding Galactic thin disk. To express this more precisely, the onsky angular projection of the scale height of the OB stars exhibits clear shrinkage with increasing reddening -hinting that reddening is statistically correlated with distance. We can use this effect to estimate the approximate distance ranges we are sampling as a function of rising extinction. This method turns out to be more informative than relying on the distance moduli derived from the SED fits, in which the strong correlation between µ and effective temperature leads to considerable imprecision. Panel (a) of Fig. 18 shows that the trend in A0 versus distance, D (from µ) eventually loses credibility as distance would seem to decrease with extinction beyond A0 = 5. In, view of this, we explore the use of the angular spread of the candidates as a proxy for distance. This depends on the finding that the OB star scale height in the Galactic disk appears to be broadly independent of Galactocentric radius (Paladini et al. 2004).
We bin the objects in extinction from 2.5 > 8.5 in steps of ∆A0 = 1, anticipating that the OB stellar density, expressed as a function of Galactic latitude in each extinction slice, conforms to an isothermal population characterised by a single angular scale-height h b = hOB/D. We adopt hOB = 45 ± 5 pc (Reed 2000;Bobylev & Bajkova 2016), and D is to be regarded as the representative, if fuzzy, heliocentric distance to the reddening slice. The scale height of OB stars, hOB, is conventionally defined with reference to either a back-to-back exponential or to the square of a hyperbolic secant. For our fitting exercise, we prefer the latter for mathematical convenience. In this, we follow Conti & Vacca (1990). Specifically, we apply to each reddening slice a fit of the form: in which A is a constant, proportional to the sample size, and b0 is the Galactic latitude at which the best-fitting function peaks. With h b the angular scale-height, this makes 3 fit parameters. Panels (b), (c) and (d) of Fig. 18 show the derived distances, D, per reddening slice, for three different Galactic longitude ranges. Panel (b) shows the entire longitude range of the studied area while panels (c) and (d) split the longitude range into two halves. Panel (c), where 287.6 < < 293.2, includes the part of the footprint that contains the cluster NGC 3603, while panel (d), where 282.0 < < 287.6 takes in the rest of the foot print containing Wd 2. For use later, we set out the numerical results of panel (c) as Table 4. The relevant panels in Fig. 18 include the distance and extinction to NGC 3603 (blue triangle) taken from Sung & Bessell (2004) and the distance and extinction to Wd 2 (green diamond) taken from Dame (2007) and Mohr-Smith et al. (2015) respectively.
Panel (c) shows that for 287.6 < l < 293.2 we have a well-behaved steady increase in estimated distance as a function of extinction of 0.8 mag/kpc. This is the range within which the dependence of A0 on Galactic longitude is also more organised, tending to rise as longitude increases (see Fig 15. The literature values of extinction and distance of NGC 3603 fit as expected into this trend, in showing it is located in a relative reddening hole (see e.g. Pang et al. 2011).
However, for 282.0 < l < 287.6 shown in panel (d), there is no orderly correlation between extinction and inferred distance. This difference can be attributed to the fact that for the lower-longitude sight lines, the Carina Arm tangent (l 281, see e.g. Dame 2007) is not far away, permitting a more rapid and chaotic accumulation of dust column density with increasing distance, looking almost directly along the Carina Arm. In addition, our more limited latitude coverage at these longitudes may be implicated in the contradictory association of a long sightline with the lowest extinction bin (see Fig. 17). The lower overall density of candidate objects nearer the tangent direction may also be a clue that a more rapid accumulation of dust column brings the accessible sightlines more often than not to an end within the Arm. In effect, the view rarely reaches much beyond Westerlund 2 at D ∼ 6 kpc (Dame 2007). This stands in contrast to the general vicinity of NGC 3603 (understood to be ∼7 kpc distant Sung & Bessell 2004), where it appears from panel (c) in Fig. 18 that OB stars are being picked up at heliocentric distances up to ∼ 10 kpc.
Our optically-based mapping can be compared with the K-band mapping carried out by Marshall et al. (2006): produced a three dimensional extinction map of the Milky Way by comparing empirical colours of giant stars in 2MASS with the expected intrinsic colours from the Besançon stellar population synthesis model. The angular resolution of this IR map is 0.25 • . Fig. 19 shows the derived extinction from Marshall et al. (2006) for three square-degree patches falling within the region under examination here. The sight lines shown in blue correspond to the higher Galactic longitude side of the region containing NGC 3603 (290.5 • < < 291.5 • and −1 • < b < 0 • ) while those shown in red fall closest to the Carina tangent direction (282.5 • < < 283.5 • and −1 • < b < 0 • ). The lines shown in green pick out a region in between (285.5 • < < 286.5 • and −1 • < b < 0 • ). The conversion factor between AK and A0 is somewhat dependent on RV : for the present purpose we will use 8, appropriate for RV ∼ 3.8, to scale AK up to A0.
We over-plot on the converted Marshall et al. (2006) relations in Fig. 19 the extinction-distance trends already presented in panels (c) and (d) of Fig. 18. The diamond markers represent the lower-longitude end of the footprint while the triangle markers show the higher-longitude end.
Here we can see that the pattern apparent in the Marshall et al. (2006) data at ∼ 291 • is consistent with our data (the blue curves, and triangles). On the other hand, the chaos in the OB-star data at lower longitudes (nearer the tangent, diamond symbols in the diagram), relative to the IR-based green and red curves, is underlined. In the remaining discussion we restrict attention to the better behaviour seen at > 287.6 • .
We now evaluate how the OB-star defined mid-plane, as specified by the fit parameter, b0, deviates from the geometrically-flat mid-plane, at latitude bm, along the observed pencil beam. The fit results relevant to this are collected together in Table 4. The parameter, bm, is itself subject to some uncertainty as it depends both on D and on the assumed height of the Sun above the ideal flat mid-plane. To complete our calculation we adopt estimates for bm that follow from the prescription set out by Goodman et al. (2014), in which the Sun is offset above the mid-plane by 25 pc. The picture emerging from this is of a slowly growing offset, such that at ∼7 kpc the OB-star layer is about 60 pc below the geometric mid-plane, falling further to 80 − 100 pc below at heliocentric distances of 9 − 10 kpc. At ∼ 290 • , this heliocentric distance range corresponds to a Galactocentric distance of ∼ 10 kpc. The uncertainties in the estimates of warp in Table 4, arise only from the computed fit errors in distance-extinction trend shown in Fig. 18: these are likely to be optimistic. In particular, the estimated distance scale carries an as yet unknown bias due to the potentially simplifying assumption -implicit in the fit procedure -that the average rise in A0 with distance has no strong latitude dependence near the mid-plane.
Neutral hydrogen 21-cm line observations of the Galactic gas disk imply little warping of the Galactic plane out to Galactocentric radii of RG ∼ 9 kpc (Kalberla & Kerp 2009). What we see here -evidence of just the beginnings of a negative slowly growing warp -fits in with this. Wellbeyond RG = 9 kpc, they and Levine et al. (2006) propose a rapid increase in the warp such that an offset of ∼ 500pc is reached at a Galactocentric distance of RG ∼ 15 kpc.
DISCUSSION AND CONCLUSIONS
In this paper, we applied our a method for the uniform and high-efficiency selection of OB stars and parametrization of their extinction, that was first laid out and validated by Mohr-Smith et al. (2015). The selection here, using VPHAS+ and 2MASS survey data, has resulted in a catalogue of 14900 stars of which 5915 are high confidence O -B2 stars, drawn from 42 square degrees in the Carina Arm region. The probable O stars number 905. The region charted here spans ∼ 11 degrees in Galactic longitude running from ∼ 282 • , close to the Carina Arm tangent direction, to ∼ 293 • , beyond the much studied massive cluster NGC 2 4 6 8 10 12 Distance ( Table 4. Data and results for the fits to extinction slices constructed from thecleaned OB star sample at Galactic longitudes > 287.6 • , using the functional form given in equation 9. Here bm, in the penultimate column is the true Galactic latitude of the geometrically flat mid-plane, according to Goodman et al. (2014). In the last column, Z 0 (OB) is the offset in parsec of the OB-star mid-plane from flatthe estimated warp in other words. Melena et al. (2008) reported 51 OB stars in the brilliant, and packed, ∼ 10 arcsec core of NGC 3603 -our catalogue lists 17 of them. This illustrates the complementarity that exists between focused studies and wide field survey selection. By bringing together VPHAS+ u, g, r, i photometry with 2MASS J, H, K photometry, we are able to determine both the value of the extinction, A0, and the extinction law, as parametrised by RV , to good precision: both are typically measured to better than 0.1 (magnitudes in the case of A0). Using a statistically much larger sample across a large area on the sky, we have confirmed and fleshed out previous results, reported by many authors, that sight lines into the Carina Arm require flatter reddening laws with 3.5 RV 4.0 for A0 > 2.0. Analysis in Section 5.3 has also demonstrated that extinction builds more quickly at Galactic longitudes closer to the Carina Arm tangent direction, where CO surface brightness is also known to rise to an evident peak (Grabelsky et al. 1987). Indeed at 286 • , g = 20 is not yet deep enough to guarantee sightlines that pass through the Arm to much beyond a distance of 6-7 kpc. However at greater longitudes, where the extinction builds at a mean rate of ∼ 0.8 mag kpc −1 , the distances sampled extend to beyond ∼10 kpc (or RG of at least 10 kpc also).
A crude impression of stellar effective temperatures (and hence distance moduli) is all that should be presumed to flow from the SED fits to the OnIR photometry of individual objects. However, it is indeed possible to achieve a reasonable separation between candidate O and candidate early-B stars. This was clearly confirmed in Section 4 where the analysis of AAOmega spectroscopy of a representative sample of 276 OB candidates was presented. Among the better quality candidate objects (χ 2 < 7.82) the cross-over rate, post spectroscopy, at the O/B boundary was only 10-20 % (the higher percentage applying on the O star side of the boundary). We also showed that the systematic offset between the photometric and spectroscopic effective temperature scales has only a modest effect on the derived extinction parameters for the B stars (A0 ∼ +0.09 and RV ∼ −0.07) and an even less of an effect on the O stars (A0 ∼ +0.03 and RV s ∼ −0.03). This is a reflection of the convergence of the O star SED onto the Rayleigh-Jeans limit as effective temperature rises upwards of ∼ 30000 K. The follow-up spectroscopy demonstrated vey clearly that there are very low levels of contamination from late type stars within the selection (under 5% of the accepted χ 2 < 7.82 candidates).
Further exploitation of the parameters derived from the photometry has also enabled an approximate distinction to be drawn between main sequence massive OB stars and lower luminosity hot stars (subdwarfs, post-AGB stars and others), and higher-luminosity evolved massive OB stars. Intriguingly, the one subluminous candidate to be followed up spectroscopically has emerged as a helium-enriched probable post-AGB object: the helium enrichment in particular is suggestive of material dredged up in a late helium flash The narrow band Hα filter in the VPHAS+ survey offers a clear path to the selection of emission line objects, and we find a fraction of B type emission line stars (∼ 7%) relative to the total B population that is consistent with the southern clus-ters study by McSwain & Gies (2005). The majority of emission line candidates are likely to be classical Be stars while a minority may also be examples of B[e] stars, luminous blue variables, or WR stars. The high-confidence broadband selection tends to disproportionately exclude new WR stars and many CBe stars, for the reason that these objects often present with NIR excesses that lead to inferior (χ 2 > 7.82) SED fits.
The catalogue created by this study is an opportunity to explore how a high angular resolution wide-field optical survey like VPHAS+ can bring a wider context to the study of star forming regions, away from the dense well-studied cores of open clusters and OB associations. The capability is now there to identify massive stars, wherever they are. A compelling example of this is the very large number of candidate reddened O stars lying in an extended halo around the brilliant cluster, NGC 3603 at Galactic coordinates (291.6, -0.5). This can be seen in Fig. 20 that shows the distribution of candidate O stars (log(T eff ) > 4.477), on their own, across the whole region. Many objects are seen around NGC 3603, spread across a sky area about a degree across -we find around 500 high-confidence O-B2 candidates in the extinction range 4.0 < A0 < 7.0, of which more than 100 are probable O stars. Very recently, Roman-Lopes et al. (2016) have used near-infrared selection to identify 10 candidate early O stars in this same region and have confirmed them spectroscopically: all are in our catalogue with log(T eff ) and A0 parameters from SED-fitting that are very close to their spectroscopic counterparts. The shape on-sky of the O-star surface density enhancement fits in well with 'star forming complex #28', one of two G291 regions, identified via longwavelength free-free emission by Rahman & Murray (2010).
Metaphorically speaking, NGC 3603 is the tip of a massivestar iceberg worthy of further investigation.
In Section 5.2 we also saw that at = 289.77 • , b = −1.22 • , there is a clustering of OB stars in the vicinity of the bright O5 supergiant, LSS 2063, that before now had evaded optical detection and cataloguing. This is sufficiently dispersed to be viewed as an OB association. As a further example, Fig. 20 contains hints of another dispersed OB complex at 283 • and b −0.5 circ : in view of the similarly high extinctions involved (A0 6), it is likely to be about as distant as Westerlund 2.
Many of the already well-known O stars in the Carina Nebula/Carina OB1 association at l ∼ 288 • are missing from the selection presented here because they are brighter than our bright selection limit (at V ∼ 12). However we do sweep up a handful of O star candidates and many B star candidates (see Fig. 17) which are far more extinguished than the typical values of AV ∼ 2.5 of known clusters such as Trumpler 14 and 16 (Hur et al. 2012). These objects are likely to be situated behind or deeper into the nebula than the well studied cluster stars. Indeed the closest distance for the majority of massive OB stars in the catalogue presented here is expected to be 2.5-3 kpc, the range in distance within which the Carina Nebula is likely to be located.
The full catalogue of blue selected objects, including spectroscopic data where they exist, is available in machinereadable form as supplementary material and will also become available via CDS: the Appendix to this paper provides a specification of the columns making up the catalogue.
The ability to efficiently and reliably select and measure thousands of fainter OB stars opens the way to using these intrinsically luminous objects to probe the structure of the Galactic disk in a more fine-grained fashion than has been possible before. Through sampling the field thoroughly, for the first time, as well as massive star clusters, this study has provided systematic evidence that the latter promote somewhat flatter optical extinction laws (i.e. increased RV ) alongside greater A0. The results of Fitzpatrick & Massa (2007, Figure 11) hint at this but lack the sampling in the field. The Carina Nebula itself has emerged as an especially striking example of raised RV . Around NGC 3603, we obtain a median extinction of 6 magnitudes, and median RV 3.75, to be compared with below 5 magnitudes and 3.55 respectively, recently measured inside the cluster (Pang et al. 2016). Further investigation of the subtle differentiations beginning to appear will help fill out the picture of dust processing arising from star formation.
The Galactic latitude distribution of the OB stars has been shown to imply incipient disk warping along sightlines near = 290 • : our approximate method of inferring distance via reddening suggests heliocentric distances on the order of 10 kpc are reached and that the OB-star layer offset below the mid-plane at this distance is likely to be 80-100 pc (Sec. 5.3). Before now, similar efforts using OB stars to trace disk warping have had to work with very much lower sky densities of bright objects (1300 stars over a third of the Galactic disc, Reed 1996) or accept data inhomogeneity (600 Carina region stars compiled from 4 catalogues Kaltcheva & Scorcio 2010). These authors, and Graham (1970), proposed stronger warping, compared to the new result, in part because of over-estimation of distances driven by under-estimation of visual extinctions (through the adoption of RV 3.1). The deep census provided here will be extended across the rest of the Galactic plane in future publications as VPHAS+, along with its northern counterparts, The INT/WFC Photometric Hα Survey (IPHAS Drew et al. 2005) and The UV Excess Survey (UVEX Groot et al. 2009), progress to fully-calibrated completion. These are set to combine transformationally with forthcoming Gaia astrometry -reaching to a similar faint limit -in enabling much more precise analysis both of Galactic disk structure, and also of the ecology and life cycles of massive Galactic clusters and their environments.
APPENDIX A: DATABASE DESCRIPTION
The catalogue of the complete set of 14900 candidate OB stars selected from the VPHAS+ (u − g, g − r) colour-colour diagram is provided as a machine readable database in the supplementary material. This will be made available via CDS.
The source positions and multi-band photometry on which the initial selection was made is provided in the first 17 columns. The RA and DEC reported are derived from the r band observations obtained with the u and g filters. Columns 18-24 list the 2MASS cross-match magnitudes and errors: note that the database does not include blue-selected objects without 2MASS counterparts. All photometric magnitudes are reported in the Vega system. For 152 (∼ 1%) of the selected objects, Hα magnitudes are presently unavailable: where this applies the database entry is left blank. Similarly the second r magnitude is missing for 59 stars. Column 24 lists the VPHAS+/2MASS cross-match separation.
The next columns, 25-38, summarise the results of the SED fits, presenting the median of the posterior distribution for all four parameters along with errors derived from the 16 th and 84 th percentiles (essentially 1-σ errors). The final important piece of information from the fits is the value of χ 2 computed for the best-fitting SED, given in column 37: where this value is < 7.82 and log(T eff ) > 4.30 (to two significant figures), column 38 in the database is set to true. We caution that the parameters for objects with χ 2 > 7.82 are less reliable: these objects are more heterogeneous and will include emission line objects, some normal OB stars as well as contaminant objects. Columns 39-41 are similar boolean columns that identify candidate emission line stars (as determined from (r − Hα) excess), and sub-luminous and evolved non-main-sequence OB candidates.
Where alternative names for an object already exist in the SIMBAD database, we write this into column 42, the 'Notes' column. We also note any other specific characteristics of the object that have already come to attention: in particular, if an AAOmega spectrum exists that shows the object to have line emission at Hβ we note it here. The small number of known contaminant latetype stars are noted here also.
The final set of columns (43-53) records whether an AAAOmega spectrum exists and reports numerical quantities derived from model atmosphere fits as appropriate. For the contaminant stars, all numerical quantities are omitted. Table A1 below provides individual specifications for all the columns in the database. | 20,505.8 | 2016-10-24T00:00:00.000 | [
"Physics"
] |
Direct Electricity Production From Coconut Oil - The Electrooxidation Of Coconut Oil In An Acid Electrolyte
Supplying more and more energy is an essential task of today's energy industry. In the last few decades, in addition to traditional methods of energy production, alternative energy sources have been developing at a fast rate. One of the devices that can use these sources is the fuel cell (FC). FCs can be a power source of the future mainly due to their high efficiency, their low impact on the environment and the possibility of powering with different fuels. Most often, FCs are powered by hydrogen. However, issues with its cheap production and storage are the reasons for seeking new fuels for FCs. Yet it must be a fuel that will provide a zero or low emission level. One of these fuels can be vegetable oil. The paper presents the measurements for the electrooxidation of coconut oil emulsion on a platinum electrode (with smooth surfaces). The electrooxidation was performed in an aqueous solution of H 2 SO 4 . Electrochemical measurements were performed in a glass cell with three electrodes. The obtained maximum current density was equal to 21 mA/cm 2 . Therefore, there is a fundamental possibility of direct electricity production from coconut oil with acid electrolyte.
Introduction
Providing more and more energy is an essential task of today's energetic industry. Energy production is based on crude oil, coal, natural gas and nuclear energy. Yet, in the last few years renewable and alternative energy sources have also been developing at a fast rate. Devices which use renewable and alternative energy sources are solar collectors, photovoltaic cells, heat pumps, wind turbines or fuel cells (FCs). The last two devices have very high real efficiency (40-80%) [1,2]. Moreover, zero or low negative influence on the environment and silent operation is what characterizes FCs [3]. Fuel cells are primarily powered mainly by hydrogen [1,2,4]. However, problems with the storage of hydrogen are the reason for the search for new fuels for FCs, eg. crude oil, petroleum derivatives [5][6][7] or biofuels [8][9][10][11].
The current density is the most important parameter of FCs. The search for new catalysts for FCs is also very important to obtain high current density and lowering the costs of electrodes production [1][2][3]12]; but first we must need to evaluate basic possibility of the electrooxidation of a new fuel with a reference (Pt) catalyst. Vegetable oil is an alternative fuel for Diesel engines and for heating with oil burners. One of these vegetable oils is coconut oil. The paper presents the electrooxidation of coconut oil with a Pt catalyst in an acid electrolyte at various temperatures and concentrations of oil.
Powering high efficiency power sources with renewable fuels will allow the development of devices using renewable energy sources and the elimination or reduction of toxic substances emissions. The FC is one kind of such a device used for electricity production.
The efficiency of a fuel cell is very high and can be calculated as: the change in Gibbs free energy divided by the change in enthalpy [1,4]. But, the relationship between Gibbs free energy in a theoretical cell and in a real cell shows that the Gibbs free energy in reality is always lower in real cell. So, the real efficiency of a fuel cell is always lower than the theoretical efficiency of a fuel cell.
The current density is the most important parameter of a fuel cell [12,13]. The correlation between current density and overpotential is described by the Butler-Volmer exponential function [12]. But, in real conditions the choice of fuels for a particular catalyst must be confirmed by measurements. Unfortunately, despite extensive knowledge in the field of solid-state physics and the kinetics of catalytic reactions, the implementation of the catalysts is mainly carried out experimentally.
Materials and method
Coconut oil is an edible oil extracted from the kernel or meat of mature coconuts harvested from the coconut palm. It has various applications. Coconut oil can be extracted through dry or wet processing. Because of its high saturated fat content, it is slow to oxidize and, thus, resistant to rancidification. Coconut oil has been used in baked goods, pastries, and sautés, for hair grooming and more [14,15]. Coconut oil has also been tested for use as a feedstock for biodiesel to use as a diesel engine fuel [16][17][18]. In this manner, it can be applied to power generators and transport using diesel engines and more [19,20]. Coconut oil is a solid substance at room temperature. For this reason it is necessary to maintain a temperature above 300K to conduct measurements of coconut oil electrooxidation.
Coconut oil is a hydrophobic substance and does not conduct electric current. To cause conduction, an intermediate agent to dissolve coconut oil in water was used. Due to its excellent emulsification properties, Syntanol DS-10 was used as a detergent [21]. Syntanol DS-10 is a mixture of primary oxygen-ethylene-glycol ethers of fatty alcohol of C10-C18 fraction, and is characterized by high superficial activity, emulgation, dispersion, solubilisation capabilities [22,23]. After electrooxidation of emulsion Syntanol DS-10 can be degraded, e.g. promoted by energy transfer reactions or by bacteria [24,25]. Previous studies on the use of different oils used to produce electricity have shown that the use of this type of detergent gives real results [5-7, 10, 11]. The concentration of coconut oil was equal to 0.0025%, 0.0050%, 0.0100%, 0.0250% and 0.0500%.
The investigated coconut oil emulsion was obtained by mixing, in various ratios of coconut oil, detergent and water, using a mechanical stirrer with a speed of about 1200 rpm. The emulsion stabilization time was approximately 2 hours. To obtain an emulsion, the coconut oil and emulsion was heated above the temperature of 300K during mixing. Measurements were according to the method of polarizing curves of coconut oil emulsion electrooxidation in a glass reactor, and on a smooth platinum electrode in an aqueous solution of sulphuric acid (aqueous solution of H2SO4 as electrolyte). Platinum was used as a catalyst of the working electrode due to its excellent catalytic properties [12]. The working electrode surface area was equal to 6.28 cm 2 . A saturated calomel electrode (SCE) was used as a reference electrode [26]. Research on the electrooxidation of the emulsion based on canola oil in acid electrolyte (aqueous solution of H2SO4), for various concentrations of canola oil and detergent, and at various temperatures (303-348K) are presented in this paper.
Electrochemical measurements were performed in a glass reactor (glass cell) with a potentiostat (AMEL System 5000 apparatus) [10]. Figure 1 shows a diagram of the measurement position. First, measurements were taken for the electrooxidation of Syntanol DS-10 in an electrolyte (aqueous solution of H2SO4), for various concentrations of the detergent at temperatures ranging from 303-348K. Next, the measurements were taken for the electrooxidation of coconut oil emulsion in an aqueous solution of H2SO4 electrolyte, for various concentrations of the oil at temperatures ranging from 303-348K.
Results
The comparison of two processes: -the electrooxidation of Syntanol DS-10, -the electrooxidation of coconut oil emulsion, allowed determining whether the electricity is generated from the electrooxidation of the oil, or only from the detergent. Figure 2-5 shows the electrooxidation of coconut oil emulsion in H2SO4 electrolyte at a temperature ranging from 303-348K. The potential of a working electrode was established in about 20 minutes and was badly reproducible. Stationary, current-free real potential depends on coconut oil concentration and is included in the potentials range of 0.58-1.24V. These values are very close to the values obtained with, e.g. canola oil or waste canola oil [10,27]. To ascertain that the emulsion (and not only the detergent) was electrooxidated, measurements of the electrooxidation process run in the scope of kinetics, but the potential on the electrode is low and establishes in a long period of time. The electrooxidation of coconut oil emulsion occurred for all temperatures (303-343K), and for all concentrations of waste canola oil.
Analysis of the data from the measurements has shown the validity of the research undertaken in order for using coconut oil for energy production without the process of combustion. The use of vegetable oil to generate electricity in fuel cells would allow developing the management of waste substances in a way that ensures low negative impact on the environment. The biggest difficulty was keeping the coconut oil emulsion at a constant temperature above 303K; because below this temperature the oil was solidified, and then precipitated from the emulsion.
A current density of about 6-15 mA/cm 2 was obtained for all concentrations of coconut oil. The highest results of current density (21 mA/cm 2 ) were obtained at the temperature of 333K. With a temperature above 348K, the first electrooxidation of Syntanol DS-10 takes place, and only then -for coconut oil emulsion. For this reason, ensuring the occurrence of the process of electrooxidation in fuel cells (with H2SO4 electrolyte) powered with emulsion of waste rapeseed oil, the temperature of 348K should not be exceeded.
A fundamental possibility of electrooxidation of coconut oil emulsion on a smooth platinum electrode in acid electrolyte was shown in this paper. It has been demonstrated that using Syntanol DS-10 detergent to prepare the emulsion of waste canola oil allows for coconut oil electrooxidation, and thus enables direct conversion of coconut oil into electrical energy. | 2,161.6 | 2018-01-01T00:00:00.000 | [
"Materials Science"
] |
An algorithm with LightGBM + SVM fusion model for the assessment of dynamic security region
With the development of energy transition, the complexity of power systems’ structure, planning and operation is continuously increasing. As to quickly and accurately assess the dynamic security region of power system, there are prominent problems with traditional manual analysis method, i.e. the rules’ roughness and a low calculation efficiency while data mining approach could provide a new way to get off such problems. Considering that the performance of SVM algorithm depends on feature selection and the LightGBM, a fast and efficient classification algorithm, can be used for feature selection, this paper proposes a new algorithm based on a fusion model. With the CEPRI-36 bus power system, the results of different algorithms are compared and the proposed algorithm verified.
Introduction
With the continuous development of energy transition, the interconnection scale, the access rate of renewable energy, the complexity of planning and operation of power systems are continuously increasing, which makes the power system security analysis much demanding. In traditional power system security analysis, a few typical operation modes are selected for transient stability calculation, and the calculation results are analyzed manually to obtain the rules about power system security. Power system are typically a complex and highdimensional nonlinear dynamic system, a simplified analysis with some dimension reduction is almost necessary. However, problems arise with simplification, such as the comprehensiveness of selected operation modes and the accuracy of security rules by manual analysis. In short words, traditional analysis method generally has the roughness of security rules and the low efficiency of analysis process.
The dynamic security region (DSR) of a pre-set fault is the operating region where power system maintains transient stability during the post-fault. DSR is usually defined in injection power space or control variable space [1] . DSR can help to understand the security margin and then to make corresponding prevention and control decisions. Theoretically, the boundary of DSR is nonknotted, compact; there has no hole in it. Therefore, DSR can be approximately described by hyperplane [2] .
In the traditional security analysis, a few operating points with critical transient stability are found by calculation, and parameters of certain buses are selected to summarizing DSR by manual and empirical fitting. The number of critical points and selected parameter are quite limited, equivalent to a dimensionality reduction of DSR, resulting in the loss of much system information. In practice, in case of riskiness, the resulted security region may be further zoomed in by a conservative coefficient, resulting in a smaller operational region and a scarification of system operation economy. Actually, it still cannot guarantee the accuracy of operational region. Figure 1 shows an example of two-dimensional DSR, where black dots are transient stability points, the blue dots the transient instability points, and the black dotted line the DSR boundary. If only the X-axis parameter is considered, DSR boundary becomes the light-blue dotted line area, therefore a smaller operational region. In addition, a selection of typical operation mode may make a coverage of operational region incorrect. For example, if operation points in the red circle are not included in typical operation mode, the security region becomes the red dotted line area, where with transient instability operating points. For a large-scale power system, with huge transient stability results of typical operating modes, manual analysis is always a formidable task. Data mining algorithm can find related information from massive data, which provides an approach for efficient and accurate search of high-dimensional DSR.
Recently, there are researches of data mining algorithms in power system security and stability analysis, such as artificial neural network (ANN), decision tree (DT) and support vector machine (SVM) [3][4][5] . However, there is few research of application in DSR. Ref. [6] shows applying SVM algorithm to solve DSR, but the accuracy is unsatisfactory. To this problem, this paper proposes an algorithm based on LightGBM+SVM fusion model, applying LightGBM for feature selection, further improving the efficiency and accuracy of SVM in solving DSR. With the CEPRI-36 bus system, performances of
LightGBM + SVM fusion model 2.1SVM algorithm
SVM algorithm was proposed in 1995 [7] , a classification algorithm based on linear discriminant function, by equation (1). To realize sample classification, it uses convex optimization technology to find the optimal discriminant surfaceas. Figure 2 shows the basic principles of SVM algorithm.
(1) where, and are respectively the normal vector and displacement term of the hyperplane; the sample data. Decision rule is: if 0, it is taken as positive class, i.e. the black dots in Figure 2, namely the stable point; if 0, as negative class, i.e. the white dots in the Figure 2, namely the instable point; otherwise, it will be any class or rejected.
For the sake of classification accuracy, SVM also maximizes the gap in Figure 2 to minimize the structural risk. The objective function is shown as equation (2).
where is the relaxation variable, implying that the interval between the allowed samples and the hyperplane is less than the hard threshold 1, that is, a certain number of outliers are allowed; , the penalty parameter, implying the importance of outliers; , the number of training samples.
By Lagrange function and its duality, equation (2) can be transformed into equation (3).
where , is the introduced Lagrange multipliers; , the label of sample stability. According to KKT [8] , equation (3) can be reduced to equation (4). 1 , 1 Since data is not linearly separable in most cases, SVM introduces a kernel function , to replace in equation (4) to map the input space to a high-dimensional feature space, and find a hyperplane and realize the classification function. By the introduction of kernel function, SVM omits the high-dimensional transformation of data and directly calculates the inner product in the original input space, which goes around from the dimension explosion of high-dimensional space.
Based on the principle of structural risk minimization and the introduction of kernel function technology, SVM has good classification effect, strong interpretability and generalization ability. When a linear kernel function is used, SVM can give the expression of classification hyperplane, namely, the boundary of DSR. However, when the number of features is large, the cost of SVM training is very high and likely to overfit. As a result, a process of feature selection is needed and the results' quality has a great impact on the accuracy of SVM.
LightGBM algorithm
LightGBM was proposed in 2017 [9] , an improved version of Gradient Boosting Decision Tree (GBDT). GBDT, an integrated algorithm, consists of a series of linear combinations of submodels. Based on the principle of iteration, it takes the regression tree as the submodel and adds the submodels one by one to decrease the loss where | is the regression tree submodel newly added in the -th iteration; , parameter of the submodel; , the number of submodels; , the sample data. is obtained by minimizing the loss function, by equation (6).
where is the loss function that the learner uses for prediction. GBDT uses pre-sorting algorithm for feature selection and splitting, thus is very time-and memory-consuming, and not suitable for massive processing. On the contrary, LightGBM uses histogram algorithm and leaf growth strategy to replace GBDT's pre-sorting algorithm and layer growth strategy respectively, greatly improving the speed and efficiency of the algorithm.
LightGBM +SVM fusion model
For classification task, LightGBM is fast, efficient and difficult to over fit, especially for high-dimensional data, but it can only give label classification. SVM algorithm with linear kernel function can give hyperplane representing DSR, but its effect depends on the quality of feature selection. Taking the advantages of the two algorithms, this paper proposes a DSR algorithm based on LightGBM + SVM fusion model, shown in Figure 3. Firstly, the training set is sent to LightGBM for training. In the training process, features importance used for feature selection are determined by two parts, i.e. times being used and their gain to final classification results. Finally, selected features are sent to SVM for training to solve the DSR boundary.
Examples and analysis 3.1CEPRI-36 bus system and samples
To verify the proposed method, the CEPRI-36 bus system with 8 generators, 32 lines and 10 loads, as in [6] is taken as test system. The pre-set fault is: 3-phase short circuit occurs on the sending end of line bus16-bus20 at 0s, and the line is cut off at 0.2s. Transient process of the system within 5s after the fault appearance is simulated. By changing system's operation point, i.e. the active power of each generator and the power of each load varies in a range of 80%~120%, a total of 8000 samples are generated. Taking the injected active and reactive power, the voltage amplitude and phase angle of buses as the initial features, and the stability of the system transient as the label, there are 228 initial features, 5407 stable samples and 2593 unstable samples.
Algorithm performance test
70% of the samples are randomly selected into the training set, and the remaining 30% of the samples into the test set. Optimal parameters are found through Grid Search and 5fold Cross Validation, and test results of each data mining algorithm under parameter tuning are shown in Table 1 The results of Table 1 shows that LightGBM algorithm has the fastest training speed and highest accuracy. SVM takes a long time to train although with the advantage of domain visualization.
Various feature selection algorithms are used to be combined with SVM for training, and the test results are listed in Table 2.
Relief algorithm in Table 2 is the feature selection method in [6]. In the test, SVM uses a linear kernel function, and the penalty parameter C is 100. 30 features selected by each selection algorithm are sent to SVM training. The parameters of LightGBM algorithm are set to:
3.2.2Sensitivity analysis
Further, LightGBM is used as feature engineering to build features automatically. In LightGBM, the setting of parameter _ is generally as: It can be seen that: (1) the model accuracy with all parameters is more than 95.5%, indicating that the model is robust to parameters and thus work well without complex parameter adjustment; (2) in various cases, the model accuracy for training set and test set is almost the same, implying that the model does not incline to overfit and has good generalization ability.
Conclusion
Power system is a typical high-dimensional nonlinear dynamic system, which makes it almost impossible to solve the accurate dynamic security region manually. Data mining algorithm is a key technology of mining information from massive data, so this paper applies it to solve the problem of dynamic security region. Main work and conclusions of this paper include: (1) A dynamic security region solving algorithm based on LightGBM+SVM fusion model is proposed, where LightGBM algorithm is used for feature selection before feeding data into SVM training. Test results of SVM, RF, XGBoost, LR, KNN and LightGBM show that LightGBM classification algorithm is fast and accurate; comparing the accuracy of SVM with LightGBM, PCA, Relief, MI and VT respectively used as feature selection algorithms, results show that LightGBM has great advantages as a feature selection algorithm.
(2) Sensitivity analysis shows that the algorithm proposed in this paper has high accuracy in both training set and test set under different parameters, implying that it is insensitive to parameters, less difficult to adjust parameters, not inclines to over-fit and has strong generalization ability. | 2,662.8 | 2021-01-01T00:00:00.000 | [
"Computer Science"
] |
Durability Improvement of Concentrated Polymer Brushes by Multiscale Texturing
Concentrated polymer brushes (CPBs) are promising soft-material coatings for improving tribological properties under severe sliding conditions, even in the macroscopic scale. Therefore, they are expected to be applied to mechanical sliding components. However, the durability of CPBs has remained challenging for industrial applications. Previous studies revealed that applying a groove texture to the CPB substrate is effective in improving the durability of CPBs. In order to achieve further improvement of durability of CPBs, we attempted to apply nano-periodic structures, whereas the groove texture applied in previous studies has widths and depths in micrometres. In this study, the effect of the nano-periodic structure in addition to the groove texture applied to the CPB substrate on the durability of CPB is investigated. The results demonstrate a significant improvement in the durability of CPBs by up to 90% compared with non-textured CPB when an appropriate nano-periodic structure is applied (i.e. a nano-periodic structure oriented parallel to the groove texture).
Introduction
Polymer brushes are a kind of polymer thin films in which polymers are grafted onto a substrate with high density and form a brush shape structure; they have been extensively studied as tribo-materials [1][2][3][4][5][6][7][8]. In particular, polymer brushes with a normalised graft density higher than 10% is known as a 'concentrated polymer brush (CPB)' [9]. CPBs 1 3 99 Page 2 of 11 in good solvents have been reported to exhibit ultralow friction in both micro [10] and macro [11][12][13][14] scale sliding; therefore, their application to mechanical components such as bearings and oil seals is expected. The challenge of applying CPBs for actual industrial applications is their durability against friction. In particular, under the frictional condition where less solvent is provided to the contact area, the tribological properties and durability of CPBs will degrade [12]. An effective way to expand the potential use of CPBs in various sliding applications is to provide the solvent to the contact area while maintaining a swollen condition. Applying a surface texture to the substrate is one of the key methods to improve the durability of CPBs. Surface texturing is a surface modification technique to improve anti-wear and frictional properties by the geometrical modification of surfaces to be slid [15][16][17][18][19]. A previous study demonstrated that applying surface textures onto the substrate of CPBs effectively improved their durability; furthermore, when a groove texture, which acts as a path for lubricants, was applied, the durability of CPBs increased by 36% [20]. In this study, in order to achieve further improvement of the durability of CPBs, we applied nano-periodic structures to the substrate of CPBs in addition to groove surface textures, similar to the previous study [20]. Nano-periodic structures were fabricated based on the following processes: when a metal surface was irradiated by a femtosecond laser with its laser fluence compatible with the energy required for the laser abrasion of the metal used, a striped groove structure with a period shorter than the wavelength of the incident laser light was formed on the metal surface [21,22]. This period can be controlled by the laser fluence [21], wavelength [23], and number of pulses [23] of the femtosecond laser. The striped groove was formed orthogonal to the polarisation of the incident light such that the direction of the striped groove can be controlled via laser polarisation. For example, when a femtosecond laser with parallel polarisation in the scanning direction was scanned on an AISI 52100 surface, as shown in Fig. 1a, a nano-periodic structure (shown in Fig. 1b) was formed. By changing the polarisation of the femtosecond laser, nano-periodic structures with different orientations against the direction of laser scanning were formed, as shown in Fig. 2.
In this study, we investigated the combined effect of nanoperiodic structures that correspond to a surface roughness (Ra) of 0.02 μm and a groove texture on the friction durability of CPBs swollen by an ionic liquid. The phenomena at sliding surfaces are discussed herein.
Specimens and Lubricants
A disc (φ 24 mm × t 7.9 mm) and cylinder (φ 6 mm × l 8 mm) made of AISI 52100 (hardness: HRC 61) purchased from test materials Co., Ltd., JP, were used as test specimens. The roughness of the cylinder Ra was 0.03 μm. Nanoperiodic structures and surface textures were applied to the disc specimens by femto-and picosecond lasers (PiCooLs, L.P.S. Works, JP). The detailed texture patterns are summarised in Sect. 2.2. To prepare CPBs based on poly (methyl methacrylate) (PMMA), the disc, which was used as the substrate for the CPBs, was cleaned via ultrasonic treatment in acetone/hexane (1:1, v/v), chloroform, and 2-propanol for 30 min in each. Then, it was treated with a UV-ozone cleaner (PC440, Meiwafosis Co., Ltd., JP) for 30 min just before use. Subsequently, a thin silica layer that was approximately 1 nm thick was deposited onto the discs by immersing the discs in an ethanol solution containing tetraethoxysilane (0.03 mol/L) and 28% aqueous ammonia solution (0.24 mol/L) overnight, followed by washing with ethanol for 30 min via ultrasonic treatment. A silane coupling agent (2-bromoisobutyryloxy) propyltrimethoxysilane (BPM) was used as an initiator to treat the silica-coated discs for the subsequent graft polymerisation. During the polymerisation, the discs were immersed in a solution containing BPM, 28% aqueous ammonia solution, and ethanol at the weight ratio of 1:10:89, respectively, overnight. This was followed by washing with ethanol for 30 min via ultrasonic treatment. Methyl methacrylate (MMA) was purified by passing it through neutral alumina to remove any radical inhibitors before use. The CPB samples were prepared via surfaceinitiated atom transfer radical polymerisation (SI-ATRP) at the high pressure of 400 MPa [24]. The BPM-immobilised discs were placed in a fluoroplastic vessel containing a solution of MMA (4.7 mol/L), ethyl 2-bromoisobutyrate (EBIB) (24 μmol/L), Cu(I)Br (15 mmol/L), Cu(II)Br 2 (1.7 mmol/L), and 4,4′-dinonyl-2,2′-bipyridine (34 mmol/L) in anisole (50 wt.%). The closed vessel was covered with an Al bag and was placed in a high-pressure reaction system (Syn Corporation Ltd., JP) that was equipped with a high-pressure vessel, an automated high-pressure pump using water as the pressure medium, and a circulating thermostat bath. Polymerisation was conducted at 60 °C and 400 MPa for 4 h. Afterwards, the solution was analysed via 1 H nuclear magnetic resonance (NMR) spectroscopy to estimate the monomer conversion and gel permeation chromatography (GPC) in order to determine the number-average molecular weight (M n ) and polydispersity index for the free polymer produced in solution, which was used as an indicator of the graft polymer [24]. NMR spectra were recorded at 400 MHz on a JNM-ECS400 spectrometer (JEOL, JP) in CDCl 3 at ambient temperature. The GPC measurements were conducted on a GPC-101 (Showa Denko K.K., JP) equipped with a guard column (Shodex KF-G), two 30-cm mixed columns (Shodex KF-806L), and a differential refractometer. Tetrahydrofuran was used as the eluent at the flow rate of 0.8 mL/min. The M n and polydispersity index values were estimated using Table 1 Molecular structure of PMMA and MEMP-TFSI the calibration data obtained by the PMMA standards (Polymer Laboratories Ltd., USA, M p = 1.31 × 10 3 − 1.64 × 10 6 ) and complemented by the polystyrene standards (Polymer Laboratories Ltd., USA, M p = 1.93 × 10 3 −1.32 × 10 7 ). The CPB-grafted discs were washed with tetrahydrofuran several times using a shaking apparatus and ultrasonic treatment. The thickness of the CPBs under dry conditions was approximately 1000 nm, as measured using a spectroscopic ellipsometer with a rotating compensator (M-2000U, J. A. Woollam, USA) equipped with D 2 and QTH lamps. The CPBs were swollen using an ionic liquid, i.e. N-(2-methoxyethyl)-N-methylpyrrolidinium bis (trifluoromethanesulfonyl) imide (MEMP-TFSI, Kanto Chemical Co., Inc., JP), which is a good solvent for PMMA. A previous study showed that the thickness of CPBs after swelling with a good solvent increased by more than two times [14]. Therefore, in this study, the thickness of the CPBs was estimated to increase to above 2,000 nm via swelling by MEMP-TFSI. The molecular structures of PMMA and MEMP-TFSI are shown in Table 1. The thickness of the CPBs was controlled by the polymerisation time. In this study, the CPBs grafted on the textured discs were prepared in the same lot. MEMP-TFSI of volume 300 μL was applied onto a dried CPB disc and stored for 96 h under low vacuum conditions. The swollen CPB discs used in the friction test were unmodified.
Surface Texture
In this study, we applied nano-periodic structures and a groove texture to AISI 52100 discs. A groove texture with a depth of 300 nm, width of 10 μm, and pitch of 110 μm was applied to the AISI 52100 disc substrate. The femtosecond laser for the nano-periodic structure was scanned with a pitch of 10 μm along the groove texture. This laser scanning induced undulation on the surface, corresponding to Ra = 0.11 μm. Three types of orientations of the nano-periodic structures, namely 0°, 45°, and 90°, against the scanning direction of the femtosecond laser, were prepared; these test samples are referred to hereinafter as Nano 0, Nano 45, and Nano 90, respectively. The pitch and corresponding roughness of the nano-periodic structures were 400 nm and 20 nm, respectively. The M n value and polydispersity index of PMMA (free polymer simultaneously produced during the SI-ATRP) were 1.70 × 10 6 and 1.26, respectively. The dry thickness of the CPBs on these textured steel discs was 1102 nm, and the graft density and normalised (dimensionless) graft density were 0.46 chains/nm 2 and 0.26, respectively. The topographic images captured via Atomic Force microscopy (AFM) measurements are shown in Fig. 3.
Friction Durability Test
To analyse the durability of CPBs on surface-modified discs against friction, we performed friction tests with increasing applied loads. A reciprocating friction tester (SRV4, Optimol, DE) with a cylinder-on-disc geometry was used, and the applied load was increased from 5 to 70 N by 1 N every 1 min. The detailed conditions of the friction test are summarised in Table 2. In this study, the load when the friction coefficient exceeded 0.03 was defined as the 'limit load' of the CPBs and used as the durability index. We tested the CPBs on each textured disc three times.
The reciprocating friction tests were conducted in both the perpendicular and parallel directions against a groove texture. The nano-periodic structures comprised three orientation types; therefore, the tests were classified into six categories (3 different orientation samples × 2 sliding directions). Herein, we denote the result of the sliding test as 'sample name-sliding direction'. For example, when Nano 0 is slid to perpendicular to the groove texture, it is denoted as 'Nano 0-Per (instead of Pll in the case of sliding to the parallel direction)'. The test combinations are shown in Table 3.
Surface Analyses
The macro image of the wear track was captured using a laser microscope (VK-X 150, KEYENCE, JP). Nanoand microscale observations were conducted using AFM (S-image, SII, JP) in MEMP-TFSI, and the resultant residual polymers on the wear tracks were evaluated from force-distance curve measurements. A pyramidal Si cantilever (SI-DF20, Hitachi High-Tech, JP) with the spring constant of 20 N/m and tip radius of 10 nm was used. A 100 × 100 μm topographic image was obtained with the load of 300 nN and a scan rate of 0.3 Hz The force-distance curve was obtained with the indentation speed of 2 μm/s. The relationship between force and distance and the amount of polymers at the wear track is shown in Fig. 4.
The force-distance curve shows the behaviour where (i) the CPB was worn out; (ii) less polymers exist, allowing the sharp cantilever to penetrate into the CPB [25]; and (iii) polymers exist sufficiently. As shown in Figs. 4 (i) and (iii), we measured the force curves of the AISI 52100 substrate and unworn CPB as references, respectively. The adhesion shown in Fig. 4 (ii) was derived from the adhesion force between the tip and the chain segments of the polymers, when the tip penetrated the polymer brushes. The details of the analysis are published elsewhere [20].
Friction Durability of Textured CPB Surfaces
The representative frictional behaviours of each CPB on the non-textured and textured substrates are shown in Fig. 5. The limit load where the friction coefficient exceeded 0.03 in each test is summarised in Fig. 6. The limit loads were 26.0 N for non-textured, 44.3 N for Nano 0-Per, 43.3 N for Nano 45-Per, 31.3 N for Nano 90-Per, 49.3 N for Nano 0-Pll, 40.6 N for Nano 45-Pll, and 33.6 N for Nano 90-Pll. The Table 3 Specifications of combination of nano-periodic structures and groove texture and sliding direction Fig. 4 Assessment of amount of polymer remaining on disc specimens surface-modified samples exhibited increased durability as follows: 70% for Nano 0-Per, 67% for Nano 45-Per, 20% for Nano 90-Per, 90% for Nano 0-Pll, 56% for Nano 45-Pll, and 29% for Nano 90-Pll compared with non-textured samples. For the case where the nano-periodic structure was oriented 0° and 45° against the groove texture, the durability improved significantly; meanwhile, that oriented at 90° indicated a moderate increase in durability.
Mechanism of Durability Improvement by Multi-Scaled Surface Texturing
To clarify the mechanism of wear and exfoliation of CPBs, it is important to analyse the surface being worn rather than after it has worn out. Therefore, in addition to the duration friction tests, we performed a test that halted when the friction coefficient exceeded 0.06 and observed the surface. For the 0° and 45° orientations of the nano-periodic structures shown in Fig. 7a, b, respectively, the exfoliation of the polymers starting from the edge of the groove texture was not observed; however, the exfoliation from the edge of the texture was observed in the 90° orientation of the nano-periodic structure. This result indicates that the appropriate nanoperiodic structure is effective in suppressing the exfoliation starting from the edge of the groove texture. Notably, the wear of the CPB occurred from the centre of the reciprocating surface, whereas the sliding condition of the edge of the reciprocating was more severe owing to the sliding speed.
To discuss the detailed mechanism of the wear of CPBs on textured substrates, we performed force-distance curve measurements on the wear track of the surface halfway during the friction test (at the same point as shown in Fig. 7). The topographic images and force-distance curves of Nano Fig. 8a, b, and c, respectively. In the cases of Nano 0-Per and Nano 45-Per shown in Fig. 8a, b, respectively, the force curves at both inside (blue and black circles) and outside (red and green circles) the groove texture suggest the wear of polymers. The 3D topographic images are shown in Supporting Information (S-1). In the case of Nano 90-Per shown in Fig. 8c, the exfoliation of polymers starting from the edge of the groove texture was observed.
The topographic images and force-distance curves of Nano 0-Pll, Nano 45-Pll, and Nano 90-Pll are shown in Fig. 9a, b, and c, respectively. Groove structures were not indicated from these results. In the cases of Nano 0-Pll and Nano 45-Pll shown in Fig. 9a, b, respectively, the force-distance curves suggest the wear of polymers. Note that the inside and outside the wear track could not be distinguished from the topographic images. In the case of Nano 90-Pll shown in Fig. 9c, the exfoliation of polymers occurred at many points.
Discussion
First, we consider the effect of the nano-periodic structure on the CPB substrate. Ramakrishna et al. reported the effect of the nanoscale surface roughness on the lubrication properties of semi-diluted polymer brushes [26]. They reported that the polymer brushes on spherical surfaces with a radius of 6 nm resulted in a higher friction owing to the less-stretched polymer chains, resulting in a smaller repulsion force between the polymer brush and the counter surface. In our study, we did not observe an increase in the friction coefficient when a nano-periodic structure was applied. The radius of the nanoperiodic surface in this study is estimated to be 202 nm [the details of the calculation are described in the Supporting Information (S-2)]. The thickness of the CPB after swelling is estimated to be above 2000 nm, which is much larger than the radius of the nano-periodic structure. Furthermore, the curved surface of the nano-periodic structure continuously appeared in contrast to the sparse appearance of the embedded particles in a previous study [26]. Therefore, it can be hypothesised that polymer chains grafted on a certain asperity are affected by the steric hindrance with other polymer chains on the neighbouring asperity. This causes the polymer brushes to stretch vertically. Based on this hypothesis, the nano-periodic structure induces an increase in the grafted area and leads to a denser polymer brush layer than that on a flat surface. Further, the graft density at the nano-periodic structure surface (0.46 chains/nm 2 ) is larger than that at the flat surface (0.35 chains/nm 2 [20]). This increase in the graft density contributed to better durability of the CPB. Another aspect of the effect of multiscale textures is the reduction in the contact area. Previous studies have reported that the nanotextured surface of soft materials reduces the contact area at the interface, thus reducing the adhesion and friction compared with flat analogues [27][28][29]. Hence, the multiscale textures in this study are also effective in reducing the contact area, which will reduce adhesion and friction and consequently improve durability.
Subsequently, we consider the effect of the orientation of the groove texture and nano-periodic structures. A previous study reported that the exfoliation of polymers starts from the edge of the groove texture [20]. The results of the limit loads shown in Fig. 6 indicate that sliding parallel to the groove texture tends to yield better durability than sliding perpendicular to the same orientation of the nano-periodic structures. In addition, the exfoliation of the CPB was observed for Nano 90-Per by AFM measurements, as shown in Fig. 8c. Therefore, we consider that the edge of groove texture worked as the origin of exfoliation when the groove slid vertically, as mentioned in a previous study [20]. Focussing on the effect of the orientation of the nano-periodic structures and the groove textures, the parallel orientation of the nano-periodic structure along the groove texture tends to yield better durability than the perpendicular orientation analogue. A previous study verified that the supply of an ionic liquid, which is a good solvent, to the contact region plays an important role in maintaining the CPB [12]. From the laser microscope image shown in Fig. 7, it is found that the wear of the CPB started from the centre of the reciprocating direction. This indicates that the Fig. 10 Progress ratio of durability of surface-modified sample compared with that of non-textured CPB sample CPB wear was caused by the starvation of MEMP-TFSI. Based on this mechanism of wear of the CPB, we consider that the orientation of the nano-periodic structure along with the groove texture acts as a lubricant path at the nanoscale and contributes to providing the MEMP-TFSI to the sliding area, which prevents the starvation of the MEMP-TFSI and improves the friction durability.
The comparison of the progress ratio of durability of the surface-modified sample with that of the non-textured CPB sample is summarised in Fig. 10. The data for the samples having a groove texture are based on previous research [20], in which the data were obtained under exactly the same test conditions. The result demonstrates that the application of nano-periodic structures together with a groove texture to the CPB substrate significantly improved the durability of the CPB.
Conclusion
Applying nano-periodic structures and a groove texture to the CPB substrate effectively improved the durability of the CPB through nano-periodic structures, which increased the graft density and induced the formation of a semi-diluted polymer layer at the outermost surface. The results demonstrated an improvement in the durability of the CPB by up to 90% compared with that of the non-textured sample. To achieve such improvements, the nano-periodic structure must be oriented along the groove texture and the laser track, which is formed during the fabrication of nano-periodic structures. | 4,690 | 2021-04-01T00:00:00.000 | [
"Materials Science"
] |
Propagation of Quasi-plane Nonlinear Waves in Tubes
This paper deals with possibilities of using the generalized Burgers equation and the KZK equation to describe nonlinear waves in circular ducts. A new method for calculating of diffraction effects taking into account boundary layer effects is described. The results of numerical solutions of the model equations are compared. Finally, the limits of validity of the used model equations are discussed with respect to boundary conditions and the radius of the circular duct. The limits of applicability of the KZK equation and the GBE equation for describing nonlinear waves in tubes are discussed.
Introduction
Propagation of nonlinear sound waves in waveguides is a very interesting physical problem.In the case that nonlinear waves travel in a gas-filled waveguide, we can observe phenomena such as nonlinear distortion, nonlinear absorption, diffraction, lateral dispersion, boundary layer effects, etc.All these phenomena can be described by means of the complete system of the equations of hydrodynamics, see e.g.[1]- [4]: the Navier-Stokes momentum equation, the continuity (mass conservation) equation, the heat transfer (entropy) equation and the state equations.Unfortunately, there is no known general solution of this system of equations, and numerical solutions bring many problems regarding stability of the solutions and their time consumption.Consequently, it is sensible to simplify the fundamental system of equations if we ignore some phenomena or consider some of them weak.This simplification leads to the derivation of model equations of nonlinear acoustics.
There have been a number of papers devoted to various aspects of the propagation of nonlinear waves in waveguides.The viscous and thermal dissipative effects on the nonlinear propagation of plane waves in hard-walled ducts are treated for instance in papers [5], [6], [7].The authors deal with the dependence of the frequency on the dissipative and dispersive effects induced by the acoustic boundary layer.Experimental results focused on propagation of finite-amplitude plane waves in circular ducts are presented in [8] and [9].Here, a very good agreement is demonstrated between experimental data and results obtained by means of the Rudnick decay model for the fundamental harmonic.Burns in [10] obtained a fourth-order perturbation solution for finite-amplitude waves.However, his expansion breaks down for large times because it contains secular terms.He took into account dissipation, but he neglected mainstream dissipation with respect to boundary dissipation.Keller and Millmann in [11] found the solution of the model equation for inviscid isentropic fluids, where they used perturbation expansion adapted to eliminate secular terms and determined the nonlinear wavenumber shift for dispersive modes.In [12], Keller utilized the results from [11].He rewrote the results in a form that is useful near the cutoff frequency, in order to show that the cutoff frequencies and resonant frequencies of modes in acoustic waveguides of finite length depend upon the mode amplitude.Nayfeh along with Tsai in [13] presented the nonlinear effects of gas motion as well as the non-linear acoustic lining material properties on wave propagation and attenuation in circular ducts.They obtained a second-order uniformly valid expansion by using the method of multiple scales.These authors presented [14], where they investigated nonlinear propagation in a rectangular duct whose side walls were also acoustically treated by means of the method of multiple scales.Ginsberg in [15] dealt with nonlinear propagation in rectangular ducts.He determined by an asymptotic method the nonlinear two-dimensional acoustic waves that occur within a rectangular duct of semi-infinite length as the result of periodic excitation.In [16], he utilized the perturbation method of renormalization to study the nonlinearity effect on a hard-walled rectangular waveguide.Nonlinear wave interaction in a rectangular duct was also investigated by Hamilton and TenCate in [17] and [18].Multiharmonic excitation of a hard-walled circular duct was treated by Nayfeh in [19].He used the method of multiple scales to derive a nonlinear Schrödinger equation for temporal and spatial modulation of the amplitudes and the phases of waves propagating in a hard-walled duct.
Foda presented his work in [20], which is concerned with the nonlinear interactions and propagation of two primary waves in higher order modes of a circular duct, each at an arbitrary different frequency and finite amplitude.He used the renormalization method to annihilate the secular terms in the obtained expression.If we take no diffraction effects into account, we can use the generalized Burgers equation to describe nonlinear plane waves in circular ducts.It is the Burgers equation that is supplemented by the term that represents boundary layer effects, see [21]- [25].The generalized Burgers equation enables the description of dissipative and dispersive effects that are caused by the boundary layer.Asymptotic and numerical solutions of this equation were presented by Sugimoto [26].In [27], there is a description of the solution of the Burgers equation in the time domain.The approximate solutions of the generalized Burgers equation for harmonic excitation in both the preshock and the postshock region are presented in [28].In the case that only weak diffraction effects are considered, the KZK equation can be used, see [22], [25], [29].However, the boundary layer is incorporated into the boundary condition in [22] and [25].
Basic equations
From the equations of continuum mechanics we can obtain in quadratic approximation an equation describing weakly nonlinear waves in thermo-viscous fluids ( ) ( Here j is the velocity potential, t is time, c 0 is the small-signal sound speed, b is the dissipation coefficient of the medium, r 0 is the ambient density, g is the adiabatic index, equal to the ratio of the specific heat at constant pressure c p to that at constant volume, c V , and L is the second-order Lagrangian density, which is given as ( ) The symbol D represents the Laplacian operator and the symbol Ñ is the gradient operator.The operators are defined for axisymmetric waves in the cylindrical coordinates by where z is the coordinate along the axis of the tube, r is the coordinate perpendicular to the axis of the tube, e z is the unit vector along the z axis and e r is the unit vector along the r axis.We shall assume that the profile of the wave distorts slowly as it propagates in the positive z direction.The term "slowly" means that the wave must travel a distance of many wavelengths l for its profile to be distorted significantly.Then it is reasonable to seek a solution having this functional form ( ) where t is retarded time and m is the small dimensionless parameter which is given by the acoustic Mach number -the ratio of the particle velocity amplitude v m to the small-signal sound speed c 0 .If we use the new coordinate system (t, z 1 , r 1 ), then transformation of the partial derivatives yields Substitution of the partial derivatives (6) into the operator (4) gives Here ^denotes directions transverse to propagation.We can write the linear wave equation directly from Eq. ( 1) If we use the operator (10) in Eq. ( 11) for the divergence operator, then after neglecting a quadratic order term we obtain If we suppose the transverse partial velocity then we can omit the last term in Eq. ( 12): Equation ( 14) represents the plane progressive wave impedance relation.
When conditions ( 13) and ( 14) are satisfied we can suppose ).This enables us to modify Eq. ( 1) Substituting relation (14) to the second-order term of Eq. ( 15) we get where After using the transformation of derivatives ( 6) we can neglect the cubic and higher terms.This yields the well- . The KZK eqatuion was derived on the condition that v z ~m and v ^~m 2 (i.e.v z v ^).v z and v ^are connected by the irrotationality condition of the velocity field If we do not take into account the wall friction we have to use for the solution of the KZK the following boundary conditions where R 0 is the tube radius and ( ) F r, t represents the prescribed sound field at z = 0.
If we assume the wall friction in the case that nonlinear waves propagate in a rigid tube, then a thin boundary layer appears near the tube wall.Within the boundary layer, the velocity component in the direction of the tube axis decreases from a mainstream value to zero at the tube wall.The boundary layer affects the acoustic waves not just near the walls but in the entire volume.The boundary layer causes both energy dissipation and wave dispersion.
If the boundary layer is assumed to have a small displacement effect on the mainstream, the following relation can be obtained, see [24] Here B is the coefficient which is given as where n is the kinematic viscosity, Pr is the Prandtl number, the fractional derivative of the order1 2 in Eq. ( 22) represents the following integrodifferential operator ( ) , , and b T is the thermal expansion coefficient of the fluid b r ¶r where T is temperature.If we suppose a perfect gas then b g Relation ( 22) is valid on condition that where d is the boundary layer thickness where w is an angular frequency.
Differentiating Eq.( 14) with respect to r, we get the equation (the irrotationality condition) If we take into account Eqs. ( 29) and ( 22), we can modify boundary condition (21) for tubes with wall friction as follows , , d ¶t After space-averaging over a whole tube cross section, if we take into account boundary condition (30), the KZK equation is reduced to the generalized Burgers equation where ¢ = B B R 0 .The solution of the linearized GBE for the boundary condition ( ) ( ) where a is the attenuation coefficient for the classical thermo--viscous loss mechanism and the attenuation coefficient a b represents the losses due to the wall friction The ratio of the two attenuation coefficients can be written as It is obvious that d l >1for high frequencies but R 0 l 1 because the first of the conditions (27) has to be satisfied.This means that the classical thermo-viscous losses dominate for high frequencies in comparison to the boundary layer losses.
Consequently, the condition d l 1 cannot be satisfied for higher wave form harmonics.
Conditions for the quasi-plane wave in a tube
The condition for validity of the KZK equation in a tube is given by the relation between the values of the longitudinal and transverse velocity components v v ^.This condition follows from the derivation of the KZK equation in the tube given above, see section Basic equations.
The transverse velocity component relates to transverse diffraction.The value of v ^depends on wave frequency, the non-quasi planar boundary condition, the tube radius and the boundary layer.
Supposing that the tube is narrow, the influence of the boundary layer is significant.Let us assume that the source frequency is lower than the cut-off frequency, thus only plane--wave mode propagation is possible.Then the diffraction is given by the influence of the boundary layer only.When we now gradually increase the frequency, the transverse component of velocity v ^also gradually rises.As soon as the frequency exceeds the cut-off frequency of the tube, the transverse mode arises, thus the effect of transverse diffraction increases considerably and the transverse component of the velocity significantly rises.Oscillations appear on the propagation curves for the harmonic amplitudes which were obtained by means of a numerical solution of the KZK equation and consequently the KZK equation loses its accuracy.This means that in the case of a narrow tube we can study wave propagation only below the cut-off frequency.In addition, it is not possible to study wave propagation if we use a boundary condition of any distinct velocity distribution along the tube radius (non-quasi planar boundary condition).
The influence of the boundary layer is less significant in wide tubes.The amplitudes of transverse components of velocity are much lower than in the case of narrow tubes.Therefore the propagation can be studied far above the cut-off frequency even with distinct velocity distribution along the tube radius for the boundary condition.
However, the KZK equation cannot be used for the boundary condition with distinct velocity distribution along the radius when the source frequency is less than the cut-off frequency for a given tube.This restriction holds for any tube radius.
If the used frequency is less than the cut-off frequency, then all higher modes are evanescent and only the plane wave propagates along the waveguide.
However, the KZK equation cannot describe this process because the transverse component of the velocity is large and we cannot consider the KZK equation to be valid.
The cut-off frequency of the first symmetric mode in a circular waveguide is given by the formula where k 1 is the radial wave number of the first mode and 38317 is the first zero point of the Bessel function derivative: ( ) . Now, let us suppose that the time dependency of the dimensionless longitudinal component near the source is given as where x = r R 0 and q wt = is the dimensionless retarded time, which means that we suppose a mono-frequency harmonic source.Here ( ) g 0 x represents the function describing the distribution of the longitudinal component along the radius.Then for the transverse component of the velocity we have ( ) where W is the dimensionless transverse component of the velocity normalized in the same way as the longitudinal component V.
Assuming wave propagation with frequency ¢ f equal to one half of the cut-off frequency we can see that W is equal to Taking into account the fact that the maximum of the derivative of the commonly used velocity distributions (Gauss, Fermi) at the boundary of a tube is of the order O(1), we can see that the values of v ^and v z are comparable.Therefore the validity condition of the KZK equation is not fulfilled.We can say that the KZK equation is valid only for a moderate distribution along the tube radius below the cut-off frequency (for instance, a plane wave which is affected by the boundary layer).
We often read (e.g., in [4], [29]) the condition kR 0 1 from which follows the relation between wave vector components k k ^.This means that a sound wave is quasi-plane and diffraction effects are weak in tubes.With regard to the text above we can say that the condition kR 0 1 represents only a sufficient, but not a necessary, condition for the use of the KZK equation as a model equation for nonlinear waves propagating in tubes.
Numerical solution
Equation ( 17) was solved in the frequency domain.When the solution is periodic in time (i.e., the sound source is periodic in time), it can be expressed in the form of Fourier series.For a numerical solution it was necessary to truncate the infinite number of terms in the Fourier series to * terms.Then the solution was sought in the form where s b w = z v c zm 0 2 and x = r R 0 are dimensionless coordinates.The finite number of terms in series (41) causes instability in the numerical solution.When the solution is approaching the region of shock wave formation, all harmonics are excited and the energy flow stops with the last harmonic, i.e., the M-th harmonic.This effect causes the Gibbs oscillations in the numerical solution.These oscillations were damped by the method described, e.g., by Fenlon [31].Each harmonic was multiplied by the coefficient Y n given by ( ) where H is the frequency damping coefficient.This causes the additional artificial attenuation of the solution.The value of H was chosen so that Gibbs oscillations practically did not arise.During the assembling of the numerical schema we proceeded from the well known Bergen code [32], which was extended by terms including the boundary layer influence.Simple iteration by the LU decomposition method was used to calculate the solution in the next layer.If we use LU decomposition, then the calculations take approximately three times longer than in the case of calculation by means of simple iteration.However, LU decomposition is not restricted by the condition on the step size in the direction of propagation.Application of this method is very convenient in the case when it is necessary to carry out a very large number of iterations by means of the simple iteration method.For example, we need 500000 steps for the simple iteration method and only 400 steps for LU decomposition for a tube 4 mm in radius.
The Burgers equation was solved in the frequency domain by means of the standard Runge-Kutta method of the fourth order.
A narrow tube
The presented distributions represent the deformation of a plane wave under the influence of the boundary layer for a narrow tube, where the boundary layer effect is very important.The calculations are done for particle velocity amplitude v m = 2.76 m×s -1 , tube radius R 0 = 0.004 m, and for the following six frequencies 1 kHz, 10 kHz, 40 kHz, 60 kHz, 100 kHz and 500 kHz.The cut-off frequency of the first symmetric mode for the given tube is approximately equal to 52 kHz.The first 100 harmonics were used in the numerical calculation, the numerical step in the direction of the wave propagation was Ds = 0.01 for the Burgers equation.The value of the numerical step for the KZK equation was determined from this step, so the total number of steps was identical for the GBE and KZK equation.The KZK equation was solved with the plane boundary condition.The numerical step in the direction of the tube radius was chosen Dx = 0.05.The calculations are realized for the case of propagation in air.The source oscillated harmonically with one frequency.For all calculations we used the numerical attenuation coefficient H = 40.
Figures 1-3 contain three curves: curve 1 is the numerical solution of the GBE, curve 2 is the longitudinal component of the obtained by the numerical solution of the KZK equation, and curve 3 represents the transverse velocity component which is calculated from the longitudinal velocity across the tube radius using eq.( 18).The values of curve 3 are multiplied 100 times and calibrated in the same way as the longitudinal component of the velocity to enable the two velocity components to be compared easily.Curves 2 and 3 are depicted for the radius x = 05 . .Owing to the fact that the resultant space evolutions correspond to practically plane waves, the choice of this radius is not important.Figures 1-3 contain the first harmonic.
The graphs illustrate the speculation about the validity of the KZK equation for a narrow tube, where the influence of the boundary layer is dominant.We see that with increasing frequency the transversal velocity component progressively rises.We can observe the significant growth of the transversal velocity component when the cut-off frequency is exceeded.The first oscillations of the transversal velocity component are noticeable in the case of 60 kHz.These oscillations still grow and they are conspicuous when the frequency is equal to 100 kHz.The longitudinal component of the velocity was scarely affected, as can be seen from the comparison with the velocity from GBE.The further increase in frequency causes the lon- gitudinal component of velocity also to become disrupted, as can be seen for frequency equal to 500 kHz.These variations are readily noticeable, especially for the first harmonic, and they are weaker for higher harmonics.The presented phenomena are in harmony with the deductions mentioned above.
A wide tube
Results for a tube with radius R 0 = 0.5 m are also presented.The calculations were made for frequency 100 kHz.
The cut-off frequency of the first symmetric mode for this tube is approximately equal to 911 Hz, thus the frequency of the described waves is considerably higher than the cut-off frequency.The Fermi distribution was chosen as the initial condition for the KZK equation.All other parameters of the computation were the same as in the previous case of the narrow tube.
Summary
This paper shows the derivation of the KZK equation in the parabolic approximation.The following validity condition of this equation for the waveguide has to be satisfied v ~m, v ^~m 2 (that is v v ^).The validity conditions of the KZK equation in the case of the description of quasi-linear waves propagation in the circular waveguide are further discussed by means of these conditions.It is shown that the condition kR 0 1 represents only the sufficient condition for validity of the KZK equation.The equation remains valid in the case of the small radius waveguide (and consequently with strong influence of the boundary layer) for frequencies below the cut-off frequency though kR 0 <1 under the condition that v v ^.The results of numerical solution of the KZK equation are presented for waveguides of both small and large radius which demonstrate these two cases.The numerical solution of the KZK equation was performed by means of a method based on the Bergen code [32], which was modified by the authors because it was necessary to incorporate the boundary condition, taking into account the boundary layer at the waveguide lateral walls.The new method for calculating the diffraction effects generated by the boundary layer effects is described in the text.When the plane wave with a frequency below the cut-off frequency propagates in a small radius tube, then its space evolution along the radius varies only a little and the results of the KZK and the Burgers equation are comparable.Solving the KZK equation also enables us to get the distribution of the perpendicular component of velocity.By means of the perpendicular component of the velocity we can see whether the validity limits of the KZK are fulfilled.In the waveguide of the large radius we can describe by means of the KZK equation the high frequency wave propagation for non-planar distribution of the velocity along the tube radius (it is no longer possible to use the generalized Burgers equation here).Again we can decide from the magnitude of the perpendicular component of the velocity whether we will use the KZK equation within the limits of its validity for the given parameters f, R 0 , v m and for the given velocity distribution along the radius near the source.
Fig. 8 :
Fig. 8: KZK equation solution of the longitudinal (V 3 ) and transversal (W 3 ) velocity component of the third harmonic | 5,146.4 | 2002-01-04T00:00:00.000 | [
"Physics",
"Engineering"
] |
ELIMINATION OF RESONANCES IN CODIMENSION ONE FOLIATIONS
The problem of reduction of singularities for germs of codimension one foliations in dimension three has been solved by Cano in [3]. The author divides the proof in two steps. The first one consists in getting pre-simple points and the second one is the passage from pre-simple to simple points. In arbitrary dimension of the ambient space the problem is open. In this paper we solve the second step of the problem. 2010 Mathematics Subject Classification: 32S45, 32S65, 37F75.
Introduction
Reduction of singularities for germs of holomorphic codimension one foliations in (C n , 0) is an unsolved problem.
In ambient dimension n = 2, the first complete proof has been given by Seidenberg in [9].It is one of the main tools for the understanding of germs of vector fields and foliations in (C 2 , 0).For instance, it is absolutely necessary to support a holonomic study of those foliations (see [8]) or to prove the existence of invariant analytic curves (separatrices) (see [1]).
In ambient dimension n = 3, the problem has been first solved in the non-dicritical case ( [2], [4]) and the result has been used to prove the existence of germs of invariant surfaces in this case.In the general case, it has been solved in [3].
Although there are invariant hypersurfaces in the non-dicritical situations and higher dimension [6], the general solution of the problem of reduction of singularities for n ≥ 4 is still widely open.
In [4] and [3] the authors have identified two kinds of points for codimension one singular foliations in higher dimensional ambient spaces.They are the pre-simple points and the simple ones.Reduction of singularities consists in obtaining at most simple points after a finite sequence of blow-ups with non singular invariant centers.To get pre-simple points is the first step in that problem, and the passage from pre-simple to simple points is the second and last step.In fact, pre-simple points are defined in terms of upper-semicontinuous invariants such as the multiplicity and the transversality positions of the initial forms.The definition of simple points adds non-resonance requirements to the conditions defining pre-simple points.This paper is devoted to a global solution of the second step of reduction of singularities.
The first example of a pre-simple but not simple point is the radial vector field, or equivalently, the foliation defined by After a first dicritical blow-up we obtain simple points (in this particular case even non-singular points).Precise definitions of the notions are given below.Up to some considerations about the Jordan Block singularities, the second step of the problem consists in the elimination of the resonances appearing on the residual vectors of the pre-simple singularities.
In order to do that in a complete global way, we construct a Control Variety X with a normal crossings divisor E. We consider some divisors whose support is contained in E in such a way that the problem of eliminating the resonances is solved once we have eliminated the indeterminacies of these divisors (in the sense of Subsection 7.2).
We end the paper by showing how to eliminate the indeterminacies of a divisor by means of a combinatorial game.In this way we complete the passage from pre-simple to simple points by means of blow-ups with invariant centers of codimension two.
Preliminaries
Contents of this section can be essentially found in [3].Let M be a germ around a non singular compact analytic subset of a complex analytic variety of dimension n.Given a point P ∈ M we denote by O M,P the ring of analytic functions at P and by M M,P its maximal ideal.Let ν : O M,P \ {0} −→ Z ≥0 be the M M,P -adic order.Given a ∈ M M,P we denote by La := a + M 2 M,P its linear part.A holomorphic singular codimension one foliation F of M (for short, a foliation of M ) is given locally at each point P ∈ M by an equation Ω = 0 where is an integrable 1-form germ whose coefficients have no common factors.Such an Ω is called a local generator of F at P .
Let Ω be a local generator of F at P and h a unit of O M,P .Then h • Ω is also a local generator of F at P .
Remark 3. Any meromorphic integrable 1-form ω gives locally a unique foliation that is also denoted by (ω = 0).To see this we consider a local generator Ω where Ω = f /g•ω for an appropriate meromorphic germ f /g.The point of multiplication by f /g is to achieve that all coefficients of Ω are holomorphic functions having no common factors.
The singular locus of F is the subset locally given by Since the coefficients of ω have no common factors, the codimension of Sing F is at least 2. If we say that the foliation F is regular at P .In this case there are local coordinates such that F is generated by ω = dx 1 .
Definition 1.Let L = {Y 1 , . . ., Y s } be a finite list of analytic irreducible subsets Y j ⊂ M .We say that L has normal crossings at a point P ∈ M if there are local coordinates (x 1 , . . ., x n ) such that These coordinates are called adapted to D.
The foliation F of M can always be given locally at each point P ∈ M by an equation ω = 0 where is an integrable 1-form whose coefficients have no common factors.Such an ω is called a local generator of F adapted to D.
Definition 3.
Let H ⊂ M be a hypersurface given locally at each point P by a reduced equation f = 0, f ∈ O M,P .We say that H is an invariant hypersurface of F if f divides Ω ∧ df , where Ω is a local generator of F at P .
The invariant components of D are also called non-dicritical components.The dicritical components are then generically transversal to F. Denote by D nd the union of the non-dicritical components of D and by D dic the union of the dicritical ones.We have D = D nd ∪ D dic and locally at a point P we write where A = A nd ∪ A nd .Note that (x i = 0) is dicritical if and only if x i divides a i .With this notation we can write equation (2) as follows: Definition 4. Let F be a foliation of M , D a normal crossings divisor, P ∈ M and ω an adapted local generator of F as in (2).The point P is pre-simple for (F, D) if it satisfies one of the following conditions: I. ν(a 1 , . . ., a n ) = 0. II.There exists i ∈ A such that the linear part La i is linearly independent of {Lx j : j ∈ A}.Equivalently, Remark 4. If P is pre-simple for (F, D) then it is also pre-simple for (F, D nd ).This follows directly from equation (3).In fact, if x i = 0 is dicritical then a i = x i b i , so ν(a i ) ≥ 1 and a i ≡ 0 mod (x i | i ∈ A) + M 2 M,P .A vector field ξ ∈ T P M is tangent to F at P if ω(ξ) = 0.If ξ is a regular vector field tangent to F at P , we say that ξ trivializes F at P .Definition 5.The dimensional type τ of F at P is τ := n−k, where k is the dimension of the C-vector space spanned by the tangent vectors ξ(P ), ξ being a germ of vector field tangent to F.
If τ is the dimensional type of F at P , as a consequence of the rectification theorem of vector fields, there are local coordinates such that F is given by a local equation ω = 0 where ω has the form Proposition 1.The dimensional type is upper semicontinuous.
Proof: Let P be a point of dimensional type τ .By definition there are n − τ trivializing vector fields independent at P .These vector fields are independent at the points of an open neighborhood U .Therefore, the points of U have at most dimensional type τ .Proposition 2. Let e be the number of non-dicritical components of D passing through a pre-simple point P .We have that e ≤ τ ≤ e + 1.
Proof: Take the notation as in equation ( 3).If we are in case I of Definition 4, there are two options: • There is i ∈ A nd with a i unit.In this case the vector fields trivialize F at P .So the dimensional type is τ = e.• For all j ∈ A nd we have ν(a j ) ≥ 1.In this case there is an index i / ∈ A such that b i = a i is a unit.The vector fields trivialize F at P .In this case τ = e + 1.In case II of Definition 4, the trivializing vector fields may be obtained thanks to the integrability condition.Details can be found in Lemma 5 of [3].
We say that a pre-simple point P is a corner point relatively to (F, D) if τ = e.If τ = e + 1 we say that P is a trace point relatively to (F, D).
Remark 5.If P is a corner point, we only can have the types A or B of the theorem, and in this case ω is a formal adapted generator for F. For trace points, the three types are possible.The type C provides an adapted generator for F. In the cases A and B, in order to adapt ω to the divisor, we have to multiply ω by the variable xi which does not correspond to a component of the divisor, therefore, xi ω = 0 is an adapted generator.Remark 6.We state this theorem without proof, but it is desirable to sketch some parts of the proof.Suppose that we are in the corner case.The formal coordinates x which give us the formal normal forms, are obtained as a limit of convergent coordinates.Starting with convergent coordinates x adapted to D, we make coordinate changes x (1) , x (2) , . . ., following a process known as Jordanization.All of these coordinate changes are of the form where the u (s) i are units.Therefore we have that where û is a formal unit.This implies that locally the components of the divisor (x i = 0) are equal to the formal hypersurfaces (x i = 0).
In the case of a trace point, the situation is similar except for at most one of the variables.The difference appears when we have a trace point of type A or B. In this situation the convergent coordinates give us τ − 1 invariant hypersurfaces, but the formal coordinates show one more germ of formal invariant hypersurface.Suppose that locally D = ∪ τ i=2 (x i = 0).First, it is shown that there is an additional germ of formal invariant hypersurface with equation where φ is a formal series vanishing at the origin.Now the process is exactly like in the corner case, but replacing x 1 by x1 .
Let us recall the case of foliations on surfaces studied by Seidenberg in [9] (see [5] for a more detailed study).Let F be a foliation given locally at a point P by ω = a dx + b dy.Consider the vector field X = b ∂ ∂x − a ∂ ∂y determined by ω.Let L X be the linear part of X , and λ, µ ∈ C its eigenvalues.The point P is a pre-simple singularity if λ or µ are non zero.A pre-simple point P is simple if one of the following conditions holds: • λµ = 0 (saddle-node), • λµ = 0 and λ/µ / ∈ Q >0 .
If λ/µ / ∈ Q >0 we say that the pair (λ, −µ) is non-resonant.The following definitions generalize this notion to arbitrary dimension.
We say that β is non-resonant if its only resonance is m = 0.
We use the formal normal forms given by Theorem 1 in order to define simple singularities.
Definition 8. Let P be a pre-simple singularity for (F, D).It is a simple sigularity if it has a formal normal form of type A or B, and the residual vector is non-resonant.
Stratification of Sing F
Let P be a point and x = (x 1 , . . ., x n ) a local coordinate system adapted to D defined in a neighborhood U of P .For all I ⊂ {1, . . ., n} denote Theorem 1 gives a formal description of the singular locus Sing F around a pre-simple point for (F, D).In adapted formal coordinates x = (x 1 , . . ., xn ) we have We have that this formal description is in fact convergent.We present this result in the following proposition, whose proof follows from Remark 6.
Proposition 3. Let P be a pre-simple point for (F, D) of dimensional type τ .There are local coordinates x = (x 1 , . . ., x n ) adapted to D such that locally at P , and such that the vector fields ∂/∂x τ +1 , . . ., ∂/∂x n are tangent to F.
From now on, we assume that Sing * (F, D) = ∅.
Consider the sets for s = 1, . . ., n.By Proposition 1 all these sets are closed.Note that in particular Sing F = M 2 .
Proposition 5.The set M s is a finite union of irreducible components of codimension s with normal crossings with D. In addition, all points of a connected component of M s \ M s+1 are analytically equivalent.
Proof: Let P ∈ M s \M s+1 and let x be a local coordinate system adapted to D. By Proposition 3 we have that the points of T x 1,...,τ are analytically equivalent to P (the analytic triviality is given by the flow of the vector fields ∂/∂x τ +1 , . . ., ∂/∂x n ), and outside this set the dimensional type decreases.
By Proposition 3 we have that the sets M s and D locally have normal crossings.Note that each subvariety T x I is contained in different components of the divisor, consequently, they are all different from each other.From this fact follows the global normal crossings.We have that Sing F is the union of finitely many codimension two regular subvarieties.Let TrSing F ⊂ Sing F be the set of all the trace points.As we shall precise below, we know that TrSing F is the union of some irreducible components of Sing F that we call trace components.The next proposition is due to Cano and Cerveau.Remark 9. We are not supposing that all points are simple, therefore we cannot use Proposition 6.If all points are pre-simple, we do not have a unique germ of formal hypersurface invariant for F, due to its possible dicriticalness.However, the connected components of TrSing F are well defined, and this fact is the property that we need.Proposition 5 allows us to stratify Sing F considering the connected components of M s \ M s+1 , for s = 2, . . ., n, as strata (where M n+1 = ∅).Since we are working with a divisor which may have dicritical components, it is useful to add this data to the stratification.Thus, the points of a stratum are characterized by being analytically equivalent and belonging to the same components of the divisor.If we denote by τ (Γ) the dimensional type of the stratum Γ and by d(Γ) the number of dicritical components which contain it, we have For simplicity, it is useful to extend the stratification to the whole variety M .We just need to add to the stratification some strata of dimensional type 1: one trace stratum for the points outside the divisor, a corner stratum for each non-dicritical component (formed by the regular points), and the strata corresponding to regular points over dicritical components.
We say that the stratum Γ has the property P if that property is satisfied by its points (note that all points of a stratum are analytically equivalent).To describe F at a stratum Γ we use as a local generator one corresponding to an arbitrary point P ∈ Γ.From now on we will talk about strata rather than points.
Let Γ be a stratum of dimensional type τ contained in d dicritical components.By Proposition 2, we know that Γ can be a corner stratum or a trace one.If it is of corner type, then it is, locally at Γ, the intersection of τ non-dicritical components of the divisor and d dicritical ones.However, if Γ is a trace stratum, it is the intersection of τ − 1 non-dicritical components, one connected component of TrSing F and d dicritical components.
Transforming foliations by non singular blow-ups with codimension two centers
In this work we only use blow-ups with regular centers of codimension two, which are irreducible components of the singular locus.Denote by E 1 , . . ., E t the non-dicritical components of D and by F 1 , . . ., F s the connected components of TrSing F.
Remark 10.Note that there are only two options for a stratum: either it is contained in the center, or they are disjoint.
Let π : M −→ M be the blow-up with center Y .In M we have a foliation F and a divisor D where: • F is the foliation of M defined locally in the following way.Let Γ ⊂ M be a stratum and let Γ = π(Γ ) ∈ M be its image by π.
Let ω = 0 be a local equation of F at Γ.We have that F is given locally at Γ by ω = 0, where ω := π * (ω) is the pull-back of ω by π.
, where D i is the strict transform of D i for i = 1, . . ., t, and D t+1 = π −1 (Y ) is the exceptional divisor.We need to describe how the stratification is modified by the blow-up.Proposition 7. Let Γ ⊂ M be a stratum.Let π be the blow up with center Y .If Γ ⊂ Y , then there is just one stratum Γ ⊂ M such that π(Γ ) = Γ.In this case, Γ is analytically equivalent to Γ. Nevertheless, if Γ ⊂ Y , there are three strata in M that are projected by π onto Γ. Denoting these strata by Γ 1 , Γ 2 , and Γ, we have Proof: We use codimension two centers, so it is useful to recall here the dimension two case.Let us consider the plane with the divisor formed by both coordinate axes.The exceptional divisor obtained after blowing-up the origin is a projective line.We can divide this line into three subsets: the origin of each chart (defined by the intersection between the exceptional divisor and each component of the strict transform of the divisor), and the rest of the points.The blow-up induces an isomorphism between the punctured plane and the new variety without the exceptional divisor.
Without loss of generality, suppose that Y is a corner center, say Y = E i ∩ E j (for trace centers the reasoning is the same).
Outside the center, the blow-up is a birational morphism, thus, the strata disjoint from the center are not modified, and they are in one to one correspondence with the strata of M \ π −1 (Y ).
Let Γ be a stratum contained in Y .We have that, as sets, As in the two dimensional case described above, divide π −1 (Γ) in three subsets: The subset Γ 1 (respectively Γ 2 ) corresponds to the origin of the first (respectively second) chart.It is contained in E i (respectively E j ) and in the exceptional divisor, but it is disjoint to E j (respectively E i ).The remaining points of π −1 (Γ) are only contained in the exceptional divisor.
The analytic triviality along these subsets can be obtained by lifting the corresponding diffeomorphisms for Γ.
Remark 11.Note that it does not matter if the blow-up is dicritical or not, these sets are always well defined.In fact, this is the reason to consider the dicritical components in the stratification.
Let (x 1 , . . ., x n ) be a coordinate system adapted to D at Γ. Let ω be a local generator of F adapted to D at Γ. Suppose that locally we have E s = (x i = 0) and E t = (x j = 0).To obtain the expression of π * (ω) we just need to substitute the equations of the blow-up in the expression of ω.In the first chart we have that where depends on the point we are looking at.The value = 0 corresponds to Γ 1 , and the different values = 0 correspond to the points of Γ. Interchanging the indices i and j we obtain the equations for the second chart (thus for Γ 2 ).Proposition 8. Let Γ ⊂ Y be a simple stratum.Then π is non-dicritical and Γ 1 , Γ 2 , and Γ are simple strata.
Proof: Suppose that Γ is a stratum of type A, and fix adapted coordinates x such that Y = T i,j .Let λ be the residual vector of Γ.A direct calculation shows that Γ 1 is a type A stratum whose residual vector is λ := λ + λ j e i (where e i is the i-th vector of the canonical basis).Let p ∈ Z τ be a vector orthogonal to λ .We have that p := p + p i e j is orthogonal to λ.If p ∈ Z τ ≥0 , then p ∈ Z τ ≥0 and therefore λ is nonresonant.This reasoning works for the other strata, and for the case of a type B singularity.
Statement of the main theorem
Let us make a precise statement of the result of reduction to simple singularities: Theorem 2. Let M be a germ around a non singular compact analytic subset of a complex analytic variety of dimension n, D ⊂ M a divisor with normal crossings, and F a foliation of M .Assume that all points of M are pre-simple for (F, D).There is a finite sequence of blow-ups such that all points of M are simple for (F , D ).
We divide the proof in two parts.First we eliminate the type C singularities (Theorem 3) and after this we eliminate the resonances (Theorem 4).
Elimination of type C singularities
In the two dimensional case, type C points are completely characterized by their behavior under blow-up.We recall here this case since it is very similar to the arbitrary dimension case.Consider the foliation of C 2 given by ω = dx − px dy y + y p α dy y , and suppose that p > 1.If we blow-up the origin, we obtain two singularities in the exceptional divisor: a saddle node in the origin of the first chart and a type C singularity in the origin of the second chart.Replacing p by p − 1 in the above expression we obtain a local generator at the new type C point.After blowing-up p − 1 times we obtain one type C singularity with p = 1.If we blow-up one more time, the only singularity that appears is a saddle node in the origin of the first chart.
As illustrated by the two dimensional case, if we blow-up type C points enough times, they disappear.Our strategy for eliminating all type C points consists in blowing-up all the trace components of the singular locus which contains type C strata.Proof: As Proposition 7 states, there is nothing to do for strata disjoint from Y .Using again Proposition 7 we know that there are three strata over the ones contained in the center.Using the same arguments as in Proposition 8 we see that type A and B strata only produce the same kind of strata (or even non singular strata).So, if there are no type C strata contained in Y , the statement is true.
Depending on the values of τ , k, p k , and α k the behavior of Γ under the blow-up centered at Y is different.First, suppose that τ ≥ 3.
• If p k > 1 the blow-up is non-dicritical.Thus, Γ and Γ 1 are corner strata and consequently they cannot be of type C. Replacing p k by p k − 1 in ( 5) we obtain a local generator at Γ 2 .• If p k = 1 and α k = 0 the blow-up is also non-dicritical.The situation is like in the previous case.Note that now p k − 1 = 0, and therefore the index k drops to k − 1.
, and Γ are analytically equivalent to the ones of ∆ 1 , ∆ 2 , and ∆ respectively, but they belong to one more dicritical component of the divisor.Note that in the three strata the dimensional type has dropped.Replacing p k by p k − 1 = 0 in the expression (5) we obtain a local generator for Γ 2 , and this is the unique type C stratum created.If τ = 2 we cannot have the third case (if α 2 = 0 then Γ is a trace stratum of type A).In the other cases the situation is similar, but note that if the index k becomes 0, Γ 2 is a non singular stratum.Theorem 3. Let M be a germ around a non singular compact analytic subset of a complex analytic variety of dimension n, D ⊂ M a divisor with normal crossings, and F a foliation of M .Assume that all points of M are pre-simple for (F, D).There is a finite sequence of blow-ups such that there are no type C points in M .
Proof: For each stratum Γ consider the invariant ι(Γ) ∈ Z 3 ≥0 defined by where the numbers k and p 2 + • • • + p k are exactly the ones that appear in a formal normal form.Let π be the blow-up of M with allowed center Y of trace type.By Proposition 9 we know that there is at most one type C stratum in M over a stratum of M .Then, for each type C stratum Γ of M there is one stratum Γ in M such that π(Γ ) = Γ.As we can see in the proof of Proposition 9 we have that for the lexicographic order.Moreover, the inequality is strict for strata contained in the center of the blow-up.
There are finitely many strata of type C. Number them by Γ 1 , . . ., Γ N and consider the global invariant Each time we blow-up an allowed trace center containing type C strata, the invariant ι C decreases for the lexicographic order.Consequently, after a finite chain of such blow-ups there will not be any type C stratum.Therefore the strategy consists in blowing-up all the allowed trace centers containing type C strata.We can do this by choosing the centers arbitrarily, or, for example, taking each time one which contains a stratum that reaches the maximum value of the invariant.
Elimination of resonances
After eliminating all type C singularities, the only non simple strata are resonant of type A or B. The following proposition allows us to know when a stratum is resonant without using the formal normal forms.
Proposition 10.Let Γ be a pre-simple stratum of type A or B. The following conditions are equivalent: (1) Γ is resonant.
(2) There is a finite chain of blow-ups and there is a stratum and it is the only one in the chain with this property.
Proof: Let λ be the residual vector of Γ.If Γ is a type B stratum we only use centers of blow-up involving the variables which give the residual vector.Thus we can think without loss of generality that Γ is a type A stratum.
(1) ⇒ (2) Let r 0 = (r 1 , . . ., r τ ) be a resonance of Γ 0 := Γ such that gcd(r 1 , . . ., r τ ) = 1.Fix two indices i, j with r i , r j > 0. Let Y 0 be the subvariety locally equal to T x i,j , and let π be the blow-up centered at Y 0 .If r i ≤ r j then the stratum Γ 1 has r 1 = r 0 −r i e j as resonance.If instead we have r i > r j the stratum Γ 2 has r 1 = r 0 − r j e i as resonance.Take Γ 1 equal to one of the resonant strata and denote by r 1 its resonance.We have that |r 1 | < |r 0 |.We can repeat this process until we reach a stratum Γ N −1 with resonance r N −1 = e s + e t .Let Y N −1 be the subvariety locally equal to T x s,t , and let π N be the blow-up centered at Y N −1 .This last blow-up is dicritical and therefore the described sequence of blow-ups is the desired chain.
(2) ⇒ (1) We need to construct a resonance of Γ using the chain of blow-ups (6).We know that r N −1 = e s + e t is a resonance of Γ N −1 since π N is dicritical.The stratum Γ N −1 is in the origin of one of the charts of the blow-up π N −1 .If for example, it is in the first chart, we have that r N −2 = r N −1 + r N −1 i e j is a resonance for Γ N −2 .Iterating this process we get a resonance for Γ.
Proposition 11.Let Γ and ∆ be strata of M .If ∆ ⊂ Γ and Γ is resonant, then ∆ is also resonant.
Proof: By Proposition 10 we know that there is a finite chain of blow-ups satisfying certain conditions related to Γ.The same sequence of blowups satisfies the same conditions with respect to ∆.Using again the equivalence of the previous proposition we have that ∆ is resonant.
Proposition 12. Suppose that all type A strata are non-resonant.Then, all type B strata are also non-resonant.
Proof: Let Γ be a type B stratum and suppose that it is resonant.Let x be an adapted to D coordinate system such that Γ is locally equal to S x 1,...,τ and let be a formal normal form.The residual vector of Γ is λ = (α k+1 , . . ., α τ ).
Let r be a resonance of Γ with the maximum amount of zeros and let I ⊂ {k + 1, . . ., τ } be the set of indices I := {i | r i = 0}.Let ∆ be the stratum locally equal to S x I .Using the arguments of the proof of Proposition 10 we can determine a chain of blow-ups in the conditions of the proposition involving only the variables corresponding to I.This chain of blow-ups also satisfies the conditions with respect to ∆.Thus, by Proposition 10, we have that ∆ is resonant.This stratum is resonant involving all the variables, and therefore it is of type A contradicting the hypothesis.
Theorem 4. Let M be a germ around a non singular compact analytic subset of a complex analytic variety of dimension n, D ⊂ M a divisor with normal crossings, and F a foliation of M .Assume that all points of M are pre-simple for (F, D), and that there are no type C points.There is a finite sequence of blow-ups such that all points of M are simple for (F , D ).
The idea is to reduce the problem to a combinatorial process of elimination of indeterminacies.First we need to treat all the strata together, both the trace and the corner ones.Then we define the Control Variety: a variety with a divisor which represents the properties of Sing F that we need.In this variety we define and solve a combinatorial game.Finally we show that this solves also the problem of eliminating resonances.
In order to treat all the strata together, we will represent all the residual vectors and resonances in a common space.Let Γ be a type A strata of dimensional type τ .Note that Γ is contained in exactly τ elements of K. Let I(Γ) ⊂ {1, . . ., N } be the set of indices corresponding to these elements.Let λ ∈ (C * ) τ be the residual vector of Γ.Each coefficient λ i corresponds to one of the components of K, say Kni .Consider the injective map Using the same idea we can represent the resonances r ∈ Z τ ≥0 into Z N ≥0 .For short, we will write λ instead of ι(λ) (and we do the same for the resonances).
Definition 10.Let p ∈ Z N be a vector of integers.If p ∈ Z N ≥0 or p ∈ Z N ≤0 , we say that the vector p has pure sign.Remark 12.Note that a resonance is a vector with pure sign.Lemma 1.If all the elements of B(Γ) have pure sign, then Γ is nonresonant.
Proof: By definition, two vectors with pure sign can not be orthogonal.Since the resonances have pure sign, Γ has to be non-resonant.
7.1.The Control Variety.Let à ∈ M N ×N be the matrix defined by Ãi,j = 1 if Ki ∩ Kj = ∅ and Ãi,j = 0 otherwise.We refer to this matrix as the codimension two incidence matrix of K. Let (i 1 , j 1 ) < • • • < (i s , j s ) be the pairs of indices such that i < j and Ãi,j = 0, ordered by the lexicographic order.
Consider the affine space X 0 = C N and let K 0 = ∪ N i=1 K i be the divisor defined by K i := (z i = 0), where (z 1 , . . ., z N ) are coordinates of C N .Note that the codimension two incidence matrix of K 0 is defined by A 0 := (A 0 i,j = 1) N i,j=1 .We will modify this variety by blow-ups until we get a new one in which the codimension two incidence matrix of the strict transform of the divisor is exactly Ã.
Let π 1 : X 1 −→ X 0 be the blow-up with center K i1 ∩ K j1 and let K 1 ⊂ X 1 be the strict transform of K (for simplicity, we denote the strict transform of each component equal to the initial one).Replacing A i1,j1 and A j1,i1 by 0 we obtain the codimension two incidence matrix of K1 .Repeating this process with the pairs (i 2 , j 2 ) < • • • < (i s , j s ), we finally get a projective variety X := X s and a divisor K := K s whose codimension two incidence matrix is exactly A := Ã.where n i ∈ Z. Suppose that we perform the blow up of X centered at K s ∩K t .By abuse of notation denote the strict transforms of K 1 , . . ., K N with the same symbols, and denote by K N +1 the exceptional divisor.We define the strict transform of Φ as where n i = n i for i = 1, . . ., N and n N +1 = n s + n t .
Let µ i,j (Φ) be the integer defined by µ i,j (Φ) = −n i n j if i < j, K i ∩ K j = ∅ and n i n j < 0, 0 otherwise.
we are close to the classical results of Zariski [10]; there he uses only codimension two centers.
Definition 12. Let Φ = N i=1 n i K i and Ψ = N i=1 m i K i be divisors.We say that Ψ is a subdivisor of Φ if for all index i we have m i = n i or m i = 0.
Remark 14.Note that if Φ is a locally determined divisor, so are all its subdivisors.Since p has pure sign we have that Φ p is not locally determined.
Suppose that π is the blow-up of X centered at K s ∩ K t .Let Φ * p be the strict transform of Φ p and consider the following subdivisors: Let π be the blow-up of M centered at Ks ∩ Kt .Suppose that Γ 1 is resonant.In the proof of Proposition 8 we saw how to compute the resonances of Γ 1 using the ones related to Γ.We have that where p 1 is exactly the vector of integers appearing in the expression of Φ 1 p .Thus, if we associate a divisor to p 1 we get Φ 1 p .In the same way, if Γ 2 or Γ are resonant, its associated divisors are Φ 2 p and Φp respectively.Lemma 2 gives us a finite chain of blow-ups in X which transforms Φ p into a locally determined divisor.Let Y 1 , . . ., Y m be the centers of such blow-ups.Each center is the intersection of two components of K, so we can write Y i = K si ∩ K ti where {s i , t i } ⊂ {1, 2, . . ., N + i − 1}.
Let π 1 be the blow-up of M with center Ỹ1 = Ks1 ∩ Kt1 .We obtain three strata over Γ, which may be resonant.We need to control these three strata, but as we saw previously, we can do this with subdivisors of Φ * p .The key is in Remark 14: if we transform Φ p into a locally determined divisor, then all its subdivisors will be also locally determined.Now we can continue the process by blowing-up the center Ỹ2 = Ks2 ∩ Kt2 , and so on.In the final step, we have that all the strata over Γ are non-resonant.
In the same way we did before, using Lemma 2 we can determine a finite chain of blow-ups which transform Φ 1 into a locally determined divisor.This chain of blow-ups transforms also the other divisors.Now, we can use Lemma 2 again so that Φ p 2 (its strict transform) becomes locally determined (note that if we transform a locally determined divisor by blow-ups, it stays locally determined).Using Lemma 2 enough times, we determine a chain of blow-ups which makes all the divisors become locally determined.With the corresponding chain of blow-ups in M we reach the situation desired.
Remark 7 .
If P is a point of dimensional type τ , and x is a local coordinate system adapted to D, then M r = #I=r I⊂{1,...,τ } S x I , locally at P .Remark 8.Note that if Sing * (F, D) = ∅ the proposition is false.Consider for example the foliation of C 3 given by d(xy(x − y)(x − zy)) = 0.In this case M 3 = (x = y = 0) has codimension two.
Proposition 6 .
If all points are simple, each connected component of TrSing F defines the germ of a formal invariant hypersurface.Proof: See [4, Part II, §5].
Proposition 9 .
Let π be the blow-up of M with allowed center Y .Each type C stratum of M produces at most one type C stratum in M .
7. 2 .
Elimination of local indeterminacies of a divisor.The objects for the combinatorial game mentioned above are divisors with support contained in K.They are all of the form Φ := N i=1 n i K i ,
7. 3 .
End of the proof of Theorem 4. Suppose that there is just one resonant stratum Γ ⊂ M with B(Γ) = {p}.Consider the divisor Φ p in X defined byΦ p := N i=1 p i K i .
A finite list of analytic subsets has normal crossings if and only if the list whose elements are the irreducible components of these subsets has normal crossings.Definition 2. Let H 1 , . . ., H t be hypersurfaces of M .We say that H = ∪ t i=1 H i is a normal crossings divisor if: • each hypersurface H i is non singular, • the list L = {H 1 , . . ., H t } has normal crossings at every point of M .Consider a normal crossings divisor D ⊂ M .Since M is a germ around a compact, D has finitely many irreducible components.At each point P ∈ M , there are local coordinates (x 1 , . . ., x n ) such that D is locally given by s, locally at P , where A j ⊂ {1, . . ., n} for j = 1, . . ., s. | 9,674 | 2015-01-01T00:00:00.000 | [
"Mathematics"
] |
MiR-146a-5p suppresses activation and proliferation of hepatic stellate cells in nonalcoholic fibrosing steatohepatitis through directly targeting Wnt1 and Wnt5a
Nonalcoholic fibrosing steatohepatitis is a uniform process throughout nonalcoholic fatty liver disease (NAFLD). MicroRNAs (miRNAs) have been suggested to modulate cellular processes in liver diseases. However, the functional role of miRNAs in nonalcoholic fibrosing steatohepatitis is largely unclear. In this study, we systematically analyzed the hepatic miRNAs by microarray analysis in nonalcoholic fibrosing steatohepatitis in C57BL/6J mice induced by methionine-choline deficient (MCD) diet. We identified 19 up-regulated and 18 down-regulated miRNAs in liver with fibrosis. Among these dysregulated miRNAs, miR-146a-5p was the most significant down-regulated miRNA. Luciferase activity assay confirmed that Wnt1 and Wnt5a were both the target genes of miR-146a-5p. Hepatic miR-146a-5p was down-regulated in fibrosing steatohepatitis, but its target genes Wnt1 and Wnt5a and their consequent effectors α-SMA and Col-1 were significantly up-regulated. In addition, miR-146a-5p was downregulated, whilst Wnt1 and Wnt5a were up-regulated in the activated primary hepatic stellate cells (HSCs) compared to the quiescent primary HSCs. Overexpression of miR-146a-5p in HSCs inhibited HSC activation and proliferation, which concomitant with the decreased expressions of Wnt1, Wnt5a, α-SMA and Col-1. In conclusion, miR-146a-5p suppresses activation and proliferation of HSCs in the progress of nonalcoholic fibrosing steatohepatitis through targeting Wnt1 and Wnt5a and consequent effectors α-SMA and Col-1.
miRNAs targets
. Many studies demonstrated that miRNAs play essential roles in a variety of cellular processes such as metabolism, immune function, cell proliferation, and apoptosis [7][8][9] . Aberrant expression of miRNAs is associated with a variety of liver diseases, including viral hepatitis, autoimmune liver disease and liver cancer 10,11 . Recent studies showed that miRNAs could regulate the activation of HSCs and fibrogenesis [12][13][14] . These may particularly contribute to the pathogenesis of nonalcoholic fibrosing steatohepatitis. However, the functional significance of miRNAs in the fibrogenesis process remains unclear. Identification of abnormally expressed miRNAs in the important pathologic state of NAFLD is helpful to further understand the molecular mechanism of nonalcoholic fibrosing steatohepatitis. In this study, we evaluated the differentially expressed miRNAs in nonalcoholic fibrosing steatohepatitis induced in mice fed with methionine-choline deficient (MCD) diet [15][16][17] and demonstrated for the first time that miR-146a-5p suppresses activation and proliferation of HSCs in the pathogenesis of nonalcoholic fibrosing steatohepatitis through targeting Wnt1 and Wnt5a and their consequent effectors alpha-smooth muscle actin (α -SMA) and type I collagen (Col-1).
Results
Differential expression of hepatic miRNAs in mice with fibrosing steatohepatitis. As shown in Fig. 1, the liver sections from mice fed an MCD diet exhibited disordered lobule structure, macrosteatosis in Zone 3, spot or focal hepatocyte necrosis, inflammatory infiltration and perisinusoidal fibrosis (Fig. 1A), which companied with significantly higher serum ALT and AST levels (P < 0.01) compared to the control diet-fed mice (Fig. 1B). To investigate the potential involvement of miRNAs in nutritional fibrosing steatohepatitis, we performed the miRNAs microarray analysis to assess the miRNAs expression profiles in the livers of mice with fibrosing steatohepatitis and those with normal histology. There were 37 dysregulated hepatic miRNAs in fibrosing steatohepatitis compared to the normal liver, including 19 up-regulated and 18 down-regulated miRNAs (> 2-fold changes) (Fig. 1C).
Microarray-based gene ontology analysis and pathway analysis for differentially expressed miRNAs. We performed a gene ontology (GO) term and Kyoto Encyclopedia of Genes and
Genomes (KEGG) pathway annotation of the predicted miRNA targets using gene annotation tool. The high-enrichment GO terms were regulation of transcription, transferase activity, protein phosphorylation, negative regulation of canonical Wnt receptor signaling pathway, Wnt receptor signaling pathway, etc ( Fig. 2A). KEGG pathway analysis identified 25 pathways that were over-represented (P < 0.05) (Fig. 2B), including insulin signaling pathway, apoptosis, Wnt signaling pathway, etc. Thus, the GO term and KEGG pathway annotations for the predicted miRNA targets illustrated the likely roles for these differentially expressed miRNAs during nonalcoholic fibrosing steatohepatitis.
Validation of miRNA expression by quantitattive real-time PCR (qRT-PCR).
In accordance with the microarray assay results, qRT-PCR confirmed that miR-15b-5p was significantly up-regulated, whereas miR-146a-5p and miR-203-3p were down-regulated in fibrosing steatohepatitis. Given miR-146a-5p was one of the most significant down-regulated miRNAs in fibrosing steatohepatitis, we chose it as a candidate for further investigation (Fig. 1D). miR-146a-5p was down-regulated in the activated HSCs in vitro. We further isolated primary HSCs in mice liver. On average, 5 × 10 6 HSCs were harvested from each mouse. The purity of freshly isolated living HSCs was more than 95% determined by the trypan blue exclusion method. The immunofluorescent staining of α -SMA, a marker of HSC activation, showed a significant increase in primary activated HSCs in vitro (Fig. 3A). The expression of miR-146a-5p was found to be significantly down-regulated in the activated HSCs (Fig. 3B).
Overexpression of miR-146a-5p suppressed proliferation of HSCs. In light of the decreased expression of miR-146a-5p in activated HSCs, we next investigated the effect of miR-146a-5p on the proliferation of two HSC cell lines LX-2 and HSC-T6. The miR-146a-5p expression was markedly up-regulated by miR-146a-5p mimics (Supplementary Figure S1). As determined by desmin immunofluorescence and CCK-8 assay, overexpression of miR-146a-5p led to an inhibition of cell proliferation in LX-2 and HSC-T6 as compared to the control cells (Fig. 4A,B).
Effects of miR-146a-4p on HSC activation and collagen deposition. To clarify the roles of miR-146a-5p overexpression in HSC activation and collagen deposition, we transfected miR-146a-5p mimics into HSCs. As shown in Fig. 4C,D, overexpression of miR-146a-5p significantly suppressed mRNA and protein expression of α -SMA, Col-1, matrix metalloproteinase-2 (MMP-2) and up-regulated the mRNA and protein expressions of Smad7, which were characterized genes in the activation process of HSCs. On the contrary, the mRNA and protein expressions of these genes were reversed by miR-146a-5p silence (Fig. 4C,D) suggesting that miR-146a-5p may suppress HSC activation as well as ECM deposition. miR-146a-5p directly acted on the 3'UTR of Wnt1 and Wnt5a mRNA. Among the predicted targets of miR-146a-5p, Wnt1 and Wnt5a were predicted as potential target genes of miR-146a-5p. Examination of the homology showed that the 7 nucleotides in the seed region of miR-146a-5p were complementary to bases of Wnt1 (Fig. 5A) and Wnt5a (Fig. 5C), respectively. No perfect binding site predicted for miR-146a-5p in the coding region of Wnt1 and Wnt5a was identified. To determine whether miR-146a-5p directly binds to the predicated sites of the Wnt1 and Wnt5a 3′UTR, we performed luciferase reporter assays. miR-146a-5p mimics significantly reduced Wnt1 3′UTR-dependent and Wnt5a 3′UTR-dependent luciferase activity but not affect mutant reporter luciferase activity, whereas mimic control had no effect on wild type or mutant reporter luciferase activity. On the other hand, miR-146a-5p inhibitor enhanced wild type or mutant reporter luciferase activity (Fig. 5B,D). These results suggested the interaction between miR-146a-5p and the 3'UTR of Wnt1 and Wnt5a mRNA. miR-146a-5p down-regulated Wnt1 and Wnt5a at the posttranscriptional level. We further explored the regulation level of miR-146a-5p on Wnt1 and Wnt5a gene expression. Accompanied with the down-regulation of hepatic miR-146a-5p, the mRNA and protein expressions of Wnt1 and Wnt5a were markedly elevated in mice fed with MCD diet compared with mice fed with control diet (Fig. 5E,F). The consistent results were observed in vitro. MiR-146a-5p target genes Wnt1 and Wnt5a were significantly enriched in HSC activation (Fig. 5G,H). Wnt1 and Wnt5a protein but not mRNA expression was significantly decreased in miR-146a-5p mimic-transfected-HSCs compared with the mimic control-transfected-HSCs. Silencing miR-146a-5p by miR-146a-5p inhibitor increased the expression of Wnt1 and Wnt5a protein levels (Fig. 5I,J). These results suggest that miR-146a-5p regulated Wnt1 and Wnt5a genes expression at the posttranscriptional level.
Effects of overexpression and inhibition of miR-146a-5p on the downstream target genes of Wnt signaling pathway. To investigate whether down-regulation of Wnt1 and Wnt5a by miR-146a-5p could affect the downstream factors in Wnt signaling pathway, we analyzed the β -catenin, glycogen synthase kinase-3β (GSK-3β ), and nuclear factor of activated T-cells 5 (NFAT5) mRNA and protein levels by qRT-PCR and Western blot, respectively. As compared to the control, the hepatic mRNA and protein expressions of β -catenin and NFAT5 were significantly increased, GSK-3β expressions was significantly decreased (Fig. 6A,B). In vitro, miR-146a-5p mimics significantly down-regulated β -catenin and NFAT5 expressions, and upregulated GSK-3β expression on both mRNA and protein levels, and silencing of miR-146a-5p showed the contrary changes ( Fig. 6C,D), indicating that miR-146a-5p might modulate Wnt signaling pathway.
Knockdown of Wnt1 or Wnt5a inhibited the gene expressions of Wnt signaling downstream and fibrogenesis.
To seek an explanation for the effect of Wnt1 or Wnt5a on liver fibrosis, we knockdown Wnt1 and Wnt5a in HSC-T6 cells by siRNA transfection. QRT-PCR and Western blot confirmed that Wnt1 and Wnt5a were significantly downregulated after siRNA transfection (Fig. 7A,B). Knockdown of Wnt1 or Wnt5a significantly reduced the mRNA and protein expressions of β -catenin and NFAT5, and elevated GSK-3β expression (Fig. 7C,D). Moreover, it was also observed that knockdown of Wnt1 or Wnt5a significantly suppressed pro-fibrotic genes α -SMA, Col-1 and MMP-2 expressions and enhanced an inhibitory Smad, Smad7 expression (Fig. 7E,F).
Discussion
The MCD model is a well-known rodent model for the study of steatohepatitis and liver fibrosis. The advantage of MCD diet model was being more efficient and reproducible for inducing severe liver damage and progressive fibrosis. Following MCD diet for 8 weeks, mice rapidly and consistently developed a severe pattern of steatohepatitis with mixed inflammatory cell infiltration, fibrosis in the pericellular, perisinusoial and portal area. Thus, this diet approach models the subgroup of NASH patients with histologically advanced NASH, and it is ideal for studying mechanisms driving NASH-related inflammation/ fibrosis.
In this study, we identified the aberrant expression of miRNAs in nonalcoholic fibrosing steatohepatits in mice. Among the differential expressed microRNAs, we identified 19 up-regulated and 18 down-regulated miRNAs (> 2-fold changes) in fibrosing steatohepatits. Coordination of aberrant expression of these miRNAs may contribute to hepatic fibrosis in nonalcoholic steatohepatits. The potential targets of differentially expressed miRNAs were known to play a role in the regulation of signal transduction, cell proliferation, differentiation and apoptosis. The KEGG signaling pathway analysis of Values are mean ± SD, **P < 0.01 compared with 1d, # P < 0.05 compared with 3d, ## P < 0.01 compared with 3d. (I) HSC-T6 cells were transfected with miR-146a-5p inhibitor or inhibitor control, miR-146a-5p mimics or mimics control for 48 h. mRNA and (J) protein expression of Wnt1 and Wnt5a were reduced by miR-146a-5p mimics and increased by miR-146a-5p inhibitor in HSC-T6 cells. β -actin was used as loading control. Values are mean ± SD, **P < 0.01 compared with control.
Scientific RepoRts | 5:16163 | DOi: 10.1038/srep16163 the miRNA microarray data was performed to cluster the signaling information involving predicted targets of the differential miRNAs. Oxidative stress, cell apoptosis, Wnt signaling and Toll-like receptor pathway are enriched in MCD diet induced hepatic fibrosis. All these genes and signaling pathways may play key roles in developmental processes of nonalcoholic fibrotic steatohepatits.
It was proved consistent by both the microarray assay and the real-time PCR that the expression of miR-146a-5p and miR-203-3p were significantly down-regulated and miR-15b-5p expression was significantly up-regulated in the fibrotic liver in mice. The effects of various miRNAs on liver fibrosis have been illustrated in recent studies. miR-29 was reported to play a crucial role in CCL4-induced liver fibrosis 18 . miR-199 and 200 family was up-regulated in the progression of liver fibrosis 19 . Moreover, miRNAs were demonstrated to play an important role in regulating HSCs function, such as activation, cell proliferation and production of ECM. miR-27a/b maintain HSCs a more quiescent phenotype and inhibit cell proliferation 20 . Overexpression of miR-122 in HSCs led to significant inhibition of the production of mature Col-1 21 . In our study, among the validated miRNAs, hepatic miR-146a-5p showed the most significantly dysregulated. Similarly, the down-regulation of miR-146a-5p was observed in the activation process of primary HSCs isolated from the mouse livers compared to their quiescent phenotype. Collectively, these data suggested that miR-146-5p might play a crucial role in the development of nonalcoholic fibrosing steatohepatitis and its suppression may be associated with HSC activation.
As miR-146a-5p expression was down-regulated during the HSC activation and hepatic fibrogenesis, the effect of miR-146a-5p on the biological behavior of HSCs was evaluated. We transducted miR-146a-5p mimics into activated human (LX-2) and rat (T6) HSCs. Notably, the cell proliferation assay by CCK-8 results revealed that miR-146a-5p significantly inhibited the proliferation of both HSC cell lines, which could be also confirmed by desmin immunofluorescent staining. In fact, activation of HSCs disrupts the balance between matrix production and degradation 2 . In our study, miR-146a-5p inhibited pro-fibrotic genes α -SMA, Col-1 and MMP-2 expressions, enhanced the expression of Smad7, a negative mediators of TGF-β signaling. MMPs, a family of ECM degradative enzymes, are promptly expressed by activated HSCs 22 . MMP-2 promotes hepatic fibrosis by increasing HSC proliferation and it is required for degradation of the accumulated collagen. Smad7 is a crucial negative regulator of TGF-β signaling, and antagonizes the activity of the Smad4. Increased Smad7 expression could attenuate the fibrogenic response of hepatic stellate cells induced by TGF-β 1 23 . In line with our results, another investigation revealed a potential mechanism for the role of miR-146a in fibrosis through regulating the expression of Smad4 24 . These findings implied that miR-146a-5p might negatively regulated liver fibrogenesis through inhibiting the HSC activation and collagen synthesis in HSCs.
In consideration of the important role of miR-146a-5p in repressing liver fibrogenesis through suppressing the activation of HSCs, we investigated the impact of Wnt1, Wnt5 and thier downstream effectors participating in this function. In fact, one single miRNA can regulate tens to hundreds targeted genes. Wnt1 and Wnt5a were predicted to be direct targets of miR-146a-5p by bioinformatics analysis and were confirmed with dual luciferase report assay and western blot. Moreover, miR-146a-5p overexpression in HSCs resulted in up-regulation of Wnt1 and Wnt5a in protein levels but no change in mRNA expression, confirming that miR-146a-5p regulated Wnt1 and Wnt5a expression at a post-transcription level. Wnt1 and Wnt5a are key elements of the canonical and non-canonical Wnt signaling pathway, respectively 25 . Wnt signaling promotes hepatic fibrosis by enhancing activation and survival of HSCs and is one of the major signal transduction pathways associated with hepatic fibrogenesis [26][27][28] . In our study, knockdown of Wnt1 or Wnt5a led to the suppression of α -SMA, Col-1, MMP-2 and increase of Smad7 expression, which was consistent with the efficacy of miR-146a-5p. To demonstrate whether Wnt1 and Wnt5a are major targets to mediate the activity of miR-146a-5p, we used a combined loss-of-function approach to functionally characterize Wnt1 and Wnt5a in fibrogenesis. Results showed that knockdown of Wnt1 or Wnt5a mimicked the roles of miR-146a-5p, further indicating that Wnt1 and Wnt5a are the primary functional targets of miR-146a-5p in nonalcoholic fibrosing steatohpatitis.
Given that Wnt signaling was reported to maintain the quiescent state of HSCs 29 and Wnt1 and Wnt5a were demonstrated to be the targets of miR-146a-5p for suppressing the activation of HSCs, we further investigated the possible downstream effectors participating in this function. The studies have shown that Wnt1 and Wnt5a exerted their effects by regulating β -catenin, GSK-3β and NFAT5, respectively. Our data indicated that miR-146a-5p inhibited β -catenin, NFAT5 and activate GSK-3β by down-regulation of Wnt1 and Wnt5a. β -catenin, a core component of canonical Wnt signaling, has been shown to be an important regulator of cellular proliferation and differentiation 30 . The knockdown of β -catenin in HSC-T6 cells inhibited cells proliferation and synthesis of Col-1 and Col-3 31 . This might be another reason for the inhibition effect of miR-146a-5p on HSC proliferation and collagen secretion. GSK-3β , a negative regulator of canonical Wnt signaling 32 , is implicated in various biological processes including cell growth, differentiation and apoptosis 33 . Inhibition of GSK-3β impeded synthesis of α -SMA by reducing β -catenin phosphorylation in HSCs 29 . NFAT5 is a transcriptional target of Wnt5a signaling, was reported to accelerate cell proliferation 34 and could also stimulate the production of TGF-β 1 and subsequent activation of Smad3 35 . In the present study, knockdown of Wnt1 or Wnt5a inhibited the expression of downstream factors, β -catenin, NFAT5, and increased the expression of GSK-3β . Taken together, the results implicated a possible mechanism that miR-146a-5p negatively modulated Wnt signaling pathway via direct interaction with Wnt1 and Wnt5a.
In conclusion, we identified hepatic miRNAs and evaluated their expression patterns in nonalcoholic fibrosing steatohepatitis induced by MCD diet using microarray. Among the validated miRNAs, miR-146a-5p was significant down-regulated in nonalcoholic fibrosing steatohepatitis and in activated HSCs. Overexpression of miR-146a-5p contributed to the development of liver fibrosis through inhibiting the proliferation, activation of HSCs and deposition of collagen, suppressing Wnt signaling pathway. Therefore, miR-146a-5p might serve as a novel regulator in the pathogenesis of nonalcoholic fibrosing steatohepatitis.
Methods
Animal models of nonalcoholic fibrosing steatohepatitis. Eight-week-old male C57BL/6J mice were bred and housed as previously described. Nonalcoholic fibrosing steatohepatitis was induced by feeding the mice with MCD diet (Research diets, Inc., NJ, New Brunswick, USA) for 8 weeks. Meanwhile, mice were fed with diet supplemented with choline bitartate and DL-methionine (Research diets, Inc., NJ, New Brunswick, USA) as controls. At the end of the experiment, all the animals were sacrificed under anesthesia, and blood samples were collected from femoral artery for biochemical analysis. The livers were partly fixed in 10% formalin for histological analysis or snap-frozen in lipid nitrogen followed by storage at − 80 °C freezer until required. All the protocols and procedures were performed following the guidelines of Hebei Committee for Care and Use of Laboratory Animals and were approved by the Animal Experimentation Ethics Committee of Hebei Medical University.
Histological analysis and Biochemical analysis. Hematoxylin and eosin stained and Masson
trichromatism stained paraffin-embedded liver sections (5 μ m thick) were scored for hepatic steatosis, inflammation and fibrosis as described previously in accordance with the Brunt's criteria and the histological scoring system for NAFLD issued by the Pathology Committee of the Nonalcoholic Steatohepatitis Clinical Research Network. Serum ALT and AST levels were measured by the enzymatic kinetic method using an automatic biochemical analyzer (Olympus AU2700, Japan) according to the manufacturer's instructions.
MicroRNA microarray Assay. Total RNA was extracted from 20 mg liver tissue of MCD diet-fed mice and control diet-fed mice (n = 3 mice/group) using TRIzol reagent (Invitrogen) according to the manufacturer's instructions. The μ Paraflo ™ MicroRNA microarray Assay was performed using a service provider (LC Sciences, Houston, TX, USA). The assay started from 4 to 8 μ g total RNA sample were 3'-extended with a poly (A) tail using poly (A) polymerase. An oligonucleotide tag was then ligated to the poly (A) tail for later fluorescent dye staining. Hybridization was performed overnight on a μ Paraflo microfluidic chip using a micro-circulation pump (Atactic Technologies). After RNA hybridization, tag-conjugating Cy3 dye was circulated through the microfluidic chip for dye staining. Fluorescence Scientific RepoRts | 5:16163 | DOi: 10.1038/srep16163 images were collected using a laser scanner (GenePix 4000B, Molecular Device) and digitized using Array-Pro image analysis software (Media Cybernetics). Data was analyzed by first subtracting the background and then normalizing the signals using a LOWESS filter (Locally-weighted Regression).
QRT-PCR analysis. Total RNA was isolated and extracted from frozen liver tissues with TRIzol reagent (Invitrogen). cDNA was synthesized using reverse transcriptase with miRNAs-specific stem-loop primer (RiboBio, Guangzhou, China) or oligo dT primers (Thermo, Waltham, MA, USA). Differentially qRT-PCR was performed on an ABI 7500 Real-Time PCR system (Applied Biosystems, Foster City, CA, USA) using SYBR Green master mixture (CoWin Biotech, Beijing, China). The relative abundance of miRNA was normalized to small nuclear RNA U6, and the expression levels of genes were normalized against an endogenous reference gene glyceraldehyde-phosphate dehydrogenase (GAPDH). The relative amount of each miRNA and genes were measured using the 2 −ΔΔCt method. All qRT-PCR reactions were conducted in triplicate. The primers used for qRT-PCR are shown in Table 1.
Identification of potential miRNA gene targets. Predicted gene targets of all differentially expressed miRNAs were identified using three databases including TargetScan, PicTar, and miRanda 36 . All predicted targets indentified in any database were then subjected to gene GO (www.geneontology. org) analysis to uncover the miRNA-gene regulatory network on the basis of biological processes and molecular functions 37 . Enrichment provided a measure of the significance of the function. Pathway analysis was used to determine the significant pathways of the differential genes according to KEGG. Fisher's exact test and χ 2 test were used to classify the GO category and the significant pathway. The false discovery rate (FDR) was calculated to correct the P-value. P-value of < 0.001 and a FDR of < 0.05 was considered to statistically difference.
Gene
Length of production (bp) Primers Isolation, culture, and identification of HSCs. Primary HSCs were isolated from 12-to 16-week-old male C57BL/6J mice (weighted about 30 g) in situ perfusion with pronase-collagenase digestion and fractionation on a discontinuous gradient of Percoll (50% and 25%). Stellate cells were harvested from the 25% media interface. Cell purity and viability were confirmed by trypan blue staining. HSCs were cultured in Dulbecco's modified Eagle medium (DMEM, GIBCO, Grand Island, NY, USA) supplemented with 10% fetal bovine serum (FBS, BioInd, Israel), 100 U/L penicillin, 100 μ g/mL streptomycin, and 2 mmol/L glutamine in a humidified 5% CO 2 atmosphere. On average, 5 × 10 6 HSCs were harvested from each mouse. The purity of freshly isolated living HSCs was more than 95% determined by the trypan blue exclusion method.
miR-146a-5p transfection in HSCs. The HSCs (LX-2, HSC-T6) cells were seeded at a density of 2 × 10 5 /ml and the medium was replaced with fresh DMEM medium without antibiotics. 50 nM miR-146a-5p mimic or 100 nM miR-146a-5p inhibitor (Ribo Bio, Guangzhou, China) was transfected into HSCs using lipofectamine 2000 (Invitrogen, Carlsbad, CA, USA) for gain and loss of miR-146a-5p function experiments, respectively. The corresponding negative sequence (mimic control or inhibitor control) were used with the same concentration as controls in miRNA experiments. After 5 h culture with transfection mix, the cell culture medium was replaced with 10% FBS/DMEM with antibiotics. At 48 h after the transfection, cells were harvested by mild trypsinization, washed in phosphate-buffered saline. All experiments were repeated in triplicate.
RNA interference and transfection. HSC-T6 cells were transfected with siRNA against Wnt1 or siRNA against Wnt5a, and control siRNA (Ribo Bio, Guangzhou, China) consisting of a scrambled sequence that will not lead to specific degradation of any cellular message. The siRNAs were transfected into HSC-T6 cells using lipofectamine 2000 (Invitrogen). Knockdown efficiency was evaluated by qRT-PCR and Western blot. The synthesized oligos were shown in Table 1 Immunocytochemistry analysis. HSCs were grown on chamber slides, and the transfection experiments were carried out as described before. The cells were fixed in 4% paraformaldehyde for 15 min and washed with PBS three times. The cells were permeated with X-Triton100 for 20 min and washed with PBS three times. Then the cells were blocked with 5% bovine serum albumin in PBS for 1 h followed by incubation with primary antibodies against desmin (ProteinTech Group, Chicago, USA) and α -SMA (Novus Biologicals, Littleton, USA) for 16 h at 4 °C overnight. After washing with PBS three times, secondary antibody was applied and incubated for 1 h. After additional washing, the cells were analyzed by fluorescence microscopy.
Cell proliferation assay. Five hours after transfection with miR-146a-5p mimics or mimics control, LX-2 cells and HSC-T6 were reseeded on 96-well plates, at a density of 5 × 10 3 cells per well for 1, 2, 3, 4, 5d. The cells were assayed for proliferation using the Cell Counting Kit-8 (CCK-8, Dojindo, Kumamoto, Japan), according to the manufacturer's instructions. The experiments were conducted three times independently.
Luciferase activity assay. Sequence of segments with the wild-type (WT) or mutant (Mut) seed region of Wnt1 and Wnt5a were synthesized and cloned into psiCHECK TM -2 luciferase vector (Promega, Madison, WI, USA) between Xho I and Not I restriction sites. An empty luciferase reporter vector was used as a negative control. HEK-293T cells were cultured in 24-well plated and each well was transfected with 200 ng of the respective psi-CHECK2 3′UTR constructs, and 50 nM miR-146a-5p mimics or mimics control, and 100 nM inhibitor or inhibitor control, using lipofectamine 2000 transfection reagent (Invitrogen, Carlsbad, CA), according to manufacturer's protocol. After 5 hours, OptiMEM (Invitrogen, CA, USA) transfection medium was replaced with DMEM. Cells were harvested and assayed 48 hours after transfection using the Luciferase Assay System (Promega). The synthesized oligos were shown in Table 1. | 5,688.2 | 2015-11-05T00:00:00.000 | [
"Medicine",
"Biology"
] |
An Efficient Snapshot Strategy for Dynamic Graph Storage Systems to Support Historical Queries
,
I. INTRODUCTION
As an important part of big data, dynamic graph data are widespread in many applications such as social networks [1]- [3], communication networks [4], [5], biology and disease networks [6], [7], coauthor networks [8], [9], etc. Graph is also a useful tool in areas such as manufacturing [10]. Recently people not only make analysis of the real time state of a graph, but also pay attention to how a graph evolves to obtain more knowledge [11], [12]. For example, Leskovec et al. [13] studied diameter changes of an evolving social network. Semertzidis and Pitoura [14] investigated the The associate editor coordinating the review of this manuscript and approving it for publication was Guangdong Tian . most durable graph pattern that exists for the longest period of time.
The increasing demands for evolving analysis pose great challenges to the dynamic graph storage system. The system is required to be capable of handling historical queries.
In other words, it should be able to recreate any historical states [15], [16].
There are three optional storage models for dynamic graph storage systems to support historical queries. The first is called 'sequence of snapshots'. A dynamic graph is regarded as a sequence of snapshots. Each snapshot is a static graph representing the state of the dynamic graph at a certain moment. The second is 'log file'. All the updates of a dynamic graph are saved in a log file. Therefore, any historical state of the graph can be regenerated through redoing the update operations recorded in the log file. The third is named 'set of varying instances'. A dynamic graph is regarded as a set of dynamically changing instances. Each instance contains the information about the evolving process of one single vertex, e.g., when the vertex is created, how and when the attribute of the vertex is updated, and how and when its relationships with other vertices change.
The first model enables high recreation performance at the cost of very high storage consumption, while the second one consumes least storage space suffering from poor recreation performance. The third one saves storage consumption as well as provides high performance in recreating the historical state of a single vertex or a small sub-graph. However, it is inefficient to recreate the historical state of the whole graph [17].
The combination the first two models named 'snapshot plus log' has been investigated in the area of fault tolerance [18]. It provides storage consumption as well as high performance in state recovery. In the scenario, snapshots are stored at regular intervals. Besides, since only the latest state is required to be recovered, the older snapshots could be discarded to reduce storage consumption as time goes by.
We investigate how to apply this 'snapshot plus log' model in the dynamic graph storage system for supporting historical queries. The main challenge lies in the snapshot strategy. The traditional one that stores snapshots at regular intervals is inefficient in this new situation, since the historical states do not share the same frequency of being requested. With the traditional snapshot strategy, some snapshots may be seldom accessed by any historical queries, while some historical queries may request historical states not near to any snapshot. The former case leads to waste of storage space, while the latter case leads to recreation performance degradation.
The contribution of this paper includes three aspects. First, we formally define the snapshot optimization problem. It is stated as the minimization of the number of redone and undone operations in the historical state recreation process through the optimal selection of the timestamps for the snapshots. Second, a new snapshot strategy is proposed to solve the problem. The historical queries are clustered according to the timestamps of the requested historical states and the centroids are used to determine the location of the snapshots. The novelty lies in that the distribution of the snapshots is not uniform in the time axis but consistent with the density of the historical queries. Last but not least, we conduct experimental analysis to validate the efficiency of the proposed strategy. The results show that with the same number of snapshots, the proposed strategy greatly improves the performance of historical state recreation. Meanwhile, with the same creation performance guarantee, the proposed strategy sharply reduces the storage consumption.
The paper is organized as follows. Section II summarizes the related work; Section III formally defines and analyzes the problem; Section IV elaborates upon the proposed snapshot strategy; Section V shows the experimental results; Section VI concludes the whole paper.
II. RELATED WORK
Recently the research on the storage of dynamic graphs with support for historical queries attracts much attention [19], [20]. The fundamental challenge here is the tradeoff between recreation performance and storage consumption [21]. The storage model can be classified into the following three categories: the snapshot sequence model, the log file model and the set of varying instances model. The snapshot sequence model regards the evolution of a dynamic graph as a set of static graph snapshots. One graph snapshot represents the state of the graph at a certain moment. This approach may be suitable for small-size and slowly evolving graphs [22]. Both Yang et al. [23] and Ren et al. [24] adopted the snapshot sequence model for historical analysis. To improve space efficiency, Ren et al. [24] used a compression method to reduce data redundancy at the cost of update time increase. Zaki et al. [25] proposed a method for storing the sequence of snapshots in a compact manner while maintaining a very low update overhead. The main idea is to separate the parts of the data that may change in the future from other parts. For a given set of graph snapshots which correspond to the state of an evolving graph at different time instances, Semertzidis et al. [26] discussed the Best Friends Forever (BFF) problem, i.e., how to identify the set of nodes that are the most densely connected in all snapshots. Nelson et al. [27] investigated several problems of interest on time-evolving graphs and proposed corresponding algorithms that run on compressed time-evolving graphs. The advantage of the methods based on the snapshot sequence model is that the requested historical state can be quickly obtained without any recreation cost, while the disadvantage is that the storage consumption is too high. The log file model saves all the update operations of a dynamic graph in a log file. Theoretically, all the historical states can be recreated by redoing the update operations, and the storage consumption is the minimum. However, it is not feasible in practice, since it takes too long to recreate a historical state.
In the third storage model, a dynamic graph is regarded as a set of varying instances. Each instance contains the update history of a single vertex [17], [28]. Han et al. [29] proposed a method that divides the graph into multiple spatio-temporal chunks with each chunk covering a subset of vertices and spanning a certain time interval. The method is suitable for graph state recreation in a distributed manner. Aridhi et al. [30] also discussed the distributed processing of large scale dynamic graphs. The advantage of this model lies in the efficient historical query of a single vertex or a small sub-graph, but the disadvantage is the inconvenience for recreating the whole historical state for a given timestamp.
In order to make a tradeoff between the performance of historical state recreation and the storage reduction, some researchers try to combine the first two models [31]. It is called as 'snapshot plus log'. The main idea is to save the state of the graph as a snapshot at some moments, and record the update operations such as vertex or edge addition, deletion, VOLUME 8, 2020 and attribute modification in a log file. When a historical query arrives, the snapshot nearest to the requested historical state is retrieved, and the update operations happened between the requested historical state and its nearest snapshot will be redone or undone depending on whether the snapshot is earlier or later than the requested historical state. After redoing or undoing the update operations, the historical state will be recreated. Bhattacherjee et al. [21] also discussed the tradeoff between recreation performance and storage cost. However, the method is designed for handling multiple-versioned data, not for dynamically changing data.
In the 'snapshot plus log' storage model, it is difficult to determine when to save a snapshot. The objective is to store a minimum number of snapshots while maintaining a small number of redone and undone operations in the recreation process, or minimizing the number of redone and undone operations for a given number of snapshots. At present, there are two typical snapshot strategies. One is based on time interval, and the other is based on update operation. The first stores snapshots at regular intervals, while the second stores a snapshot whenever the number of the update operations accumulates to a certain value. However, whether the snapshots are appropriate depends on whether they hit the historical queries, or at least near to the requested historical states. Snapshots far away from the historical states do not favor the recreation process at all while consuming storage space.
III. PROBLEM STATEMENT
We use U as the set of the update operations that have happened on the dynamic graph G, with each element u i representing the ith update operation. Here each u i is a tuple consisting of sn i , ut i and o i , with sn i denoting the serial number of the update operation, ut i representing the time when the update operation u i happened and o i describing how the graph G was updated at time ut i . Let M denote the number of elements contained in U , and then there are totally M different historical states. The valid timestamps corresponding to the ith historical state can be described as an interval [ut i , ut i+1 ). It means that at every time instant during the time interval [ut i , ut i+1 ), the state of the graph G is always the same to that at time ut i .
We use Q as the set of historical queries that are predicted to happen in the near future, with the element q j representing the jth kind of historical query. Here each q j is a tuple consisting of ht j and n j , with ht j representing the timestamp related to the requested historical state of the graph G and n j representing the frequency of the jth kind of historical query in the near future. In other words, the historical state of the graph G at time ht j will be queried n j times. It should be noted that, Q is a predicted set, and the more exact it is, the better. A simple prediction method is to take the latest query set as the predicted value. The prediction technique is out of the scope of this paper. We just assume that Q is available through some prediction methods.
We use S as the set of the snapshots and T as the set of the timestamps corresponding to the snapshots in S. To serve a historical query that requests the historical state of the graph G with the timestamp ht j , the system works as follows. First, it finds the two neighboring snapshots s left and s right . Let ts left and ts right respectively represent the timestamps of the two neighboring snapshots. We obtain that ts left is the largest snapshot timestamp in those not greater than ht j , and ts right is the smallest snapshot timestamp in those not smaller than ht j . Second, the system calculates the distances from the requested historical state to the two neighboring snapshots. The nearer neighboring snapshot is chosen for further computation. Here the distance between a historical state and a snapshot is evaluated by not the time interval itself, but the number of the update operations occurred during the time interval. Finally, the requested historical state is recreated by redoing or undoing operations on the nearer snapshot. If s left is the nearer snapshot, the update operations during the interval (ts left , ht j ] need to be redone and the process is called forward recreation. Otherwise, the update operations during the time interval (ht j , ts right ] need to be undone and the process is called backward recreation. The update operation details could be looked up in the log file that records the whole updating process of the graph. The number of the update operations that are redone and undone greatly affects the performance of historical queries. Constrained by the storage cost, we assume that only N snapshots of the graph G are allowed to be created. The problem is how to determine T for the N snapshots such that the average number of redone and undone operations served for the historical queries is minimized. Suppose that ts k (1 ≤ k ≤ N ) represents the timestamp of the kth snapshot. The optimization problem is then stated as follows: In Equation (5), we use O 2 (j) rather than O(j), because the former promises lower variation.
IV. THE PROPOSED SNAPSHOT STRATEGY A. MAIN IDEA
The two traditional snapshot strategies (i.e., the time interval based strategy and the update operation based strategy) make decisions independent of the distribution of historical queries. As a result, some snapshots are far away from all the historical states requested by the historical queries, while some historical queries request historical states that are not near to any snapshot. The former case leads to storage waste, while the latter case leads to recreation performance degradation.
Therefore, we propose a new snapshot strategy that determines the timestamps of the snapshots according to the distribution of historical queries. Firstly, a clustering method is used to aggregate the historical queries into a number of groups. The number of the groups equals the number of the snapshots to store. Secondly, the cluster centroids are used to determine the timestamps of the snapshots. Historical queries aggregated to the same group will be served by the same snapshot. Some of the historical queries are served in a forward recreation manner by redoing update operations on the snapshot, while others are served in a backward recreation manner by undoing update operations on it.
To make a further explanation of the idea of our snapshot strategy, we take an example as shown in FIGURE 1. In the figure, the graph has been updated 10 times during the period from the time instant 0 to 20, and the update operations are represented with u 1 . . . u 10 . There are eight historical queries, i.e., h 1 . . . h 8 , and the timestamps of the requested historical states are marked in the figure. Suppose that only two snapshots are allowed to be stored.
With the time based snapshot strategy, the timestamps of the two snapshots are 10 and 20 respectively. All of the historical states requested by the eight historical queries are created from Snapshot1. For serving the historical query either h 1 or h 2 , four update operations, i.e., u 3 , u 4 , u 5 and u 6 , need to be undone. For serving either h 3 or h 4 , three update operations, i.e., u 4 , u 5 , and u 6 , need to be undone. For serving either h 5 or h 6 , no operation needs to be undone or redone, because the requested historical state is equal to Snapshot1. For serving either h 7 or h 8 , one update operation, i.e., u 7 , needs to be redone. Therefore, the average number of redone or undone operations for serving each historical query equals 2.
With the update operation based snapshot strategy, the first snapshot is created once the number of the update operations reaches five, and so the timestamps of the two snapshots are six and twenty respectively. All of the historical states requested by the eight historical queries are created from Snapshot1. For serving the historical query either h 1 or h 2 , three update operations, i.e., u 3 , u 4 , and u 5 , need to be undone. For serving either h 3 or h 4 , two update operations, i.e., u 4 and u 5 , need to be undone. For serving either h 5 or h 6 , one operation, i.e., u 6 , needs to be redone. For serving either h 7 or h 8 , two update operations, i.e., u 6 and u 7 , need to be redone. Therefore, the average number of redone or undone operations for serving each historical query also equals 2.
With our cluster based snapshot strategy, the two snapshots are located at the centroids of the historical queries, and the two timestamps are four and eleven. For the two historical queries h 1 and h 2 , the requested historical states are recreated from Snapshot1 by undoing the update operation, i.e., u 3 . For the two historical queries h 3 and h 4 , the requested historical states are equal to Snapshot1 without redoing or undoing any update operation. For the two historical queries h 5 and h 6 , the requested historical states are recreated from Snapshot2 by undoing the update operation, i.e., u 7 . For the two historical queries h 7 and h 8 , the requested historical states are equal to Snapshot2 without redoing or undoing any update operation. Therefore, the average number of redone or undone operations for serving each historical query equals 0.5.
Our cluster based snapshot strategy ensures that the historical queries are served by a very near snapshot with a very high probability, and the number of redone and undone operations is minimized in recreating the requested historical states. VOLUME 8, 2020 FIGURE 2. A scenario for explaining the distance between a historical query and a centroid.
B. ELABORATIONS
As stated in the above subsection, there are two phases in our strategy for determining the snapshot timestamps. One is to cluster the historical queries, and the other is to obtain the timestamps of the snapshots through the cluster centroids. We elaborate upon the two phases in the following.
1) PHASE 1: CLUSTERING THE HISTORICAL QUERIES
We use the K-means algorithm for clustering historical queries. Although other clustering algorithms may also work, we verify that the simple K-means algorithm already meets our requirements in the situation, as shown in Section V.
The K-means algorithm clusters the samples in an iteration way. It initializes the centroids with random values. In each iteration, there are three tasks. The first is to calculate the distance between each sample and each centroid. The second is to classify the samples into groups. According to the values of the distances calculated in the first step, the nearest centroid for each sample is figured out, and samples with the same nearest centroid are classified into the same group. The third is to update the centroids according to the samples in the group, and start the next iteration step.
In the K-means algorithm, a central part is to calculate the distance between a given sample and a given centroid. In our situation, the samples are the historical queries, and the centroids are the timestamps of the snapshots. A simple indicator for the distance is the time interval between the timestamp of the historical state requested by the historical query and the timestamp of the snapshot. However, not the time interval length but the number of update operations occurred during the time interval actually matters, as it determines the cost of redoing and undoing in the historical state recreation. Therefore, we adopt the number of update operations occurred during the time interval between the timestamp of the requested historical state and that of the snapshot as the criterion of the distance.
For example, in FIGURE 2, the time interval between the timestamp of the requested historical state and that of Centroid1 is 4, while the time interval between the timestamp of the requested historical state and that of the Centroid2 is 6. However, the distance between the requested historical state and Centroid1 is longer than that between the requested historical state and Centroid2. The reason is that there are three update operations during the former time interval, while two update operations during the latter.
For the convenience of calculating the distance defined above, we take the serial number of the latest update operation to substitute the timestamp for describing the historical state. Suppose that the timestamp of the requested historical state is ht j . Among all the update operations in U , we look for u i satisfying that the element ut i is the maximum one among those not greater than ht j , and then sn i is the serial number of the latest update operation. In the clustering method, we use sn i to denote the requested historical state requested by q j .
The historical query clustering algorithm in shown in Algorithm 1. The input of the algorithm includes the update operation set U , the historical operation set Q, and the number of snapshots to be stored N , while the output C is the set of cluster centroids in the form of the sequential numbers of the update operations. Each element c k in C will be transformed into snapshot timestamps in Phase 2. Here we just describe the transformation as ts k = g(c k ).
From Lines 1 to 11, the algorithm transforms the historical query set from Q to Q . The timestamp of a requested historical state is substituted by the serial number of the latest update operation. As stated above, it is more convenient to calculate the distance in this way. From Lines 12 to 13, the cluster centroids are initialized with random values, and they are optimized in an iteration way as shown from Lines 14 to 25. In each iteration, each historical request q v is attributed to the nearest centroid as shown from Lines 17 to 20, and then the cluster centroids are updated according to the belonging historical queries as shown from Lines 21 to 24. Besides, the cluster centroids are saved as C old at the beginning of each iteration shown in Line 15, and are compared with the newly updated cluster centroids C at the end of each iteration shown in Line 25. If there is no difference between C and C old , the iteration process is finished, and the cluster centroids are returned.
In each iteration, each c k is updated with the average of the sequential numbers of the latest update operations with regard to the historical states requested by the historical queries belonging to the cluster. The reason is explained below.
f (ts 1 , . . . ts N ) = f (g(c 1 ), . . . , g(c N )) 90842 VOLUME 8, 2020 Algorithm 1 Historical Query Clustering Algorithm Input: The update operation set U = {u i |u i is a tuple <sn i ,ut i ,o i >}; the historical query set Q = {q j |q j is a tuple <ht j ,n j >}; the number of clusters to aggregate N Output: The cluster centroid set C = {c k |1 ≤ k ≤ N } 1: Q = ∅ 2: num = 0 3: for each q j in Q do 4: Traverse U to find sn max that is the maximum of i satisfying that ut i is not greater than ht j 5: for r from 1 to n j do 6: num + + 7: sn num = sn max ; 8: q num =< num, sn num > 9: end for 11: end for 12: Find both the minimum and the maximum of sn j in Q , namely min and max respectively 13: Initialize each c k in C with a value randomly chosen between min and max 14: repeat 15: C old = C 16: for each v from 1 to num do 18: Find k 0 satisfying that |sn v − c k 0 | is the minimum among all the |sn v − c k | with 1 ≤ k ≤ N 19: end for 21: for k from 1 to N do 22: Calculate avg k that is the average of sn j for all the q j in Cluster k
2) PHASE 2: CALCULATING THE SNAPSHOT TIMESTAMPS FROM THE CLUSTER CENTROIDS
The centroids obtained in Phase 1 are described with the serial numbers of the update operations, and we need to convert them to snapshot timestamps. First, according to the serial number, the time instant when the update operation occurred can be obtained from the information contained in the set U . Second, the time instant when the following update operation occurred can also be obtained. Any time between the two time instants could be taken as the timestamp of the snapshot. Without loss of generality, we take the first time instant as the snapshot timestamp. for each u i in U do 4: if not sn i <c k then 5: break 7: end if 8: end for 9: end for The calculation of the snapshot timestamps based on the cluster centroids is shown in Algorithm 2.
Since the centroids of historical queries may change as time goes by, the timestamps of the snapshots will be updated periodically. The snapshots can be created according to their timestamps.
The serving of the historical queries is the same to other traditional strategies. First, according to the timestamp of the requested historical state, two nearest snapshots are found, i.e., the left nearest snapshot and the right nearest snapshot. Second, the number of update operations between the timestamp of the left nearest snapshot and the timestamp of the requested historical state is obtained, and that between the right nearest snapshot and the historical state is also obtained. Third, according to the number of update operations, the real nearest snapshot is determined. If the left one is the real nearest, forward recreation is adopted, and the update operations will be redone. Otherwise, backward recreation is adopted, and the update operations will be undone.
V. EXPERIMENTAL EVALUATION
We mainly concentrate on the performance improvement in serving historical queries and the reduction in storage consumption provided by our proposed snapshot strategy. The average number of redone and undone operations in serving each historical query is taken as the criterion for evaluating the recreation performance, while the total number of snapshots is taken as the criterion for storage consumption.
A. EXPERIMENTAL SETUP
We adopt the Monte Carlo simulation method for evaluation. The three snapshot strategies (including the time interval based strategy, the update operation based strategy and our clustering method based strategy) are implemented in Python 3.7 with SKlearn. The computer is equipped with 8-core Intel i5 processor and 8GB of RAM.
Two kinds of datasets are required for evaluation. The first one is a sequence of arrival time instants of graph update operations, and the second one is a sequence of timestamps representing the historical states requested by the historical queries.
We use the dataset 'CollegeMsg temporal network' which is released by SNAP (Standford Network Analysis Project) at the website [32] for evaluation. The 'CollegeMsg temporal network' is a dynamic graph which had been updated 59,835 times spanning 193 days. The time instants of all the updates are available for generating the sequence of time instants of graph update operations. The statistics of the dataset are listed in TABLE 1.
In many applications, a minor part of the data tends to be frequently accessed while the majority part is rarely accessed. The Zipf distribution is widely adopted to describe the skewness of popularity in many real-world applications [33]. We also use the Zipf distribution to randomly generate the timestamps of the historical states requested by the historical queries.
1) ANALYSIS OF IMPROVEMENT IN RECREATION PERFORMANCE
In this experiment, the sequence of arrival time instants of graph update operations is composed of 59,835 elements as depicted in the above subsection. We totally generate 10,000 random values as the timestamps of the requested historical states. The frequency of the historical state being requested obeys the Zipf distribution with the parameter α = 1.2. The number of snapshots N varies from 10 to 200.
For each given number of snapshots, we use the three snapshot strategies to calculate the timestamps of the snapshots. After that, the average number of redone and undone operations in serving a historical query is obtained. We compare the three strategies in FIGURE 3. As shown, our proposed clustering based strategy greatly improves the recreation performance compared with the two traditional strategies.
As the number of snapshots increases, the average number of redone and undone operations decreases with all the three strategies. However, the storage consumption becomes higher as well. In practice, we should tradeoff the recreation performance and the storage consumption. As shown in FIGURE 3, the average number of redone and undone operations decreases sharply when the number of snapshots varies between 10 and 100, but very slowly between 100 and 200. Therefore, we choose 100 as the number of snapshots for evaluation.
For N = 100, we demonstrate the distribution of the number of redone and undone operations in serving each historical query in FIGURE 4. Each point (x, y) in the curve means that the proportion of the historical queries that require no more than x redone or undone operations equals y. As shown in the figure, the historical queries that require no more than 50 redone or undone operations nearly take a proportion of 77.2% with our cluster based snapshot strategy, while the proportion is 45.7% with the time-based strategy and only 8.7% with the operation-based strategy. The historical queries that require no more than 200 redone or undone operations take a proportion of nearly 100% with our cluster based snapshot strategy, while the proportion is about 90.3% and 58.2% respectively with the other two strategies.
We assign the Zipf distribution parameter α with 1.5, and keep all the other parameters unchanged. The results are shown in FIGURE 5, indicating that the superiority of our strategy is more apparent when the distribution of the historical queries is more skewed. As a comparison, we list the average number of redone and undone operations for each historical query with N = 100 in TABLE 2. The reduction of our strategy is between 70.7% and 95.5% compared with the two traditional strategies.
2) ANALYSIS OF REDUCTION IN STORAGE CONSUMPTION
We try to find the minimum number of snapshots to meet the recreation performance satisfying that the average number of redone and undone operations does not exceeding 15 and 100 respectively. The sequence of arrival time instants of graph update operations is also composed of 59,835 elements, and we totally generate 10,000 random values as the timestamps of the requested historical states with the frequency of the historical state being requested obeying the Zipf distribution with the parameter α = 1.5.
The comparison results are shown in FIGURE 6. With the same recreation performance guarantee, our strategy sharply reduces the storage consumption (nearly 78.9% on average). It should be noted that we do not differentiate the redoing or undoing cost of different kinds of update operations, and neither differentiate the storage cost of different snapshots.
In a word, our proposed strategy leads to recreation performance improvement and storage consumption reduction compared with traditional time-based and operation-based snapshot strategies. However, it should continually analyze the distribution of the historical queries and make adjustment dynamically, while the traditional ones require little analysis and make no dynamic adjustment. The analysis and adjustment process itself leads to computation overhead.
VI. CONCLUSION & FUTURE WORK
This paper studies the snapshot strategy for the 'snapshot plus log' solution to support historical queries of dynamic graphs. It points out that the inefficiency of the traditional snapshot strategies lies in the contradiction between the uniform distribution of snapshots and the skewed distribution of historical queries. In other words, the historical states are not equally requested, while the snapshots are evenly distributed under the traditional snapshot strategies. Therefore, this paper proposes a new snapshot strategy that determines the timestamps of the snapshots based on the distribution of the historical queries, such that the snapshots are near to the requested historical states with a very high probability. The experimental results show that the proposed strategy greatly improves the performance of historical state recreation and sharply reduces the storage consumption.
In the future, we will investigate how to apply this 'snapshot plus log' model in a distributed storage system of dynamic graph data. In a distributed environment, not only the snapshot strategy but also the placement strategy will affect the recreation performance. It is a big challenge to place the snapshots with variable timestamps onto distinct storage nodes to balance the historical query workload as well as to maximize the recreation performance. | 7,765.8 | 2020-05-12T00:00:00.000 | [
"Computer Science"
] |
Integration of Computer Vision and Wireless Networks to Provide Indoor Positioning
This work presents an integrated Indoor Positioning System which makes use of WiFi signals and RGB cameras, such as surveillance cameras, to track and identify people navigating in complex indoor environments. Previous works have often been based on WiFi, but accuracy is limited. Other works use computer vision, but the problem of identifying concrete persons relies on such techniques as face recognition, which are not useful if there are many unknown people, or where the robustness decreases when individuals are seen from different points of view. The solution presented in this paper is based on an accurate combination of smartphones along with RGB cameras, such as those used in surveillance infrastructures. WiFi signals from smartphones allow the persons present in the environment to be identified uniquely, while the data coming from the cameras allow the precision of location to be improved. The system is nonintrusive, and biometric data about subjects is not required. In this paper, the proposed method is fully described and experiments performed to test the system are detailed along with the results obtained.
Introduction
Indoor Positioning Systems (IPS) are taking on a key role in many domains, creating multiple opportunities in the era of artificial intelligence. Tracking the movement of robots/people and the use of data engineering makes it possible to optimize energy and costs and improve user experience by means of a proactive and reactive environment. These systems are also useful in improving medical applications.
Among active localization techniques, WiFi-based Positioning Systems (WPS) are a well-known option for tracking the movements of people in indoor environments. WPS is a geolocation system that uses the characteristics of nearby WiFi hotspots and other wireless access points to discover where a device like a smartphone is located. Recent WPSs have obtained an average error of 1.67 m [1,2], which is not very accurate for people tracking. Due to the error produced by these techniques, other systems have been developed. Technologies based on computer vision offer a different approach to the localization problem, but are not able to identify people easily. In these systems, identification is carried out by means of face detection [3] and recognition [4], appearance features [5], or color or patterns code [6]. Computer vision techniques have problems with occlusions and they need information about the users in the system.
A previous work of the authors [7] presented an indoor positioning system to estimate the location of people navigating complex indoor environments. The developed technique combines WiFi and RGB-D cameras in complex inhabited environments, consisting of various connected rooms, where people are moving freely. However, that paper considered that the number of people detected by WiFi positioning and detected by RGB-D needed to be equal, and required the installation of RGB-D cameras, such as Kinect v2-not usually available in common environments.
A new approach is presented in the present paper that combines WiFi and RGB cameras instead of RGB-D sensors, which results in a much simpler infrastructure requirement. A proper transformation to get a 3D model, based on the camera calibration parameters, is also used. The proposed approach is based on the method presented in [8] to extract the bird's-eye view of the scenario and people's trajectories. However, the method presented in [8] is restricted to the localization and tracking of people in single rooms and does not identify them. The method has been extended for use in more complex environments, such as hospitals or office environments, where there may be several rooms. To identify people and improve the localization, a new algorithm that integrates visual data with WiFi positioning is proposed.
The article is structured as follows: Section 2 explores the state-of-art of the technologies considered in this paper. Section 3 shows how the system works with RGB, WiFi, and the process of integrating both technologies. In Section 4, the different experiments and results carried out on people navigating indoors are reported and the results obtained are discussed. Finally, Section 5 notes the advantages and limitations of the presented system and suggests future developments based on this method.
Overview of Related Work
Modern IPSs use different technologies to track the location of persons. For these technologies, Koyuncu and Yang [9] suggest four different groups: (1) IPSs based on infrared or ultrasonic distances; (2) based on signal triangulation or Bluetooth/WiFi/RFID fingerprint map; (3) based on computer vision or the combination of such technologies as RFID or WiFi; and (4) inertial technologies (e.g., accelerometers and gyroscopes) or other types of sensor.
A survey of an optical indoor positioning system is presented in [10], where the authors classify the existing alternatives, according to the reference used, to figure out the position of users in the scene (e.g., 3D models, images, coded markers, or projected patterns). Different works have been developed in computer vision to track people positioning. Some of these, such as OpenPTrack [11] or the systems presented by Saputra et al. [12], Sevrin et al. [13], or Nakano et al. [14], consider a multicamera solution based on the use of RGB-D sensors. Others, like the works published by Mohedano et al. [8] or Elhayek et al. [15], follow an approach using common RGB cameras. Vision-based solutions can track people, but do not easily identify concrete persons. Other techniques, such as face recognition [4] or pattern recognition [6], look for a solution to the problem of identification.
WiFi Positioning Systems are mostly founded on the fingerprinting technique [16,17]. The Received Signal Strength Indication (RSSI) is used to generate a map of the environment with 2D coordinates and the values of signals received by different Access Points (APs), such as routers. A recent comparison between these systems has been presented by He and Chan [18]. Among the most advanced techniques, the authors explain how to make use of temporal or spatial signal patterns, user collaboration, and motion sensors.
Torres-Sospedra et al. [19] have recently presented the comparison between results obtained in IPIN (2014-2017) and Microsoft ISPN (2014-2017). The best results are obtained with a LIDAR system (IPIN 2017), which has an error below 0.1 m. This system is not available in small devices and has a bigger cost than other solutions. A WiFi fingerprinting-based system using a Bayesian filter was the winner of the infrastructure-free category in MS-ISPN 2014, obtaining an average error of 1.67 m [1,2]. Infrastructure-free solutions do not require modifications in the scenario. In IPIN 2016, Guo et al. [20] presented a WiFi and a Pedestrian Dead Reckoning-based system (PDR), which considers factors such as speed to calculate the next location starting from a fixed known position. An error of 1.5 m was obtained. Other authors [21][22][23] have also studied this combination of technologies, WiFi and PDR, but considering several limiting problems, such as the variation of WiFi signals and the drift of PDR. Formulating the sensor fusion problem in a linear perspective and using a Kalman filter, an average localization accuracy of 1 m was obtained. It is important to note that WiFi systems using the 2.4 GHz range obtained better results than others [1].
The combination of different technologies is a way of improving the efficiency of traditional WPSs [18,24,25]. The integration of data from RGB-D sensors and WiFi signals to provide more accurate positioning was proposed in [7]. However, the installation of RGB-D sensors is not usual in buildings and, in addition, it is not economical. The patent presented by Barton et al. [26] cited this previous work, integrating RGB cameras and WiFi signals by posing a theoretical idea of computing a proximity parameter to associate a person detected by a camera and the location data of a wireless device. This approach is prepared for identifying people using smartphones by means of cameras, but it does not cover a whole linear problem of multiple users, considering the trajectory of people in WiFi and RGB. Other hybrid systems combine WPS with such technologies as Bluetooth [27], RFID [28] or GSM [29], or Bluetooth beacon-based crowdsourced landmarks with inertial sensors [30] or GPS with inertial sensors [31]. A different approach is followed by Biswas and Veloso [32], who use a different technology (laser range-finder, RGB-D, or RSSI signals) depending on the position of a robot.
The IPSs are a useful way of creating reactive and proactive environments to enrich the experience of users. Several authors, such as Tsetsos et al. [33], Dudas et al. [34], Matuszka et al. [35], or Lee et al. [36] have integrated indoor navigation with semantic web technologies that focus on user activities.
The work presented in this article considers the trajectory of people in WiFi and RGB as a linear problem and calculates an association matrix to improve WiFi location with computer vision. RGB stereo-vision algorithms are used to track people in 3D and a novel algorithm integrates different numbers of people detected by RGB/WiFi.
Analysis of the System
This section is composed of three subsections: Section 3.1 explains how the system works to extract people's trajectories from the RGB cameras. Section 3.2 presents how WiFi positioning works to obtain their respective trajectories. Section 3.3 illustrates the proposed integration between these two technologies: WiFi and RGB.
People-Tracking in RGB
Instead of developing a different approach to human detection in 2D using RGB, the problem is solved by considering a well-known alternative based on neural networks. Among the previously developed systems, some rely on the use of Haar filters [37] or Histograms of Oriented Gradients [38]. Recent systems use Deep Convolution Neural Networks (DCNN), such as the Faster RCNN Inception V2 COCO Model [39]. All of them are available in OpenCV, working simultaneously with TensorFlow. Systems based on DCNN offer better results, detecting more people with a lower number of false positives. However, these systems are slower, requiring more time to process images. Considering that, the experiments have been carried out with a 2-s time stamp, so DCNN systems are feasible for providing useful data. Concretely, Faster RCNN Inception V2 has been used to extract people from images. Results obtained in this stage are a set of rectangles framing the different people detected.
For each rectangle obtained in the previous stage, a region has been extracted by comparing the image with the static background of the scenario (obtained by each camera before the experiments). Otsu-based segmentation on the Gaussian-filtered images, followed by some morphology, produces a final binary image of each person, as shown in Figure 1. The top region of points is then used to obtain the coordinates of the person, provided that the region has more than a particular number of points. These coordinates, corresponding to the top of the person's head, represent a better approach to avoid variances due to static foreground occlusions produced at other points [8]. 3D coordinates are subsequently obtained by means of a Linear Triangulation Method [40] applied to the 2D coordinates obtained from each camera. This method is carried out in 2 steps: 1. A first step consists of determining the camera projection matrix, L, associated to each camera, before the experiments. It is important to mention that all cameras involved in the process must satisfy the epipolar constraint. The L matrix allows the 3D coordinates to be related to the 2D image perceived by the camera, according to LX i = u i , where X i are the 3D coordinates of a given point and u i are its corresponding image coordinates. To obtain L, six different normalized points are registered in the scenario, indicating the 3D coordinates with respect to the room and 2D position in each image obtained by its respective camera. A Direct Linear Transformation (DLT) algorithm estimates L from 2D/3D coordinates. 2. A second step, performed during execution time, allows 3D X i coordinates to be identified from a set of different 2D points for each camera: u i , u i , u i , etc., (see Figure 2). Each camera has its respective L matrix, relating 3D common coordinates with their respective 2D ones, such as Based on these expressions, each perspective camera model produces two equations. The complete set of equations represents an overdetermined homogeneous system of linear equations which is solved with SVD, obtaining a 3D point that is optimal in a least squares sense.
When cameras detect more than one person in a room, the best geometrical association between persons detected by different cameras is the combination that minimizes the residual value r of the previous overdetermined linear equation [41,42].
Once the 3D coordinates have been obtained, they are transformed into a 2D UCS Universal Coordinates System. This 2D map is the aerial view of people obtained from different cameras. Figure 3 shows two images obtained by cameras I 1 and I 2 and its representation in the 2D zenithal view. Finally, the trajectory between consecutive time stamps is computed by comparing results obtained in the 2D aerial view. As soon as new coordinates are calculated, they are compared with the previous ones to track persons. People follow a path where two points are part of the same trajectory of the person if both are situated at less than a concrete distance.
People-Tracking in WiFi
A fingerprint map is a table that relates a set of signal intensities (RSSI) with the 2D aerial coordinates where they were obtained. Once a fingerprint map has been created, it is possible to estimate the position of a new set of RSSI values calculating the Euclidean distance with the previous There are different ways of creating the fingerprint map [43][44][45], but a convenient method is using RGB-D cameras to register the 2D coordinates. They are more accurate than other solutions, such as normal cameras or manual measurements. For this reason, the creation of the map has been carried out using RGB-D sensors. Once the map has been created, the positioning process only relies on the use of normal RGB cameras.
During the creation of the map, a user freely moves around the environment. Figure 4 shows a person who moves following a given trajectory (in green) and the created table. The RSSI values from the cell phones, received from the APs, together with their position estimated by the RGB-D sensors, are recorded in the map every time the user clicks a button of an application developed for this purpose. RSSI values from 16 different APs have been recorded. Considering that the Kinect v2 returns the coordinates of different body joints, the coordinates of the neck have been considered, as they are the joint less prone to be occluded by elements in the scenario. In addition, a general universal coordinate system has been created for the full scenario. As the map is created exclusively by one person, two RGB-D sensors return the coordinates of the same person. When the data collection ends, in order to simplify the positioning process without significant loss of precision, another essential task is carried out at the end of this stage: the complete scenario is divided into cells (e.g., 1 × 1 m) and RSSI data are grouped in each cell using the corresponding position of the 2D aerial coordinates. An RSSI vector is created for each cell, pairing each component to the centroid for all of the RSSI measurements of a certain AP. RSSI scans are grouped according to the distance between their original associated 2D coordinates and the coordinates of the centre of each cell. This step reduces the size of the fingerprint map to improve the performance of the system and obtain more reliable RSSI values, avoiding variations in the measurements.
It is worth noting that RGB-D sensors are not strictly necessary to create a fingerprint map. They have been used for convenience in our experiments, but will no longer be required during the system operation.
People positioning is carried out by comparing the RSSI values obtained from the smartphones with the RSSI centroids of the map and returning the coordinates of the virtual cell with less difference. These comparisons are implemented by the Euclidean distance between the RSSI vectors [46]. The trajectory of each person with WiFi is related to their smartphone.
However, systems based on WiFi do not deliver accurate results in indoor environments. The integration with a different technology, such as computer vision, improves the accuracy and offers promising results.
RGB and WiFi Integration
WiFi positioning is improved with computer vision by associating the trajectory of a person obtained by WiFi and the trajectory of the same person by RGB. Initially, there is a set of RGB and WiFi trajectories that are disassociated, that is, the system does not know which WiFi trajectory an RGB one corresponds to, and vice versa. The problem presented in this section solves the association regardless of whether there is a different number of people detected by each of the technologies. The diagram of the proposed system is shown in Figure 5, describing the steps explained in the previous sections for RGB and WPS. The association between both trajectories, represented in the schema as Calculate Positions based on Synchronized Euclidean distance, is explained below. The problem is approached as an optimal combination of WiFi and RGB trajectories for all people detected in a set of time stamps. The solution to the algorithm is to find the matrix S, valid for the complete dataset, such that the best combination is achieved when the sum of the distances from all possible trajectories is minimum, as shown in where d E represents the Euclidean distance between the coordinates of a person detected in RGB and WiFi. For WiFi, the coordinates used are the centroids of the virtual cells in the 2D aerial map. This equation minimizes the Synchronized Euclidean distance [47], computing the sum of the distances between each pair of points of WiFi and RGB. The problem is subject to the following restrictions: if n 1 > n 2 , if n 1 = n 2 , if n 2 > n 1 , In the case of Equation (2), not all people detected by WiFi are detected by cameras. In the case of Equation (3), all people detected by WiFi are detected by cameras. In the case of Equation (4), there are more people detected by cameras than from WiFi.
The problem is solved using a Mixed Integer Linear Programming (MILP) solver, based on the revised simplex method and the Branch-and-bound method for the integers [48]. The Branch-and-bound algorithm finds a value x that minimizes a function f (x) among some set C of candidate solutions. It recursively divides the search space into smaller spaces and minimizes f (x) on these spaces. Instead of performing a brute-force search, the Branch-and-bound algorithm keeps in memory the bounds on the minimum to be found, and uses these bounds to prune the space, eliminating candidates that will not be optimal. The result of the algorithm produces the matrix S, matching each WiFi trajectory with the corresponding RGB one. If there is no RGB trajectory for a person, the system uses the WiFi trajectory as it is the one directly obtained by the smartphone. Figure 6 shows an example of matrix S, matching a different number of people detected by WiFi, n 1 = 10, and RGB, n 2 = 7. Continuous tracking in RGB is carried out using the 2D zenithal coordinates of people. When new coordinates are calculated, they are compared with the previous ones to find those with the smallest Euclidean distance. This principle is used when a person leaves a room and enters a different one. When a person is occluded or overlapped by another person for a given camera, the position is calculated from the remaining cameras given that DLT/SVD algorithms can work with only two cameras. Continuous tracking in WiFi is directly obtained by smartphones because each set of RSSI scans is associated to a concrete device. After the algorithm, each RGB trajectory is associated to a WiFi one in m time stamps. For this association, data from t k to t k+m−1 time stamps are considered. In the next time stamp, the algorithm moves one slot of time and considers data from t k+1 to t k+m .
Experiments and Discussion
The scenario is an 80 m 2 office, with 8 rooms and a central corridor, as shown in Figure 7. Kinect v2 cameras were used to generate the WiFi fingerprint map. Afterwards, they were replaced by conventional RGB cameras, as only RGB images have been considered for computer vision positioning.
To create the fingerprint map, RSSI values were obtained from a person at the same time as skeletons were received by the Kinect sensors. Whenever the person clicked a button, a complete scan of APs and skeletons was done. Then, head coordinates and RSSI values were stored in a database. Figure 8 shows one person creating the fingerprint map with 2 RGB-D sensors, moving them between different rooms.
A set of 36 RGB cameras of different models were deployed in the scenario. The calibration of the RGB cameras, matrix L, was calculated using eight different normalized points registered in each room, considering the 3D coordinates with respect to the room and the 2D position in each image obtained by its respective camera. The points were visible from the different cameras of the room. Once the group of cameras had been calibrated, the error in obtaining the coordinates of a concrete fixed point in the scenario was 0.03 m. The error in locating a person was 0.13 m, similar to other works [15].
As shown in Figure 9, an Android-based application was created. In this application, different users called a web service named obtainLocation(), passing the RSSI values at a synchronized time. Once all RSSI values had been received, the central web server called different services to obtain 2D coordinates of people (obtainPeoplePositions()). For performance reasons, each camera was connected to a dedicated server to compute the Faster RCNN Inception V2 model [39] (extractPeopleRegions()). Every 2 seconds, the application sent RSSI data to a central web server, which was connected to each camera by means of the intermediate computer. A 2-second slot between time stamps was valid for the experiments. Finally, after the synchronization of the results, Linear Triangulation (applyLinearTriangulation()) and the positioning algorithm (calculatePositioning()) were executed.
Four people participated directly in this experiment, following previously established trajectories. A value of m = 10 time stamps was used for the experiments. A bigger value improves the efficiency of the algorithm, but requires excessively long trajectories. At the same time, a high value of m increases computing cost. m = 10 has been found to produce good results with a short trajectory. The system properly associated the RGB and WiFi trajectory in 99.10% of cases. When a person was not detected by the RGB cameras, the success was 96.80% for associating the rest of the trajectories. Different cases were evaluated for two, three, and four people. Figure 10 shows three people following a concrete trajectory. Two of them (persons 1 and 2) go together until a point where they separate. Table 1 presents data related to person 1 in the previous trajectory, where the RSSI values obtained by smartphone and the RSSI values corresponding to the WPS cell of the fingerprint map are shown. RGB coordinates in the UCS are also presented. These results can be extrapolated for a greater number of people. To this end, after the completion of the real experiment, 50 different WiFi and RGB trajectories were obtained. Each person moved around the scenario following different trajectories that were recorded in a database with their WiFi and RGB information. When data collection finished, these 50 trajectories were associated, indicating the WiFi trajectory corresponding to the RGB one. The efficiency of the system was validated, randomly combining these 50 trajectories from 5 to 20 people, producing more than 1 million different combinations. The experiments considered the trajectory of different numbers of people, taking into account both technologies during 10 time stamps of 2 s. In every test, a random WiFi trajectory was selected for each person. RGB and WiFi trajectories were disassociated and the evaluation checked if the WiFi trajectory was again associated with the corresponding RGB one. Table 2 shows the success of associating all the trajectories of the people detected by WiFi with their respective trajectory in RGB. Considering that the 50 trajectories include their respective WiFi/RGB data, the evaluation of the system is performed by determining whether the WiFi trajectory associated to the RGB is the same as the one recorded for that trajectory. When a lower number of people is detected by a concrete technology, this reflects that all users of that technology have been properly linked to it. When the number of people detected by both technologies is equal, the success rate increases because there are fewer false-positives. People not linked properly with RGB obtain the location based on WiFi. (1, 1) (0. 28, 1.49) A Mixed Integer Linear Programming (MILP) solver, based on the revised simplex method and the Branch-and-bound method for the integers [48], has been used to solve the problem. The algorithm was run on a server with an Intel i9-9900K processor and 32 GB of RAM. It took from 0.6 ms to associate the simplest situations (n 1 < 10 and n 2 < 10) to 1.95 ms for the most complex one (n 1 = 20 and n 2 = 20).
The computational cost follows an exponential function t = 0.08 · 1.16 n + 0.42, where t represents the processing time in milliseconds and n the maximum number of users. When n = 50 people, the processing time is 134 ms, which works properly in aspects of time. However, in an 80 m 2 scenario, that amount of people is overcrowded. For larger scenarios with more than 50 people, the scenario must be divided using the APs detected by smartphones. A person will be associated in the zone corresponding to the APs detected.
Considering a verified average distance error of 0.13 m for RGB and 2.0 m for WiFi, an average error of 0.53 m has been estimated for 20 people. This error is calculated by multiplying the positive associations by the RGB average error and the rest by the WiFi error. In Figure 11, in blue, an average error in meters is shown, considering the same number of people being detected simultaneously by WiFi and RGB. In red is the error computed assuming that WPS only works for 80% of the people detected by the RGB cameras, which could correspond to people not carrying their smartphones. In this case, the number of people detected by RGB corresponds to the radius.
There are positioning systems that make use of computer vision to track people, such as [6], where the authors present a system to follow a group of workers using the color of their hardhats, or OpenPTrack [11], a scalable and multicamera solution. However, these systems do not identify concrete persons. Computer vision produces accurate results, but it requires other techniques, such as face recognition [4] or appearance features [5], to solve the problem of identification. The comparison between the results obtained and the existing ones has to be made with other systems that are able to identify people, such as WiFi fingerprinting-based systems. Concretely, the error obtained (0.53 m) is lower than previous exclusive WiFi fingerprinting-based systems, such as [2] (1.67m), [20] (1.5 m), or [23] (1 m). It should be noted that the presented algorithm can be easily integrated with other computer vision systems, such as OpenPTrack [11].
associations by the RGB average error and the rest by the WiFi error. In Figure 11, in blue, an average error in meters is shown, considering the same number of people being detected simultaneously by WiFi and RGB. In red, is the error computed assuming that WPS only works for 80% of the people detected by the RGB cameras, which could correspond to people not carrying their smartphones. In this case, the number of people detected by RGB corresponds to the radius. Figure 11. Average error of the system (in meters) for different numbers of people 5 There are positioning systems that make use of computer vision to track people, such as [6], where the authors present a system to follow a group of workers using the color of their hardhats, or OpenPTrack [11], a scalable and multi-camera solution. However, these systems do not identify concrete persons. Computer vision produces accurate results, but it requires other techniques, such as face recognition [4] or appearance features [5], to solve the problem of identification. The comparison between the results obtained and the existing ones has to be made with other systems that are able to identify people, such as WiFi fingerprinting-based systems. Concretely, the error obtained (0.53m) is lower than previous exclusive WiFi fingerprinting-based systems, such as [2] (1.67m), [20] (1.5m) or [23] (1m). It should be
Conclusions
This work presents an integrated indoor positioning system for use in complex environments where multiple people carry smartphones and which makes use of computer vision to provide an accurate position. The system uses WiFi positioning and several RGB cameras installed in each room to reduce occlusions. The algorithm is able to manage a different number of people detected by RGB/WiFi and is focused on tracking people, but it could easily be extended to the localization of nonhuman targets such as mobile robots, Automated Guided Vehicles (AGVs), etc. on work floors.
The system successfully links the trajectory of all the people detected by the computer vision with their respective trajectory in 79% of cases for 20 persons moving freely around the scenario. Considering an average error for RGB/WiFi detection, a positioning error of 0.53 m has been calculated. Of course, the successes would decrease consistently if there was a large difference between the number of people detected by each technology. The error is, however, lower than previous exclusive WiFi fingerprinting-based systems, such as [2] (1.67 m), [20] (1.5 m), or [23] (1 m). The algorithm presented could be improved and integrated with these previous WPS methods or others which make use of inertial sensors or Kalman filters. It could also be integrated with algorithms based on Bluetooth, such as [30], which use Bluetooth beacon-based landmarks and exploits inertial sensors composed of an accelerometer, magnetometer, and gyroscope.
The experiments were carried out using common RGB cameras to obtain images and exploit the process of people-tracking by DCNN. Four cameras were installed in each room, covering an 80 m 2 office. Although four cameras were used to improve the results, only two cameras are needed, since DLT/SVD algorithms can work with just two cameras. The difference in accuracy using two cameras with respect to four is ±0.02 m, although they do not work so well with occlusions or overlaps and they may not capture all the angles of the room. Moreover, two Kinect v2 sensors were used only to create the WiFi fingerprint map, as this is a fast and accurate way to build it. It is important to note that, regarding scaling, the system is prepared to work in large environments. A computational cost has been analyzed, indicating a recommended limit of about 50 people per zone. In a large environment, when there are more than 50 people, the scenario would be split into different zones.
From the point of view of cost, the solution presented is an economical way to increase the performance of WPS in interiors. Previously installed surveillance cameras are candidates for implementing the RGB tracking while smartphones are widespread. There are multiple applications of the system, mainly focused on the creation of reactive and proactive environments to enrich the user experience. For example, the work [49] integrates an indoor positioning system with Europeana [50], a data source about artworks, to proactively show information about the pieces situated near a person inside a museum. Future works will consider the use of this system in more complex scenarios, such as medical or industrial environments or private facilities, deploying a complete set of cameras. Funding: The present research has been partially financed by the "Programa Retos Investigación del Ministerio de Ciencia, Innovación y Universidades (Ref. RTI2018-096652-B-I00)" and by the "Programa de Apoyo a Proyectos de Investigación de la Junta de Castilla y León (Ref. VA233P18)", cofinancied with FEDER funds. The work has also been supported in part by the Spanish Ministry of Economy and Competitiveness under Project DPI2016-77677-P, and the RoboCity2030-DIH-CM Madrid Robotics Digital Innovation Hub ("Robótica aplicada a la mejora de la calidad de vida de los ciudadanos. Fase IV"; S2018/NMT-4331) funded by the "Programas de Actividades I + D de la Comunidad de Madrid". | 7,621.6 | 2019-12-01T00:00:00.000 | [
"Computer Science",
"Engineering"
] |
Optical response of two-dimensional few-electron concentric double quantum rings: A local-spin-density-functional theory study
We have investigated the dipole charge- and spin-density response of few-electron two-dimensional concentric nanorings as a function of the intensity of a perpendicularly applied magnetic field. We show that the dipole response displays signatures associated with the localization of electron states in the inner and outer ring favored by the perpendicularly applied magnetic field. Electron localization produces a more fragmented spectrum due to the appearance of additional edge excitations in the inner and outer ring.
Progress in nanofabrication technology has allowed to produce self-assembled, strainfree, nanometer-sized quantum complexes consisting of two concentric, well-defined GaAs/AlGaAs rings 1,2 whose theoretical study has recently attracted some interest. 3,4,5,6 Most of these works are concerned with the properties of their ground state, although the optical properties of one-and two-electron concentric double quantum rings (CDQR) at zero magnetic field have been addressed using a single-band effective-mass envelope model discarding Coulomb correlation effects. 2 The singular geometry of CDQR has been found to introduce characteristic features in the addition spectrum compared to that of other coupled nanoscopic quantum structures. As a function of the inter-ring distance, the localization of the electrons in either ring follows from the interplay between confining, Coulomb and centrifugal energies. Each of them prevail in a different range of inter-ring distances, affecting in a different way the CDQR addition spectrum. 6 It is thus quite natural to investigate whether and how localization effects may show up in the dipole response, using a perpendicularly applied magnetic field instead of the inter-ring distance to control the electron localization in either ring.
The aim of this paper is to use local-spin-density-functional theory (LSDFT) as described in detail in Ref. 7, to investigate the dipole longitudinal response of CDQR. The method has been used in the past to address the response of single quantum rings (see e.g. Ref. 8 and references therein). We address here the few-electron case, and consider the CDQR's as strictly two-dimensional systems.
Within LSDFT, the ground state of the system is obtained by solving the Kohn-Sham (KS) equations. The problem is simplified by the imposed circular symmetry around the z axis, which allows one to write the single particle (sp) wave functions as ϕ nlσ (r, σ) = u nlσ (r)e −ılθ χ σ , being −l the projection of the sp orbital angular momentum on the z axis.
The confining potential has been taken in a form that slightly generalizes that of Ref. 4: with R 1 = 20 nm, R 2 = 40 nm, ω 1 = 30 meV, and ω 2 = 40 meV. confining potentials, better suited to model the experimental devices, 2 have been considered. 6 On the CDQR system it may act a constant magnetic field B in the z direction, to which a cyclotron frequency ω c = eB/mc is associated. We have taken for the dielectric constant, electron effective mass, and effective gyromagnetic factor, the values appropriate for GaAs, namely, ǫ = 12.4, m * = 0.067, and g * = −0.44, and have solved the KS equations for up to N = 6 electrons, and for B values up to 4-5 T, depending on N. In the following, we discuss some illustrative results. 3 It is known that for an N-electron single quantum ring, sp states with small l values become progressively empty as B increases. This can be intuitively understood as follows.
If only nodeless radial states are occupied, the Fock-Darwin wave functions are proportional to x |l| e −x 2 /4 , where x = r/a, being a = h/(2mΩ) with Ω = ω 2 0 + ω 2 c /4. Of course, this is so for a harmonic confining potential of frequency ω 0 , and not for the ring confining potential, but some of that wave function structure remains even in this case. These wave functions are peaked at r max ∼ 2|l| a, and consequently, as B increases, the |l| values corresponding to occupied levels must increase so that r max sensibly lies within the range of r values spanned by the ring morphology. The same appears to happen for the CDQR we have studied, as illustrated in Fig Yet, they can be localized in either ring if the resulting configuration has a lower energy.
It is relevant for the analysis of the dipole response to notice that electron localization is best achieved when, due to the double well structure of the confining CDQR potential, KS orbitals corresponding to an intermediate l value are not occupied. In the present case, it happens for l = 3. Intuitively, the missing l is the one whose KS orbit has a 'radius' similar to that of the maximum of the inter-ring barrier.
A full delocalization situation produces a very regular sp energy pattern since, due to it, electrons 'feel' simultaneously the confining potential produced by both constituent rings.
This happens e.g. for B = 0 and other low-B values. The situation may change at higher magnetic fields. Indeed, Fig. 2 shows that around B = 3 T, the two lowest parabolic-like bands tend to cross between l = 2 and 3. Roughly speaking, each parabolic-like band arises The present study can be extended to the case of many-electron CDQR and to other multipole excitations, or to incorporate on-plane wave-vector effects for the analysis of Ra-8 man experiments. 8 A more realistic description of the CDQR confining potential 6 demands a three-dimensional approach. 11 Work along this line is in progress.
We would like to thank Josep Planelles for useful discussions. This work has been performed under grants FIS2005-01414 and FIS2005-02796 from DGI (Spain) and | 1,324.4 | 2006-10-30T00:00:00.000 | [
"Physics"
] |
A polymer dataset for accelerated property prediction and design
Emerging computation- and data-driven approaches are particularly useful for rationally designing materials with targeted properties. Generally, these approaches rely on identifying structure-property relationships by learning from a dataset of sufficiently large number of relevant materials. The learned information can then be used to predict the properties of materials not already in the dataset, thus accelerating the materials design. Herein, we develop a dataset of 1,073 polymers and related materials and make it available at http://khazana.uconn.edu/. This dataset is uniformly prepared using first-principles calculations with structures obtained either from other sources or by using structure search methods. Because the immediate target of this work is to assist the design of high dielectric constant polymers, it is initially designed to include the optimized structures, atomization energies, band gaps, and dielectric constants. It will be progressively expanded by accumulating new materials and including additional properties calculated for the optimized structures provided.
Workflow
The workflow in Fig. 1 summarizes the preparation of the polymer dataset. In the first step, crystal structures of polymers and related compounds were collected from various available sources, including the reported literature, the Crystallography Open Database (COD) 15 , and our structure prediction works [20][21][22][23][24][25][26] . Those obtained from structure prediction runs were subjected to a preliminary filter (described below), removing any obvious redundancy of identical structures. Then, the selected structures were optimized by DFT calculations, yielding the equilibrium structures and their atomization energies E at . The energy band gap E g was then calculated on a dense grid of k points while their dielectric constant ε, which is composed of an electronic part ε elec and an ionic part ε ion , was computed within the framework of density functional perturbation theory (DFPT) 33 . In the next step, the computational scheme and the calculated results were validated with available measured data, including the measured band gap E g , the dielectric constant ε and/or the infrared spectroscopy (IR) measurements. Those which do not agree with the available experimental data are subjected to further calculations at tighter convergence criteria of residual atomic force (see Technical Validation for more details), and if better agreement is not reached, these points are removed from the dataset. A post-filtering step was finally performed on the whole dataset, keeping only distinct data points. Relaxed structures of all the materials are finally converted into the crystallographic information format (cif) using the pymatgen library 34 . A note was also provided together with the dataset, indicating the convergence criteria of the datapoints reported herein.
Structure accumulation
Our dataset includes three primary subsets, each of them originating from a distinct source. Subset 1 consists of common polymers which have already been synthesized, resolved, and reported elsewhere. This set contains 34 polymers, listed in Table 1. Collecting polymer structures of this class is challenging because the reported data is widely scattered, and in case the information obtained is sufficient to reconstruct structures, this work has to be done manually and hence, substantially laborious. We further note that only for a few of them, measurement for band gap, dielectric constant, and/or infrared (IR) spectrum have been performed. This data was used for the validation step.
Subset 2 includes 314 new organic polymers (284 of them have been used in ref. 11) and 472 new organometallic polymers. Their structures were generated from a computation-driven strategy 19,20 which has been used to rationally design various classes of polymeric dielectrics 11,[20][21][22][23][24][25][26] . The starting point of this strategy is a pool of common polymer building blocks, which are either organic, e.g., -CH 2 -, -NH-, -CO-, -O-, -CS-, -C 6 H 4 -, and -C 4 H 2 S-, or inorganic (metal-containing) like -COO-Sn(CH 3 ) 2 -OCC-, -SnF 2 -, and -SnCl 2 -. The repeat unit of an organic polymer is then created by concatenating a given number of organic building blocks while that of an organometallic polymer contains at least one inorganic block linked with a chain of several CH 2 groups. Next, chains of the repeat units (illustrated in Fig. 2) are packed in low-energy crystal structures which are determined by Universal Structure Predictor: Evolutionary Xtallography (USPEX) 23,35 or minima-hopping (MH) 36,37 , two of the currently most powerful structure prediction methods. In brief, these methods allow for predicting the low-energy structures of a material as the local minima of the potential energy surface, constructed from DFT energy. The efficiency of these methods have been successfully demonstrated for many different materials classes [38][39][40][41] , including a large number of organic 20,23 and organometallic polymers [24][25][26] .
The material structures used to prepare subset 3 were collected from COD. Generally, materials provided by COD are not polymers, but a number of them are collected in this dataset as they are closely related to the examined polymers. Although collecting materials structures from this database is straightforward, we limited ourselves to only those whose cell volumes are not too large, i.e., roughly 1,500 Å 3 and below. This subset contains 253 molecular organic and organometallic crystals, 178 of them have recently been used in ref. 10 by some of us. Table 2 summarizes the contents of the polymer dataset, which contains both polymers (subset 1 and 2) and non-polymers (subset 3). In terms of chemistry, the included materials can be classified as either organic or organometallic, incorporating different metals in their backbone. The complete list of chemical elements that appear in this dataset is given in Table 3.
Numerical calculations
The computed data reported in our dataset was prepared with density functional theory (DFT) 31,32 calculations, using the projector augmented-wave (PAW) formalism 42 as implemented in Vienna Ab initio Simulation Package (vasp) [43][44][45][46] . The default accuracy level of our calculations is``Accurate'', specified by setting PREC = Accurate in all the runs with vasp. The basis set includes all the plane waves with kinetic energies up to 400 eV, as recommended by vasp manual for this level of accuracy. PAW datasets of version 5.2, which were used to describe the ion-electron interactions, are also summarized in Table 3. The van der Waals dispersion interactions, known 47 to be important in stabilizing soft materials dominated by non-bonding interactions like polymers 48 , were estimated with the non-local density functional vdW-DF2 (ref. 49). The generalized gradient approximation (GGA) functional associated with vdW-DF2, i.e., refitted Perdew-Wang 86 (rPW86) 50 , was used for the exchange-correlation (XC) energies.
Because the examined material structures are significantly different in terms of the cell shape, the sampling procedure of their Brillouin zones must be handled appropriately. For each structure, a Monkhorst-Pack k-point mesh 51 of a given spacing parameter h k in the reciprocal space was used. For the geometry optimization and dielectric constant calculations, h k = 0.25 Å − 1 while the band gap calculations have been performed on a finer Γ-centered mesh with h k = 0.20 Å − 1 . We further set the lower limit for the Monkhorst-Pack mesh dimensionality, that is, the number of grid points along any reciprocal axis is no less than 3, regardless of how short the reciprocal lattice dimension along this axis is.
During the relaxation step, we optimized both the cell and the atomic degrees of freedom of the materials structures until atomic forces are smaller than 0.01 eV Å − 1 . Calculations for band gap E g was then carried out on top of the equilibrium structures. Because E g is typically underestimated with a GGA XC functional like rPW86 (ref. 52), this important physical property has also been calculated with the hybrid Heyd-Scuseria-Ernzerhof (HSE06) XC functional 53,54 with an expectation that the calculated result would become much closer to the true material band gap. Both E GGA g and E HSE06 g , the band gap calculated at the GGA-rPW86 and HSE06 levels of theory, are provided in all the entries of the dataset (see File format for more details). Finally, the dielectric constant ε of these structures was calculated within the DFPT formalism as implemented in vasp package. Calculations of this type involve the determination of the lattice vibrational spectra at Γ, the center of the Brillouin zone. This information is also used to compute the IR spectra of some structures for the purpose of validation.
Post-filtering
Given that the sources of the polymer dataset reported herein are diversified, any clear duplicate and/or redundancy should be identified and removed. Because the preliminary filtering step was performed only on subset 2 based on their DFT energy and band gap estimated during the structure prediction runs with a limited accuracy, an additional filtering step was performed on the whole dataset. Within this step, all cases with the same chemical composition but different by less than 0.1 eV in E g , less than 5 meV per atom in E at , and less than 0.1 in both ε elec and ε ion , are clustered. At this point, the number of clustered points is not large, and all of them were inspected visually, keeping only distinct materials.
Data Records
The complete dataset of 1,073 polymers and related materials can be downloaded as a tarball from Dryad Repository (Data Citation 1) or can be accessed via http://khazana.uconn.edu/ (all the records with ID from 0001 to 1073). All 4,292 DFT runs of the entire dataset (for each structure, there are 4 runs, including relax, dielectric, GGA band gap, and HSE06 band gap) are hosted by NoMaD Repository (Data Citation 2).
File format
All the information reported in the dataset for a given material is stored in a file, named as 0001.cif, where a cardinal number (0001 in this example) is used for the identification of the entry in the dataset. The first part of a file of this type is devoted to the optimized structure in the standard cif format which is compatible with majority of visualization software. Other information, including the calculated properties, is provided as the comments lines in the second part of the file as follow While most of the keywords are clear, we used Source to provide the origin of the material structure and Class to refer to the class of materials which can either be ''organic polymer crystal'', ''organometallic polymer crystal'', ''organic molecular crystal'', or ''organometallic molecular crystal''. Keyword Label was used to provide more detailed information on the material, which can be the common name of the material if it is available, the ID of the record obtained from COD, or the repeat unit of the polymer structure predicted.
Graphical summary of the dataset
To graphically summarize the polymer dataset, we visualize it in the property space. Because the band gap and the dielectric constant are the primary properties reported by this dataset, three plots, namely E HSE06 g -ε elec , E HSE06 g -ε ion , and E HSE06 g -ε, were compiled and shown in Fig. 3. Materials from different classes are shown in different colors to clarify the role of the polymer chemical composition in controlling E g and ε. Within the recent effort of developing polymers for high-energy-density applications [19][20][21][22][23][24][25][26] , such plots are useful for identifying promising candidates, i.e., those which have high dielectric constant while maintaining sufficient band gap (E g ≥ 3 eV). Figure 3a clearly indicates a limit of the form ε elec $ 1=E g between ε elec and E g , which is applicable for both organic and organometallic classes of materials. We note that this behavior has also been reported elsewhere 10,19 . Figure 3c, on the other hand, demonstrates that the classes of organic and organometalic polymers and molecular crystals occupy different regions in the property space. At a given value of band gap, the organometallic polymers are generally much higher than the organic polymers in terms of the dielectric constant. While a fairly large number of organometallic polymers were already developed [24][25][26] , this observation suggests that there remains significant room for manipulating the dielectric constant of the organometallic polymers.
Technical Validation
Among the materials properties reported in the present dataset, the atomization energy E at is physically relevant and has always been used as a standard method for examining the thermodynamic stability of various classes of materials, including inorganic crystals [38][39][40][41] and polymers [19][20][21][22][23][24][25][26] . While the band gap E GGA g calculated at the GGA level of DFT is not ready to be compared with the measured data due to the aforementioned well-known underestimation 52 , E HSE06 g (the band gap calculated with the HSE06 XC functional) is expected to be rather close to the true band. We show in Fig. 4a E HSE06 g of 11 polymers for which the band gap has been measured experimentally. The calculated band gap seems to agree pretty well with the measured data with a numerical discrepancy of about 20% and below.
We now consider the calculations of the dielectric constants, namely ε elec and ε ion . Overall, the theoretical foundations and the implementations for calculating ε elec and ε ion are well developed and tested, leading to rather accurate results. Within the DFT-based perturbative approach, ε elec is computed via the response to the external field perturbations while ε ion is evaluated through the phonon frequencies at the Γ point of the Brillouin zone. To be precise, the dielectric response of a crystalline insulator to an external electric field E is given in terms of a frequency-dependent tensor ε αβ ðωÞ. To linear order, the electronic contribution of the dielectric tensor is given by where P α is the component along the α direction of the induced polarization P. On the other hand, the ionic part of the dielectric tensor is determined as In this expression, Ω is the volume of the simulation cell, appearing as a normalization factor. The sum is taken over the index m of the phonon normal modes, which assumes the frequency ω m,q = 0 at the Brillouin zone center (q = 0) while the mode oscillator strength S mαβ is determined through the Born effective charge Z s,αβ * of the atom s. For an isotropic material, the dielectric constant of the practical interest is taken to be the average value of its diagonal elements at the static limit, i.e., ε ¼ 1 3 P α ½ε αα ðω-0Þ. Equation 2 implies that at the limit of ω → 0, ε αβ ion ðωÞ is rather sensitive to the numerical accuracy of ω m,q = 0 , which, in turn, suggests highly equilibrated materials structures for the DFPT calculations. As mentioned in the Workflow Section, if the calculated dielectric constant ε of a polymer is different from its measured data (this information is available for just a limited number polymers in subset 1 and 2) by more than 20%, the structures are further optimized until the residual atomic forces are smaller than 0.001 eV Å − 1 . Only those with calculated dielectric constant within 20% of the experimental data [shown in Fig. 4b] are kept.
Within our dataset, the IR spectrum was measured for some materials. From the computational side, this material characteristic can also be calculated rather accurately from the byproducts of the dielectric constant calculations with DFPT. In particular, the intensities of the infrared-active modes are given by 56 where e m,sβ is the β component of the normalized vibrational eigenvector of the mode m at the atom s. Obviously, all of the necessary quantities needed to calculate I m according to Equation 3 can be obtained within the DFPT-based computational scheme of ε, thus requiring essentially no computational overhead. This approach has widely been used in characterizing various classes of materials 57,58 . We show in Figure 4c-f the IR spectra calculated for four polymers, including orthohombic polyethylene, orthohombic polyoxymethylene, poly(dimethyltin glutarate) 24 , and polythiourea 20 , each of them is compared with the corresponding measured IR spectrum. The excellent agreement between the calculated and the measured IR spectra can be regarded as a supportive validation of the computational scheme based on DFT calculations used for this polymer dataset.
Usage Notes
This dataset, which includes a variety of known and new organic and organometallic polymers and related materials, has been consistently prepared using first-principles calculations. While the HSE06 band gap E HSE06 g is believed to be fairly close to the true band gap of the materials, the GGA-rPW86 band gap is also reported for completeness and for further possible analysis. The reported atomization energy and the dielectric constants are also expected to be accurate.
The polymer dataset is one among many recently developed datasets which can be used for designing materials by various data-driven approaches. To be specific, this dataset is expected to be useful in the development of polymers for energy storage and electronics applications. Moving forward, the development of this dataset will be continuously validated and updated, and the most recent version can be accessed at repository http://khazana.uconn.edu/. | 3,957.8 | 2016-03-01T00:00:00.000 | [
"Materials Science"
] |
Impact of CIR Storms on Thermosphere Density Variability during the Solar Minimum of 2008
The solar minimum of 2008 was exceptionally quiet, with sunspot numbers at their lowest in 75 years. During this unique solar minimum epoch, however, solar wind high - speed streams emanating from near-equatorial coronal holes occurred frequently and were the primary contributor to the recurrent geomagnetic activity at Earth. These conditions enabled the isolation of forcing by geomagnetic activity on the preconditioned solar minimum state of the upper atmosphere caused by Corotating Interaction Regions (CIRs). Thermosphere density observations around 400 km from the CHAMP satellite are used to study the thermosphere density response to solar wind high - speed streams/CIRs. Superposed epoch results show that thermosphere density responds to high - speed streams globally, and the density at 400 km changes by 75% on average. The relative changes of neutral density are comparable at different latitudes, although its variability is largest at high latitudes. In addition, the response of thermosphere density to high - speed streams is larger at night than in daytime, indicating the preconditioning effect of the thermosphere response to storms. Finally, the thermosphere density variations at the periods of 9 and 13.5 days associated with CIRs are linked to the spatial distribution of low - middle latitude coronal holes on the basis of the EUVI observations from the STEREO.
Introduction
The solar minimum of 2008 was exceptionally quiet, with sunspot numbers at their lowest since 1913. This placed the ionosphere and thermosphere properties in a steady, low solar flux preconditioned state. It was expected that this deep solar minimum would provide a unique opportunity to minimize the magnetospheric and solar-driven disturbances to study dynamics in the ionospherethermosphere system driven from the lower atmosphere (Sojka et al., 2009). However, accompanying this epoch of low, nearly constant solar EUV flux were recurrent high -speed solar wind streams and the resultant geomagnetic disturbances associated with large, long-lived low latitude solar coronal holes (Gibson et al., 2009).
Coronal holes of substantial size near the Sun -Earth line can create high -speed solar wind.
High speed solar wind can interact with the slower solar wind in interplanetary space leading to disturbances in the solar wind called corotating interaction regions (CIRs) (e.g., Tsurutani et al., 1995Tsurutani et al., , 2006. These disturbances lead to modest enhancements in Earth's geomagnetic activity with typical Kp values around four. Additionally, coronal holes can persist for many solar rotations in the solar atmosphere. Consequently, solar wind disturbances occur at harmonics of the solar rotation period leading to recurrent geomagnetic activity. The recurring periodicity in CIRs enables a correlation analysis with periodicities in geomagnetic activity and changes in the ionosphere -thermosphere system. Oscillations at multi-day periods (near 7 and 9 day subharmonics of solar rotation) associated with recurrent high -speed solar wind streams were recently discovered in the thermosphere and ionosphere properties during the declining phase of Solar Cycle 23 (Lei et al., 2008a(Lei et al., , 2008b(Lei et al., , 2008cMlynczak et al., 2008;Thayer et al., 2008;Crowley et al., 2008).
One important outcome of Lei et al. (2008aLei et al. ( , 2008c and Thayer et al. (2008) was that the solar EUV flux did not vary appreciably at these shorter sub-harmonic periods suggesting that geomagnetic forcing on the thermosphere could possibly be isolated. However, this discovery was found during the declining phase in the solar cycle such that the solar EUV flux was gradually decreasing over multiple periods of recurrent geomagnetic activity, thus changing the base state of the thermosphere over time and leading to a different response for each particular storm. The solar minimum period in 2008 showed nearly constant EUV flux over many recurrent geomagnetic storms enabling isolation and identification of the thermospheric response solely to CIR-forced geomagnetic activity. In this study, we will investigate the thermosphere response in the solar minimum 2008 to CIR storms, including its latitude and local time dependence in a quantitative way through a superposed -epoch analysis.
Data Sets
The primary data source used in this work is thermospheric density from the Challenging Minisatellite Payload (CHAMP) satellite. The Spatial Triaxial Accelerometer for Research (STAR) Level 2 observations were processed by the GeoForschungsZentrum Potsdam (GFZ) to remove maneuvers and anomalous spikes and smoothed over 10s. Thermosphere mass densities from pole to pole are then obtained from accelerometer measurements using standard methods (Sutton, Nerem, and Forbes, 2007). The measured densities at satellite altitudes are normalized to a constant altitude of 400 km using NRLMSISE00 (Picone et al., 2002), and this normalization process is necessary in order to minimize the effect of slight changes of the satellite altitude. coordinates, geomagnetic activity index Kp, and CHAMP ascending orbit-averaged neutral density at 400 km in 2008. The most striking feature in solar wind density N n is the sharp spikes, closely followed by the peaks in B. The subsequent enhancement in solar wind speed can be seen clearly, which follows each peak in N n and B. In addition, B z shows rapid fluctuations with a typical amplitude of ~8 nT in the stream -stream compression region and around 2 -4 nT in the high-speed streams in a higher time -resolution plot (not shown). These are the classical features of a CIR as described by Tsurutani et al. (1995Tsurutani et al. ( , 2006; and references therein). There were 38 high -speed streams/CIRs in the entire year of 2008, according to the criterion of McPherron, Baker, and Crooker (2009). Additionally, B x oscillates in direction alternately between "toward" (+) and "away" (-) from the Sun in each Carrington Rotation (CR) period delimitated by vertical lines, which is suggestive of the dominant two-sector structure. The corresponding oscillations with multi-day periods are clearly seen in Kp as a result of the CIR storms. Consequently, thermosphere densities from CHAMP present high-frequency peaks (within each solar -rotation period), which are imbedded in the larger time -scale variations due to the seasonal variation of the thermosphere and local time progression of the satellite.
Results
The Lomb -Scargle (Lomb, 1976;Scargle, 1982) amplitude spectra of the corresponding parameters in Figure 1 are presented in Figure 2 including thermosphere density from CHAMP descending-orbits as well. Obviously, all variables display strong 9-and 13.5-day periodicities except that the 9-day periodicity is absent in the IMF B x and B z components. The 9-day periodicity is also absent in B y (no plotted), but it is strongly present in the total B ( Figure 2b) due to compression effects at the beginning of the CIRs (see Figure 1). Note that the 9-and 13.5-day periodicities are not due to mathematical artifacts since the oscillations at these periods are clearly seen in the time series ( Figure 1). The results of this study indicate again that these strong 9-and 13.5-day oscillations in the thermosphere are associated with the solar-wind energy input, which is in accordance with our previous studies (e.g., Lei et al., 2008aLei et al., , 2008cThayer et al., 2008). Figure 3 shows the same variables as those in Figure 1, except zooming into the two solar rotation periods of CR2068 and CR2075 in Spring and Fall seasons, respectively. Again, the CIR storms in both CR2068 and CR2075 share the common features with those in the schematic diagram of Tsurutani et al. (1995Tsurutani et al. ( , 2006. It should be pointed out that CR2068 is the focus period of the Whole Heliosphere Interval (WHI) campaign (Gibson et al., 2009). Three high -speed streams occurred during the WHI period. The oscillations with the dominant periods of 9 and 13.5 days also prevailed in solar wind, geomagnetic activity, and neutral density in this interval. Furthermore, they were recurrent at least for the first half of 2008 as seen in Figure To examine the thermosphere response to the CIRs quantitatively, we carried out a superposed epoch analysis on 29 of 38 total CIRs that were isolated events with a duration of more than three days, regardless of recurrence of the stream interfaces. The percentage changes of both ascending and descending orbit-averaged neutral densities (equivalent to 58 events for thermosphere density) during the CIRs to the reference of one day prior to the CIR interfaces are computed to minimize the seasonal and local time effects. In Figure 4, from top to bottom, are the superposed epoch results for solar wind density N n , solar wind speed, solar wind dynamic pressure, B z component, Kp, and the relative changes in neutral density for both ascending and descending orbits. The initial, main, and recovery phases of the CIR storm defined in Tsurutani et al. (1995) can be seen from this figure. Both solar wind density N n and dynamic pressure show a strong increase during the initial phase of the CIR associated with the crossing of the heliosphere current sheet. B z has a weak southward component (in an averaged sense) at the stream interface and it shows larger variability during the main phase because of the stream-stream compressive effects. Kp increases rapidly during the initial phase.
However, it is unclear why the increase of neutral density during the initial phase is not as sharp as that 5 seen in Kp. This is probably because the geomagnetic activity may start in the midnight sector auroral zone and expand to the dayside. Neutral density takes about 7-8 days to recover back to its value under quiet conditions, which is the imprint of the long recovery of the solar wind speed and the resultant geomagnetic activity. Interestingly, the relative change of neutral density to the CIR is as large as 75% on average, which indicates that high -speed streams/CIRs have a significant impact on the day-to-day variability of the thermosphere and satellite drag even during the "quiet Sun" period, although the resultant geomagnetic activity is weak or moderate.
The CHAMP density measurements from pole to pole also allow us to further investigate the latitudinal dependence of the thermosphere response to CIRs. Although its variability (i.e., the spread of the standard deviation) is largest at high latitudes (Figures 5a-c), it is surprising that the relative changes of neutral density are comparable at different latitudes (Figures 5d-e). In addition, the nighttime density at 400 km ( Figure 5e) increases by 85% on average during the main phase, which is larger than the increase in daytime, indicating the preconditioning effect of the thermosphere response to storms, as explained next. Lei et al. (2010) showed that the increase of neutral temperature during geomagnetic storms results in the integration effects of the changes of all scale heights below the satellite altitude. Consequently, the increase in neutral density is larger at night when the scale height of the neutral gas is smaller than that in daytime because neutral density falls off rapidly as a function of scale height. It is clear in Figure 5 that neutral density is quietest one day prior to the stream interface, which accords well with the geomagnetic calm before the CIR storm (Figures 1 and 4) (also see Tsurutani et al., 1995, andBorovsky andSteinberg, 2006). An important application of this result is that the ionosphere-thermosphere observations one day prior to the stream interface might be more suitable to minimize the effect of the magnetospheric energy input to investigate the variability of the ionosphere -thermosphere solely due to the influence from the lower atmosphere or anthropologic sources.
Discussion
Recent studies demonstrated that the 9-day solar wind variations in 2005, which contribute to the corresponding oscillations in the thermosphere and ionosphere (Lei et al., 2008a(Lei et al., , 2008bMlynczak et al., 2008), are due to the existence of a triad of solar coronal holes distributed roughly 120 degrees apart in solar longitude (Temmer, Vršnak, and Veronig, 2007). The remaining question is what spatial distribution of coronal holes results in the strong 9-and 13.5-day periodicities in solar wind parameters and thermosphere density in 2008. Figure 6 illustrates the distribution of coronal holes made from the STEREO-A EUVI 195Å measurements as a function of solar latitude and Carrington longitude along with temporal variations of solar wind speed and thermosphere density during the WHI period. There were two large equatorial -low latitude coronal holes marked by the red circles. The coronal hole in the northern hemisphere is responsible for the high-speed stream during DoY 86 -95 (around the period of 9 days) and the 6 broader coronal hole in the southern hemisphere is the cause of the high -speed stream during DoY 95 -107 (near the period of 13.5 days). It is immediately apparent that the 9-and 13.5-day periodicities in solar wind and thermosphere density during WHI (Figures 6b -d) are associated with these two coronal holes extending from the northern and southern hemispheres, respectively. In addition, the third stream during DoY 107 -113 is associated with the coronal hole from higher latitudes in the southern hemisphere. Thereby, both the width and separation of low latitude coronal holes play an important role in determining the temporal variations of high -speed streams, geomagnetic activity, and the corresponding geospace response.
Finally, it is worth noting that the coronal holes shown in Figure 6a actually lasted over several solar rotations as seen in the STEREO EUVI measurements (http://secchi.nrl.navy.mil/synomaps), and these long-lasting coronal holes contributed to the high -speed streams/CIRs which occurred frequently in the deep solar minimum of 2008. Additionally, the low -middle latitude coronal hole from the southern hemisphere was diminished in the second half of 2008. Therefore, the resultant high -speed streams evolved as peaks with much shorter duration in comparison with the corresponding streams in the first half of 2008 (see Figure 1).
Conclusion
During the unique solar minimum of 2008 when solar EUV flux was low and nearly constant, solar wind high -speed streams emanating from near-equatorial coronal holes occurred frequently and were the primary contributor to the continuous geomagnetic activity at the Earth. These conditions enabled the isolation of forcing by geomagnetic activity on the preconditioned solar minimum state of the upper atmosphere caused by CIRs. Intense magnetic field regions or CIRs are due to the interaction of high -speed corotating streams with the upstream low speed solar wind, and high density heliospheric current sheet. There were 38 high -speed streams/CIRs in 2008. Thermosphere density observed from CHAMP was significantly disturbed due to CIRs even though their resultant recurrent geomagnetic activity was weak or moderate. Therefore, the variations of thermosphere density provide a potential trace of solar wind/magnetospheric energy input into the upper atmosphere.
The main conclusions of this study are summarized as follows: ⅰ) Superposed epoch results have shown that thermosphere density responds to high -speed streams globally and the density at 400 km changes by 75% on average. ⅱ) The relative changes of thermosphere density are comparable at different latitudes, although its variability is larger at high latitudes. ⅲ) Thermosphere density has a larger response (in a relative sense) at night than in daytime due to their differing scale heights. ⅳ) The thermosphere is calmest one day prior to the stream interface. ⅴ) According to the STEREO EUVI observations, the thermosphere density variations at the periods of 9 and 13.5 days associated with CIRs are linked to the spatial distribution of low-middle latitude coronal holes. | 3,535 | 2010-04-26T00:00:00.000 | [
"Environmental Science",
"Physics",
"Geology"
] |
Quantum sensing of electric field distributions of liquid electrolytes with NV-centers in nanodiamonds
To use batteries as large-scale energy storage systems it is necessary to measure and understand their degradation \textit{in-situ} and \textit{in-operando}. As a battery's degradation is often the result of molecular processes inside the electrolyte, a sensing platform which allows to measure the ions with a high spatial resolution is needed. Primary candidates for such a platform are NV-centers in diamonds. We propose to use a single NV-center to deduce the electric field distribution generated by the ions inside the electrolyte through microwave pulse sequences. We show that the electric field can be reconstructed with great accuracy by using a protocol which includes different variations of the Free Induction Decay to obtain the mean electric field components and a modified Hahn-echo pulse sequence to measure the electric field's standard deviation $\sigma_E$. From a semi-analytical ansatz we find that for a lithium ion battery there is a direct relationship between $\sigma_E$ and the ionic concentration. Our results show that it is therefore possible to use NV-centers as sensors to measure both the electric field distribution and the local ionic concentration inside electrolytes.
I. INTRODUCTION
Rechargeable batteries play an important role for our society and are a key ingredient for the transition towards renewable energy sources [1][2][3].As the production of batteries is accompanied with a considerable use of resources, recyclable [4] batteries with a long lifetime are needed.The latter is limited by degradation mechanisms, such as the formation of solid-electrolyte interfaces [5] or lithium-plating [6] which can reduce the battery's capacity with increasing cell age [7].As these processes happen on a molecular level within nanometer scales [5], a sensor which is capable of monitoring the ionic concentration in-situ and in-operando with high spatial and temporal resolutions is needed.Even though MRI allows to reconstruct transport properties [8,9] of a battery, tools which allow to perform measurements inside the electrolyte are still absent [5].
It has been demonstrated that nitrogen-vacancy (NV) centers in diamond (see Fig. 1(b)) are high-resolution quantum sensors, which can detect oscillating or fluctuating [10][11][12][13] magnetic fields with nano- [14,15] and even subpico-Tesla [16] sensitivities.Besides this, NV-centers have great ability for the detection of electric fields.They can not only detect DC [17,18] or AC [19] electric fields with remarkable precision, but are additionally capable of detecting single fundamental charges [20] even within the diamond lattice [21].This electric field sensitivity was used by Ref. [22] to show that, based on theoretical con-siderations, bulk NV-centers can work as electrochemical sensors if they are in contact with an electrolyte solution.
Here we show that nanodiamonds equipped with single NV-centers can act as in-situ electric field sensors inside liquid electrolytes (Fig. 1(a)).By exploiting how transverse and axial electric fields act on the NV-center's ground state spin states, we find variations of the freeinduction decay (FID) pulse sequence, which allow to measure the mean electric field components.Further, we show that it is possible to use variants of the Hahnecho pulse sequence to additionally obtain the electric field's standard deviation σ E .From a semi-analytical ansatz we demonstrate exemplarily for a lithium ion battery (LIB) that there is a direct relationship between the electric field's standard deviation and the local ionic concentration.A nanodiamond with a single NV-center can therefore work as a sensor which allows to simultaneously reconstruct the electric field distribution and to measure the ionic concentration with nm spatial resolution.
II. ELECTRIC FIELD DISTRIBUTION IN LIQUID ELECTROLYTES
Before introducing measurements of the electric field distribution by the NV-center, we would like to develop an analytic expression of the electric field induced inside the nanodiamond by the positive and negative ions of the electrolyte.
The potential Φ at position r inside the nanodiamond due to a single charge q at position b, is described by and inside a sphere of radius R. The relative permittivities are ND = 5.8 [22] and e = 17.5 [23].Solid lines are fits following Eq.( 3) with A as a fit parameter.(d) Fit parameters A obtained from (c), compared to the theory value.
Poisson's equation Here = 0 i with i = e, ND, are the permittivities of, respectively, the electrolyte and the nanodiamond in terms of the vacuum permittivity 0 and ρ is the charge density induced by q.The solution inside the nanodiamond, Φ ND (see Methods for the detailed derivation), allows to obtain the electric field at the center of the nanodiamond, which is By considering the positions of ions of a molar concentration c to be normally distributed within a sphere of radius R around a nanodiamond (radius r ND ), the standard deviation of the electric field distribution at the center of the nanodiamond is To validate Eq. ( 3), we simulated the standard deviation of 500 sets of uniformly and randomly placed ions for different molar ionic concentrations (see Fig. 1(c)).As it is the most widely used electrolyte of LIBs [24], we chose LiPF − 6 with e = 17.5 [23].The total electric field was calculated as the linear sum of Eq. ( 2) for all randomly placed ions around a 200 nm spherical nanodiamond [25].As it can be seen from Fig. 1(d), the expected A value is in fair agreement with the simulations.From Eq. (3) it can be calculated that for R = 500 nm, the fluctuations will increase only by 3%, compared to σ E (R = 400 nm).
As σ E therefore saturates for R 500 nm, this implies that electric field fluctuations only affect the nanodiamond within sub-micrometer range and the system is limited by the confocal volume of the experimental setup, which typically is ∼ 1 µm 3 [26,27].
III. SENSING OF STATIC ELECTRIC FIELDS INSIDE ELECTROLYTES
An electric field E can in cylindrical coordinates be expressed by its axial component E z , its transverse projection E ⊥ = E 2 x + E 2 y and an angle φ E , which defines the projections onto the x and y axis as E x = E ⊥ cos φ E and E y = E ⊥ sin φ E .The total Hamiltonian which describes the NV-center in presence of electric and axial magnetic fields will in the following be denoted as Ĥ0 .By taking into account that the NV-center can be driven by two perpendicular microwave wires (see Fig. 1(a)) with amplitude Ω, frequency ω d and a phase φ between each other, the total ground state Hamiltonian in a frame rotating with ω d is Ĥ = Ĥ0 + Ĥd (see Methods), where Here ∆ = D − ω d is the detuning between the zerofield splitting, D = 2.87 GHz [28], and the microwave drive frequency.S i , i = x, y, z, are the spin-1 operators, which can be used to define ladder operators S ± = S x ± iS y .σ 0,±1 = |0 ±1| are operators which describe transitions between |0 and, respectively, |±1 .Frequency contributions generated by electric and axial magnetic fields are considered through ) and β z = γ e B z (γ e = 28 GHz/T [30]).
The phase factors ± = 1 − ie ∓iφ /2 which enter into Eq.( 4), allow to describe the transitions which are caused by circularly (φ = ±π/2) or linearly (φ = 0) polarized microwave drives [31].The time-evolution operators of Ĥd , R (t) = e −i Ĥd t (see Methods), show that one can induce Rabi oscillations between |0 and |1 for right circularly polarized drives and |0 ↔ |−1 for left circular polarizations.Linearly polarized drives allow to drive transitions between |0 and both |±1 .In absence of microwave drives, the |±1 states are symmetrically mixed by ξ ⊥ and axial electric fields effectively shift |0 from |±1 , which can be seen from F (τ ) = e −i Ĥ0τ (see Methods).As axial and transverse electric fields thus act differently on the |m s = 0, ±1 states of the NV-center, one can derive variations of the Free Induction Decay (FID), which allow to extract these electric field components.
A. Measurement of electric field components
The FID consists of two microwave pulses separated by a free evolution period τ .Electric field contributions ξ ⊥ , φ E and ξ z can be sensed through FID-variations, as shown in Fig. 2(a).The NV-center can be initialized into its |0 state via excitation with green laser light, followed by intersystem-crossing [32].This state can then be driven to −i |1 through a right-polarized π-pulse, denoted as R (T π ) + , and will be influenced by both axial magnetic as well as transverse electric fields.The latter induce mixing with |−1 .By using a microwave π-pulse with the same polarization as the initial one, the transferred population from |1 to |−1 can be obtained from the FID-signal which is a measure of the population which has been transferred from |1 to |−1 .In Fig. 2(b) one can see this FID-signal as a function of the free evolution time τ for β z values up to 2.8 MHz, which corresponds to B z = 1 G.Besides having a decreased contrast for β z = 0, the frequency β 2 z + ξ 2 ⊥ of the FID-oscillations depends on both axial magnetic and transverse electric fields.It is therefore strongly recommended to perform the measurements in a magnetically shielded environment, for exam-ple by a µ-metal as in Ref. [33].In the following it will be assumed that all measurement are performed without any magnetic field being present.
The transverse electric field components are uniquely defined through φ E , as ξ x = ξ ⊥ cos φ E and ξ y = ξ ⊥ sin φ E .A superposition state −e iπ/4 (|1 + |−1 ) / √ 2 generated through a linearly polarized π-pulse (considered via R (T π ) 0 , see Methods) will additionally to ξ ⊥ also be affected by φ E as this phase differs in its sign for |1 and |−1 (see Methods).If either |1 or |−1 is projected to |0 through the final microwave pulse, one obtains an FID-signal, which both depends on ξ ⊥ and φ E , One can obtain φ E as the relative fraction between the value of the FID-signal at τ = 0 and its first maxima at 2τ ξ ⊥ = π/2, By using FID ξ ⊥ and FID ξ ⊥ ,φ E , it is therefore possible to not only determine the electric field's transverse component, but also to obtain the projection onto the x and y axes, which are determined through φ E .
Axial electric field contributions ξ z cause a Stark shift between |0 and |±1 .A superposition state (|0 − i |−1 ) / √ 2 generated by a circularly polarized π/2-pulse (see Fig. 2(a)) will therefore be affected both by ξ z and ξ ⊥ .If the final microwave π/2-pulse has the same polarization as the initial one, an FID-signal is obtained which depends both on ξ ⊥ and ξ z , if the NV-center was driven with ω d = D.The Fourier transform of Eq. ( 8) (see Methods), shows, that ξ z can be measured if it is possible to spectrally resolve ξ ⊥ ± ξ z .To study this, we numerically [34,35] simulated FID ξz,ξ ⊥ and included dephasing at rates 1/T * 2 through a Lindblad operator 1/T * 2 S z for T * 2 in the range up to 15 µs (see Fig. 2(c)).One can resolve ξ ⊥ ±ξ z for nanodiamonds with T * 2 > 10 µs, which is higher than the value of typical nanodiamonds [36].For a nanodiamond with T * 2 ≈ 15 µs it would be possible to distinguish between ξ ⊥ and ξ z and therefore to determine the projection of the electric field onto the symmetry axis of the NV-center.
IV. INFLUENCE OF FLUCTUATING ELECTRIC FIELDS
It can be assumed that the ions surrounding the nanodiamond will not stay static for the timescales in which measurements are performed but will be subject to, for instance, drift and diffusion.These fluctuations will affect the electric field inside the nanodiamond.Due to the limited T * 2 of nanodiamonds, the FID pulse sequences as introduced before will be mainly suitable for the measurement of the average electric fields (see Methods).The coherence time of a nanodiamond can be significantly prolonged if instead of an FID, a Hahn-Echo pulse sequence is used [25].As it is shown in Fig. 3(a), we propose a modified version of the Hahn-Echo, where after the first free evolution interval, a πpulse with right-circular polarization is performed, before the spin is allowed to precess freely during a second free evolution interval τ .Before being read out, a right-circularly polarized π-pulse is applied, which leads to a signal Hahn (τ ) = (1 − cos (2τ ξ ⊥ )) 2 /4.Simulations of this Hahn-Echo variation show that the averages (see Methods for an example) can be fit by Here T 2 is the sum of the intrinsic spin coherence time T 2,int.= 100 µs [25] and a contribution due to the fluctuating electric fields, In Fig. 3(b), one can see T 2 as a function of the electric field's standard deviation σ E , where solid lines are T 2,E = αE m /σ 2 E in terms of a fit parameters α.The total spin coherence time is therefore strongly affected by σ E and the mean electric field value E m .If the mean transverse electric field has been sensed by the FID sequence as shown in Eq. ( 5), it is therefore possible to derive the electric field's standard deviation, which together with ξ ⊥ , φ E and ξ z defines the electric field distribution.As there is a direct relationship between σ E and the local ionic concentration (see Fig. 1(c)), the proposed Hahnecho pulse sequence additionally allows to use the NVcenter inside the nanodiamond as a local concentration sensor.
FIG. 3. (a)
Hahn-echo pulse sequence used to simulate Eq. ( 10).(b) Total T2 for numerically [34,35] simulated Hahn-Echoes with T2,int = 100 µs, with the electric field components sampled from a normal distribution with mean Em and standard deviation σE.For the simulations a drive of Ω = 10 MHz was used.Solid lines are fits of αEm/σ 2 E .Every trajectory was obtained from 1000 individual simulations.Error bars of one standard deviation are smaller than the data points.
V. CONCLUSION AND OUTLOOK
In conclusion we have shown here a full reconstruction of the mean electric field generated in a liquid electrolyte, through the spin control of a quantum sensor immersed in the electrolyte.We have found exact expressions correlating the electric field components with the free-induction decay of the sensor spin, and the dependence of the variance on the spin-echo measurements.Together we were able to deduce the electric field distribution and also measure the local ionic concentration, a key parameter in characterizing the performance of the liquid electrolyte for battery applications.We envisage that with improved modeling of the electric field distribution in liquid electrolytes and using better quantum control methods, for example using correlation spectroscopy [37], we could enhance the sensitivity of the sensor to the local electric-field environment, allowing for an in-situ monitoring of the battery using the liquid electrolyte.
project QMNDQCNet and DFG (Project No. 507241320 and 46256793).S. V. K. and D. D. would like to acknowledge the funding support from BMBF (Grant No. 16KIS1590K).A. F. is the incumbent of the Elaine Blond Career Development Chair and acknowledges sup-port from Israel Science Foundation (ISF grants 963/19 and 418/20) as well as the Abramson Family Center for Young Scientists and the Willner Family Leadership Institute for the Weizmann Institute of Science.
Quantum sensing of electric field distributions of liquid electrolytes with NV-centers in nanodiamonds -Supplementary Information
I. ELECTRIC FIELD AT CENTER OF NANODIAMOND
In the following we would like to deduce the electric field of a single point charge q at a distance b from the origin of the nanodiamond with radius r ND by following Ref.[S1].Poisson's equation describes the electrostatic potential Φ, where = 0 i , i = e, ND is the permittivity of, respectively, the electrolyte and the nanodiamond in terms of the vacuum permittivity 0 .By exploiting azimuthal symmetry of the problem, the above expression reduces to Laplace's equation for r = b, which in spherical coordinates with |r| = r and θ the angle spanned by r and b is The general solution of this partial differential equation can be expressed in terms of the associated Legendre polynomials P l of order l and in terms of two constants A l and C l as [S1, S2] As the potential inside the nanodiamond must be finite at r = 0, C l needs to vanish and one therefore has (S5) The general solution would then be given as a superposition of this expression with Eq. (S3), i.e.Φ e = Φe + Φ, which reads where it was used that in this case A l = 0 to ensure a vanishing potential at infinite distances to the origin, i.e.Φ e → 0 for r → ∞.The constants A l and C l , which enter into, respectively, Eq. (S4) and Eq.(S6), can be determined by requiring continuity at the interface between electrolyte and nanodiamond, e E e − ND E ND • n ND = 0 (S7) where n ND = r/r is the unit vector normal to the surface of the nanodiamond.These boundary conditions are satisfied, if . (S10) The electrostatic potential inside the nanodiamond therefore is b l+1 e (2l + 1) ND l + e (l + 1) and the electric field at the center, i.e. for r = 0, can be calculated as if it is used that in cartesian coordinates one has e z = cos θe r − sin θe θ with e z the azimuthally symmetric unit vector and e r and e θ the radial and altitudinal unit vectors.
A. Electric field variance
The probability of an ion to be located at b witin a sphere of radius R around the nanodiamond is It can be easily verified that this distribution is normalized, i.e.R 3 d 3 b p (b) = 1.Direct calculation reveals E z = 0 and therefore (2 e + ND ) Under the assumption that the electric fields generated by the single ions are uncorrelated, the total fluctuations are given by multiplying the above expression with the number of ions inside the sphere.The standard deviation σ 2 Ez = cN A V σ 2 Ez,ion of the electric field components with N A Avogadro's number, c the molar ionic concentration and V the volume in which the ions reside therefore is From this it can be seen that the expected electric field fluctuations increase with the molar concentration, i.e. σ Ez ∝ √ c.
II. HAMILTONIAN IN ROTATING FRAME
As derived by Doherty et al. in Ref. [S3], the Hamiltonian of the NV-center in presence of axial magnetic fields B z and electric field components E i with i = x, y, z and = 1 is with γ e = 2.8 MHz/G the NV's gyromagnetic ratio [S4] and d = 0.35 Hz • cm/V and d ⊥ = 17 Hz • cm/V the axial and transverse dipole moments [S5].By rewriting this Hamiltonian in terms of its frequency contributions β z = γ e B z , x + E 2 y and by introducing the electric field polarization φ E , which defines the transverse electric field projections via ξ x = ξ ⊥ cos φ E and ξ y = ξ ⊥ sin φ E , Eq. (S16) can be rewritten as where Ŝ± = Ŝx ± i Ŝy are spin-1 ladder-operators and h.c.means the hermitian conjugate.To understand how fluctuating electric fields alter the FID-signal, we numerically [S7, S8] simulated FID ξ ⊥ (Eq.( 5) main text) for normally distributed electric fields.Hereby, at every timestep at which the time-evolution is calcuated, the electric field components are passed from a beforehand sampled normal distribution with mean E m and standard deviation σ E .It can be seen from Fig. S1 that the average FID ξ ⊥ signal decays rapidly to its steady-state value of 1/2, which is due to the short T * 2 time of 1 µs.For this reason it is proposed to use the Hahn-Echo pulse sequence for measurements of strongly fluctuating electric fields.The total T2 value obtained from this fit is T2 = (39.87± 0.86) µs.
As described in the main text, the numerically obtained Hahn-echo trajectories (see Fig. S2 for an example) are well fitted by Hahn (τ ) = 1 4 1 − cos (2τ ξ ⊥ ) e −τ /T2 2 .Here both the intrinsic T 2,int.= 100 µs and T 2,E due to fluctuating elecric fields contribute to the total T 2 via The latter can be fitted in terms of E m and σ E via The values of the fit parameter α can be found in Fig. S3.
FIG. 1 .
FIG. 1.(a) Experimental setting.A nanodiamond which is dissolved in the liquid electrolyte of the battery is surrounded by positive (orange) and negative (blue) ions.Two perpendicular aligned gold wires allow to generate polarized microwave drives.(b) To work as a quantum sensor, the nanodiamond contains a vacancy (V) next to a nitrogen atom (red).(c) Standard deviation of Ez, calculated from 500 repeated sets of randomly placed ions of concentration c around the nanodiamond (rND = 100 nm)and inside a sphere of radius R. The relative permittivities are ND = 5.8[22] and e = 17.5[23].Solid lines are fits following Eq.(3) with A as a fit parameter.(d) Fit parameters A obtained from (c), compared to the theory value. | 5,079.2 | 2023-01-11T00:00:00.000 | [
"Physics"
] |
Environmental regulation, environmental responsibility, and green technology innovation: Empirical research from China
Innovation and green are the directions to promote the circular economy and environmental sustainability at the corporate level. This paper examines the impact of environmental regulation (pollution charge) on green technology innovation and the mediating role of corporate environmental responsibility. Our results indicate that: (1) Environmental regulations stimulate manufacturing enterprises’ environmental responsibility and green technology innovation. It is worth noting that corporate environmental responsibility strengthens the relationship between environmental regulation and green technology innovation. (2) Further investigation reveals that R&D expenditure and environmental investment have greatly strengthened the positive effect of environmental regulation on green technology innovation. (3) With more detailed disclosure about enterprises’ environment-related information, the more outstanding stimulation effects of environmental regulation. Discussions on the features of enterprise location have revealed that, if the goal of environmental protection is set too high or if the fiscal decentralization is too strong, implementation of environmental regulation would not achieve desirable results. Accordingly, we need to optimize the collection of environmental taxes, strengthen the enterprises’ environmental responsibility, and increase investment in R&D and environment protection. Meanwhile, the execution of environmental regulation should also take into account the institutional environment and governance features of the enterprise locations.
Introduction
The key projects faced in contemporary China are to accelerate the green transformation of development modes and to achieve high-quality economic development. The green innovation capabilities and environmental responsibility levels of heavily polluting listed companies in China are relatively low. Therefore, the government has adopted various means of environmental regulations to restrain the enterprises, to form a green, efficient, and economical way of production. Then, did environmental regulation has improved corporate environmental responsibility and green innovation activities? Corporate environmental responsibility (CER) means that enterprises take the responsibility that benefits sustainable development. Green innovation runs through the entire process of an enterprise's production, consumption, and service, involving renovations of technology, organization, and institutions [1]. Existing studies on environmental regulation are mostly conducted on the level of regions and industry, lacking in-depth discussion on the environmental regulation effects and inner mechanism of enterprises [2]. It is of great significance to evaluate the response of manufacturing enterprises to environmental regulation policies. We examine the impact of environmental regulation on green technology innovation (GTI) and the mediating effect of CER. This paper also presents the heterogeneous effect of environmental regulations on innovation in different governance environments, thereby providing a theoretical basis for promoting the green development of manufacturing enterprises. Numerous scholars have agreed that the economic effects of environmental regulations from two major perspectives, namely the "compliance cost" and the "Porter Hypothesis" [2][3][4][5]. On the one hand, pollution control action has consumed large amounts of resources for manufacturing enterprises. Enterprises may have to cut down on R&D spending to improve their financial situation, and innovation may not be the primary option for them to implement green development [3,4]. On the other hand, Porter [5] pointed out that moderate environmental regulation stimulates corporate innovation and creates an innovation compensation effect. In particular, market-incentive environmental policies like pollution charges and carbon permits trading will enhance an enterprise's competitiveness by inspiring technology innovation [6,7]. Kesidou and Wu [8] suggest that stricter environmental regulatory frameworks in emerging economies are not only combating pollution but also shifting the innovation activities of manufacturing firms. For heavily polluting companies, a proactive environmental strategy and energy policy will help promote enterprises' energy-saving transformation and improve their future performance [9,10]. Acemoglu et al. [11] believe that the cooperation of two environmental regulation tools-pollution emission charges and environment subsidies-can achieve enterprises' green technology innovation. With the spread and reinforcement of environmental regulations, green technology innovation holds a better advantage for enterprises [12].
Firms' correct choices on environmental governance methods and implementation strategies can arguably have a positive impact on their innovation capacity [13,14]. Various studies establish that the interlinkages of CSR, CER, and innovation, studying the impact of CSR and CER on the economic consequences of enterprises [15][16][17][18]. From the perspective of stakeholder theory, stakeholders have a markedly impact on the industry's greening [19]. CSR can help firms to gain external resources, such as government support and social support [16]. Imed et al. [20] hold that corporate innovation is driven only by the environmental dimension of CSR. As the main part of CSR, CER is the result of enterprises responding to the government's environmental regulations [21]. CER depends on environmental management strategies, and a better effective environmental governance is beneficial for enterprise performance [22][23][24]. Ferri [25] found that enterprises with a stronger social responsibility are more likely to make green investments. Liu et al. [26] believe that improvement of governance structure may enhance heavily polluting firms' environmental performance and eventually promote their capability of sustainable development. While inefficient corporate governance may bring down the enterprise's environmental performance and inhibit its green innovation [27]. In this sense, firms focusing on CER can capture stakeholders' preferences, turning external resources into innovation support.
Environmental regulations affect enterprises' green technology innovation via more than one route. However, there has not been much research on the internal mechanism of environmental regulations affecting corporate behavior, especially from the perspective of environmental responsibility. Enterprises can choose non-green innovation, green innovation, and take environmental responsibility when subject to environmental regulation. Heavily polluting manufacturing enterprises have to enhance their inner governance to improve environmental performance. In particular, environmental regulation stimulates environmental management certification and improves environmental responsibility [28]. As an important part of social responsibility, environmental responsibility is becoming a decisive factor influencing company green performance.
This paper focuses on the impact of environmental regulation on manufacturing enterprises' green technology innovation, analyzing the regulating functions of R&D expenditure and environmental protection investment. We find that environmental regulation has a positive effect on corporate green technological innovation. Part of the role of environmental regulation in promoting green innovation is achieved by strengthening corporate environmental responsibility. The conclusion still stands after robustness tests of replacing independent variables and econometric models. Further investigation reveals that the input of R&D and environment protection have both greatly strengthened the positive effect of environmental regulation on green technology innovation. The environmental information disclosure will enhance the positive effect of pollution charges on green technological innovation. In addition, excessive environmental protection goals or fiscal decentralization in the area where the company is located is not conducive to the implementation of environmental policies.
This study offers a two-fold contribution. First, this paper reveals the relationship between environmental regulation, corporate environmental responsibility, and green technology innovation. To this end, we shed light on the mediating effect of CER. Second, this paper explores the regulating effect of factors such as R&D expenditure and environment protection investment, thus offering theoretical guidance for enterprises to deal with environmental regulation. By studying the regional differences concerning environmental regulation's impact on green technology innovation, this paper puts forward policy recommendations for coordinated growth of regional economy and environment.
The remaining parts of this paper are organized as follows: Section 2 provides the formulation of the research hypotheses; Section 3 describes the quantitative analysis concerning (a) the sample selection and data sources, (b) the choice of the variables, (c) the econometric models; Section 4 sets out the empirical research findings and robustness test; Section 5 provides further research and heterogeneity analysis; Section 6 provides the discussion of findings and conclusions.
Environmental regulation and green technology innovation
Under the pressure of regional environmental regulations, enterprises have to pay pollution charge and increase investment in environmental governance. These environmental governance behaviors take up a lot of resources and create new production costs, which is not conducive to innovation input. In addition, strict environmental regulation measures will inhibit the financial activities of heavily polluting companies [29]. While some scholars believe that only the long-term benefits of innovation can compensate for the costs of environmental regulations. According to the Porter Hypothesis, moderate environmental regulation stimulates technology innovation and thereby bringing "innovation compensation" of increased competitiveness. The competitive advantage formed through technological innovation gains longterm profits for enterprises and maintains their market competitiveness. External knowledge adoption and green absorptive capacity strengthen the positive impact of environmental regulation [30]. Accordingly, the enterprise's continuing innovation depends on the interaction between the "costs compliance effect" and the "innovation compensation effect". Alongside the accelerated construction of ecological civilization, environmental regulation has become a standardized restraint on manufacturing enterprises, making innovation the only way for companies to gain a competitive advantage [31].
Unlike innovations of non-green technology, green innovation means the implementation of green concepts to the entire process of corporate production and operation. It involves innovation of green technology, green management, and green marketing. Green innovation promotes the sustainable development of enterprises by improving the technical level of products and reducing environmental pollution [32]. Heavily polluting manufacturing enterprises have to increase R&D investment for improving green innovation. Green innovation fundamentally enhances product competitiveness and brings competitive advantages to enterprises. Firstly, enterprises can obtain government's environmental protection and innovation subsidies with technological innovation, which in turn brings a product's marketing profits. Secondly, the pressure from stakeholders compels listed enterprises to implement green development strategies and green innovation into business management decisions. It can be inferred that environmental regulation will stimulate the enterprise to transform external pressure into a "motivating factor" encouraging innovation. Innovation is the starting point for a company to obtain the "compensation effect" of environmental regulation. For heavily polluting manufacturing enterprises, green technology innovation has far more competitive strengths compared with other forms of innovation. Ultimately it is the environmental regulation policy that encourages manufacturing enterprises to perform green technology innovation. Based on the above, this paper proposes the following hypotheses: Hypothesis 1: Environmental regulation is positively associated with the green technology innovation of manufacturing enterprises.
The mediating roles of corporate environmental responsibility
Companies will pay more attention to environmental responsibility under the influence of environmental regulation. CER including environmental protection investment, environmental information disclosure, green marketing, and these factors are conducive to innovation. Apart from direct supervision, the government will urge enterprises frequently to be more responsible via compulsory environment reports. Companies with better environmental performance will actively disclose environmental information in their social responsibility reports. [33]. Environment responsibility is a major component of corporate social responsibilities and is under the scrutiny of both stockholders and the capital market. As required by the Company Law of the People's Republic of China, listed manufacturing enterprises should publish their conduct of social responsibility in time and make detailed disclosure on their environmental responsibilities. Manufacturing enterprises should evaluate the impact of their behavior on the natural environment, actively undertake their environmental responsibilities and promote sustainable development. Multiple pressures from the public, the capital market, and the government compel enterprises to undertake effective environmental management measures as a response to the demands of environmental supervision [34]. CER increases heavily polluting companies' long-term economic effects through improving companies' operational efficiency and reducing their credit costs [18]. It brings sufficient financial support for corporate innovation. First, we argue that environmental regulations can promote enterprises to take environmental responsibility. Environmental regulation is conducive to guiding listed companies to strengthen environmental management system certification and environmental information disclosure [35]. According to the stakeholder theory, environmental information disclosure wins favor from investors and protection from supervisors, thereby reducing the risks of investment and promote transparency [36]. Inspired by stakeholders, enterprises prefer to pay attention to CER, carry out active measures of environmental governance, and increase investment in environmental protection [37]. Environmental supervision has certainly changed corporate behavior, promoting business executives to carry out different environmental strategies in response to various types of environmental regulation [38,39].
Second, we argue that CER can promote green innovation. Green innovation demands more regulatory commitment and concern than other types of innovation. Environmental responsibility can encourage companies to allocate more resources to green innovation when making business decisions [22]. Several past studies suggest that green strategy and green human resource management have a positive influence on the green process and product innovation [17,40]. Tseng et al. [41] suggest that environmental responsibility is the foundation of sustainable development, which drives corporate financial and governance performance. Mishra [42] shows that innovative enterprises benefit from engaging in CSR activities through their environmental dimensions. Environmental responsibility can promote the enterprise to form the concept of green development and encourage managers and staff's identification with environment protection awareness. Transformation of corporate R&D mode requires the corresponding transformation of a green organization, i.e. the company's inner procedure should be redesigned with additional development of green innovation capability [27]. Enterprises' internal features define the effects of environmental regulation policies on environmental performance. Environment management system certification is beneficial to the formation of a corporate green innovation culture and encourages activities of green technology innovation. In addition, corporate environmental responsibility also improves the reputation of society and enables it to receive more external support. Based on the above, this paper proposes the following hypotheses: Hypothesis 2: Environmental regulation impels manufacturing enterprises to improve environmental responsibility.
Data source and descriptive statistics
According to the Guideline for Environment Information Disclosure of Listed Companies released by China's Ministry of Environmental Protection, the heavily polluting industries include 16 industries in total: thermal power generation, steel making, cement, electrolytic aluminum, coal mining, metallurgy, chemical engineering, petrochemical engineering, construction materials, paper-making, brewing, pharmaceutical production, fermentation, textiles, tannery, and mining.
Model construction
Based on the Mediating Effect Model of Baron and Kenny [43] and the research design of Li and Xiao [38], here we construct the following metrological model: Benchmark model (1) is constructed based on Hypothesis 1, with subscript indexes i and t representing the enterprise and the year respectively. GTI serves as the explanatory variable, representing the green technology innovation level of listed manufacturing enterprises. The Charge is the explanatory variable representing the environmental regulation for enterprises. Model (2) and model (3) are constructed based on Hypotheses 2 and 3. CER is a mediating variable representing the level of corporate environmental responsibility, α is the constant term, and ε is the random disturbance term. The Control k, i, t is a series of controlled variables, including the share of the largest shareholder (SHR1), asset size (SIZE), asset-liability ratio (LEV), the proportion of male executives (GENDER), CEO duality (DUAL), state ownership (STATE), return on assets (ROA), and operating life (AGE). In addition, we control the annual (Year), industry (Industry), and regional (Region) fixed effect.
It should be mentioned that θ 1 is the total effect of environmental regulation on corporate green innovation; θ 2 is the impact of environmental regulation on corporate environmental responsibility; θ 3 is the direct effect of environmental regulation on corporate green innovation; θ 4 is the impact of environmental responsibility on corporate green innovation after environmental regulation is under control. θ 2 θ 4 represents the mediating effect transmitted via corporate environmental responsibility, i.e. the indirect effect.
For further research, model (4) and model (5) are constructed to discuss the moderating effect of R&D expenditure and environment protection investment under environmental supervision. We use the ratio of R&D expenditure to main business income to evaluate RD and use the natural logarithm of the enterprise environmental investment to measure ENVI.
Explanation of variables
Explained variable. We use the natural logarithm of patents authorization plus one to measure the green technology innovation (GTI), including the green invention and green utility patents. Although data on patent applications are more timely, the number of green patents authorized can better reflect the true innovation level of an enterprise [44,45].
Explanatory variable. Environmental regulation is mainly measured by indicators, such as investment expenditure in environmental governance, composite emission index, or numbers of environmental violations [2,3,7,38]. Most measurements are based on macro-data at the city level or above, which could not be directly used to measure the environmental supervision of the company [46]. Following Li and Xiao [38], this study uses the proportion of pollution charge (Charge) to total assets of listed manufacturing enterprises to measure the degree of environmental regulation. The system of pollution charge has been widely applied in China, motivating enterprises to incorporate environmental responsibility into production decisions. As an environmental regulation measure targeting enterprises, the governance effect created by billing pollution discharge is immediately evident.
Mediation variables. We take CER as the mediating variable, measured by the ratio of CER to CSR of listed manufacturing enterprises. The CSR score of listed companies includes the dimensions of shareholder responsibility, employee responsibility, supplier, customer and consumer rights and interests, environmental responsibility, and social responsibility. CER score is calculated based on assessments of listed companies' environment governance actions, including environment protection awareness, environmental management system certification, environment protection investment, and energy conservation. These dimensions comprehensively reflect a listed company's level of environment governance [47].
Other control variables. Enterprise innovation is affected by factors such as company characteristics, board characteristics, and so on. We add these variables to control for unobserved heterogeneity as follows.
Share of the largest shareholder (SHR1): The ownership concentration ratio is measured by the shareholding ratio of the first majority shareholder. Based on the Principal-Agent Theory, senior management is more likely to be affected by the interests of major shareholders.
Asset size (SIZE): The size of Enterprises is measured by natural logarithms of corporate total assets. The large company attracts more government and public attention [1].
Asset-liability ratio (LEV): The asset-liability ratio is a comprehensive index to evaluate the company's debt and risk level. Low financial risk is conducive to enterprises to increase R&D expenditure and environmental protection investment.
The proportion of male executives (GENDER): Under external pressure, senior executives of different genders place different levels of emphasis on corporate innovation and environmental performance [48].
CEO duality (DUAL): 1 if the CEO also chairs the board and 0 otherwise. CEO duality improves the company's operational efficiency, a powerful CEO will result in greater innovation performance [49].
State ownership (SOE): 1 if enterprise for the state-owned and 0 otherwise. Enterprises with different ownership systems have different governance characteristics, which affect the policy effects of environmental regulation.
Return On Assets (ROA): Return on assets often represents the company's performance and own profitability.
Operating life (AGE): The life cycle of a company will not only affect the business performance but also indirectly affect innovation. We use the age of the company to measure its operating life. Table 1 is a statistical description of the main variables in this paper. More than half of the heavily polluting enterprises have no green patents, and their innovation outputs are mainly non-green ones. Enterprises with more green patent authorization are chemical raw materials, chemical products manufacturing, and pharmaceuticals, ferrous metal smelting, and rolling procession, nonferrous metal mining, and dressing. Industries with higher marks of environmental responsibility include chemical products manufacturing, pharmaceuticals, and beverage manufacturing. Industries with higher profit margins are pharmaceuticals and chemical products manufacturing. The average pollution charge is 0.036(%), indicating that listed heavy-pollution manufacturing enterprises spend a large amount of money on pollution discharge. And the enterprises that pay the pollutant discharge fees account for a relatively low proportion. We find that manufacturing enterprises with excellent performance of green innovation, environmental responsibility, and financial results are mostly of the chemical products manufacturing, pharmaceuticals, and beverage manufacturing. Based on whether companies pay pollution charges, we conduct a T-mean difference test of sample groups (Table 2). For enterprises not paying pollution charges (G1), their GTI average
PLOS ONE
Environmental regulation, environmental responsibility and green technology innovation and CER average are half of those that pay pollution charges (G2). Their difference in mean value and median is at the significant level of 1%. Remarkably, enterprises paying pollution charges are better at green innovation and environmental responsibility performance.
Analysis of the main model's regression results
Columns (1)- (3) in Table 3 are the regression results of models (1) to (3) respectively. The regression coefficient of environmental regulation on heavily polluting manufacturing enterprises' green technology innovation is 0.297, at the significant level of 1%. In other words, should the percentage of pollution charges incorporate total assets increase by 1%, the number of green patents held by these enterprises will increase by 0.297%. Overall, the environmental regulation has a promoting effect on the green innovation activities of Chinese heavily polluting manufacturing enterprises, consistent with Hypothesis 1. In reality, innovation is the sole solution for enterprises to gain competitive gains and reduce costs of environmental regulation.
Columns (2) and (3) in Table 3 show the regression results of the mediating effect. The regression coefficient of environmental regulation on CER is 0.05, at the significant level of 5%. In other words, should the percentage of pollution charges incorporate total assets increase by 1%, the score of environmental responsibility by these enterprises will increase by 0.05%. Environmental regulation can strengthen heavily polluting enterprises' environmental responsibility, consistent with Hypothesis 2. The regression results demonstrate that the impacts of both environmental regulation and environmental responsibility on green technology innovation are remarkably positive.
It demonstrates the existence of the "partial mediating effect" of corporate environmental responsibility, namely, part of environmental regulation's stimulating effect on green technology innovation is achieved by strengthening CER. This paper proves that, as an important channel to affect corporate management in the form of environmental regulation, environmental responsibility can effectively improve a company's level of green innovation. CER includes environmental protection awareness, environmental management system certification, environmental investment, and other aspects, and the impact of these factors on green technology innovation is positive. The results demonstrate that CER has strengthened the relationship between environmental regulation and green technology innovation. Performing environmental responsibility and developing green innovation are the main measures of enterprises in solving environmental problems.
We use the stepwise regression method to verify the mediating effect and continues to use the Sobel test to examine the mediating effect of CER. The Sobel test results are shown in Table 4. The Z statistic of indirect effects is significant at the 5% level, indicating that there is a mediating effect, which accounts for 5.4%. At the same time, the results of the Sobel test are consistent with the results of the full-sample regression.
The results of the control variables are summarized as follows. The share of the largest shareholder (SHR1) and operating life (AGE) both have a significant negative effect on GTI, suggesting that higher ownership concentration and operating life go against green innovation. The asset size (SIZE) and asset-liability ratio (LEV) both have a significant positive effect on GTI, suggesting that companies with large scale and better financial situations pay more attention to green innovation. The gender ratio (GENDER) has a significant positive effect on innovation, which means that male executives are more concerned with green innovation and environmental responsibility. The coefficients of CEO duality (DUAL) and accounting earnings (ROA) are not significant. Besides, there is no clear distinction between state-owned enterprises' level of green technology innovation and that of private enterprises.
PLOS ONE
Environmental regulation, environmental responsibility and green technology innovation
Robustness test and instrumental variable test
In this paper, we conduct robustness tests as follows: (1) replacing independent variable and dependant variable respectively; (2) lag one-year processing on independent variables and control variables; (3) adopting Logit regression for empirical analysis. First, we select the ratio of corporate charges to regional sewage charges as a substitute indicator for environmental regulation. Then, we change the dependant variable, representing the corporate level of green technology innovation with the number of authorized patents on green utility models.
Considering the lagging impact of environmental policy, this paper conducts lag one-year processing on independent variables and control variables to retest the model (1). In addition, we define corporate green technology innovation as a dummy variable T and use Logit regression for empirical analysis. The results of our robustness tests are given in Table 5. We find that pollution charge (Charge) is still significant and positive for green technology innovation in the model (1). The results listed in Table 5 show that the regression coefficient of pollution charge on GTI is remarkably positive and consistent with previous conclusions. It also indicates that
PLOS ONE
Environmental regulation, environmental responsibility and green technology innovation enterprises should pay more attention to green technology innovation and environmental responsibility in the future in response to environmental regulation.
To deal with the possible endogeneity between environmental regulation and GTI, Our manuscript reports the results of a robustness test based on the two-stage instrumental variable method and GMM instrumental variable method (Table 6). We choose the word frequency of environmental information disclosure in company quarterly and annual reports and the average annual pollution charge of other listed companies in the industry as the instrumental variables for Charge. Table 6 shows that the pollution charge of heavily polluting listed companies in China significantly increases their green technology innovation.
R&D expenditure and environment protection investment
The mediating effect test shows that the indirect effect of environmental regulation on innovation is lower than the direct effect. For further investigation, this study discusses enterprises' responses to environmental regulation under two situations. First, enterprises can increase their R&D expenditure and launch green innovation or other kinds of innovation for promoting green development and competitiveness. Secondly, enterprises can also increase their environment protection investment for either environmental responsibility or green innovation, to reduce environmental pollution and improve environmental performance. According to theoretical analysis, enterprises can choose both green technology innovation and nongreen technology innovation to enhance their competitiveness under the pressure of environmental regulation. The results of our empirical analyses concerning interaction terms are given in Table 7.
The interactive Charge × RD is significantly positive, the interactive Charge × ENVI is positive but not significant. This result shows that corporate R&D expenditure has strengthened the stimulus given by pollution charge on corporate green innovation, and thus performing a positive moderating role. Manufacturing enterprises can strengthen green technology innovation by increasing R&D expenditure and environment protection investment.
Heterogeneity analysis
Political connection is more than just an important route affecting corporate innovation. It also affects the execution of environmental regulations. On the one hand, private enterprises and weak technology companies have enhanced their innovation capabilities via political connections [50]. CEO's support for environmental protection policies also helps promote corporate green technology innovation [51]. The stricter the environmental regulation, the higher the deployment effect of politically-related R&D resources, which in turn improves R&D effects [52]. On the other hand, political connections tend to reduce the due punishments of environmental violations and lead to the "protection effect". Strong political connections amplify enterprises' advantages at bargaining, and thus restrains environmental regulation from uplifting the total green factor productivity dynamically [15]. Political connections of CEOs could also strengthen the execution of environmental regulation policies, amplifying the policy effect of environmental regulation. In this paper, we categorize samples into those politically connected and those not, based on whether their CEO is a Communist Party member, Deputy to the National People's Congress, or member of the National Committee of the Chinese People's Political Consultative Conference. Column (1)-(2) in Table 8 reports that the pollution charge has a greater positive role in the green innovation of enterprises that lack political connection. The political associations of CEO somewhat suppress the policy effect of environmental regulation. External pressure is an important reason for pollution charges to drive the green innovation of enterprises [38]. Such a disclosure mends the issue of unbalanced information between enterprises and investors, reducing the financing restraints and costs for a company [53]. The excellent financial condition helps enterprises carry out their duties of environmental governance and implement green innovation. Accordingly, the more transparent the environment disclosure, the more stimulation of environmental regulation on corporate innovation [54]. Here we categories sampled enterprises into two groups based on whether they publish annual environmental reports and conduct examination. This paper conducts a group regression of sample companies according to whether the number of environmental information disclosure items exceeds the industry average. The results of Columns (3) to (6) in Table 8 show that the pollution charge is positively correlated with GTI, significantly at the 5% level. In the group of disclosing public environmental annual reports, the regression coefficient of pollution charges is 0.44, while the regression coefficient of companies that does not disclose environmental reports is 0.21. Pollution charge has a greater incentive for green innovation in manufacturing companies that disclose environmental information promptly. Green innovation and environmental responsibility are mutually beneficial, manufacturing enterprises with better environmental responsibility tend to achieve better policy effects of environmental regulations. As is part of environmental responsibility, environmental information disclosure has also strengthened the relationship between environmental regulations and corporate innovation.
In China, the central government's policies of environmental regulation serve as the foundation for regional governments to draft their respective policies. Considering regional differences, the central government has classified them into various functional zones, each bearing a unique task of ecological protection and with the respective goal of economic development. Some regional governments aim at maximized economic benefits and often loosen the restraints of environment protection for economic advancement, other regional governments aim at ecological assessment, hence stricter execution of environmental regulations. Even within the same province, cities differ in their execution of environmental regulation. According to Du et al. [55], the transformation of regional governance contributes to the realization of the "Porter Hypothesis" in the Chinese context and increases industrial green competitiveness. The size of a government is closely related to environmental regulation. A minor government and loose regulation have reduced enterprises' environmental responsibilities [33]. Regional features like governance goals and financial decentralization affect the effect of implementing environmental regulation policies. Environmental regulation is under the sway of external circumstances, and competition among regional governments will alter the degree to which they implement environmental regulations. For instance, neighboring districts are economically competing against each other, yet they are also imitating each other in terms of drafting and implementing environmental regulation policies [56]. Therefore, the external governance environment will change the degree of impact of environmental regulations on corporate green innovation.
We continue to discuss the impact of external governance factors on the implementation of environmental regulations like regional government's environment restraint goals and financial decentralization. Following Yu et al. [57], we collect data of environment goal restraint disclosed in every city governments' reports. According to whether the local government of the enterprise puts forward the target of industrial pollution reduction, the sample data has been divided into two groups. At the same time, we also classify the sample into two groups according to whether the fiscal decentralization of the company's location exceeds the median of the year. Table 9 is the regression results of how pollution charge affects corporate GTI under different regional governance characteristics. We find that the regression coefficient of pollution charge on GTI of heavily polluting firms is still significantly positive. In low-environment target cities, environmental regulations have a greater impact on the green innovation of manufacturing companies in heavily polluting industries.
In regions with strong fiscal decentralization, environmental regulations have a weaker impact on green innovation in manufacturing companies in heavily polluting industries. Environmental regulation policy depends on the execution of respective governments, and regional governments with a higher degree of financial decentralization tend to be more capable at execution.
In China, the eastern, central, and western regions have differences in the market environment and economic development, thus affecting the implementation effect of environmental Table 9. Heterogeneity test of regional differences.
PLOS ONE
Environmental regulation, environmental responsibility and green technology innovation policies. In the results of Column (5) and Column (6), we find environmental regulation has a greater impact on GTI in eastern China. The heterogeneity test of regional differences suggests that, as a market-incentive environmental regulation policy, the pollution charge is less dependent on the government's executive power.
Conclusions
According to the Porter Hypothesis, moderate environmental regulation can make the internalization of external issues like corporate pollution and encourage corporate innovation activities. In particular, the effect of environmental policy on innovation depends on the policy means and the strategic behavior of the enterprise [58,59]. This paper analyses the transmission mechanism of how environmental regulation affects corporate environmental responsibility and green technology innovation, in addition to the theoretical discussion on how various governance conditions adjust environmental regulation. Pollution charge is a market-incentive environmental regulation method that directly faces enterprises, which produces higher regulatory effects. Compelled to pay, heavily polluting manufacturing enterprises have to strengthen their environmental responsibility and green technology innovation. In the meantime, increasing R&D expenditure and environment protection investment is better to enhance the effect of implementing environmental regulation policies, thus promoting the green innovation output of manufacturing enterprises. The research in this article shows that corporate environmental responsibility is closely related to green innovation, which theoretically guides the sustainable development of manufacturing companies.
The study makes a profound analysis of the relation of pollution charges on green technology innovation by using microdata of heavily polluting manufacturing enterprises listed in Chinese A Stock Markets, providing a more targeted reference for making policies. We have manually collected information on corporate pollution charges, corporate environmental responsibility, environment protection investment, and green patents, and empirically prove that the mechanism of pollution charges affecting corporate environmental responsibility and green technology innovation. We find that corporate environmental responsibility also significantly enhances its green technology innovation capability via improving manufacturing enterprises' environmental responsibility. As the main response of manufacturing enterprises to environmental laws and regulations, corporate environmental responsibility has improved the level of green technological innovation of manufacturing enterprises. Further investigation reveals that investment in R&D and environment protection can greatly strengthen the positive effect of environmental regulation on the manufacturing enterprises' green technology innovation. On the contrary, the CEO's political connections inhibit the policy impact of pollution charges on corporate green technology innovation.
Innovation and environmental responsibility are the directions to promote the circular economy at the corporate level [60,61]. For enterprises that disclose environmental information promptly, environmental regulations have a greater incentive for green technological innovation. The discussion of the heterogeneity of external governance factors shows that in regions with lower environmental goals, environmental regulations have a stronger influence on the green technology innovation of heavily polluting manufacturing enterprises. Environmental regulations have less impact on the green innovation of manufacturing companies in regions with a higher degree of fiscal decentralization. If local governments set higher environmental protection targets, it will be difficult for companies to charge pollutants to stimulate green technological innovation in heavily polluting companies. This paper has examined the mechanism of environmental responsibility's stimulation on green technology innovation. Such governance behavior includes R&D expenditure, environment protection investment, and environment information disclosure. We have provided new proofs for existing studies on the economic effects of environmental regulation, thus offering theoretical support for the realization of corporate environmental responsibility and green technology innovation. The policy significance of the research conclusions of this paper mainly lies in the following.
First of all, attention should be paid to the construction of a pollution discharge charging mechanism for enterprises. The public sector should optimize the environmental taxation system so that the pollution charges do not become a burden for corporate production. We propose to strengthen the administration of pollution charges and environment taxes, to fully unleash the moderator capacity of market-stimulating environmental regulation on heavily polluting manufacturing enterprises' environmental responsibility, and to achieve the "positive" effect of environmental regulations on green technology innovation.
In addition, it is urgent to increase R&D expenditure and environmental protection investment. Specifically, environmental protection investment is the performance and result of environmental responsibility. Manufacturing enterprises should improve internal governance and enhance environmental responsibility that strengthens their green innovation activities. Therefore, manufacturing enterprises need to be encouraged and rewarded for undertaking environmental management system certification, disclosing environmental information, and increasing input of environmental governance.
Finally, policymakers should design different environmental regulation policies following each district's governance features. Meanwhile, it is very necessary to fully consider the institutional environment and governance characteristics of the enterprise location when implementing environmental policy. The sustainable development of enterprises can be promoted only by setting reasonable environmental protection goals and providing financial incentives for green innovation behavior. | 8,386 | 2021-09-22T00:00:00.000 | [
"Environmental Science",
"Business",
"Economics"
] |
Single-imprint moth-eye anti-reflective and self-cleaning film with enhanced resistance
This work presents nanoimprinted moth-eye surface nanocomposite fi lms exhibiting multifunctional broadband anti-refl ective and photo-induced self-cleaning properties with improved mechanical resistance. The anti-refl ective fi lms are produced in combined processing steps of titanium dioxide nanoparticle coating and surface imprinting of moth-eye nanostructures. Nanoparticle polymer blending and formation of reinforced sub-wavelength surface nanocomposite features is achieved simultaneously. This methodology represents a practical approach for producing nanoimprinted surfaces with superior mechanical properties and multi functionality. The fi lms are suitable for fl exible and portable solar devices. As featured in:
Introduction
A large number of products require strategies to avoid undesirable reflections and glare for example electronic displays, optics and lighting, solar panels, architectural glazing, storefronts, etc.A low cost solution employed today is the application of antiglare coatings to eliminate external reflections.These coatings make use of diffuse scattering to disperse the reflected light.Diffusion works by reducing the coherence of the image that is reflected, making it appear unfocused and as a trade-off, resolution and clarity are reduced.
Anti-reflective (AR) coatings represent a much more efficient approach. 1The current AR coating strategies are based on the multilayer interference and quarter-wave principles. 2 Multilayer interference coatings are produced by interlayering non-absorbing, high and low refractive index materials.While this strategy is very effective and well established, it is costly and it is not suitable for low value added products.Quarter-wave coatings consist of a single quarter-wave layer of transparent material whose refractive index is the square root of the substrate's refractive index.Quarter-wave coatings are optimized for one single wavelength and one angle of incidence; hence, they have a very intense reflection colour and lack broadband antireflective properties.
An additional approach to realize AR optical properties is by creating a graded refractive index interface by means of surface texturization at subwavelength dimensions.These surfaces are also called moth-eye AR surfaces from where they were initially inspired. 3,4Moth-eye AR surfaces impart antireflective properties to an interface not only over a broad spectral range but also over wide angles of incidence. 5,6An additional important advantage is that they are very low cost potentially as they do not require additional materials or processing steps for production.High aspect ratio moth-eye like structures can sometimes display self-cleaning behaviour derived from superhydrophobicity by minimizing the adhesion of dirt particulates or easing their removal. 7ontinuous nanoimprint processing is possibly the technology most suitable to produce moth-eye AR surfaces at the industrial scale for low value added products such as architectural windows or solar collectors where high volumes and large areas are required.In these products, not only reflection reduction is required, but additional functions, such as transparency, self-cleaning abilities, mechanical strength and durability will be of clear advantage.The fabrication of effective moth-eye AR polymer films by nanoimprinting has been reported before [8][9][10][11][12][13] by large scale 14 and roll to roll 15 processes.However, for the practical implementation of the technology there are still several issues to resolve.Firstly, it is the fragility of the sub-wavelength cone-like features needed to produce moth-eye AR surfaces.In addition, the high transmittance of AR surfaces can be drastically reduced by the adsorption of contaminants from the atmosphere and or deterioration over time primarily due to photodegradation and wear in exterior environments. 16,17itanium dioxide (TiO 2 ), also known as titania, remains as one of the most widely used additives for its chemical stability and properties derived from its semiconductor nature.9][20][21] In organic coatings or paint formulations, TiO 2 is employed for its dual function as a photocatalyst and as a photoabsorber. 22As a photoabsorber, TiO 2 is an effective UV radiation screener of wavelengths from 280 nm to 400 nm and consequently it helps to inhibit polymer photodegradation and embrittlement due to polymer chain scission. 23s a photocatalyst, with a band gap of 3.2 eV, TiO 2 (anatase) absorbs photons with a wavelength of 388 nm and in the presence of water and oxygen, highly reactive radicals such as hydroxyl and hydroperoxyl radicals and activated oxygen species are produced which are capable of causing oxidative degradation of organic matter including contaminants. 24hese species may also give rise to photocatalytically induced hydrophilicity that is, the conversion of hydrophobic surface character to a hydrophilic one upon exposure to UV light. 25][28] To prevent photocatalytic oxidative degradation in the case of organic host matrices, several strategies have been developed.Traditionally this has been avoided by using an inert interlayer to insulate the photooxidation activity often using a silica 29 or a polysiloxane layer. 30More recently, TiO 2 functionalization with silane coupling agents 31 or hybrid sol-gel silane coatings 32 have emerged as more practical approaches for the preparation of photocatalytic coatings with reduced impact on the organic matrices.A more straightforward strategy employed in outdoor coating formulations is to use a low particle loading (i.e.≤2%) where a compromise between achieving a sufficient photo-oxidation and UV shielding efficiency for a weathering resistance during the particular service life can be achieved. 33here have been a number of reports where graded refractive index surfaces have been conferred with self-cleaning ability primarily derived from TiO 2 photooxidation reactions together with an enhancement of surface wettability.In this line of work, Guldin et al. developed anti-reflective coatings based on a highly porous silica based network produced by silica sol gel chemistry incorporating TiO 2 nanocrystals. 34The process required the steps of coating, annealing and plasma etching of the organic components, which makes processing complicated and difficult to implement in practice, particu-larly on flexible substrates.Moreover, porous AR thin films may be prone to water absorption, which will give rise to variations in the RI and degradation of transmittance.Nakata et al. coated TiO 2 nanoparticles onto a commercial PET prepatterned with moth-eye structures.A strong self-cleaning effect was achieved based on the hydrophilicity imparted by TiO 2 after UV irradiation.However, due to the thick layer of nanoparticles employed, a marked decrease in the film transparency was observed. 35Kang et al. developed a nanoimprinted TiO 2 moth-eye layer on perovskite solar cells, reporting an improvement in the light harvesting efficiency.However, due to the high refractive indices of both TiO 2 layer and perovskites, the reflection reduction was only moderate. 36iO 2 has also been recently incorporated into a moth-eye inspired topography made of PDMS to act as a UV filter while preserving transparency. 37ue to the high elastic modulus of titania nanoparticles, the incorporation of the nanoparticles has in addition a reinforcement effect on polymer matrices. 38However, a low load and adequate dispersion of nanoparticles within the polymer matrix is necessary to preserve transparency in optical films.
Here, we describe a first of its kind approach targeted to improve the current limitations of polymer based moth-eye AR surfaces.The methodology involves the fabrication in a single processing step of AR flexible polymer transparent films by nanoimprinting sub-wavelength moth-eye features onto a polymer surface loaded with TiO 2 nanoparticles.The surface acquires multiple properties including photoinduced selfcleaning and enhanced mechanical resistance while improving the optical transparency compared to the neat flat films.This methodology could be readily adapted via roll-to-roll to large area processing for applications such as architectural windows or flexible solar devices.
Synthesis of TiO 2 nanoparticles
TiO 2 nanoparticles were prepared following the hydrothermal synthesis method described by Grätzel. 39For this, 20 ml of titanium isopropoxide(IV) (Acros Organics) was added to 36 ml of deionised water and the mixture was stirred for one hour.The resulting product was filtered and washed three times with deionised water.The filtered product was placed into a Teflon-lined titanium autoclave and mixed with 3.9 ml of 0.6 M tetramethylammonium hydroxide (Sigma Aldrich).The reaction was carried out for 14 hours at 120 °C.Finally, the resulting colloid was centrifuged two times at 10 000 rpm for 10 min to remove aggregates.The final colloidal aqueous solution contained a concentration of nanoparticles of approximately 24 wt% with a mean diameter of 24 nm as measured by dynamic light scattering (Malvern Zetasizer).Wide angle X-ray diffraction (WAXD) measurements were performed at the BM26 beamline of the European Synchrotron Radiation Facility (ESRF, Grenoble) to confirm the formation of the anatase phase of TiO 2 .The detailed characterization of the nanoparticles is included in Fig. S1.†
Preparation of TiO 2 -polymer substrates
Initially, a poly(methyl methacrylate) (PMMA) (Sigma Aldrich) solution in toluene (7.5 wt%) was spin-coated (1000 rpm) onto a PET (Hifi Industrial Film, 125 μm thickness) film disk of 5 cm diameter employed as a carrier.A PMMA layer of about 660 nm was obtained (see Fig. S2 †).Next, the aqueous dispersion of TiO 2 nanoparticles was diluted with methanol at three different concentrations (0.1, 0.5 and 1 wt%) and these dispersions were spin-coated (3000 rpm) onto the previously layered PMMA film generating a TiO 2 nanoparticle film for the 0.5 and 1 wt% dispersions and a discontinuous particle layer for the case of 0.1 wt% dispersion (see Fig. S3 †).
Nano-imprinting of the moth-eye AR TiO 2 composite films
The AR structures were created by a thermal nanoimprint process.Initially, a working mould of polydimethylsiloxane (PDMS) with the AR moth-eye topography was prepared from a master nickel anti-reflective mould (HT-AR-02, Temicon).This was achieved using two layers of PDMS: hard-PDMS (h-PDMS) (Gelest) and soft PDMS (Sylgard 184, Dow Corning).The h-PDMS was first mixed and cast onto the master nickel mould.After a period of 30 min for the filling the cavities, the mould was spin-coated (1000 rpm for 1 min) in order to obtain a homogeneous thin layer of h-PDMS.Subsequently, the h-PDMS was partially cured in an oven for 10 min at 80 °C.Then the PDMS precursor and initiator mixture were cast on the partially cured h-PDMS and placed in an oven at 80 °C for 24 hours to cure completely.Finally, the replicated working mould was peeled off and kept in a clean room environment.
Using the PDMS working mould, the prepared TiO 2 -PMMA surfaces were imprinted at 170 °C at 45 bar of pressure for 5 min (Eitre 3 Nanoimprint Lithography System, Obducat).The different samples prepared were labelled as P-XT-AR, where "X" refers to the concentration of the TiO 2 dispersion employed.
Property characterization of AR TiO 2 composite films
The topography of the imprinted substrates was characterized by scanning electron microscopy (SEM) (Auriga FIB-SEM system, Zeiss) and atomic force microscopy (AFM) in tapping mode (Multimode 8 AFM with a Nanoscope V controller, Bruker).
The specular transmission and total reflection measurements were obtained using a Lambda 650 UV-Vis spectrophotometer (PerkinElmer) fitted with a 150 mm integrating sphere.
The photo-catalytic capacity of the AR composite films was measured through degradation assays of Rhodamine B (RhB) aqueous solution (5 mg L −1 ).For this, the AR films were placed on a Petri dish with 12 ml of RhB solution.The substrates were first stored in darkness for 120 min to reach an adsorption-desorption equilibrium of RhB.Subsequently, the substrates were irradiated with UV light (UVASPOT 400/T, Honle) providing 80 mW cm −2 of light intensity for periods of 10 min while kept in an ice bath to avoid evaporation caused by heating.At these intervals, an aliquot was measured with a spectrophotometer at the peak of maximum absorbance (554 nm).The results of 4 different experiments were averaged for each of the 4 different substrates.
The wettability of the prepared substrates was assessed by measuring the static water contact angle (WCA) using an optical tensiometer (Attension Theta, Biolin Scientific).The tests were conducted under sequential 10 min UV irradiation while the substrates were submerged under a thin layer of deionised water.After UV exposure, the samples were dried before WCA measurement.For this, 3 μL droplets of deionised water were deposited onto the substrates.The static WCAs were obtained by fitting the drop profile to a Young-Laplace curve.
Accelerated weathering tests were performed following the standard norm: ISO 11507 Method A using a weathering chamber (QUV/basic model, Micom Laboratories Inc.).A cycle with two steps was selected.During the first step, the samples are irradiated with UV light (0.71 W m −2 ) at 60 °C for 4 hours.The second step consists of water condensation at 50 °C.These steps were repeated consecutively and the samples were taken for analysis at four different times: 100 h, 200 h, 400 h and 600 h.
Evaluation of the artificial weathering effects on the AR films was carried out by SEM imaging, optical transmittance measurements and chemical changes detected by infrared spectroscopy (FT-IR) in attenuated total reflectance mode (Alpha FTIR, Bruker).
The nanomechanical characterization of the AR nanostructured surfaces was performed by nanoindentation and nanoscratch tests using a Hysitron TriboIndenter (TI 950 instrument).A spherical diamond tip with a radius of 10 µm was employed as the indenter probe.Each nanoindentation test consisted of 20 load-controlled load-hold-unload cycles unloading to 50% of the maximum load in each cycle until a maximum total load of 200 µN was reached.A minimum of 10 indentations were performed on each sample.The nanoscratch testing consisted of scratches of 16 µm in length, using a constant normal force of 100 µN.Two additional scans with a low normal force of 2 µN were programmed before and after each scratch in order to obtain the topography profile of the scratched line before and after the test to calculate the residual depth of the scratch.
Results and discussion
The production of nanostructured multifunctional AR surface composite films is carried out using a single thermal nanoimprint process.PMMA is employed as a base polymeric material due to its exceptional optical properties, such as low light absorption and transmittance values higher than 90% in the visible spectrum.The fabrication method of the composite nanostructured films is outlined in Fig. 1.Initially, the required TiO 2 nanoparticles were synthesized following the hydrothermal method described by Grätzel 39 (see Fig. S1 and Table S1 † for characterization details).The fabrication starts by layering a PMMA film of 660 nm onto a flexible PET substrate via spin coating of a PMMA solution (Fig. S2 † shows the profilometer profile).Subsequently, a methanol dispersion of the TiO 2 nanoparticles is spin-coated onto the PMMA film.Three different dispersion concentrations were employed (0.1, 0.5 and 1 wt%) in order to determine the impact of the nanoparticle load on the nanoimprinting pattern fidelity as well as on the final properties of the AR films.The spin coating process of the TiO 2 particles produces a monolayer of particles on the surface of the PMMA substrate with a maximum height of 33 nm (see AFM images in Fig. S3 †).In the next step, the films are imprinted in a thermal process using a PDMS working mould patterned with the moth-eye topography.After cooling, the film is de-moulded obtaining the polymer motheye structures filled with polymer dispersed nanoparticles.The fabrication process is shown in the scheme of Fig. 1a.Doublesided AR films were also fabricated by imprinting a doublesided coated substrate placed between two PDMS AR moulds.The neat PMMA imprinted film is denoted as P-AR and the imprinted composite films are denoted as P-01T-AR, P-05T-AR, and P-1T-AR in reference to the initial TiO 2 dispersion concentrations employed.The quality of the replication was assessed by SEM and AFM imaging.The height of the cone-like features obtained ranged from 340 nm for the P-AR film to 290 nm for the P-1T-AR nanocomposite film (see AFM profiles in Fig. S4 and S5 † and geometrical parameters in Table S2 †).This gradual decrease in the cone height is presumably caused by the increase in viscosity of the softened polymer with the particle load impacting the flow of the polymer into the cavities of the mould during the imprinting process.The AFM and SEM images in Fig. 1b and c show a moth-eye topography imprinted on the 0.5 wt% TiO 2 composite (P-05T-AR); Fig. 1d corresponds to a SEM cross-section image of this film.Both images show well-formed cone-like nanostructures with TiO 2 nanoparticles distributed on the imprinted layer of nanocone tips as well as on the valleys.
The optical performance of the nanocomposite moth-eye surfaces was characterized using a spectrophotometer equipped with an optical integrating sphere.This equipment allowed determining the total reflectance at an incidence angle of 8°.The optical performance of the nanocomposites prepared with different loads of TiO 2 imprinted on a single side and on both sides was characterized and compared to a neat polymer flat surface as a reference.The optical characterization results are summarized in Fig. 2. As can be seen, the moth-eye nanostructures reduced significantly the broadband reflectance seen on the flat film from values of about 9% to 6% (Fig. 2b).Due to the high refractive index of titania (∼2.5), a reduction in the transmittance and therefore, an increase in the reflected component was seen as the amount of nanoparticles increased on the films.The P-01T-AR film presented similar reflectance values to those of the neat film, while these increased slightly for P-05T-AR and P-1T-AR films signifying the absorption and scattering effects by the TiO 2 particles as the load increased.Nonetheless, these results also reveal that a thin monolayer of nanoparticles such that applied on the surfaces does not deteriorate the optical properties of the AR films significantly and in fact, all the AR composite films showed a strong broadband reflectance reduction over the reference neat PMMA flat film.Remarkably, the total reflectance of P-01T-AR and P-05T-AR films imprinted with motheye features on both sides, reached values below 1% for wavelengths in the region of 600 nm, and below 2% in most of the visible part of the spectrum.The specular transmittance measurements are shown in Fig. 2a.In this figure, it can be seen that in accordance with the level of reflection, the transmittance values were above 90% within the range from 400 nm to 700 nm, which is higher than that of the flat film (∼88%).
The extended transmission and reflection spectra (200-2000 nm) are shown in Fig. S6.† The substrates being made of two layers of different plastic materials showed the typical UV absorption in the 300-400 nm range.In addition, the higher amount of titania in the P-1T-AR substrate produced a discernible decrease in transmittance below the 425 nm wavelength range, while the transmittance observed through the P-01T-AR substrate was very close to that of the neat P-AR substrate.Likewise, the transmission spectra of the substrates P-01T-AR and P-05T-AR imprinted on both sides displayed values as high as 98%, indicating that there were practically no optical losses due to absorption or diffuse scattering effects by the TiO 2 nanoparticles.
A consistent decrease in optical transmittance for all imprinted substrates (with or without titania) in the region from 435 to 400 nm was also noted.To ascertain the origin of this drop, the transmittance of substrates with no TiO 2 particles and with and without structures were comparatively measured (see transmission spectra in Fig. S7 †).These measurements proved that the optical scattering losses caused by the moth-eye nanostructures are responsible for the slight drop in transmittance seen in that region.The thin layer of well-dispersed TiO 2 nanoparticles within the polymer matrix in fact did not impair the optical transparency of the moth-eye films and this is illustrated by the digital photograph in Fig. 2c.The photograph shows the high transparency and the reflection reduction brought about by the moth-eye structures on the P-05T-AR printed film (right) compared to a non-patterned PMMA film where the reflected image of the ceiling can be clearly perceived (left).
The photo-induced self-cleaning effect was assessed by monitoring the degradation of the dye Rhodamine B (RhB) with UV radiation.For this, the AR substrates prepared with different TiO 2 loads were exposed to UV radiation at regular intervals of 10 min immersed under a thin layer of water to emulate a humid or wet environment. 40Fig. 3a shows the relative RhB concentration variation due to photo-catalytic degradation after sequential UV radiation doses.As a control substrate, a neat P-AR film was used (red line).The slight degradation with the exposure time observed for the RhB on this control can be attributed to the photobleaching induced by the UV light on RhB.For the imprinted nanocomposite films, all showed a photocatalytic activity that increased with the TiO 2 load and exposure time.As expected, the maximum degradation was obtained for the P-1T-AR composite.On this substrate, the RhB was degraded approximately 70% after 70 min of UV exposure.In this period of time, P-01T-AR showed 30% degradation only.Tests were carried out to determine the effect of the thermal imprint process on the photocatalytic activity of the TiO 2 loaded on the three different substrates (see Fig. S8 † for the plotted results).The substrates with 0.5 and 1% TiO 2 surface load, moth-eye imprinted and non-imprinted or flat, showed a similar catalytic efficiency.However, in the case of 0.1% TiO 2 load, the imprinted AR substrates displayed a marked reduction in photocatalytic efficiency.This result signifies that in the case of the P-01T-AR substrate, with more dispersed nanoparticles, the incorporation of these into the nanocones by the polymer flow during imprinting is more efficient which is in good agreement with the height of the nanocones obtained (see profile in Fig. S5 †).In the case of higher loads, (0.5% and 1%), the titania particles form a quasi-continuous film (see AFM images in Fig. S3 †) whereby the interaction forces among nanoparticles are stronger which possibly results in a less efficient integration of the nanoparticles into the matrix and as a result, the nanoparticles are less embedded showing similar photocatalytic efficiency to the non-imprinted substrates.
To evaluate the photoinduced surface wettability, the different AR composite films were irradiated with UV light through a thin water layer and after drying, the wettability of the substrates was determined through water contact angle (WCA) measurements at the same regular intervals.Newly imprinted AR surfaces displayed a WCA of about 135°.This angle was the same for both the neat or composite AR surfaces.The consistency found in all the surfaces indicates that the surface roughness of all the substrates was alike with nanoparticles embedded into the polymer topography as confirmed by AFM (Fig. 1b).The WCA on the neat and P-01T-AR surfaces remained hydrophobic with only a slight drop in the WCA value.However, the WCA for the P-05T-AR and P-1T-AR substrates decreased over time after exposure to UV light and at around 40 min of irradiation, the surfaces became hydrophilic as shown in Fig. 3b.The initial hydrophobicity recovered minimally over a period of months (see Fig. S9 †) and only after heating at temperatures above 80 °C, the initial hydrophobicity was restored.These results concur with the photocatalytic activity observed for the TiO 2 composites where the surfaces with higher TiO 2 load (0.5-1 wt%) sustained a higher degree of photocatalysis.The wettability switch of TiO 2 polymer nanocomposite surfaces has been reported before. 25,41From X-ray photoelectron spectroscopy (XPS) measurements the switch has been associated with an increase in the content of Ti-OH on the surface upon UV exposure. 25n accelerated weathering test was programmed in order to investigate the aging resistance of the different substrates.The test was performed applying UV radiation, temperature and humidity cycles following the standard ISO 11507 utilizing a climate chamber.The morphological changes induced by the accelerated weathering were determined by SEM.The images indicate that the P-01T-AR nanostructures remained unchanged even after 600 h.However, for the P-05T-AR and P-1T-AR films an appreciable increase in roughness and exposure of nanoparticles on the surfaces could be seen with increasing radiation time signifying the loss of the polymer matrix due to photocatalytic degradation (see Fig. S10 † for SEM images of the surfaces after weathering).These results underline the need for an optimal content of TiO 2 nanoparticles to achieve the desired photocatalytic effect with minimal polymer degradation.The optical quality of the AR film tested was studied after each weathering cycle by measuring the specular transmittance (see Fig. S11 †).The substrates show a decrease in transmittance when the ageing time and amount of titania nanoparticles increased.The resistance to wear of the P-01T-AR films with 0.1 wt% of titania nanoparticles is worth remarking, showing values of 88% transmittance after 600 h of weathering.The chemical changes taking place after the aging process were also evaluated by attenuated total reflection Fourier transform infrared spectroscopy (FTIR-ATR) (Fig. S12 † summarizes the FTIR-ATR spectra obtained).The P-AR and P-01T-AR did not show any appreciable chemical change after 600 h of weathering cycles.However, after 200 h of weathering, the P-05T-AR and P-1T-AR substrates showed a marked reduction of the PMMA IR bands indicating a significant degradation of the PMMA matrix due to photooxidation reactions.The absence of new peaks corresponding to degraded compounds after weathering suggests that chain scission and de-polymerization are the most prevalent degradation mechanisms of PMMA. 42he mechanical robustness of the AR nanocomposite surfaces was characterized by nanoindentation.Nanoindentation has demonstrated to be a valuable technique for the mechanical characterization of polymer nanocomposites and because of its high sensitivity to small surface deformations, has also become a useful tool for the measurement of mechanical properties of surface nanostructures. 43,44Here, nanoindentation and nanoscratch experiments were specifically designed for studying the deformation resistance of the imprinted AR nanostructures to normal and lateral stresses, respectively.Nanoindentation tests were performed applying incremental load-unload cycles onto the sample surface using a nanoindenter equipped with a 10 μm radius spherical tip until a final load of 200 µN was applied.This load was preselected from load-displacement curves where the penetration depths attained were smaller than the height of the moth-eye nanocone structures.Representative load-depth curves obtained for each of the tested samples are plotted in Fig. 4a.The flat substrate presented initially an elastic response for which the loading and unloading segments in each loading cycle overlapped, while the imprinted samples presented less elastic recovery with more permanent deformation at lower loads.The maximum indentation depth at 200 µN was substantially lower for the flat sample (≈50 nm), than for the P-AR sample (≈120 nm).The addition of TiO 2 nanoparticles improved considerably the mechanical resistance of the moth-eye imprinted surfaces due to their higher elastic modulus with a reduction in maximum depth up to ≈90 nm.It is worth noting that in all experiments the maximum indenter depth reached was lower than the height of nanostructures that ranged from 290 to 340 nm and therefore, the experiments essentially are indicative of the mechanical behaviour of the nanostructures.Interestingly, the moth-eye imprinted surfaces with three different TiO 2 loads (P-01T-AR, P-05T-AR, P-1T-AR) did not show apparent differences in the mechanical strength (Fig. 4a), suggesting that the quantity of nanoparticles that is incorporated inside the nanostructures is comparable regardless of the initial concentration applied onto the surface.The contact stiffness did however change with the load of TiO 2 nanoparticles.Fig. 4b plots the contact stiffness obtained from the initial slope of the indentation load-depth curve in the elastic region, at a penetration of ≈10 nm where plastic deformation is negligible.The stiffness decreased from 2.5 to 1.9 μN nm −1 upon imprinting the moth-eye nanostructures on the neat PMMA film.This is presumably due to the decrease in the effective area in contact upon imprinting the surface.However, the stiffness increased successively with the TiO 2 particle loading and reached up to ≈2.6 μN nm −1 in the P-1T-AR substrate.This corresponds to a stiffness enhancement of 37% over the neat P-AR substrate and a value similar to that of the flat PMMA surface.Considering that the geometrical parameters of the nanostructures were equivalent for all the imprinted AR composites, this result indicates that increasing nanoparticle concentration does increase the stiffness owing to the higher nanoparticle loading remaining at the base of the AR nanocones rather than on the cones themselves, which as seen above, appears equivalent.Thus, this result confirms the good integration of the TiO 2 nanoparticles on the matrix and its reinforcement effect. 34anoscratches with a length of 16 μm were performed at a constant normal force of 100 μN to evaluate the scratch resistance (see the load profile in Fig. S13 †).The results are presented in Fig. 4c.The normal force during scratching was selected to maintain a maximum penetration below the height of the moth-eye nanostructures.Initially a pre-scan was performed whereby the length of the scratch was first scanned with a small contact force (2 µN) to acquire the topographical height profile.Subsequently, the scratch was produced and afterwards, a post-scan was performed at low contact force to evaluate the residual scratch depth.The arrows on the plots indicate the direction of the scans during the experiment (leftto-right for the pre-and post-scans, right-to-left for the scratch experiment).The differences between the height profiles of the pre-and post-scans indicate the permanent residual deformation left by the scratch, while the difference between the height profiles obtained during scratching and the post-scan corresponds to the elastic recovery.As can be seen in Fig. 4c, the flat PMMA surface undergoes a scratch depth of ≈35 nm but it does not suffer any permanent deformation under the selected working force because the pre and post-scans overlap completely (black and blue lines).Imprinting moth-eye features on the neat PMMA (P-AR graph) results in a substantially reduced scratch resistance, with a total scratch depth of ≈120 nm, of which, only ≈30 nm are elastically recovered leaving a residual scratch depth of ≈90 nm.However, loading the imprinted surfaces with TiO 2 nanoparticles resulted in a substantially enhanced scratch resistance with a residual scratch depth below 60 nm for the P-05T-AR substrate.Comparable results were obtained for P-01T-AR and P-1T-AR substrates (see Fig. S14 †).Consistent with the results obtained through the nanoindentation experiments, the scratch tests support the presumption that the incorporation of the nanoparticles inside the nanostructures is size constrained by the nanocone volume.SEM images of the scratch regions in Fig. S15 † show a scratch damage limited to the tip of the nanocones corroborating the nanoscratch measurements.
Conclusions
This paper has presented a practical methodology to produce broadband anti-reflective and photo-induced cleaning polymer composite surfaces with improved durability and mechanical resistance.These multifunctional films have been produced on titania polymer nanocomposite surfaces via nanoimprinting of an antireflective moth-eye inspired topography.The films presented excellent optical performance being anti-reflective and highly transparent while containing a thin titania load.Additionally all the nanocomposite films presented a self-cleaning function derived from photocatalytic activity and photoinduced hydrophilicity activated by UV light.The accelerated weathering tests indicated that with 0.1% TiO 2 loading, the film matrix does not experience an apparent photo-degradation after 600 h, maintaining higher optical quality.Conversely, a larger amount of nanoparticles induced the degradation of the PMMA nanostructure matrix, deteriorating the optical properties after 100 h of accelerated weathering.Hence, considerations have to be made on the loading quantity of titania nanoparticles based on the specific application and the desired lifetime.Alternatively, a polymer matrix more stable towards photo-degradation such as fluorinated polymers can be used.Nanomechanical tests provided evidence for an enhanced mechanical robustness of the nanocomposite AR surfaces to both normal and lateral loadings with respect to neat AR surfaces.It is perfectly plausible to adapt the fabrication of the multifunctional AR-TiO 2 composites to coating-imprinting sequential roll-to-roll processing methodology for large scale and low cost production.Moreover, the approach presented can be adopted for other polymer/nanoreinforced systems with added functionalities.
Fig. 1
Fig. 1 (a) Scheme of the fabrication process of AR moth-eye nanocones on PMMA-TiO 2 nanocomposites.(b-d) Morphological characterization of a P-05T-AR substrate surface, (b) 3D-AFM topography image, (c) SEM image of a tilted sample, (d) SEM image of the cross-section.
Fig. 2
Fig. 2 Characterization of the broadband transmission and anti-reflective properties.(a)Specular transmission spectra.(b) Total reflection spectra.(c) Photographs demonstrating the reflection reduction caused by the moth-eye structures on P-05T-AR film (right) over a PET film and a PMMA coated PET film (left).
Fig. 3
Fig. 3 (a)Photocatalytic activity for different TiO 2 loads on the composite substrates with UV radiation time measured as the decrease in concentration of Rhodamine B by photocatalytic decomposition; (b) wettability conversion on the TiO 2 composite surfaces (hydrophobic-hydrophilic) measured by changes in contact angle as a function of the UV irradiation time under wet conditions.
Fig. 4
Fig. 4 Mechanical properties of the nanocomposite surfaces measured by nanoindentation: (a) indentation load-depth curves, (b) stiffness values obtained in the elastic region, (c) scratch test results for three representative samples: PMMA flat, P-AR and P-05T-AR. | 7,420 | 2018-08-23T00:00:00.000 | [
"Materials Science"
] |
EasyPrimer: user-friendly tool for pan-PCR/HRM primers design. Development of an HRM protocol on wzi gene for fast Klebsiella pneumoniae typing
In this work we present EasyPrimer, a user-friendly online tool developed to assist pan-PCR and High Resolution Melting (HRM) primer design. The tool finds the most suitable regions for primer design in a gene alignment and returns a clear graphical representation of their positions on the consensus sequence. EasyPrimer is particularly useful in difficult contexts, e.g. on gene alignments of hundreds of sequences and/or on highly variable genes. HRM analysis is an emerging method for fast and cost saving bacterial typing and an HRM scheme of six primer pairs on five Multi-Locus Sequence Type (MLST) genes is already available for Klebsiella pneumoniae. We validated the tool designing a scheme of two HRM primer pairs on the hypervariable gene wzi of Klebsiella pneumoniae and compared the two schemes. The wzi scheme resulted to have a discriminatory power comparable to the HRM MLST scheme, using only one third of primer pairs. Then we successfully used the wzi HRM primer scheme to reconstruct a Klebsiella pneumoniae nosocomial outbreak in few hours. The use of hypervariable genes reduces the number of HRM primer pairs required for bacterial typing allowing to perform cost saving, large-scale surveillance programs.
procedure for the discrimination of sequence variants on the basis of their melting temperature. This method allows to perform bacterial typing in less than five hours 7 .
To develop a novel HRM-based typing procedure, it is necessary to: i) select one or more core genes; ii) design a primer pair in conserved regions flanking a gene portion where the melting temperature varies among the strains.
Andersson and colleagues have developed the "MinimumSNP" tool 8 , which identifies, in a gene alignment, the variable positions that can lead to a melting temperature change (called informative SNPs). MinimumSNP identifies single informative positions, not necessarily grouped in a single portion of the gene. In other words, it does not indicate which regions are more suitable for primer design: two low-variable regions neighbouring a SNP-rich informative stretch. Thus, the user of MinimumSNP has to choose one (or few) SNPs and then design primers around it (or around them).
Herein, we present EasyPrimer, a web-based tool for the identification of the gene regions suitable for primer design to perform HRM studies and any kind of pan-PCR experiments. Moreover, we validated EasyPrimer by designing HRM primers for the discrimination of clinical isolates of Klebsiella pneumoniae, an important opportunistic pathogen frequently cause of infections in humans and animals 9 .
This article was submitted to an online preprint archive 10 .
easyprimer: a tool for primers design. EasyPrimer is a user-friendly open-source tool developed to
assists primer design in difficult contexts, e.g. on an alignment of hundreds of sequences and/or on hypervariable genes. The tool uses as input a nucleotide multi-fasta file and identifies the best regions for primer design: two low variable regions flanking a highly variable one. The on-line and the stand-alone versions of the tool are freely available at https://skynet.unimi.it/index.php/tools/easyprimer. primers design. We downloaded pgi, gapA and wzi gene sequences from BigsDB database (https://bigsdb. pasteur.fr) and we run EasyPrimer to identify the best regions for primer design. The EasyPrimer output for the wzi gene is reported in Fig. 1, while the outputs relative to pgi and gapA genes are reported in Supplementary Figs. S1 and S2, respectively. Then we designed a total of four novel primer pairs: one for pgi, one for gapA and two for wzi (reported in Table 1).
High-resolution melting analysis.
In this work we considered three clinical strains collections: • the "background" collection, which includes 17 K. pneumoniae strains belonging to 17 different Sequence Types (STs); • the "outbreak" collection, which includes 11 K. pneumoniae strains isolated during a nosocomial outbreak; • the "validation" collection that includes 54 K. pneumoniae strains belonging to six of the most epidemiologically relevant STs (i.e. ST258, ST512, ST11, ST101, ST15 and ST307) 11,12 .
The strains of the background and outbreak collections were analysed using all the ten primer pairs listed in Table 1. The strains of the validation collection were subjected to HRM experiments using only the two primer pairs designed on wzi gene (wzi-3 and wzi-4 primer pairs). Four out of the ten primer pairs were newly designed in this work (see above), while the remaining six were already available in literature 7 . The obtained melting temperatures ("Tm") of the three HRM replicates and their relative average temperature ("aTm") values are reported in Supplementary Table S1. primer pairs and schemes comparison. For each of the ten primer pairs we calculated the strain distance matrix among the background collection strains based on the aTm values (see Methods). The calculated aTm distances ranged from zero to three degrees, and the median distances varied among the genes (as shown in Fig. 2). In particular, the two wzi primer pairs showed median distance values significantly higher than those obtained for many of the other primer pairs (see Supplementary Table S2 for details). EasyPrimer output for the wzi gene (563 alleles on https://bigsdb.pasteur.fr). The consensus sequence calculated from the gene alignment is reported on the x-axis. Residues under the peaks of the blue curve are highly conserved and thus suitable for primer design. Conversely the red curve increases over the highly variable regions suggested to be amplified. The grey peaks represent all the Single Nucleotide Polymorphisms (SNPs) with their own frequency. The dotted lines are used to highlight the "HRM-detectable" SNPs, i.e. the ones causing a change in the GC content. The blue arrows were manually added to show the positions of the two primer pairs designed on wzi in this work.
The median pairwise distance did not significantly change among the three schemes (Wilcoxon test with Holm post-hoc correction, p-value > 0.05) and the relative boxplot graphs are reported in Supplementary Fig. S3.
Furthermore, we compared the aTm distance matrices of wzi and MLST8 schemes for each strain pair of the background collection, subtracting the two matrices (see Fig. 3). We found that, among all the 136 possible strain pairs, 66 (48.5%) showed a higher distance for wzi scheme than MLST8 scheme. More in detail, the ST258 wzi_29 (also known as ST258 Clade 1 13 ) was better discriminated from the ST512 wzi_154 (which is part of the ST258 Clade 2 14 ) by wzi scheme than MLST8 (see Fig. 3). ST307 was better or equally discriminated from all the other strains by wzi scheme than MLST8 (except for the ST512 and ST147 strains). Similarly, ST15 (wzi_89) strain was better discriminated from all the background strains by wzi scheme than MLST8, apart from the ST147 strain (see Fig. 3). Furthermore, the ST101 strain was better discriminated by wzi than MLST8 scheme from ST258 (wzi_29), ST307, ST512 and ST15 (wzi_89). ST11 (wzi_75) was better discriminated by wzi scheme from ST15 (wzi_89), ST307, ST258 and ST512. Conversely, ST11 (wzi_75) and ST101 were better discriminated by MLST8 than wzi. Lastly, ST147 was the only ST better discriminated by MLST8 scheme than wzi for all the strains pairs (see Fig. 3).
Whole genome sequencing-based strain typing. A total of 82 K. pneumoniae strains have been subjected to WGS-based typing in this work. 24 out of 82 strains have been previously subjected to NGS sequencing as part of two published works: • 12 from Gaiarsa and colleagues 14 (10/12 for the background and 2/12 for the validation collection). For these strains, the NGS sequences were retrieved from public database.
For the remaining 58 out of 82 K. pneumoniae strains, the reads and genomic sequences were obtained in this work (see Supplementary Table S3): • 11/58 strains of the outbreak collection (all from Papa Giovanni XXIII hospital).
The wzi allele, the ST, the K-type as well as the accession numbers of these 82 K. pneumoniae strains are reported in Supplementary Table S3. WGS-based outbreak reconstruction. Ten out of the 11 outbreak isolates belonged to the ST512 while the isolate "BG-Kpn-22-18" belonged to the ST307 (see Supplementary Table S3). An alignment of 66 core-SNPs Arithmetic difference between the average melting temperature distance matrices computed among the 17 Klebsiella pneumoniae strains (selected to belong to 17 different STs) using the MLST8 scheme (eight primer pairs on seven genes) and wzi scheme (two primer pairon one gene). The heatmap colours range from blue to white to red: if the temperature distance between two strains is greater for the MLST8 than the wzi scheme the relative position on the heatmap is coloured in blue, otherwise in red.
HRM-based outbreak reconstruction. The three dendrograms obtained by hierarchical clustering on the aTms strain distances for the schemes MLST6, MLST8 and wzi are reported in Supplementary Figs. S5 and S6 and Fig. 4, respectively. All the schemes correctly discriminated the outbreak ST512 strains from the ST307 one. Notably, only the wzi scheme correctly clustered the outbreak strains with the background strain of the same ST.
Repeatability of the wzi HRM protocol. To validate the repeatability of the wzi HRM typing protocol, we included in the analysis 54 additional strains belonging to the most epidemiologically relevant clades (ST258 Clade 1, ST258 Clade 2, ST307, ST101, ST11 and ST15) 11,12 , for a total of 82 strains (see Supplementary Table S3).
For each of these clades, the aTms obtained for wzi-3 and wzi-4 primer pairs varied in a range < = 0.5 °C, corresponding to the sensitivity of the machine used for the HRM experiments (see Table 2).
Clustering analysis on wzi-3 and wzi-4 melting temperatures grouped the strains in seven clusters (see Figs. 5 and 6). Among the most epidemiologically relevant clades, all the strains of the ST258 Clade 1 (ST258 wzi_29), ST258 Clade 2 (ST258 wzi_154 and ST512 wzi_154) and ST307 were correctly clustered; while ST11 and ST101 strains fell in the same cluster. The three ST15 strains fell in two different clusters coherently to their wzi alleles: the one harbouring wzi_89 clustered alone, while the other two strains, both harbouring wzi_24, fell in the ST11/ ST101 cluster (see Figs. 5 and 6).
Discussion
High Resolution Melting (HRM) is a real-time PCR analysis for the detection of mutations and polymorphisms 3,4 , also applicable for fast bacterial typing in hospital surveillance and real-time nosocomial outbreak detection 5 . Several works applied HRM to bacterial typing, exploiting Multi Locus Sequence Type (MLST) genes 7,16,17 which have been considered the gold standard genes for bacterial typing for almost 20 years 18 . These genes have been selected to be housekeeping therefore they display low variability. In this work we show that it is possible to increase HRM discriminatory power using hypervariable genes.
On the other hand, the identification of the regions suitable for primer design can be challenging when the number of aligned sequences is high or when the gene is hypervariable. Thus, we developed EasyPrimer, a tool for the identification of the best regions for primer design for HRM analysis and, more in general, for any kind of www.nature.com/scientificreports www.nature.com/scientificreports/ pan-PCR study. EasyPrimer shows, with an easy-to-read graphical output, which are the best regions for primer design: two conserved regions flanking a highly variable one. The on-line and the stand-alone versions of the tool are freely available at https://skynet.unimi.it/index.php/tools/.
We validated the tool designing HRM primers for the nosocomial pathogen Klebsiella pneumoniae. A scheme including six HRM primer pairs for five out of the seven K. pneumoniae MLST genes was already available in literature 7 (MLST6 scheme). Thus, we used EasyPrimer to design the primers for the remaining two MLST genes (pgi and gapA), obtaining a larger scheme with eight primer pairs (MLST8 scheme). Furthermore, we designed two HRM primer pairs for the hypervariable capsular gene wzi (wzi scheme). We tested the discriminatory power of these schemes on 17 K. pneumoniae strains belonging to 17 different STs (background collection) and we used the HRM approach to study an outbreak occurred in an Italian hospital.
Notably, most of the epidemiologically relevant K. pneumoniae clades (and/or STs) emerged after large recombination events that involved the capsule locus (which includes wzi gene), often leading to K-type change. For this reason, the emergence of a novel clade/ST is often associated to wzi allele change 19 . This makes wzi gene particularly suitable for K. pneumoniae typing. Our analyses on the background collection showed a good discriminatory power for both the MLST-based and wzi-based HRM assays: both schemes successfully discriminated most of the analysed strains. Wzi scheme discriminated better than MLST8 scheme all the highly epidemiologically relevant clades (ST258 Clade 1, ST258 Clade 2, ST307, ST11, ST101 and ST15), except for the pairs ST258 Clade 2 -ST307 and ST11 -ST101 (see Fig. 3). Nonetheless, wzi scheme is able to discriminate the ST258 Clade 2 from ST307 as well (see Fig. 4). Conversely, wzi scheme does not discriminate ST11 from ST101 (see Figs. 5 and 6). The latter may represent a minor flaw of the wzi HRM protocol as the two STs are mostly isolated in geographically distant areas of the globe (namely: ST11 in Asia 20 , ST101 in Europe-Africa 21 ).
Clustering analysis on the 82 strains, including multiple strains from the same clade (see Materials), allowed to evaluate with more precision the discriminatory power of the wzi HRM protocol. The analysis clearly showed that the protocol is able to discriminate five of the six most epidemiologically relevant K. pneumoniae clades, discriminating ST258 Clade 1, ST258 Clade 2, ST307, ST11/ST101 and ST15 (see Figs. 5 and 6). In our dataset we found strains of the ST15 and ST11 harbouring different wzi alleles. This is not surprising, considering that the capsule locus (which contain the wzi gene) is a recombinational hotspot in ST11 19 . Wzi scheme discriminated among the different ST15 strains present in the collections, according to the different wzi alleles they harbour (see Figs. 5 and 6). This highlights the benefits of using hypervariable genes instead of MLST genes in typing methods: e.g. wzi HRM protocol can rule out an ST15 outbreak of strains harbouring different wzi alleles, any MLST-based protocol cannot.
As stated above, K. pneumoniae clades are often associated to specific wzi alleles and K-types. Despite the wzi HRM protocol was designed on wzi gene, it correctly discriminates most of the epidemiological relevant clades. Furthermore, we found that every K-types correspond to a specific wzi allele (see Supplementary Table S3).
Moreover, the analysis of the 82 strains clearly showed that the wzi HRM protocol is highly repeatable: wzi-3 and wzi-4 aTms ranged within 0.5 °C (the machine sensitivity) among the strains of the same clade (see Table 2). For this study, dozens of independent HRM experiments have been performed in different months by two different operators (M.P. and A.P.). The observed stability of HRM aTms for each clade clearly shows that the results of wzi HRM protocol are portable. This makes the method suitable for studies involving several isolates, such as large hospital surveillance programs.
Additionally, we want to highlight that the observed HRM discriminatory power was obtained using a BioRad CFX Connect real-time PCR instrument (BioRad, Hercules, California): a machine not specifically designed for HRM experiments but for real-time PCR, with a melting temperature sensitivity of 0.5 °C (i.e. a lower sensitivity compared to HRM machines).
We applied the wzi scheme to the reconstruction of a nosocomial outbreak occurred in an Italian hospital. During the outbreak, 11 patients resulted colonized or infected by K. pneumoniae and the WGS typing revealed that the isolates belonged to two different clones. These clones were identified on the basis of core SNP distance (SNP distance < 5) and MLST profile (one isolate belongs to the ST307 and ten isolates to the ST512). As shown in Fig. 4, the wzi scheme not only correctly discriminated the outbreak isolates of the two clones but it also clustered them with the background isolates of the corresponding ST profile.
During the last years, WGS has revolutionized clinical microbiology, allowing the precise description of bacterial genomic features in few days (including the presence of resistance and/or virulence factors). Despite this, its application during real-time outbreak reconstructions still shows some limits: the time required to be completed, the cost and the necessity of qualified personnel for library preparation, bioinformatic analyses and results interpretation. Indeed, the complete sequencing of a bacterial strain genome costs at least ~100 euros (using an Illumina MiSeq machine) and requires one or two days for library preparation and 5-36 hours for sequencing. During the first days of a nosocomial outbreak the number of cases still increases slowly. In this time frame, it is crucial to quickly understand if the bacterial strains are genetically related, and if the clone is spreading in the nosocomial environment. In this situation HRM is a "first-line" typing technology to figure out when an Figure 5. Strain-to-strain network of the 82 isolates analysed, generated on the basis of wzi-3 and wzi-4 HRM melting temperatures. Two strains were connected if both wzi-3 and wzi-4 gave difference in melting temperature < 0.5 °C. Clusters were identified as separated sub-networks on the strain-to-strain network and they were named from the major Sequence Type they include.
Scientific RepoRtS | (2020) 10:1307 | https://doi.org/10.1038/s41598-020-57742-z www.nature.com/scientificreports www.nature.com/scientificreports/ outbreak is starting. Indeed, HRM is less precise than WGS but it can be reliable for a fast, preliminary bacterial typing, fundamental in the first days of a nosocomial outbreak. If the outbreak is identified, WGS could be used to further investigate the transmission dynamics. HRM assay represents a fast, simple and time/cost saving approach for bacterial typing, allowing to analyse several bacterial samples per days. Furthermore, this technique does not require advanced skills in molecular biology and the results can be analysed without the use of any specific software. This method can be useful also in veterinary and dairy farming settings: K. pneumoniae is a relevant veterinary pathogen and one of the most frequent cause of mastitis in dairy cattle 9 .
We found that the discriminatory power of an HRM scheme does not strictly depend on the number of genes but also on their genetic variability. Indeed, comparing the MLST6 and MLST8 schemes, we found that the median distance among the strains did not change significantly. Wzi scheme contains two primer pairs and this reduces drastically the amount of time and costs required for typing. For instance, using only two primer pairs on a 96-well PCR plate, it is possible to type 15 isolates per run (five hours, including DNA extraction, HRM run and analysis of results) with a cost of ~5 euros each. This makes the HRM a feasible method for real-time surveillance and for a preliminary typing step in large epidemiological studies. Lately, Multi-Drug Resistance (MDR) K. pneumoniae strains have become a major burden for public health worldwide. Despite WGS represents an important Figure 6. On the left the dendrogram obtained from the strain-to-strain network reported in Fig. 5. In the middle, the average melting temperatures of wzi-3 and wzi-4 primer pairs, the Sequence Type, the wzi allele and the K-type of the 82 isolates analysed. On the right, the names of the clusters identified by network analysis, corresponding to the clusters in Fig. 5. tool for precise bacterial typing, it remains too demanding for developing countries healthcare systems. Low cost and simple protocols, as the wzi HRM typing proposed here, represent a real opportunity for surveillance programs.
The use of hypervariable genes in HRM-based bacterial typing, such as wzi in K. pneumoniae, can drastically increase the discriminatory power of the method. With the large number of genomes available in databases, it is now possible to find the most variable genes for a species. Unfortunately, it is not easy to identify the best regions to design primers in such hypervariable genes, particularly when hundreds of different alleles are available. EasyPrimer can represent a useful tool to overcome this limit.
Methods
isolates collections. We considered three strain collections: the background, the outbreak and the validation collections. The background collection includes 17 strains belonging to 17 different STs retrieved from two previously WGS typed bacterial collections: nine strains from Gaiarsa and colleagues 14 and eight strains form Gona and colleagues 15 (for details see Supplementary Table S3). The outbreak collection includes 11 K. pneumoniae isolates gathered during a 16 days nosocomial outbreak occurred in April 2018, in the Papa Giovanni XXIII hospital (Bergamo) (For details see Supplementary Tables S3 and S4). The validation collection includes 54 K. pneumoniae isolates belonging to six of the most epidemiologically relevant clades 11,12 : • 17 strains belonging to ST307. • 15 strains belonging to ST258 Clade 2, including ST258 wzi_154 and ST512 wzi_154.
• two strains belonging to ST11.
• two strains belonging to ST15. 45/54 strains were isolated at San Raffaele hospital (Milan), 2/54 strains were isolated at Papa Giovanni XXIII hospital (Bergamo), 4/54 retrieved from the K. pneumoniae collection of Gona and colleagues 15 3/54 retrieved from the K. pneumoniae collection of Gaiarsa and colleagues 14 .
Neither ethics committee approval, nor informed consent were required as all collected data are fully anonymized, there was no contact with patients and/or their families and no interventions or changes to treatment and management were made, in accordance with institutional guidelines.
DNA extraction and whole-genome sequencing. The genomic DNA of the 45 strains isolated from San Raffaele hospital (Milan) were extracted using Maxwell 16 Cell DNA purification kit. The extracted DNA was sequenced using the NextSeq. 500 platform with 2 × 150 bp paired-ends runs, after Nextera XT library preparation.
The genomic DNA of the 13 strains isolated from Papa Giovanni XXIII hospital (Bergamo) was extracted using the DNeasy blood and tissue kit (Qiagen, Hilden, Germany) following the manufacturer's instructions. The extracted DNA was sequenced using the Illumina Miseq platform with a 2 × 250 bp paired-end run, after Nextera XT library preparation.
The genomic DNA of the 12 strains previously sequenced by Gaiarsa and colleagues 14 were extracted using QIAsymphony Virus/Pathogen minikit, version 1 (Qiagen, Hilden, Germany) with the automated instrument QIAsimphony (Qiagen, Hilden, Germany) according to manufacturer's instructions.
The genomic DNA of the 12 strains previously sequenced by Gona and colleagues 15 were extracted using the DNeasy blood and tissue kit (Qiagen, Hilden, Germany) following the manufacturer's instructions.
Details about strains hospital isolation are reported in Supplementary Table S3.
High resolution melting primer design using easyprimer. The EasyPrimer tool was developed for the identification of the most suitable regions for primer design in HRM and, more in general, in pan-PCR experiments. Briefly, the tool starts from gene sequences in multi-fasta format. The sequences are considered as not aligned by default and they are aligned by Muscle software 22 as the first step of the pipeline (see Supplementary Fig. S7 and Supplementary Note S1). The user can also decide to submit aligned sequences (in multi-fasta format) and skip the alignment step. EasyPrimer evaluates the amount of genetic variation for each position of the alignment and identifies the most reliable regions for primer design. EasyPrimer flags as good candidates for primer design two conserved regions flanking a highly variable one (taking into consideration, in advance, the optimal lengths of primers and amplicon). The user can decide either to evaluate the variability of the amplicon considering HRM-detectable SNPs only (the best option for HRM primer design) or all the SNPs (the best setting for pan-PCR experiments). A detailed description of the algorithm is reported in the Supplementary Note S1.
To develop an HRM-based protocol for K. pneumoniae typing, we focused on the seven MLST genes and on the hypervariable capsular gene wzi 23 . The HRM primer pairs for five out of the seven K. pneumoniae MLST genes were already available in literature 7 (infB, mdh, phoE, rpoB and two pairs on tonB). For the remaining two MLST genes (pgi and gapA) and for the wzi capsular gene (two primer pairs) the primers were designed using EasyPrimer. For each gene, the sequences were downloaded from the BigsDB database (https://bigsdb.pasteur.fr, 218 alleles for pgi, 183 for gapA and 563 for wzi), EasyPrimer was run and primer pairs were designed on the basis of its output.
High-resolution melting assays. We performed HRM assays using the genomic DNA extracted from each of the 82 K. pneumoniae strains included in this work. On the strains of the background and outbreak collections we used each of the ten primer pairs mentioned above. On the validation collection strains we used wzi-3 www.nature.com/scientificreports www.nature.com/scientificreports/ and wzi-4 primer pairs only. HRM analyses were performed on the BioRad CFX Connect real-time PCR System (BioRad, Hercules, California). Each 10 µl reaction contained: 5 µl of 2x SsoAdvanced Universal SYBR ® Green Supermix (BioRad, Hercules, California), 0.4 µl of each primer (0.4 µM) and 1 µl of template DNA (25-50 ng/ µl). The thermal profile was as follows: 98 °C for 2 min, 40 cycles of [95 °C for 7 s, 61 °C for 7 s, and 72 °C for 15 s], 95 °C for 2 min, followed by HRM ramping from 70-95 °C with fluorescence data acquisition at 0.5 °C increments. Three technical replicates were performed for each strain and for each gene analysed. Negative controls were added in every run and for each gene.
comparison of the HRM primer pairs and schemes. We compared the discriminatory power of the ten HRM primer pairs on the 17 background collection strains. For each primer pair we calculated the average melting temperatures (aTms) of the three replicates for each strain and the relative strain distance matrix based on the obtained aTms. Thus, we compared the discriminatory power of the different primer pairs by comparing the relative distance matrix values using Wilcoxon test with Holm post-hoc correction.
Furthermore, we grouped the primer pairs in three schemes (MLST6, MLST8 and wzi) and we compared the relative strain distance matrices using Wilcoxon test with Holm post-hoc correction. The scheme compositions were as follows: the MLST6 scheme included the six primer pairs proposed by Andersson and colleagues 7 for five MLST genes (with two primer pairs for tonB); the MLST8 included all the MLST6 primer pairs, the primers for pgi and gapA (newly designed in this work using the EasyPrimer tool); the wzi scheme included the two primer pairs for the wzi gene (newly designed in this work). For details see Table 1 and Fig. 2.
Then, we compared the discriminatory power of MLST8 and wzi schemes by subtracting the relative distance matrices (wzi -MLST8) and studying the obtained matrix with a heatmap.
All these analyses were performed using R (https://www.r-project.org/) and the R libraries Ape and Gplots.
HRM-based outbreak reconstruction.
From the aTms of the outbreak and background collections we calculated the distance matrices for MLST6, MLST8 and wzi primer schemes (for more details see above) and clustered the strains using the hierarchical clustering method implemented in the Hclust function in R.
Repeatability of the wzi HRM protocol.
To test the repeatability of the wzi HRM typing protocol we analysed the wzi scheme aTms for all the strains of the three collections (17 background strains, 11 outbreak and 54 validation, see above). This allowed to compare the wzi-3 and wzi-4 aTms of multiple strains for each of the most epidemiologically relevant clades 11,12 (eight ST258 clade 1, 26 ST258 Clade 2, 19 ST307, 12 ST101, two ST11 and three ST15 strains) (see Table 2 and Supplementary Table S3). We clustered the strains on the basis of wzi scheme aTms. Given the 0.5 °C sensitivity of the machine, we considered the strains with differences both in wzi-3 and wzi-4 aTMs < 0.5 as indistinguishable. Thus, we built a strain-to-strain network, in which the indistinguishable strains pairs were connected. Clusters were extracted from the network using the decompose igraph R function (https://www.r-project.org/). Lastly, the strain-to-strain network was converted to a dendrogram and merged to wzi aTms in a heatmap plot, using R (https://www.r-project.org/). | 6,491.8 | 2020-01-28T00:00:00.000 | [
"Computer Science",
"Medicine",
"Biology"
] |
Single-cell transcriptome of Nepeta tenuifolia leaves reveal differentiation trajectories in glandular trichomes
The peltate glandular trichomes (PGTs) on Nepeta tenuifolia leaves can secrete and store bioactive essential oils. ScRNA-seq is a powerful tool for uncovering heterogeneous cells and exploring the development and differentiation of specific cells. Due to leaves rich in PGTs, the young leaves were used to isolated protoplasts and successfully captured 33,254 protoplasts for sequencing purposes. After cell type annotation, all the cells were partitioned into six broad populations with 19 clusters. Cells from PGTs were identified based on the expression patterns of trichome-specific genes, monoterpene biosynthetic genes, and metabolic analysis of PGT secretions. The developmental trajectories of PGTs were delineated by pseudotime analysis. Integrative analysis of scRNA-seq data from N. tenuifolia leaves and Arabidopsis thaliana shoot revealed that PGTs were specific to N. tenuifolia. Thus, our results provide a promising basis for exploring cell development and differentiation in plants, especially glandular trichome initiation and development.
The peltate glandular trichomes (PGTs) on Nepeta tenuifolia leaves can secrete and store bioactive essential oils. ScRNA-seq is a powerful tool for uncovering heterogeneous cells and exploring the development and differentiation of specific cells. Due to leaves rich in PGTs, the young leaves were used to isolated protoplasts and successfully captured 33,254 protoplasts for sequencing purposes. After cell type annotation, all the cells were partitioned into six broad populations with 19 clusters. Cells from PGTs were identified based on the expression patterns of trichome-specific genes, monoterpene biosynthetic genes, and metabolic analysis of PGT secretions. The developmental trajectories of PGTs were delineated by pseudotime analysis. Integrative analysis of scRNA-seq data from N. tenuifolia leaves and Arabidopsis thaliana shoot revealed that PGTs were specific to N. tenuifolia. Thus, our results provide a promising basis for exploring cell development and differentiation in plants, especially glandular trichome initiation and development.
Introduction
The leaf cell types in dicotyledonous plants are relatively conservative and are composed of mesophyll, vascular, and epidermal cells, despite the leaves varying in size, shape, and color in the different species (Ramsperger et al., 1996). Specific plant organs are used for many medicinal purposes. The leaves of Artemisia annua, Mentha haplocalyx, Perilla frutescens, Pogostemon cablin, Lavandula angustifolia, and Ocimum basilicum, are widely used in medicines, cosmetics, and other industries (Giuliani et al., 2009;Ahmed andTavaszi-Sarosi, 2019: Li et al., 2020). In aromatic medicinal plants, leaves are covered with special multicellular structures, trichomes, which are divided into glandular trichomes (GTs) and non-glandular trichomes (NGTs) depending on their secondary metabolism capability (Liu et al., 2019). GTs are known as cell metabolic factories due to their powerful biosynthetic secretion and accumulation capabilities (Tissier, 2012). For example, the antimalarial drug, artemisinin, is produced in A. annua GTs, and pharmaceutical essential oils of M. haplocalyx accumulate in the GTs (Tissier, 2012). Some genes controlling GTs initiation and development have been identified, such as AaMXITA1 AaHD1, and AaHD8 in A. annua, and SlMX, and SlMYC in tomato (Chalvin et al., 2020). However, our knowledge of these biological process is still limited.
Nepeta tenuifolia is an annual plant of Lamiaceae family, which is widely used as traditional medicine in Asia (Fung and Lau, 2002). Volatile oil is considered the main active ingredient of N. tenuifolia, which has antibacterial, anti-inflammatory, antiviral, and other pharmacological effects. For its excellent antibiotic effect, N. tenuifolia has played a crucial role in the treatment of SARS, COVID-19 and other pneumonia (Huang et al., 2020;Chang et al., 2021). Monoterpenes are the most common constituents of N. tenuifolia oils. Its volatile oil has been mainly accumulated in peltate GTs (PGT), a type of GT widely distributed on the leaves, and the content of volatile oil is positively related to PGTs density (Jiang et al., 2016). Promoting PGTs initiation is a potential strategy to increase the volatile oil content of N. tenuifolia. Hence, investigations on the molecular basis of GTs initiation and development are needed in N. tenuifolia and other medicinal plants.
scRNA-seq has recently been performed in the plant kingdom to investigate plant cell fate decisions and to unravel cell continuity and heterogeneity, which were not detected by traditional bulk RNA-seq. These technologies have been used to isolate cells and include glass microcapillaries, flow cytometric sorting, laser microdissection, and enzymatic hydrolysis (Dinneny et al., 2008;Efroni et al., 2015;Frank and Scanlon, 2015;Han et al., 2017). For plant cells, the existence of cell walls has hampered the acquisition of protoplasts, and the limited prior knowledge of cell identity has become a technical obstacle for plant scRNA-seq. Thus, the application of scRNA-seq is limited to a few plant species, such as Arabidopsis thaliana, rice, and maize (Nelms and Walbot, 2019;Zhang et al., 2019;Zhang et al., 2021a;Zhang et al., 2021b), and enzyme-isolated protoplasts are mostly used in plants . For example, the scRNA transcriptome landscape of A. thaliana vegetative shoots reconstructed the continuous developmental trajectories of epidermal cells and vascular tissues, exploring new regulators of shoot development (Zhang et al., 2021b). In addition to discovering new cell types, scRNAseq can also be used to explore the regulation of cellular gene networks, as well as the trajectories of transcriptional changes behind cell fate selection. Overall, scRNA-seq has great potential for plant physiology and development (Seyffert et al., 2021). Recent studies have led to significant advances in cell lineage trajectories, so scRNA-seq may help us to uncover GT cells differentiation and development (Nelms and Walbot, 2019;Zhang et al., 2019;Zhang et al., 2021a;Zhang et al., 2021b).
This study presents the first scRNA-seq atlas of leaves of N. tenuifolia in medicinal plants. In total, the leaf cells were divided into 19 cell clusters corresponding to six broad populations, and specific marker genes for the main cell types were inferred. We annotated the PGT cell types and delineated their pseudo-time trajectories to explore their differentiation and development. Comparing the scRNA-seq data of available A. thaliana shoots and N. tenuifolia leaves revealed that the conservation and divergence of different species and PGTs were specific to N. tenuifolia. The scRNA-seq data paved the way for improving the medicinal quality of N. tenuifolia and constructing a molecular regulatory network for GT development.
Results
Protoplast isolation from N. tenuifolia leaves To select suitable plant materials, cell isolation (i.e., protoplasting) was performed on young leaves from 10-d, 15d, 25-d, 30-d, 35-d, and 40-d old plants. The young leaves near the shoots were harvested ( Figure S1) and were further cut into small strips (~1 mm in length, m = 0.5 g), and the leaf strips were added to 5 mL enzyme solution containing cellulase and macerozyme. The mixture was shaken at 60 rpm for 2.5 h to digest the cell wall to obtain protoplasts (plant cells without cell walls, Figures S2, S3). Protoplast viability and counts were assessed using 0.4% trypan blue staining before nextgeneration scRNA-seq. The number of protoplasts is listed in Table S1. Live protoplasts were not stained with trypan blue ( Figure S2I). At the same time, the number of PGTs on sampled leaves were also calculated (Table S1). Based on the number of live protoplasts and PGTs, together with impurities and broken protoplasts, the 25-d-old plants seemed to be a better selection for scRNA-seq of N. tenuifolia. Final protoplasts of approximately 6 × 10 5 /mL per sample were used for the 10x Genomics scRNA-seq assays ( Figures 1A, S3A, B).
Generation of a cell atlas of N. tenuifolia young leaves The scRNA-seq libraries were generated from leaf protoplasts, and data were pre-filtered at both the cell and gene levels with 33,254 single-cell transcriptomes obtained from three biological replicates (JJ1, JJ2, and JJ3). In detail, 15,672 cells with 21,582 genes for JJ1, 7352 cells with 21,314 genes for JJ2, and 10,275 cells with 21,501 genes for JJ3 were successfully detected ( Figure S4 and Table S2). After deleting low-quality cells ( Figure S6), the sequencing data were visualized by reducing dimensionality through principal component analysis (PCA), and cell clusters were visualized by tdistributed stochastic neighborhood embedding (t-SNE) (Laurens and Hinton, 2008) and uniform manifold approximation and projection (UMAP) (Mcinnes and Healy, 2018;Becht et al., 2019). Three replicates, JJ1, JJ2, and JJ3, exhibited similar proportions of cell identity in UMAP and t-SNE, revealing reproducibility in data quality ( Figure S5). With no need for known markers, significant principal components were first constructed using Seurat (Satija et al., 2015) in a knearest neighbor graph of the cells. Then, it optimized the edge weight between any two cells according to the shared overlap in the Jaccard distance. Significant principal components were ultimately partitioned into 19 transcriptionally distinct clusters, from 33,254 high-quality cells from the young leaves of N. tenuifolia. A comparison of differentially expressed genes (DEGs) among the clusters revealed a series of cluster-enriched genes in each cluster ( Figure S7A and Table S3). As there were very few known marker genes for N. tenuifolia, the genes that were orthologs of Arabidopsis known marker genes (method homologous gene annotation) were applied to annotate these clusters ( Figures 1D, S7B and Table S4).
A continuum of epidermal cells differentiating towards glandular trichomes
GTs are types of trichomes capable of producing various secondary metabolites, mainly terpenoids and are multicellular structures derived from aerial epidermal cells (Duke and Paul, 1993;Huchelmann et al., 2017). PGTs, types of GTs on N. tenuifolia, are the predominant source of oil and contain bioactive ingredients with high medicinal and economic value (Liu et al., 2018). Many efforts have been made to promote secondary metabolic productivity in GTs such as artemisinin (Schuurink and Tissier, 2020;Qin et al., 2021). ScRNA-seq has a powerful ability to explore the continuous developmental and differentiation trajectory, as well as key genes related to cell differentiation (Ryu et al., 2019;Shulse et al., 2019;Zhang et al., 2019). Therefore, scRNA-seq is a useful tool for investigating the molecular mechanisms underlying multicellular GT initiation and differentiation.
The EC population was annotated preliminarily using known marker genes. We aimed to deduce the developmental trajectory of the GTs. Re-clustering of clusters 5, 7, 16, and 17, belonging to the epidermis/trichome population, and cluster 13, belonging to the guard cell population, revealed 13 sub-cell clusters named E0-E12, which improved the accuracy of cell clustering ( Figure 3A). The Figure 3A was EC reclusters named to be new reclusters E0-E12; the Figure 3B was named by EC clusters: cluster 5, 7, 13, 16, 17, which showed the relationship between EC reclusters and EC clusters. In the UMAP compared Figures 3A, B, the GC population was divided into two subclusters, 5 and 7; cluster 7 was re-clustered as E2, E4, and E8, and cluster 17 was also clustered in one, E11 ( Figures 3A, B). Interestingly, E10 was generated from cluster 5, and topologically connected to two trajectories, E9 and E12, in the UMAP plot, dominated by the cells in cluster 16.
In UMAP, E10 topologically bifurcated into two trajectories, E9 and E12 ( Figure 4A). To validate that E10 may differentiate into E9 or E12, pseudotime analysis was performed by ordering the cells of E10, E12, and E9, using Monocle 2, to reconstruct the trajectory ( Figures 4A, B). The inferred pseudotime analysis exhibited gradual transitions from the cells in the E10 towards two directions, E12 (PGTs) and E9 (other trichomes), which was consistent with the distribution distance on UMAP (Figures 4A, B). Monocle 2 analysis, colored by samples, showed that the cells from the three samples had no preference ( Figure 4C). The GO analysis of E10 showed enriched terms such as "regulation of cell development," "developmental cell growth," and "regulation of cell morphogenesis involved in differentiation" (Table S6 and Figure S12). According to the orthologs of Arabidopsis, upregulated genes in E10 were related to cell wall development (Sch000000997, Sch000013032) (Ringli et al., 2001;Adams et al., 2014) and response to defense (Sch000019518, Sch000015198) (Table S7). These findings indicate that E10 cells may be in the stage of development and differentiation towards trichomes. The genes related to p-menthane monoterpene biosynthesis were visualized along pseudotime, including DXS, DXR, CMS, CMK, MCS, HDS, HDR, IDI, GPPS, LS, L3OH, IPD, IPR, suggesting that these metabolic genes were expressed at the late developmental stage of PGTs ( Figure S13).
The differentially expressed genes (DEGs) across pseudotime (q value < 0.01) of cell differentiation fate in trichomes (E9, E10, E12) are shown in Figure 4D. These genes were clustered into four modules, in which the cell differentiation state began at cluster 1 and through towards cluster 2 (E12), or vice versa, cluster 3 (E9), consistent with their pseudotime trajectories (Table S8). A survey of our scRNA-seq dataset revealed that these DEGs may regulate the differentiation and development of PGT or other GTs. For example, the expression of Sch000025057 and Sch000027347 (cluster 1 in Figure 4D) gradually increased along branch 2 towards E12; Sch000027711 and Sch000007579 (cluster 2) were expressed from root to branch 2; Sch000027205 and Sch000017846 (cluster 3) were elevated at the late developmental stage of E9; progressive increases in Sch000018884 and Sch000021906 (cluster 4) expression were observed in E12 and E9, respectively (Figure S14), and the function of these genes needs further investigation. Thus, the Compare scRNA-seq between N. tenuifolia and Arabidopsis We explored the conservation and divergence of leaf cell types between N. tenuifolia and Arabidopsis. To this end, we merged and grouped the above species' scRNA-seq datasets and performed cell clustering analysis because the Arabidopsis shoot scRNA-seq datasets were already available which including two shoot apex samples with one leaf sample (Zhang et al., 2021b). Unfortunately, trichome cells have not been isolated from the scRNA-seq data of Arabidopsis. In total, the combined analyses generated 88,952 cells grouped into 24 panoramic cell clusters (P0-P23), with cells from Arabidopsis accounting for 63.10% and cells from N. tenuifolia 36.90%. Most of the cell clusters highly overlapped in UMAP (Figures 5A, B). Next, we annotated these clusters as MC (clusters P0, P1, P3, P5, P7, and P8), EC (clusters P6, P12, P14, P16, P17, and P21), shoot meristematic cell (SMC) (clusters P11 and P13), PC (clusters P4 and P10), VC (clusters P9 and P15 for xylem, XP; clusters P2 and P22 for phloem, PP), GC (cluster P18), CC (cluster P19), shoot endodermis (SEn, cluster P20), and U. A. (cluster P23) (Tables S9, S10) based on the known Arabidopsis marker genes, cluster-specific genes, and homologous genes in N. tenuifolia.
EC clusters P6, P12, P14, P16, P17, and P21 were further analyzed in N. tenuifolia and Arabidopsis. These cells were re- clustered into 10 subclusters named PE0-9 ( Figures 6A, B and Figures S15A, B). PE0 seemed to be divided into two clusters, although they were then clustered as one cluster ( Figure 6C and Figure S15C). PE2 is specific to N. tenuifolia. We explored the cells of E12 and E9, noted as PGTs and other trichomes, in the overlapped scRNA-seq atlas of EC. The cells of E12 were specifically enriched in PE2, while E9 cells were enriched in PE0 (Figures 6B-E and Figures S15B-E). These results suggest that cells related to PGTs identified in N. tenuifolia were unique, compared to Arabidopsis, while other epidermal cells highly overlapped, such as GC (PE4). Results from the above revealed that comparison of scRNA-seq data of different species can explore unique cell types and species characteristics, while playing an important role in species conservation and evolution.
Discussion
scRNA-seq technology has been successfully applied in the field of plant biology, thus revolutionizing our view of the identification of cell types and essential cellular activities, in plant development and differentiation at the single-cell level. In this medicinal plant study, we initially constructed a single-cell transcriptome landscape of young N. tenuifolia leaves and recontrasted the cell fate differentiation of PGTs. We annotated the cell clusters of the leaves using homologous known marker genes of Arabidopsis and in situ hybridization. This study revealed the scRNA-seq applicability of non-model plants, and could facilitate future exploration of GTs cell fate determination in medicinal plants.
Single cell isolation challenge and improvement
The first step in scRNA-seq is the dissociation of specific tissues into single cells. Enzyme-induced protoplast generation methods for removing cell walls are commonly used in plants (Seyffert et al., 2021). As the quality of protoplasts can directly affect scRNA-seq data, protoplast isolation methods must be explored to further determine the ideal conditions such as the selection of plant tissue, plant growth stage, enzyme type and concentration, and isolation time. The composition of the cell wall and cuticle varies greatly among different plants, therefore, protoplasting protocols should be tried and modified accordingly. Moreover, the cell size greatly varied among different plants and tissues, creating a major problem in the cell capture for the 10x Genomics Single Cell Instrument.
We intended to dissect the differentiation trajectories of PGTs; thus, the selection of the leaf stage, was more important. Protoplasting was performed on young leaves from 10-d, 15-d, 25-d, 30-d, 35-d, and 40-d calculated simultaneously. The statistics implied that the number of PGTs increased with plant growth, and protoplast viability was similar within 35 days, but dramatically decreased at day 40. After several experiments, we found that protoplast from 25-d old plants were purer and active ( Figure S3). We tried to obtain as many protoplasts of PGTs as possible to ensure the quality of the protoplasts. However, dissociation of trichomes was difficult. In our protoplast pools, E12 and E9 (defined as PGTs and other GTs, respectively) only had 45 and 96 cells, respectively, whereas the leaf trichome cells of Arabidopsis were lacking in scRNA-seq data because trichome cells were somewhat resistant to protoplasting (Zhang et al., 2021b). The trichome cells are covered with plenty of cutin and wax, creating a hurdle for single-cell preparation (de Luna et al., 2020;Fich et al., 2020;Konarska and Lotocka, 2020). Extraction of the nucleus and single nucleus RNA sequencing (snRNA-seq) may provide solutions for the above problems to capture different cell types regardless of cell size (Habib et al., 2017). However, snRNA-seq may lack genetic information of the cytoplasm, and it remains unclear whether snRNA-seq contains sufficient biological information to distinguish cell types at whole-cell resolution in plants. This gap hints at the urgent need for the development of a suitable and universal protocol for single-cell preparation of plants.
Identification and differentiation of PGTs
UMAP can efficiently preserve the continuity of cell clusters and cluster locations related to cellular development (Becht et al., 2019). In the reEC, clusters 5, 7, 13, 16,17 were re-generated into 13 sub-clusters, E0-E12. Cluster 16, annotated as trichomes, was further divided into E9 and E12. The new cluster, E10, was isolated from cluster 5, connected to E9 and E12 ( Figure 3A), suggesting that E10 may serve as a cell containing differentiation potential for trichomes. In favor of this hypothesis, the pseudotime trajectory confirmed that E9 and E12 were differentiated from E10 and those in E9 and E12 in the end states ( Figures 4A, B). Marker gene expression and associated biological processes suggest that E12 consists of PGTs. The DEGs in the inferred trajectory were clustered into four clusters based on their expression patterns ( Figure 4D). The significant GO term for cluster 3, with high expression in E9, enriched "cell wall macromolecule metabolic process," "cell wall macromolecule metabolic process," and "wax metabolic process," which is like the GO of rice atrichoblasts and tomato NGTs (Thoma et al., 1993;Zhang et al., 2021a). Interestingly, GT-enriched GO terms were also related to fatty acid biosynthetic and lipid biosynthetic processes (Thoma et al., 1993;Zhang et al., 2021a). It was noted that monoterpene biosynthesis genes were specifically expressed in E12, although E9 was enriched in GO terms of isopentenyl diphosphate and farnesyl diphosphate. Thus, we speculated that cells in E9 may be a mixture containing NGTs and other GTs, due to the few metabolites detected in other GTs of N. tenuifolia, and the challenges of isolating other GTs such as digitiform GTs and capitate GTs. Therefore, further research is required to annotate the E9 cell type. To confirm the cell cluster identity of PGT, we attempted to locate genes related to DXS, LS, and L3OH, which were highly expressed in E12 using in situ hybridization; however, these genes were specifically expressed in both PGTs and epidermis. This could be related to the influence of background signals, and multiple transcripts of one gene. To obtain more accurate gene localization, we will prepare immunocytochemical localizations for these genes using a polyclonal antibody, which has been successfully applied in peppermint, with key genes localized to the secretory cells of PGTs (Turner et al., 2012).
Candidate genes may be involved in trichome differentiation and development
Pseudotime trajectory analysis of trichomes, implied that E10 could differentiate into PGTs and other trichomes. Highly expressed genes along the trajectory branch point to E12, may be candidate genes involved in PGTs differentiation and development ( Figures S14A, B). In addition, we explored the homologous gene expression of reported genes regulating trichomes in pseudotime trajectory, such as WOLLY of tomato, MXITA1 of Artemisia annua. The homologous gene of AaMXITA1 and SlWOLLY were specifically expressed at the end of branch 2 ( Figures S16A, B), which played an important role in multicellular GTs (Chalvin et al., 2020) .Moreover, CUT1 and FLP1 were essential for the synthesis of cuticular waxes Dong et al., 2022), which were highly expressed in branches 1-E9 compared to branch 2 ( Figures S16C, D). Both GTs and NGTs originate from the epidermis and are regulated by precise gene regulatory networks. Their differentiation is promoted by some signals like environmental stimuli and phytohormones . GTs were wildly distributed in the plant kingdom, which were regarded as biofactories for their unique capacity to synthesize, secrete or store a wide array of valuable metabolites (Huchelmann et al., 2017). These specific metabolites were used in drugs, food additives, natural insecticides or fragrances with significant commercial value (Feng et al., 2021). Therefore, GTs has the potential to be further developed and utilized as a biochemical factory to enhance the biosynthesis of these natural metabolites. The PGTs in N. tenuifolia was one type of GTs, which the volatile compounds were stored in the subcuticular storage space, usually existed in Lamiaceae like Mentha piperita, Salvia fruticosa, Cistus creticus, and so on. These plant were produced into perfume, pigments, and medicines with great economic value. In the study, we speculated the differentiation of PGT at the single cell level, and identified some candidate genes related GT differentiation. These results may provide valuable information of molecular regulatory network of GTs and lay the foundation of increasing the density of GTs to increase the contents of special compounds.
Prospect of scRNA-seq in plant science
Sequencing at the single-cell level has shown great potential for the development of specific tissues and the identification of cell types. Although plant tissues have complex bio-contexts, scRNA-seq can examine individual cell types and identify new cell types with the richness of plant background data (Rodriguez-Villalon and Brady, 2019;Rich-Griffin et al., 2020). More complex gene regulatory principles can be explored and explained with the development of scRNA-seq technology and computer algorithms (Hebenstreit, 2013;Cortijo et al., 2019). Although isolating high-quality individual cells from various plant tissues remains difficult, separation methods with wide applicability are being developed, such as the extraction of nuclei (Denisenko et al., 2020). It is expected that scRNA-seq will be widely used in plants, particularly crops and medicinal plants.
Furthermore, scRNA-seq identifies specific cell types by combining cluster and pseudotime analyses, extending cell heterogeneity, and revealing mechanisms of plant development, which improves the investigation of the regulatory gene network of good traits and development of medicinal parts in crops (Jean-Baptiste et al., 2019;Shulse et al., 2019). Therefore, it plays an important role in discovering new resources for natural plant population phenotypes, cultivating crops with good traits, and improving the germplasm of medicinal plants (Hirsch et al., 2014;Lei et al., 2021). Specific characteristics of plant cell types are adapted to the environment. Cell stage changes occur when subjected to biological or abiotic stress. Based on cell heterogeneity, scRNAseq can explain phenotypic changes or changes in cell characteristics caused by stress. Thus, it can be applied to several domains of plant research such as transcriptome variations induced by drought, ultraviolet radiation, and mutants (Ryu et al., 2019;Long et al., 2021).
In summary, we constructed a gene expression map of young leaves at single-cell resolution and identified cell types. Pseudotime trajectory analysis of PGTs has paved the way to discover and uncover more important regulators of GT initiation and differentiation in other plants. N. tenuifolia scRNA-seq also represents a valuable resource for gene discovery, functional analysis, and the development of cell types on a molecular level and single-cell resolution.
Experimental procedures Plant materials and growth conditions
Young leaves of N. tenuifolia were used for the scRNA-seq experiments. Seeds of N. tenuifolia were sown in soil at 25°C, in a greenhouse, with a 16 h light/8 h dark cycle. Young leaves were harvested for scRNA-seq experiments on days 10, 15, 20, 25, 30, 35, and 40 after sowing. Protoplasts isolation for scRNA-seq We used~0.5 g young leaves to isolate protoplasts as previously described (Zhang et al., 2021b). Young leaves were harvested from 25-d-old seedlings, chopped, and added to an enzyme solution consisting of a mixture of cellulase R10, macerozyme R10, mannitol, KCl, CaCl 2 , and BSA. These mixtures were shaken mildly, and 8% mannitol, with 20 mM KCl and 0.1% BSA, was added to release more protoplasts. 8% mannitol was an osmotic regulator; KCl and 0.1% BSA were plasma membrane stabilizer.
The solution was then filtered twice using cell strainers (40 mm in diameter, Falcon, Cat No. /ID: 352340), and finally washed with 8% mannitol at 4°C. Protoplast viability was determined by trypan blue staining.
Construction of scRNA-seq library
The protoplasts were loaded on a chromium single-cell controller (10x Genomics) to generate single-cell gel beads-inemulsion (GEMs). The scRNA-seq library was generated with single cell 3 'Library and Gel Bead Kit V3 (10x Genomics, 1000075), and Chromium Single Cell B Chip Kit (10x Genomics, 1000074) according to the manufacturer's protocol. Approximately 20,000 protoplasts were added to each channel, and the number of target cells was estimated to be 10,000 protoplasts. cDNA libraries and sequences were generated as previously described (Zhang et al., 2021b).
In situ hybridization assays
For in situ hybridization assays, leaves were collected from 25-d old plants and washed with RNase-free H 2 O and then fixed with formaldehyde. The leaves were paraffin-embedded and sectioned (4 mm) using a Leica sliding microtome (LEICA, RM2016). The slides were dewaxed, and the experiment was performed according to the instructions of the CISH in situ hybridization kit (C001, http://www.gefanbio.com/showcp2. asp?id=3560). In short, the slides were washed multiple times with solution, and DEPC H 2 O, digested with Proteinase K, washed with 0.1 mol/L glycine solution, PBS, and 5×SSC solution, hybridized with corresponding probes, and incubated with anti-digoxigenin-AP Fab fragments. After washing, peroxidase was added to the biotin solution, and the mixture was incubated. The signals were detected using DAB. Hematoxylin was used to stain the nuclei, and the slides were dehydrated with ethanol, and sealed with neutral gum. Microscopy was carried out in bright-field mode using Nikon Eclipse Ci with a Nikon DS-RISCISH CCD. The primers used are listed in Table S11.
GC-MS analysis of secretion of PGTs
Oil in the PGTs was collected using the micropipette method. Firstly, a micropipette with an internal diameter of 100 mm was first generated from a capillary tube of 10 µL using a custom-built capillary puller. The 25-d old leaves were placed on a slide with the back facing up, under a stereomicroscope. Subsequently, a micropipette was used to absorb oil from the 300 PGTs by penetrating the thin cuticle. The contents were added to 50 µL n-hexane for GC-MS analysis. GC-MS was performed as previously reported (Liu et al., 2018). Each samle (2 mL) was injected into the system in the splitless mode.
Process of raw scRNA-seq data
The raw data were first analyzed for quality control, and valid barcodes were counted. More than 60% of the reads in all samples were aligned to the N. tenuifolia reference genome using the aligner STAR (v.2.5.1b) (Dobin et al., 2013). After the effective cells were identified, the gene-barcode matrices (named "filtered_feature_bc_matrix" by 10× Genomics) were utilized as processed raw data for a single sample. While combining data from multiple libraries, Aggregating Multiple Gem Groups (AGGR) merged the output of the Cell ranger (v5.0.0) count for multiple samples, normalizing these samples to the same sequencing depth, and then recalculating the gene-barcode, and obtaining all sample matrices for further analysis. Seurat (v4.0.0, R package) was used to avoid any batch effects and mitochondrial genes. Cells whose gene number was less than 200, gene number ranked in the top 1%, or mitochondrial gene ratio more than 25% were regarded as abnormal and filtered out. Seurat software provided us with a graph-based clustering approach for the analysis of scRNA-seq data. Dimensionality reduction was performed using PCA, and visualization was performed using t-SNE and UMAP. Notably, t-SNE is a powerful tool for visualizing and exploring scRNA-seq datasets and can visualize highdimensional data by giving each data point a location in a twoor three-dimensional map (Laurens and Hinton, 2008). UMAP is widely used to visualize the resultant clusters that can reflect the continuity and histology of differentiation between cell populations (Mcinnes and Healy, 2018).
Homologous gene annotation
Based on available data on Arabidopsis (Araport11) and tomato (ITAG4.0), we identified N. tenuifolia homologs of Arabidopsis and tomato genes. BLASTP was performed using N. tenuifolia proteins as queries against Arabidopsis and tomato proteins. The best hit, with an e-value lower than 10 -15 , and the highest bit score, was retrieved as the homologous gene.
Gene ontology enrichment analysis GO enrichment of genes in every cluster was performed using the KOBAS software with Benjamini-Hochberg multiple testing adjustment with log2 FC > 0.25, and p ≤ 0.01 as the threshold value. The results were visualized using the R package.
Pseudotime trajectory analysis
The matrix of the cells was allowed to build single-cell trajectories using Monocle 2(R package) (Trapnell et al., 2014), which introduced pseudotime. The cells in the cluster of interest were ordered, and their dimensions were reduced. The pseudotime trajectories were then visualized. The shape of the trajectory is like that of a tree with roots and branches. The cells of the tree roots can be used for differentiation purposes. Genes in the branch of the tree are often related to development and differentiation processes. Genes with similar expression trends were clustered into one group because they might share similar regulatory networks and biological functions.
Intraspecies scRNA-seq data comparison
Arabidopsis shoot and N. tenuifolia leaf scRNA-seq datasets were integrated using AGGR. In total, 88,952 cells were selected and batch effects across species were removed using Seurat. After clustering, the 24 cell clusters were extended. Cell types were annotated using known marker genes of Arabidopsis, and homologous gene of Arabidopsis in N. tenuifolia was identified by 1-to-1.
Data availability statement
The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found below: https:// www.ncbi.nlm.nih.gov/, PRJNA743551.
Author contributions
CL and QW conceived the project. PZ have isolated protoplasts. HC and PZ generated scRNA-seq data. PZ, YS, and ZS performed experiments. CL, QW, and LF revised the manuscript. All authors contributed to the article and approved the submitted version. | 7,289.8 | 2022-10-19T00:00:00.000 | [
"Biology",
"Environmental Science"
] |
Algebraic field theory operads and linear quantization
We generalize the operadic approach to algebraic quantum field theory [arXiv:1709.08657] to a broader class of field theories whose observables on a spacetime are algebras over any single-colored operad. A novel feature of our framework is that it gives rise to adjunctions between different types of field theories. As an interesting example, we study an adjunction whose left adjoint describes the quantization of linear field theories. We also develop a derived version of the linear quantization adjunction for chain complex valued field theories, which in particular defines a homotopically meaningful quantization prescription for linear gauge theories.
Introduction and summary
The aim of this paper is to generalize and extend the operadic approach to algebraic quantum field theory initiated in [BSW17]. The structures we shall formalize and investigate are functors A : C → Alg P from a small category C to the category of algebras over a single-colored operad P, which are required to satisfy a suitable generalization of the Einstein causality axiom. One should interpret C as a category of spacetimes and P as the operad controlling the algebraic structure of the observables on a fixed spacetime. Choosing the associative operad P = As, we recover the framework for quantum field theory developed in [BSW17]. There however exist also other interesting choices which are not covered by the latter work. For example, (1) classical field theories may be obtained by choosing the Poisson operad P = Pois in our construction, and (2) linear field theories, which we describe in terms of Heisenberg Lie algebras of presymplectic vector spaces, by choosing the unital Lie operad P = uLie. Therefore, our constructions provide a flexible framework to formalize and investigate a broad range of different types of field theories (linear, classical, quantum, etc.) from a common algebraic perspective based on operad theory.
One of the key observations in the present paper is that to each of such types of field theories there corresponds a colored operad which controls their algebraic structures, i.e. field theories are precisely the algebras over this colored operad. We denote the relevant colored operad by P (r 1 ,r 2 ) C and note that it depends on two different kinds of input data, which control the spacetime category of interest and the type of field theory. More precisely, the first datum is an orthogonal category C = (C, ⊥) (cf. Definition 3.1) and and the second is a bipointed single-colored operad P (r 1 ,r 2 ) = (P, r 1 , r 2 : I[2] ⇒ P) (cf. Definition 3.14). As in the previous paragraph, we interpret C as a category of spacetimes and P as the operad controlling the algebraic structure of the observables on a fixed spacetime. The data ⊥ and r 1 , r 2 are used to formalize a suitable generalization of the Einstein causality axiom of quantum field theory, see Definition 3.3. We shall provide a precise description of the colored operads P (r 1 ,r 2 ) C in Definitions 3.9 and 3.11.
We will show that the results for quantum field theories obtained in [BSW17] extend to our more general and flexible framework. In particular, from the functoriality of the assignment C → P (r 1 ,r 2 ) C of our colored operads to orthogonal categories, we obtain adjunctions between the categories of field theories corresponding to different spacetime categories. This includes generalizations of the time-slicification and local-to-global adjunctions from [BSW17], which have already found interesting applications to quantum field theory on spacetimes with boundaries [BDS18]. A novel feature of our framework, which is not captured by [BSW17], is a second kind of functorial assignment P (r 1 ,r 2 ) → P (r 1 ,r 2 ) C of our colored operads to bipointed single-colored operads. This results in adjunctions between the categories of field theories of different types. An interesting example, which we shall study in detail in this paper, is given by an adjunction whose left adjoint describes the quantization of linear field theories. This is induced by a canonical single-colored operad morphism uLie → As from the unital Lie operad to the associative operad.
Reformulating the usual quantization of linear field theories in terms of (the left adjoint of) an adjunction has profound technical advantages for studying gauge theories. Recall that the observables of gauge theories form chain complexes rather than vector spaces, which are obtained by e.g. the BRST/BV formalism. Because the category Ch(K) of chain complexes of vector spaces over a field K carries a canonical model structure with weak equivalences given by quasi-isomorphisms (see e.g. [Hov99]), it is natural ask whether field theories with values in Ch(K) form a model category as well. Based on [BSW18,Hin97,Hin15], we shall show that this is the case and moreover that the linear quantization adjunction is a Quillen adjunction. Employing techniques from the theory of derived functors (see e.g. [DS95,Hov99]), we obtain a derived linear quantization functor which provides a homotopically meaningful quantization prescription for linear gauge theories in the sense that it maps weakly equivalent linear gauge theories to weakly equivalent quantum gauge theories. A similar construction in the framework of factorization algebras [CG17] has been recently investigated in [GH18]. We shall also analyze in some detail the interplay of our derived linear quantization functor with (a homotopy theoretical generalization of) the time-slice axiom and local-to-global property of gauge theories. In a future work, we attempt to develop concrete constructions and examples of linear gauge theories from suitable geometric data such as stacks of fields and Lagrangian densities. The derived linear quantization functor from the present work then will be relevant to quantize these linear gauge theories.
The outline of the remainder of this paper is as follows: In Section 2 we shall fix our notations and briefly recall some background material on colored operads and their algebras. In Section 3 we introduce our rather broad concept of field theories which we study in this paper and show that the corresponding categories admit a description in terms of algebras over a suitable colored operad P (r 1 ,r 2 ) C . We also show that the assignment (C, P (r 1 ,r 2 ) ) → P (r 1 ,r 2 ) C of these operads to orthogonal categories C and bipointed single-colored operads P (r 1 ,r 2 ) is functorial. In Section 4 we harness this functorial behavior in order to study adjunctions between the categories of field theories corresponding to different C and P (r 1 ,r 2 ) . We first show that the results from [BSW17] on specific properties of the adjunctions corresponding to changing C easily generalize to our more flexible framework. After this we focus on our novel class of adjunctions corresponding to changing P (r 1 ,r 2 ) and investigate their interplay with the time-slice axiom and local-to-global property of field theories. A particularly relevant example of such an adjunction is the linear quantization adjunction which we study in detail in Section 5. In Section 6 we extend the results of the previous sections to the case of Ch(K)-valued field theories (which includes gauge theories) by using techniques from model category theory.
Closed symmetric monoidal categories
Throughout this paper we fix a closed symmetric monoidal category M, which we further assume to be complete and cocomplete, i.e. all small limits and colimits exist in M. The monoidal product is denoted by ⊗ : M × M → M, the monoidal unit by I ∈ M and the internal hom by [−, −] : M op × M → M, where (−) op denotes the opposite category. The symmetric braiding is denoted by τ : m ⊗ m ′ → m ′ ⊗ m, for all m, m ′ ∈ M. We shall always suppress the associator and unitors and in particular simply write m 1 ⊗ · · · ⊗ m n for multiple tensor products of objects m 1 , . . . , m n ∈ M. Because M is by assumption cocomplete, there exists a Set-tensoring ⊗ : Set × M → M, which we denote with abuse of notation by the same symbol as the monoidal product. Explicitly, for any set S ∈ Set and m ∈ M, we define where is the coproduct in M.
Example 2.1. A simple example of a bicomplete closed symmetric monoidal category is the Cartesian closed category Set of sets. Here ⊗ = × is the Cartesian product, I = { * } is any singleton set and [S, T ] = Map(S, T ) is the set of maps from S to T . The symmetric braiding is given by the flip map τ : S × T → T × S , (s, t) → (t, s). ▽ Example 2.2. Another standard example of a bicomplete closed symmetric monoidal category is the category Vec K of vector spaces over a field K. Here ⊗ is the usual tensor product of vector spaces, I = K is the 1-dimensional vector space and [V, W ] = Hom K (V, W ) is the vector space of linear maps from V to W . The symmetric braiding is given by the flip map τ :
Colored operads
We provide a brief review of those aspects of the theory of colored operads that are relevant for this work. We refer to e.g. [Yau16], [BM07] and [BSW17] for a more detailed presentation.
Let C ∈ Set be a non-empty set, which we shall call the 'set of colors'. We will use the notation c := (c 1 , . . . , c n ) ∈ C n for elements of the n-fold product set.
Definition 2.3. A C-colored operad O with values in M is given by the following data: • for each n ≥ 0 and (c, t) ∈ C n+1 , an object O t c ∈ M (called the object of operations from c to t); • for each n ≥ 0, (c, t) ∈ C n+1 and permutation σ ∈ Σ n , an cσ (called the permutation action), where cσ := (c σ(1) , . . . , c σ(n) ); • for each n > 0, k 1 , . . . , k n ≥ 0, (a, t) ∈ C n+1 and (b i , a i ) ∈ C k i +1 , for i = 1, . . . , n, an This data is required to satisfy the standard permutation action, equivariance, associativity and unitality axioms, see e.g. [Yau16, Definition 11.2.1]. A morphism φ : O → P between two C-colored operads O and P with values in M is a family of M-morphisms Colored operads generalize the concept of (enriched) categories in the following sense. In contrast to allowing only for 1-to-1 operations, such as the morphisms C(c, c ′ ) in a category C, colored operads also describe n-to-1 operations in terms of the objects of operations O t c . The operadic composition generalizes the usual categorical composition to operations of higher arity and the operadic unit is analogous to the identity morphisms in a category. Permutation actions are a new feature for operations of arity ≥ 2 and they have no analog in ordinary category theory. The following example clarifies how every category defines a colored operad with only 1-ary operations.
Example 2.4. Let C be a small category and denote its set of objects by C 0 . The following construction defines a C 0 -colored operad Diag C ∈ Op C 0 (Set) with values in M = Set, which is called the diagram operad of C, see e.g. [BM07]. For (c, t) ∈ C n+1 0 , one defines the set of operations by The permutation action is uniquely fixed because Σ 1 = {e} is the trivial group. The only nontrivial operadic compositions are γ : Diag C is given by the identity morphisms in the category C. One confirms that this defines a colored operad in the sense of Definition 2.3. ▽ Many interesting examples of (colored) operads can be conveniently defined in terms of generators and relations, see e.g. the examples below. Let us briefly explain how this construction works. We denote by Seq C (M) the category of C-colored (non-symmetric) sequences with values in M. An object X ∈ Seq C (M) is a family of objects X t c ∈ M, for all n ≥ 0 and (c, t) ∈ C n+1 , and a Seq C (M)-morphism f : X → Y is a family of M-morphisms f : X t c → Y t c , for all n ≥ 0 and (c, t) ∈ C n+1 . There exists a forgetful functor U : Op C (M) → Seq C (M) that forgets the permutation action, operadic composition and operadic unit of a C-colored operad. This functor has a left adjoint which is called the free C-colored operad functor, i.e. we have an adjunction (2.4) Given any choice of generators G ∈ Seq C (M), we consider the corresponding free C-colored operad F (G) ∈ Op C (M). In order to implement relations, we consider R ∈ Seq C (M) together with two parallel Seq C (M)-morphisms r 1 , r 2 : R ⇒ U F (G). Note that because (2.4) is an adjunction, the latter is equivalent to two parallel Op C (M)-morphisms r 1 , r 2 : F (R) ⇒ F (G), which we denote with abuse of notation by the same symbols. Because the category Op C (M) is cocomplete, the following construction defines a C-colored operad.
Definition 2.5. The C-colored operad presented by the generators G ∈ Seq C (M) and relations r 1 , r 2 : R ⇒ U F (G) is defined as the coequalizer Example 2.6. Consider for the moment M = Set. The associative operad As ∈ Op { * } (Set) is the single-colored operad (i.e C = { * } is a singleton) presented by the following generators and relations: We define the set of generators of arity n by (2.6) for all n ≥ 0. The generator µ in arity 2 is interpreted as a multiplication operation and the generator η in arity 0 as a unit element. To implement associativity and left/right unitality of these operations, we consider for all n ≥ 0, together with the two Seq { * } (Set)-morphisms r 1 , r 2 : R → U F (G) defined by where the operadic composition and unit are those of the free operad F (G). The associative operad As := F (G)/(r 1 = r 2 ) ∈ Op { * } (Set) is defined as the corresponding coequalizer.
It is instructive and useful to visualize the generators and relations in terms of rooted trees. The generators are depicted by (2.9a) and the relations (in the order they appear in (2.8)) then read as (2.9b) Let us note that the associative operad can be defined in any bicomplete closed symmetric monoidal category M. Using the Set-tensoring (2.1) and the unit object I ∈ M, we define generators G ⊗ I ∈ Seq { * } (M) and relations r 1 ⊗ I, r 2 ⊗ I : (2.10a) The relations are given by antisymmetry and the Jacobi identity where the numbers below the trees indicate input permutations.
Note that for defining the Lie relations we had to use the natural Abelian group structure on the Hom-sets of Vec K , i.e. addition of linear maps between vector spaces. Hence, the Lie operad can not be defined in a generic bicomplete closed symmetric monoidal category M. If however M is an additive category, then one can define the Lie operad Lie ∈ Op { * } (M) with values in M along the same lines as above. (2.11b) which express that µ is commutative and that {·, ·} is a derivation in the right entry (and hence by antisymmetry also a derivation in the left entry). Computing the operadic composition of the derivation relation with ½ ⊗ η ⊗ η implies that In addition to the antisymmetry and Jacobi identity relations (cf. (2.10)) for [·, ·], we demand the compatibility relation = 0 (2.14) between the Lie bracket and the unit. ▽ We shall often require a generalization of the concept of colored operad morphisms from Definition 2.3 to morphisms that do not necessarily preserve the underlying sets of colors. As a preparation for the relevant definition, note that for every D-colored operad P ∈ Op D (M) and every map of sets f : C → D, one may define the pullback C-colored operad f * (P) ∈ Op C (M). Concretely, it is defined by setting f * (P) t c := P f (t) f (c) , for all n ≥ 0 and (c, t) ∈ C n+1 , and restricting the permutation action, operadic composition and operadic unit in the evident way.
Algebras over colored operads
We have seen above that a colored operad O describes abstract n-to-1 operations, for all n ≥ 0, together with a composition law γ, specified identities ½ and a permutation action O(σ) that allows us to permute the inputs of operations. Forming concrete realizations/representations of these abstract operations leads to the concept of algebras over colored operads.
Definition 2.11. An algebra A over a C-colored operad O ∈ Op C (M), or shorter an O-algebra, is given by the following data: • for each c ∈ C, an object A c ∈ M; • for each n ≥ 0 and (c, t) ∈ C n+1 , an M-morphism α : A c i with the convention that A ∅ = I for n = 0. This data is required to satisfy the standard associativity, unity and equivariance axioms, see e.g. [Yau16, Definition 13.2.3]. A morphism κ : A → B between two O-algebras A and B is a family of M-morphisms κ : We denote the category of O-algebras by Alg O .
Example 2.12. Consider the diagram operad Diag C ∈ Op C 0 (Set) from Example 2.4. A Diag Calgebra is a family of sets A c ∈ Set, for all objects c ∈ C 0 in the category C, together with maps α : for all c, t ∈ C 0 . (Here we already used that Diag C only contains 1-ary operations.) Because Diag C t c = C(c, t) is the Hom-set, the latter data is equivalent to specifying for each C-morphism f : c → t a map of sets A(f ) := α(f, −) : A c → A t . The axioms for O-algebras imply that A(g f ) = A(g) A(f ), for all composable C-morphism, and A(id) = id for the identities. Hence, a Diag C -algebra is precisely a functor C → Set, i.e. a diagram of shape C. One observes that morphisms between Diag C -algebras are precisely natural transformations between the corresponding functors. ▽ Example 2.13. Consider for the moment M = Set and the associative operad As ∈ Op { * } (Set) from Example 2.6. An As-algebra is a single set A = A * ∈ Set together with an As-action. The latter is equivalent to providing a family of maps α : As(n) → Map(A ×n , A), for all n ≥ 0, which define an Op { * } (Set)-morphism to the endomorphism operad End(A), see e.g. [Yau16, Definition 13.8.1]. Because As is presented by generators and relations (cf. Example 2.6), this is equivalent to defining α on the generators such that the relations hold true. This yields two maps µ A := α(µ) : A × A → A and η A := α(η) : { * } → A, which because of the relations have to satisfy the axioms of an associative and unital algebra in Set. One finds that morphisms of As-algebras are precisely morphisms of associative and unital algebras.
For a general bicomplete closed symmetric monoidal category M, one obtains that the category Alg As of algebras over As ∈ Op { * } (M) is the category of associative and unital algebras in M. In particular, for M = Vec K this is the category of associative and unital K-algebras.
, the pullback functor (f, φ) * : Alg P → Alg O has a left adjoint, which is called operadic left Kan extension. We denote the corresponding adjunction by (2.16) Example 2.16. Every functor F : C → D defines an evident Op(Set)-morphism (F 0 , F ) : between the corresponding diagram operads, cf. Example 2.4. Recalling from Example 2.12 that Alg Diag C ∼ = Set C is the category of functors from C to Set (and similarly that Alg Diag D ∼ = Set D ), one shows that the pullback functor (F 0 , F ) * is the usual pullback functor F * := (−) • F : Set D → Set C for functor categories. Its left adjoint (F 0 , F ) ! is therefore the ordinary categorical left Kan extension Lan F : Set C → Set D . ▽ 3 Field theory operads
Orthogonal categories and field theories
Let us briefly recall the basic idea of algebraic quantum field theory, see e.g. [HK64, BFV03, BDFY15, FV15] for more details. Broadly speaking, a field theory in this setting is a functor from a suitable category of spacetimes to a category of algebraic structures of interest, that satisfies a list of physically motivated axioms. The prime example is given by functors A : Loc → Alg As from the category Loc of globally hyperbolic Lorentzian manifolds to the category of associative and unital algebras that satisfy the Einstein causality axiom. The latter is a property of the functor A : Loc → Alg As which demands that for every pair (f 1 : Loc-morphisms whose images are causally disjoint in M the diagram M denotes the (opposite) multiplication on A(M ). For the purpose of this paper, we consider the following generalization of the scenario sketched above. (Examples which justify this generalization are presented at the end of this subsection.) Let C be a small category which we interpret as a category of spacetimes. Instead of associative and unital algebras, let us take any single-colored operad P ∈ Op { * } (M) and consider the functor category Alg P C . An object in this category is a functor A : C → Alg P , i.e. an assignment of P-algebras to spacetimes, and the morphisms are natural transformations between such functors. To encode physical axioms which generalize the Einstein causality axiom above, we recall the concept of orthogonal categories from [BSW17].
Definition 3.1. An orthogonal category is a pair C := (C, ⊥) consisting of a small category C and a subset ⊥⊆ Mor C t × t Mor C of the set of pairs of morphisms with a common target, which satisfies the following properties: We shall also write We denote by OrthCat the category of orthogonal categories and orthogonal functors.
for all n ≥ 0. This means that each r i picks out an operation of arity 2 in P. For simplifying notation, we shall write and we call P (r 1 ,r 2 ) an (arity 2) bipointed single-colored operad.
Definition 3.3. A field theory of type P (r 1 ,r 2 ) on C is a functor A : C → Alg P that satisfies the following property: For all (f 1 : in M commutes, where α P c denotes the P-action on A(c) ∈ Alg P , cf. Definition 2.11. The category of field theories of type P (r 1 ,r 2 ) on C is defined as the full subcategory FT C, P (r 1 ,r 2 ) ⊆ Alg P C , (3.5) whose objects are all functors A : C → Alg P satisfying (3.4).
Remark 3.4. Our concept of field theories in Definition 3.3 is based on the idea that there exist two distinguished arity 2 operations in P, which act in the same way when pre-composed with an orthogonal pair f 1 ⊥ f 2 of C-morphisms. There exists an obvious generalization of this scenario to n-ary operations in P and orthogonal n-tuples of C-morphisms. We however decided not to introduce this more general framework for field theories, because all examples of interest to us are field theories in the sense of Definition 3.3. ▽ Example 3.5 (Quantum field theories). Consider the associative operad As ∈ Op { * } (M) from Example 2.6 and the two Seq { * } (M)-morphisms µ, µ op : I[2] ⇒ U (As) which select the multiplication and opposite multiplication operations. A field theory of type As (µ,µ op ) on C is a functor A : C → Alg As to the category of associative and unital algebras which satisfies the analog of (3.1). For C = Loc (cf. Example 3.2), this is a locally covariant quantum field theory [BFV03,FV15] that satisfies the Einstein causality axiom but not necessarily the time-slice axiom. As explained in [BSW17], the latter can be encoded by . A field theory of type As ([·,·],0) on C is a functor A : C → Alg As to the category of associative and unital algebras which satisfies the property that is the zero-map, for all (f 1 : .) This is equivalent to our description in Example 3.5, i.e.
FT C, As ([·,·],0) ∼ = FT C, As (µ,µ op ) . (3.7) This observation will be useful in Section 5 when we study the linear quantization adjunction. ▽ Example 3.8 (Linear field theories). In the usual construction of linear quantum field theories, see e.g. [BGP07,BDH13] for reviews, one first defines a functor L : Loc → PSymp to the category of presymplectic vector spaces, which is then quantized by forming CCR-algebras (CCR stands for canonical commutation relations). Recall that a presymplectic vector space (V, ω) is a pair consisting of a vector space V and an antisymmetric linear map ω : V ⊗ V → K. Notice that this is not an operation of arity 2 in the sense of operads because the target is the ground field and not V . Hence, PSymp is not the category of algebras over an operad and, as a consequence, functors L : Loc → PSymp do not define field theories in the sense of Definition 3.3.
However, there exists a canonical upgrade of every functor L : Loc → PSymp to a field theory in the sense of Definition 3.3. Given any presymplectic vector space (V, ω), one can define its Heisenberg Lie algebra H(V, ω). The underlying vector space of H(V, ω) is given by V ⊕ K and the Lie bracket There exists a canonical unit map η : Hence, Heisenberg Lie algebras are algebras over the unital Lie operad uLie ∈ Op { * } (M) given in Example 2.9. Because forming Heisenberg Lie algebras is functorial, we can define for every L : Loc → PSymp the composite functor H L : Loc → Alg uLie .
Consider now the two Seq { * } (M)-morphisms [·, ·], 0 : I[2] → U (uLie) which select the Lie bracket and the zero-operation. A field theory of type uLie ([·,·],0) on C is a functor A : C → Alg uLie to the category of unital Lie algebras which satisfies the property that is the zero-map, for all (f 1 :
Operadic description
In this section we show that the category of field theories from Definition 3.3 is the category of algebras over a suitable colored operad. This generalizes previous results in [BSW17] and it is the key insight that allows us to study a large family of universal constructions for field theories in Section 4. As a preparation for the relevant definition, we define an auxiliary colored operad that describes functors from a small category C to the category of P-algebras.
Definition 3.9. Let C be a small category with set of objects C 0 and let P ∈ Op { * } (M) be a single-colored operad. The C 0 -colored operad P C ∈ Op C 0 (M) is defined by the following data: • for n ≥ 0 and (c, t) ∈ C n+1 0 , the object of operations is where ⊗ is the Set-tensoring (2.1) and C(c, t) := n i=1 C(c i , t) is the product of Hom-sets; • for n ≥ 0, (c, t) ∈ C n+1 0 and σ ∈ Σ n , the permutation action P C (σ) is defined by for all f : = (f 1 , . . . , f n ) ∈ C(c, t), where ι f : P(n) → P C t c = C(c, t) ⊗ P(n) are the inclusion morphisms into the coproduct (cf. (2.1)) and f σ := (f σ(1) , . . . , f σ(n) ); • for n > 0, k 1 , . . . , k n ≥ 0, (a, t) ∈ C n+1 0 and (b i , a i ) ∈ C k i +1 0 , for i = 1, . . . , n, the operadic composition γ P C is defined by . . , f n g nkn ) ∈ C(b, t) is defined by composition in the category C; • for c ∈ C 0 , the operadic unit ½ P C is where id c : c → c is the identity morphism of c in the category C.
A straightforward check shows that this data defines a colored operad, cf. Definition 2.3.
Lemma 3.10. There exists a canonical isomorphism between the category of algebras over the colored operad P C ∈ Op C 0 (M) from Definition 3.9 and the category of functors from C to Alg P .
Proof. A P C -algebra is a family of objects A c ∈ M, for all c ∈ C 0 , together with a P C -action α : P C t c ⊗A c → A t . Because (3.11) is a coproduct, this is equivalent to a family of M-morphisms α f : P(n) ⊗ A c → A t , for all n ≥ 0, (c, t) ∈ C n+1 0 and f ∈ C(c, t), which satisfies the following compatibility conditions resulting from the axioms for algebras over colored operads Using that any f = (f 1 , . . . , f n ) ∈ C(c, t) can be written as f = id t n (f 1 , . . . , f n ), where id t n = (id t , . . . , id t ) is of length n, the diagram (3.16a) implies that α f factorizes as Hence, the P C -action α is uniquely specified by the following two types of M-morphisms: (1) α t := α idt n : P(n) ⊗ A ⊗n t → A t , for all t ∈ C 0 and n ≥ 0, and (2) The remaining conditions in (3.16) are equivalent to α t defining a P-action on A t , for all t ∈ C 0 , and A(f ) : A c → A t defining a functor C → Alg P to P-algebras. From this perspective, P C -algebra morphisms correspond precisely to natural transformations between functors from C to Alg P .
Definition 3.11. The operad of field theories of type P (r 1 ,r 2 ) on C is defined as the coequalizer The importance of this operad is evidenced by the following theorem. between the category of algebras over the colored operad P (r 1 ,r 2 ) C ∈ Op C 0 (M) from Definition 3.11 and the category of field theories of type P (r 1 ,r 2 ) on C from Definition 3.3.
Proof. Because P (r 1 ,r 2 ) C is defined as a coequalizer (3.20), its algebras are precisely those P Calgebras A ∈ Alg P C that satisfy the relations encoded by r 1,C , r 2,C : R ⊥ ⇒ U (P C ), cf. (3.19). Using the notations from the proof of Lemma 3.10, this concretely means that the diagram in M commutes, for all (f 1 : c 1 → t, f 2 : c 2 → t) ∈⊥. Using the isomorphism of Lemma 3.10, one easily translates this diagram to the diagram (3.4) for the functor A : C → Alg P corresponding to A ∈ Alg P C , which completes the proof.
Example 3.13. Recalling Examples 3.5, 3.7 and 3.8, our construction defines colored operads for quantum field theory As
Functoriality
Note that the field theory operad P (r 1 ,r 2 ) C ∈ Op C 0 (M) from Definition 3.11 depends on the choice of two kinds of data: (1) An orthogonal category C = (C, ⊥) and (2) a bipointed single-colored operad P (r 1 ,r 2 ) = (P, r 1 , r 2 : I[2] ⇒ U (P)). We will see that both of these dependencies are functorial. Recall from Definition 3.1 that orthogonal categories are the objects of the category OrthCat. The second kind of data may be arranged in terms of a category as follows.
Definition 3.14. The category of (arity 2) bipointed single-colored operads Op 2pt { * } (M) has the following objects and morphisms: An object is a pair P (r 1 ,r 2 ) = (P, r 1 , r 2 : I[2] ⇒ U (P)) consisting of a single-colored operad P ∈ Op { * } (M) and a parallel pair of Seq { * } (M)-morphisms r 1 , r 2 : I[2] ⇒ U (P) (cf. Proof. For every morphism (F, φ) : (C, P (r 1 ,r 2 ) ) → (D, Q (s 1 ,s 2 ) ) in OrthCat × Op 2pt { * } (M) one can define an Op(M)-morphism φ F : P C → Q D between the corresponding auxiliary operads from Definition 3.9. Concretely, this morphism is specified by the components We now show that the assignment of the field theory operads is functorial too. For this we first note that one can define analogously to above a morphism R ⊥ C → R ⊥ D of colored sequences and one easily checks that this defines a morphism of parallel pairs in (3.19). (For this step one uses that F is an orthogonal functor and that φ preserves the points.) Because forming colimits is functorial, this defines an to the coequalizer of the corresponding pullback operads. (With an abuse of notation, we denoted by F both the free D 0 -colored operad functor (2.4) and the orthogonal functor F : C → D.) Notice that pullback operads arise at this point because Definition 3.11 considers colimits in the categories of operads with a fixed set of colors and not in the category Op(M). From the universal property of colimits one obtains a canonical ) to the pullback of field theory operad. The composition of the latter two morphisms defines our desired Op(M)-morphism, which we denote with abuse of notation by the same symbol φ F : P (r 1 ,r 2 ) C → Q (s 1 ,s 2 ) D as the one for the auxiliary operads.
As a consequence of this proposition, we obtain for every morphism (F, φ) : (C, P (r 1 ,r 2 ) ) → between the corresponding categories of field theories. From the concrete definition of φ F given in the proof of Proposition 3.15 and the identification in Theorem 3.12, one observes that the right adjoint (φ F ) * admits a very explicit description in terms of either of the two compositions in the commutative diagram In this diagram F * is the restriction to the categories of field theories of the pullback functor for functor categories for O = P and O = Q, and (φ * ) * is the restriction to the categories of field theories of the pushforward functor for functor categories for E = C and E = D, where φ * : Alg Q → Alg P is the pullback functor corresponding to the single-colored operad morphism φ : P → Q.
Universal constructions for field theories 4.1 Generalities
This section is concerned with analyzing in more depth the adjunctions in (3.25) and their relevance for universal constructions in field theory. Because of (3.26), this problem may be decomposed into three smaller building blocks: 3. the interplay between these two cases via the diagram of categories and functors in which the square formed by the right adjoints commutes by (3.26) and, as a consequence of the uniqueness (up to a unique natural isomorphism) of left adjoint functors, the square formed by the left adjoints commutes up to a unique natural isomorphism.
In the following subsections we study particular classes of examples of such adjunctions, all of which are motivated by concrete problems and constructions in field theory, and discuss their interplay. A particularly interesting example, which we will discuss later in Section 5, is given by an adjunction that describes the quantization of linear field theories. exhibits FT C, P (r 1 ,r 2 ) as a full coreflective subcategory of FT D, P (r 1 ,r 2 ) , i.e. the unit η : id → j * j ! of this adjunction is a natural isomorphism.
Full orthogonal subcategories
Proof. The proof is analogous to the corresponding one in [BSW17] and will not be repeated. (4.5) The right adjoint j * is the restriction functor which restricts field theories that are defined on all of Loc to the full orthogonal subcategory Loc ⋄ of spacetimes diffeomorphic to R m . More interestingly, the left adjoint j ! is a universal extension functor which extends field theories that are only defined on Loc ⋄ to all of Loc. It was shown in [BSW17] that j ! is a generalization and refinement of Fredenhagen's universal algebra construction [Fre90,Fre93,FRS92,Lan14]. A nontrivial application of a similar construction to quantum field theories on spacetimes with boundaries has been studied in [BDS18]. ▽ Remark 4.3. The result in Proposition 4.1 that j ! exhibits FT C, P (r 1 ,r 2 ) as a full coreflective subcategory of FT D, P (r 1 ,r 2 ) is crucial for a proper interpretation of j ! as a universal extension functor and j * as a restriction functor in the spirit of Example 4.2. Given any field theory B ∈ FT C, P (r 1 ,r 2 ) on the full orthogonal subcategory C ⊆ D, one may apply the left and then the right adjoint functor in (4.4) to obtain another field theory j * j ! (B) ∈ FT C, P (r 1 ,r 2 ) on C ⊆ D. The latter is interpreted as the restriction of the universal extension of B. By Proposition 4.1, the unit η B : B → j * j ! (B) defines an isomorphism between these two theories, which means that j ! extends field theories from C ⊆ D to all of D without altering their values on the subcategory C. ▽ An interesting application of the class of adjunctions in (4.4) is that they allow us to formalize a kind of local-to-global (i.e. descent) condition for field theories. Given a field theory A ∈ FT D, P (r 1 ,r 2 ) on the bigger category D, one may ask whether it is already completely determined by its values on the full orthogonal subcategory C ⊆ D. In the context of Example 4.2, the question is whether the value of a field theory on a general spacetime M ∈ Loc is already completely determined by its values on spacetimes diffeomorphic to R m , which is a typical question of descent. The following definition provides a formalization of this idea.
Definition 4.4. A field theory A ∈ FT D, P (r 1 ,r 2 ) on D is called j-local if the corresponding component of the counit ǫ A : j ! j * (A) → A is an isomorphism. The full subcategory of j-local field theories is denoted by FT D, P (r 1 ,r 2 ) j−loc ⊆ FT D, P (r 1 ,r 2 ) .
The following result, which extends eariler results from [BSW17] to our more general framework, shows that j-local field theories on the bigger category D may be equivalently described by field theories on the full orthogonal subcategory C ⊆ D.
Corollary 4.5. The adjunction (4.4) restricts to an adjoint equivalence (4.6) Proof. This is an immediate consequence of Proposition 4.1. exhibits FT C[W −1 ], P (r 1 ,r 2 ) as a full reflective subcategory of FT C, P (r 1 ,r 2 ) , i.e. the counit ǫ : L ! L * → id of this adjunction is a natural isomorphism.
Orthogonal localizations
Proof. The proof is analogous to the corresponding one in [BSW17] and will not be repeated. (4.8) The right adjoint L * is the functor that forgets that a field theory B ∈ FT Loc[W −1 ], P (r 1 ,r 2 ) satisfies the time-slice axiom. More interestingly, the left adjoint L ! assigns to a field theory A ∈ FT Loc, P (r 1 ,r 2 ) that does not necessarily satisfy the time-slice axiom a theory that does. Hence, one may call the left adjoint functor L ! a 'time-slicification' functor. Notice that the result in Proposition 4.6 that L * exhibits FT Loc[W −1 ], P (r 1 ,r 2 ) as a full reflective subcategory of FT Loc, P (r 1 ,r 2 ) has a concrete meaning. The isomorphisms ǫ B : L ! L * (B) → B given by the counit say that time-slicification does not alter those field theories that already do satisfy the time-slice axiom, which is of course a very reasonable property. ▽ An interesting application of the class of adjunctions in (4.7) is that they allow us to formulate a suitable criterion to test whether a theory A ∈ FT C, P (r 1 ,r 2 ) satisfies the 'time-slice axiom'.
Definition 4.8. A field theory A ∈ FT C, P (r 1 ,r 2 ) is called W -constant if the corresponding component of the unit η A : A → L * L ! (A) is an isomorphism. The full subcategory of W -constant field theories is denoted by FT C, P (r 1 ,r 2 ) W −const ⊆ FT C, P (r 1 ,r 2 ) .
The following result shows that W -constant field theories may be equivalently described by field theories on the orthogonal localization C[W −1 ].
Corollary 4.9. The adjunction (4.7) restricts to an adjoint equivalence Proof. This is an immediate consequence of Proposition 4.6.
Change of bipointed single-colored operad
Our third class of examples are adjunctions that correspond to morphisms φ : P (r 1 ,r 2 ) → Q (s 1 ,s 2 ) of bipointed single-colored operads, i.e. (4.10) Let us stress that these adjunctions are conceptually very different to the ones we studied in the previous two subsections because they change the type of field theories and not the orthogonal category on which field theories are defined. In particular, such adjunctions can not be formulated within the original operadic framework for algebraic quantum field theory developed in [BSW17] as they crucially rely on our more flexible definition of field theory operads, cf. Definition 3.11. In Section 5 we study an interesting example given by an adjunction that describes the quantization of linear field theories.
We observe the following preservation results for j-local field theories (cf. Definition 4.4) and for W -constant field theories (cf. Definition 4.8) under the adjunctions (4.10).
Proof. Item a): Let A ∈ FT D, P (r 1 ,r 2 ) j−loc be any j-local field theory of type P (r 1 ,r 2 ) , i.e.
is an isomorphism. This follows from the commutative diagram where isomorphisms are indicated by ∼ =. In more detail, the top square commutes by naturality of the counit and the vertical arrows are isomorphisms because A is j-local. The middle square commutes because of (4.3). The bottom triangle is the triangle identity for the adjunction and the unit (vertical arrow) is an isomorphism because of Proposition 4.1.
Item b): Let
A ∈ FT C, Q (s 1 ,s 2 ) W −const be any W -constant field theory of type Q (s 1 ,s 2 ) , i.e. η A : A → L * L ! (A) is an isomorphism. The claim is that the field theory (φ * ) * (A) ∈ FT C, P (r 1 ,r 2 ) of type P (r 1 ,r 2 ) is W -constant as well, i.e. η (φ * ) * (A) : is an isomorphism. This follows from the commutative diagram In more detail, the top square commutes by naturality of the unit and the vertical arrows are isomorphisms because A is W -constant. The middle square commutes because of (4.3). The bottom triangle is the triangle identity for the adjunction and the counit (vertical arrow) is an isomorphism because of Proposition 4.6.
Let us emphasize that the result in Proposition 4.10 is asymmetric in the sense that j-local field theories are preserved by the left adjoints (φ * ) ! and W -constant field theories are preserved by the right adjoints (φ * ) * . The reason for this asymmetry is that the former property is formalized by a coreflective full subcategory (cf. Proposition 4.1 and Definition 4.4) while the latter property by a reflective full subcategory (cf. Proposition 4.6 and Definition 4.8). The opposite preservation properties do not hold true in general because in (4.3) only the square formed by the left adjoints and the square formed by the right adjoints commutes (up to a natural isomorphism). We however would like to note the following special case in which there exists a further preservation result. This will become relevant in Section 5 below. (s 1 ,s 2 ) ) is (naturally isomorphic to) the restriction to the categories of field theories of the pushforward functor for functor categories where the adjunction φ ! : Alg P ⇄ Alg Q : φ * corresponds to the single-colored operad morphism φ : P → Q. Then the left adjoint functor (φ * ) ! : FT(C, P (r 1 ,r 2 ) ) → FT(C, Q (s 1 ,s 2 ) ) preserves W -constant field theories.
Proof. Consider the diagram (4.3) for F = L and observe that under our hypothesis the square form by the (φ * ) ! and L * commutes (up to a natural isomorphism), i.e.
where in the second step we used that pullback and pushforward functors for functor categories commute. Replacing (φ * ) * by (φ * ) ! in the proof of Proposition 4.10 b) then proves our claim.
We conclude this section with a technical lemma that provides a criterion to detect whether the hypotheses of Proposition 4.11 are fulfilled. Recall from Definition 3.11 that there exists a natural projection Op C 0 (M)-morphism π : P C → P (r 1 ,r 2 ) C from our auxiliary operads to the field theory operads. Given any Op 2pt { * } (M)-morphism φ : P (r 1 ,r 2 ) → Q (s 1 ,s 2 ) , this yields the square of adjunctions in which the square formed by the right adjoints commutes, i.e. (φ * ) * π * = π * (φ * ) * , and hence the square formed by the left adjoints commutes (up to a unique natural isomorphism), i.e. (φ * ) ! π ! ∼ = π ! (φ ! ) * . Notice that the vertical adjunctions exhibit the field theory categories as full reflective subcategories of the functor categories. An immediate consequence is the following Lemma 4.12. If the functor (φ ! ) * π * : FT C, P (r 1 ,r 2 ) → Alg Q C factors through the full reflective subcategory FT C, Q (s 1 ,s 2 ) ⊆ Alg Q C , then the left adjoint (φ * ) ! : FT C, P (r 1 ,r 2 ) → FT C, Q (s 1 ,s 2 ) is (naturally isomorphic to) the restriction to the categories of field theories of the pushforward functor (φ ! ) * : Alg P C → Alg Q C .
Linear quantization adjunction
Throughout this section we assume that the underlying bicomplete closed symmetric monoidal category M is additive. Recalling Example 3.5 and also Remark 3.6, we define the category of quantum field theories on an orthogonal category C by which one easily confirms to be well-defined by using the relations of the associative operad (cf. Example 2.6) and the ones of the unital Lie operad (cf. Example 2.9). It is evident that φ : uLie ([·,·],0) → As ([·,·],0) defines an Op 2pt { * } (M)-morphism in the sense of Definition 3.14. By (4.10) this induces an adjunction between the category of linear field theories and the category of quantum field theories, which we shall denote by The aim of this section is to study this adjunction in detail and in particular to show that the left adjoint Q lin admits an interpretation as a linear quantization functor.
Let us first provide an explicit description of the right adjoint functor U lin = (φ * ) * . Note that the functor φ * : Alg As → Alg uLie from associative and unital algebras to unital Lie algebras is very explicit. It assigns to any (A, µ A , η A ) ∈ Alg As the unital Lie algebra φ * (A, µ A , η A ) = (A, µ A −µ op A , η A ) ∈ Alg uLie , where the Lie bracket is given by the commutator. The corresponding pushforward functor U lin = (φ * ) * : QFT(C) → LFT(C) carries out this construction object-wise on C. Concretely, for A : C → Alg As ∈ QFT(C), the functor underlying U lin (A) ∈ LFT(C) is given by U lin (A)(c) = φ * A(c) ∈ Alg uLie , for all c ∈ C.
We now provide an explicit description of the left adjoint functor Q lin in (5.4). Our strategy is to analyze the pushforward functor (φ ! ) * : Alg uLie C → Alg As C for the functor categories and to prove that it satisfies the criterion of Lemma 4.12. As a consequence of this lemma, the restriction to the categories of field theories of the pushforward functor (φ ! ) * defines a model for the left adjoint functor Q lin .
Let us describe first the left adjoint functor of the adjunction φ ! : Alg uLie ⇄ Alg As : φ * between algebras over single-colored operads. The following construction, which we will call the unital universal enveloping algebra construction, defines a model for the left adjoint φ ! . Let V ∈ Alg uLie be any unital Lie algebra, with Lie bracket [·, ·] : V ⊗ V → V and unit η : I → V . As the first step, we form the usual tensor algebra T ⊗ V := ∞ n=0 V ⊗n ∈ Alg As , i.e. the free As-algebra of the underlying object V ∈ M, with multiplication µ ⊗ : T ⊗ V ⊗ T ⊗ V → T ⊗ V and unit η ⊗ : I → T ⊗ V . We then consider the two parallel M-morphisms where ι 1 : V → T ⊗ V is the inclusion into the coproduct, which compare the commutator of T ⊗ V with the Lie bracket of V . We form the corresponding coequalizer in Alg As and notice that U ⊗ V is the universal enveloping algebra of the underlying Lie algebra (V, [·, ·]) ∈ Alg Lie . As the final step, we consider the two parallel M-morphisms which compare the unit of V with the unit of T ⊗ V , and form the corresponding coequalizer in Alg As . All of these constructions are clearly functorial.
Proof. It is easy to construct a natural bijection Hom Alg As (φ ! (V ), A) ∼ = Hom Alg uLie (V, φ * (A)), for all V ∈ Alg uLie and A ∈ Alg As . Concretely, given κ : φ ! (V ) → A in Alg As , then κ π ′ π ι 1 : V → φ * (A) defines an Alg uLie -morphism. On the other hand, given ρ : V → φ * (A) in Alg uLie , then the canonical extension to an Alg As -morphism ρ : T ⊗ V → A on the tensor algebra descends to the quotients in (5.5) and (5.6). Proof. By hypothesis, given any orthogonal pair (f 1 : As is the zero map too. This is an immediate consequence of our definition of the unital universal enveloping algebra (cf. (5.5) and (5.6)) and the fact that the commutator bracket satisfies the Leibniz rule in both entries. (Hint: The latter property is used to expand the commutator of polynomials to a sum of terms containing as a factor the commutator of generators, which is identified via (5.5) with the Lie bracket.) As a consequence of Lemma 4.12, we obtain PSymp → Alg uLie , cf. Example 3.8. It is easy to check that the composition φ ! H : PSymp → Alg As of the Heisenberg Lie algebra functor and the unital universal enveloping algebra functor is naturally isomorphic to the usual (polynomial) CCR-algebra functor CCR : PSymp → Alg As that is used in the quantization of linear field theories, cf. [BGP07,BDH13]. In particular, we obtain a natural isomorphism Q lin H L ∼ = CCR L : C → Alg As , which means that our quantization prescription via Q lin is in this case equivalent to the ordinary CCR-algebra quantization of linear field theories. ▽ We would like to emphasize that our linear quantization functor preserves both j-locality and W -constancy, i.e. it preserves descent and the time-slice axiom of field theories.
Towards derived quantization of linear gauge theories
The techniques we developed in this paper can be refined to the case where M is a suitable symmetric monoidal model category. Let us recall that a model category is a category that comes equipped with three distinguished classes of morphisms -called weak equivalences, fibrations and cofibrations -that satisfy a list of axioms going back to Quillen, see e.g. [DS95] for a concise introduction. The main role is played by the weak equivalences, which introduce a consistent concept of "two things being the same" that is weaker than the usual concept of categorical isomorphism. For example, the category M = Ch(K) of (possibly unbounded) chain complexes of vector spaces over a field K may be endowed with a symmetric monoidal model category structure in which the weak equivalences are quasi-isomorphisms, see e.g. [Hov99].
Model category theory plays an important role in the mathematical formulation of (quantum) gauge theories. In particular, the 'spaces' of fields in a gauge theory are actually higher spaces called stacks, which may be formalized within model category theory. We refer to e.g. [Sch13] for the general framework and also to [BSS18] for the example of Yang-Mills theory. Consequently, the observable 'algebras' in a quantum gauge theory are actually higher algebras, e.g. the differential graded algebras arising in the BRST/BV formalism. We refer to [Hol08,FR12,FR13] for concrete constructions within the BRST/BV formalism in algebraic quantum field theory and also to [BSW18] for the relevant model categorical perspective.
The aim of this last section is to refine the linear quantization adjunction from Section 5 to the framework of model category theory. In particular, we will construct a derived linear quantization functor, which is an essential ingredient to quantize linear gauge theories to quantum gauge theories in a way that is consistent with the concept of weak equivalences. In order to simplify our presentation, we restrict ourselves to the case where M = Ch(K) is the symmetric monoidal model category of chain complexes of vector spaces over a field K of characteristic zero, e.g. K = C. In this section we shall freely use terminology and results from general model category theory [DS95,Hov99] and more specifically the model structures for colored operads and their algebras [Hin97,Hin15]. We refer to [BSW18] for a more gentle presentation of how these techniques can be applied to Ch(K)-valued algebraic quantum field theory.
Our first (immediate) result is that the categories FT(C, P (r 1 ,r 2 ) ) of field theories with values in M = Ch(K) from Definition 3.3 are model categories, i.e. there exists a consistent concept of weak equivalences for Ch(K)-valued field theories. Furthermore, the adjunctions in (3.25) are compatible with these model category structures in the sense that they are Quillen adjunctions.
Proof. This is a consequence of Theorem 3.12 and Hinich's results [Hin97,Hin15], which show that all colored operads in Ch(K) are admissible for K a field a characteristic zero.
As a specific instance of these general results, we obtain that both the category of Ch(K)valued linear field theories LFT(C) and the category of Ch(K)-valued quantum field theories QFT(C) carry a canonical model structure. Moreover, the linear quantization adjunction (5.4) is a Quillen adjunction. Using the general technique of derived functors (see e.g. [DS95,Hov99]), this means that we can construct a left derived linear quantization functor LQ lin and a right derivation of its right adjoint RU lin . Because all objects in the model categories of field theories from Proposition 6.1 are fibrant objects, there is no need to introduce a fibrant replacement functor and we can simply define the right derived functor by By Ken Brown's lemma, it follows that this functor preserves weak equivalences. It is important to stress that it is the derived functor LQ lin and not the non-derived functor Q lin which provides a meaningful quantization prescription for linear gauge theories that is consistent with the crucial concept of weak equivalences.
Remark 6.3. Regarding applications to the construction of quantum gauge theories, we would like to note that the derived linear quantization functor LQ lin always exists, because cofibrant replacements always exist in a model category. However, finding explicit models to compute cofibrant replacements is generically quite hard, which means that making these constructions practically applicable requires further work. We hope to come back to this issue in another paper, where we also plan to discuss concrete examples of linear quantum gauge theories. ▽ We would like to conclude this section by presenting a first attempt towards a natural homotopical generalization of the j-locality property (cf. Definition 4.4) and the W -constancy property (cf. Definition 4.8) in the context of model category theory. To motivate the definitions below, let us recall that given a Quillen adjunction F ⊣ G between model categories, the ordinary unit η : id → G F and counit ǫ : F G → id are built from the non-derived functors and hence they are in general not homotopically meaningful. As a consequence, our previous concepts of j-locality and W -constancy are in general not preserved under weak equivalences. To address this issue, we will consider the derived functors LF = F Q and RG = G R and formalize j-locality and W -constancy in terms of the derived unit and counit of the Quillen adjunction where q : Q → id (respectively r : id → R) is the natural weak equivalence corresponding to the cofibrant replacement functor Q (respectively the fibrant replacement functor R). Because all objects are fibrant objects in the model categories of field theories from Proposition 6.1, we can choose in what follows R = id.
We focus first on a homotopical generalization of the j-locality property from Definition 4.4.
Definition 6.4. Let j : C → D be a full orthogonal subcategory and P (r 1 ,r 2 ) any bipointed singlecolored operad. A field theory A ∈ FT D, P (r 1 ,r 2 ) is called homotopy j-local if the corresponding component of the derived counit weak equivalences and the commutative diagram The vertical arrows in the top square are weak equivalences because A is by hypothesis homotopy j-local. The vertical arrows in the two other squares are weak equivalences because left Quillen functors preserve cofibrant objects and weak equivalences between cofibrant objects. The bottom horizontal arrow is a weak equivalence because of Lemma 6.5. Finally, the natural isomorphism in the underbraces is due to (4.3).
Corollary 6.7. The derived linear quantization functor (6.2) maps homotopy j-local linear field theories to homotopy j-local quantum field theories.
We propose a homotopical generalization of the W -constancy property from Definition 4.8.
Definition 6.8. Let L : C → C[W −1 ] be an orthogonal localization and P (r 1 ,r 2 ) any bipointed single-colored operad. A field theory A ∈ FT C, P (r 1 ,r 2 ) is called homotopy W -constant if the corresponding component of the derived unit is a weak equivalence in FT C, P (r 1 ,r 2 ) .
It turns out that analyzing the homotopy W -constancy property is in general more subtle than our study of the homotopy j-locality property above. The reason for this is the following observation, which implies that L ! ⊣ L * is only under certain conditions a Quillen reflection. Proof. This follows from (6.3), the 2-of-3 property of weak equivalences and Proposition 4.6.
In order to prove some desirable properties of homotopy W -constant field theories, we have to introduce extra assumptions on the orthogonal localization functor L. It is an interesting and relevant question whether these assumptions are satisfied for the orthogonal localization L : Loc → Loc[W −1 ] appearing in locally covariant field theory, cf. Example 3.5. To answer this question, one has to perform an explicit study of cofibrant objects in the model categories of field theories, which is very technical and beyond the scope of this work.
Assumption A. The derived counit of the Quillen adjunction L ! ⊣ L * is a natural weak equivalence, i.e. L ! ⊣ L * is a Quillen reflection.
Assumption B. The functor L * L ! Q maps to the full subcategory of cofibrant objects.
Under Assumption A, it is easy to prove that the (derived) right adjoint functor RL * = L * constructs examples of homotopy W -constant field theories.
Proof. This follows from the commutative diagram where for the right vertical arrows we used Lemma 6.9 and Proposition 4.6.
Under both Assumptions A and B, we can prove that Proposition 4.11 generalizes to our model categorical setting.
Proof. Let A ∈ FT(C, P (r 1 ,r 2 ) ) be any homotopy W -constant field theory. We have to prove that the derived unit η (φ * ) ! Q(A) : Q (φ * ) ! Q(A) → L * L ! Q (φ * ) ! Q(A) corresponding to the field theory (φ * ) ! Q(A) ∈ FT(C, Q (s 1 ,s 2 ) ) is a weak equivalence. This follows from the 2-of-3 property of weak equivalences and the commutative diagram The vertical arrows in the top square are weak equivalences because (φ * ) ! is a left Quillen functor and η A is a weak equivalence between cofibrant objects by hypothesis and Assumption B. The vertical arrows in the bottom square are the isomorphisms explained in the proof of Proposition 4.11. Finally, the bottom horizontal arrow is a weak equivalence because of Lemma 6.10, which uses Assumption A.
Corollary 6.12. Suppose that both Assumptions A and B hold. Then the derived linear quantization functor (6.2) maps homotopy W -constant linear field theories to homotopy W -constant quantum field theories. | 15,099 | 2018-09-14T00:00:00.000 | [
"Mathematics"
] |