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Building Extraction from UAV Images Jointly Using 6 D-SLIC and Multiscale Siamese Convolutional Networks
Automatic building extraction using a single data type, either 2D remotely-sensed images or light detection and ranging 3D point clouds, remains insufficient to accurately delineate building outlines for automatic mapping, despite active research in this area and the significant progress which has been achieved in the past decade. This paper presents an effective approach to extracting buildings from Unmanned Aerial Vehicle (UAV) images through the incorporation of superpixel segmentation and semantic recognition. A framework for building extraction is constructed by jointly using an improved Simple Linear Iterative Clustering (SLIC) algorithm and Multiscale Siamese Convolutional Networks (MSCNs). The SLIC algorithm, improved by additionally imposing a digital surface model for superpixel segmentation, namely 6D-SLIC, is suited for building boundary detection under building and image backgrounds with similar radiometric signatures. The proposed MSCNs, including a feature learning network and a binary decision network, are used to automatically learn a multiscale hierarchical feature representation and detect building objects under various complex backgrounds. In addition, a gamma-transform green leaf index is proposed to truncate vegetation superpixels for further processing to improve the robustness and efficiency of building detection, the Douglas–Peucker algorithm and iterative optimization are used to eliminate jagged details generated from small structures as a result of superpixel segmentation. In the experiments, the UAV datasets, including many buildings in urban and rural areas with irregular shapes and different heights and that are obscured by trees, are collected to evaluate the proposed method. The experimental results based on the qualitative and quantitative measures confirm the effectiveness and high accuracy of the proposed framework relative to the digitized results. The proposed framework performs better than state-of-the-art building extraction methods, given its higher values of recall, precision, and intersection over Union (IoU).
Introduction
Building extraction based on remote sensing data is an effective technique to automatically delineate building outlines; it has been widely studied for decades in the fields of photogrammetry and remote sensing, and is extensively used in various applications, including urban planning, cartographic mapping, and land use analysis [1,2].The significant progress in sensors and operating platforms has enabled us to acquire remote sensing images and 3D point clouds from cameras or Light Detection And Ranging (LiDAR) equipped in various platforms (e.g., satellite, aerial, and Unmanned Aerial Vehicle (UAV) platforms); thus, the methods based on images and point clouds are commonly used to extract buildings [3][4][5].
Building extraction can be broadly divided into three categories according to data source: 2D image-based methods, 3D point cloud-based methods, and 2D and 3D information hybrid methods.2D image-based building extraction consists of two stages, namely, building segmentation and regularization.Many approaches have been proposed in recent years to extract buildings through very-high-resolution 2D imagery, including the active contour model-based method [6], multidirectional and multiscale morphological index-based method [7], combined binary filtering and region growing method [8], object-based method [9], dense attention network-based method [10], and boundary-regulated network-based method [2].Although these methods have achieved important advancements, a single cue from 2D images remains insufficient to extract buildings under the complex backgrounds of images (e.g., illumination, shadow, occlusion, geometric deformation, and quality degradation), which cause inevitable obstacles in the identification and delineation of building outlines under different circumstances.Consequently, differentiating building and non-building objects that carry similar radiometric signatures is difficult by using spectral information alone.Existing methods focus more on building qualitative detection than accurate outline extraction, thus requiring further improvement in building contour extraction to satisfy various applications, such as automatic mapping and building change detection.
Unlike 2D remotely-sensed imagery, LiDAR data can provide the 3D information of ground objects, and are especially useful in distinguishing building and non-building objects by height variation.Various approaches based on LiDAR data, such as polyhedral building roof segmentation and reconstruction [11], building roof segmentation using the random sample consensus algorithm [12,13] and global optimization [14], and automatic building extraction using point-and grid-based features [15], have been proposed for building extraction.However, the utilization of height information alone may fail to distinguish building and non-building objects with similar heights, such as houses and surrounding trees with smooth canopies.The accuracy of building extraction often relies on the density of 3D point clouds, and the outline of poor-quality points at the edge of buildings is challenging to accurately delineate.Moreover, most LiDAR-based methods may only be applicable to urban building extraction and may be unsuitable for extracting rural buildings with topographic relief because of the difficulty in giving a certain height threshold to truncate non-building objects.Aside from these limitations, automatic building extraction is challenging in the contexts of complex shape, occlusion, and size.Therefore, automatically extracting buildings by using a single data type, either 2D remotely-sensed images or 3D LiDAR point clouds, remains insufficient.
Many approaches that combine spectral and height information have been proposed to overcome the shortcomings of building extraction using a single data type.In [16,17], Normalized Difference Vegetation Index (NDVI) and 3D LiDAR point clouds were used to eliminate vegetation and generate a building mask, and height and area thresholds were given to exclude other low-height objects and small buildings.A method based on LiDAR point clouds and orthoimage has been proposed to delineate the boundaries of buildings, which are then regulated by using image lines [1].However, compared with satellite and aerial imagery, LiDAR data are actually difficult to access due to the high cost involved [5].Tian et al. [18] proposed an approach to building detection based on 2D images and Digital Surface Model (DSM); unlike 3D LiDAR point clouds, height information is generated from stereo imagery by the dense matching algorithm.Moreover, the combination of 2D UAV orthoimages and image-derived 3D point clouds has been used for building extraction on the basis of low-cost and high-flexibility UAV photogrammetry and remote sensing [5,19].Most civil UAVs only acquire remote sensing images with RGB channels and do not include multispectral bands (e.g., near-infrared bands), that is, eliminating vegetation by the NDVI is not feasible.As an alternative method, RGB-based Multidimensional Feature Vector (MFV) and Support Vector Machine (SVM) classifiers were integrated by Dai et al. [5] to eliminate vegetation; in this method, buildings are extracted by using a certain height threshold (e.g., 2.5 m), and building outlines are regularized by jointly using a line-growing algorithm and a w-k-means clustering algorithm.However, this method is only useful for extracting buildings with linear and perpendicular edges and not applicable to extract buildings with irregular shapes.
On the basis of the advantages of UAV photogrammetry and remote sensing, this study concentrates on building segmentation and outline regularization based on UAV orthoimages and image-derived point clouds.First, image segmentation is implemented to cluster all pixels of UAV orthoimages; SLIC is a popular algorithm for segmenting superpixels and does not require much computational cost [20], but it easily confuses building and image backgrounds with similar radiometric signatures.We accordingly exploit a novel 6D simple linear iterative clustering (6D-SLIC) algorithm for superpixel segmentation by additionally imposing DSM that is generated from image-derived 3D point clouds; DSM helps to distinguish objects from different heights (e.g., building roof and road).Second, the vegetation superpixels are truncated by using a Gamma-transform Green Leaf Index (GGLI).Then, the boundaries of non-vegetation objects are shaped by merging the superpixels with approximately equal heights.Inspired by the progresses made in deep learning in recent years, the deep convolutional neural network is one of the most popular and successful deep networks for image processing because it can work efficiently under various complex backgrounds [21][22][23][24][25][26] and is suitable for identifying building objects under different circumstances.The Fully Convolutional Network (FCN) [27] is a specific type of deep network that is used for image segmentation and building extraction [28].U-shaped convolutional Networks (U-Nets) are extended for image segmentation [29] and building extraction [30].In this study, buildings are detected by Multiscale Siamese Convolutional Networks (MSCNs), including a feature learning network and a binary decision network, which are used to automatically learn a multiscale hierarchical feature representation and detect building objects.Finally, the building outlines are regulated by the Douglas-Peucker and iterative optimization algorithms.
The main contribution of this study is to propose a method for building extraction that is suitable for UAV orthoimage and image-derived point clouds.In this method, the improved SLIC algorithm for UAV image segmentation, which helps accurately delineate building boundaries under building and image backgrounds with similar radiometric signatures.MSCNs are used to improve the performance of building detection under various complex backgrounds, and the Douglas-Peucker algorithm and iterative optimization are coupled to eliminate jagged details generated from small structures as a result of superpixel segmentation.
The remainder of this paper is organized as follows.Section 2 describes the details of the proposed method for building extraction.Section 3 presents the comparative experimental results in combination with a detailed analysis and discussion.Section 4 concludes this paper and discusses possible future work.
Proposed Method
The proposed framework for building extraction consists of three stages, as presented in Figure 1.In the segmentation stage, 6D-SLIC is used to segment superpixels from UAV orthoimages and DSM (generated from image-derived point clouds), and the initial outlines of ground objects are shaped by merging the superpixels.In the building detection stage, a GGLI is used to eliminate vegetation, and the buildings are detected by using the proposed MSCNs (including a feature learning network for deep feature representation and a binary network for building detection).In the regularization stage, the building boundaries are decimated and simplified by removing insignificant vertices using the Douglas-Peucker algorithm.At the same time, the building outlines are regulated by using a proposed iterative optimization algorithm.Finally, the building outlines are validated and evaluated.
D-SLIC-based Superpixel Segmentation
Image segmentation is a commonly used and powerful technique for delineating the boundaries of ground objects.It is also a popular topic in the fields of computer vision and remote sensing.The classical segmentation algorithms for remotely-sensed imagery, such as quadtree-based segmentation [31], watershed segmentation [32], and Multi-Resolution Segmentation (MRS) [33], often partition an image into relatively homogeneous regions generally using spectral and spatial information while rarely introducing additional information to assist segmentation (e.g., height information) despite various improved methods for finding solutions to some image datasets [9,[34][35][36].Therefore, the commonly used segmentation methods that are highly dependent on spectral information cannot still break the bottleneck, i.e., sensitivity to illumination, occlusion, quality degradation, and various complex backgrounds.Especially for UAV remote sensing images, a centimeter-level ground resolution provides high-definition details and geometric structural information of ground objects but also generates disturbances, which pose a great challenge in accurately delineating boundaries.
Examples of four types of buildings are given in Figure 2(a).The best results of segmentation obtained from classical methods are exhibited in Figures 2(b) and (c); such results are achieved through multiple tests to find the optimal parameters (e.g., scale: 300, shape: 0.4, compactness: 0.8 in MRS).MRS performs better than quadtree-based methods do, but the building boundaries under MRS are still incomplete or confused with backgrounds relative to ground-truth outlines (Figure 2(d)) because the spectral difference is the insignificant gap at building edges.The accurate outlines of buildings are difficult to delineate from the spectral and spatial information of UAV images.Many strategies can be used to merge the segmented regions to the entities, but finding a generic rule to achieve a perfect solution in a single data source is actually difficult.Most classical algorithms (e.g., MRS) are time and memory consuming when used to segment large remotely-sensed imagery, because they use a pixel grid for the initial object representation [37].
D-SLIC-Based Superpixel Segmentation
Image segmentation is a commonly used and powerful technique for delineating the boundaries of ground objects.It is also a popular topic in the fields of computer vision and remote sensing.The classical segmentation algorithms for remotely-sensed imagery, such as quadtree-based segmentation [31], watershed segmentation [32], and Multi-Resolution Segmentation (MRS) [33], often partition an image into relatively homogeneous regions generally using spectral and spatial information while rarely introducing additional information to assist segmentation (e.g., height information) despite various improved methods for finding solutions to some image datasets [9,[34][35][36].Therefore, the commonly used segmentation methods that are highly dependent on spectral information cannot still break the bottleneck, i.e., sensitivity to illumination, occlusion, quality degradation, and various complex backgrounds.Especially for UAV remote sensing images, a centimeter-level ground resolution provides high-definition details and geometric structural information of ground objects but also generates disturbances, which pose a great challenge in accurately delineating boundaries.
Examples of four types of buildings are given in Figure 2a.The best results of segmentation obtained from classical methods are exhibited in Figure 2b,c; such results are achieved through multiple tests to find the optimal parameters (e.g., scale: 300, shape: 0.4, compactness: 0.8 in MRS).MRS performs better than quadtree-based methods do, but the building boundaries under MRS are still incomplete or confused with backgrounds relative to ground-truth outlines (Figure 2d) because the spectral difference is the insignificant gap at building edges.The accurate outlines of buildings are difficult to delineate from the spectral and spatial information of UAV images.Many strategies can be used to merge the segmented regions to the entities, but finding a generic rule to achieve a perfect solution in a single data source is actually difficult.Most classical algorithms (e.g., MRS) are time and memory consuming when used to segment large remotely-sensed imagery, because they use a pixel grid for the initial object representation [37].Many deep learning-based algorithms, such as multiscale convolutional network [38], deep convolutional encoder-decoder [39], and FCN [40], have been proposed for the semantic segmentation of natural images or computer vision applications, and prominent progress has been made.However, deep learning-based methods dramatically increase computational time and memory and are thus inefficient for the fast segmentation of large UAV orthoimages.In the current study, a 6D-SLIC algorithm is used to extract initial building outlines by joining height information.SLIC is a state-of-the-art algorithm for segmenting superpixels that does not require much computational resource to achieve effective and efficient segmentation.
In the 6D-SLIC algorithm, superpixels are generated by clustering pixels according to their color similarity and proximity in the 2D image plane space; in this way, the proposed algorithm is similar to the SLIC algorithm [20].Compared to the five-dimensional (5D) space [ ] , , , , l a b x y in the SLIC algorithm, the height information obtained from image-derived 3D point clouds is then used to cluster pixels.Hence, a 6D space [ ] , , , , , l a b x y z is used to generate compact, nearly uniform superpixels, where [ ] , , l a b is defined by the pixel color vector of the CIELAB color space and [ ] , , x y z is the 3D coordinate of a pixel.The pixels in the CIELAB color space are considered Many deep learning-based algorithms, such as multiscale convolutional network [38], deep convolutional encoder-decoder [39], and FCN [40], have been proposed for the semantic segmentation of natural images or computer vision applications, and prominent progress has been made.However, deep learning-based methods dramatically increase computational time and memory and are thus inefficient for the fast segmentation of large UAV orthoimages.In the current study, a 6D-SLIC algorithm is used to extract initial building outlines by joining height information.SLIC is a state-of-the-art algorithm for segmenting superpixels that does not require much computational resource to achieve effective and efficient segmentation.
In the 6D-SLIC algorithm, superpixels are generated by clustering pixels according to their color similarity and proximity in the 2D image plane space; in this way, the proposed algorithm is similar to the SLIC algorithm [20].Compared to the five-dimensional (5D) space [l, a, b, x, y] in the SLIC algorithm, the height information obtained from image-derived 3D point clouds is then used to cluster pixels.Hence, a 6D space [l, a, b, x, y, z] is used to generate compact, nearly uniform superpixels, where [l, a, b] is defined by the pixel color vector of the CIELAB color space and [x, y, z] is the 3D coordinate of a pixel.The pixels in the CIELAB color space are considered perceptually uniform for small color distances, and height information z is used to cluster the pixels into the building area with approximately equal heights.
Unlike that in the SLIC algorithm, the desired number of approximately equally sized superpixels K is indirectly given in the 6D-SLIC algorithm but is computed on the basis of the minimum area A min , as follows: where N is the number of pixels in an image and R denotes the ground resolution (unit: m).A min is commonly given as 10 m 2 with reference to the minimum area of buildings in The literature [5], whereas 5 m 2 is given to consider small buildings in the current study; each superpixel approximately contains N/K pixels, and a superpixel center would exist for roughly equally sized superpixels at every grid interval S = at regular grid intervals S are selected.Similar to the SLIC algorithm, the search area of the pixels associated with each cluster C k is assumed to be within 2S × 2S of the 2D image plane space.The Euclidean distance of the CIELAB color space and height are used to define pixel similarity, which is useful in clustering pixels for small distances.The distance measure D S of the proposed 6D-SLIC algorithm is defined as follows: where xy between a pixel i (i ∈ R 2S×2S ) and the cluster center C k can be computed as follows: As a result of the high-definition details of UAV images, noisy pixels may be considerable and should be avoided in the selection of a cluster center.A 3D gradient is proposed to control the sampling of K cluster centers and move them to the lowest 3D gradient position in a 3×3 neighborhood to avoid placing a cluster center at the edge of buildings.The 3D gradients G(x, y, z) are computed as where G I and G z denote the gradients of image intensity and height difference, respectively.The two gradients can be computed as where I(x, y) and DSM(x, y) represent the lab vector and height corresponding to the pixel at position (x, y), respectively; and .denotes the L 2 norm.DSM is generated from image-derived 3D point clouds.
All the pixels of the UAV images are associated with the nearest cluster center on the basis of the minimum distance of D S .The cluster center C k is then updated by where n k is the number of pixels that belong to the cluster center C k .The new cluster center should be moved to the lowest 3D gradient position again on the basis of the values of Equations ( 4) and (5).The processes of associating all pixels to the nearest cluster center and recomputing the cluster center are iteratively repeated until the convergence of distance D S .
After all pixels are clustered into the nearest cluster center, a strategy of enforcing connectivity is employed to remove the small disjoint segments and merge the segments in terms of the approximately equal height in each cluster.Therefore, the initial boundaries of ground objects are shaped by connecting the segments in the vicinity.This definition satisfies the constraint in Equation (7), and clusters i and j are regarded to belong to the same ground object.
where mean_z represents the average operation of height and z_threshold is a given height threshold, which is set to 2.5 m in this study.
We use an efficient and effective superpixel segmentation on the basis of the SLIC algorithm, which is regarded as a simple and efficient approach that is suitable for large-image segmentation.3D space coordinates, rather than a 2D image plane space, are selected as a distance measure to cluster all pixels of an image into superpixels.The algorithm is expressed below, and the comparisons of superpixel segmentation based on the SLIC and 6D-SLIC algorithms are shown in Figure 3.The building areas are identified by vegetation removal and Siamese-typed networks (described in Sections 2.2 and 2.3), except for the regions merging on the basis of height similarity.
Perturb each cluster center in a 3×3 neighborhood to the lowest 3D gradient position.repeat for each cluster center C k do Assign the pixels to C k based on a new distance measure (Equation (2)).end for Update all cluster centers based on Equations ( 5) and (6).Compute residual error between the previous centers and recomputed centers e ← D 3 depicts that the boundaries of the superpixels at the building edges obtained from the proposed 6D-SLIC algorithm are closer to the true boundaries of buildings than those obtained from the SLIC algorithm are.Additionally, other four state-of-the-art methods (e.g., Entropy Rate Superpixels (ERS) [41], Superpixels Extracted via Energy-Driven Sampling (SEEDS) [42], preemptive SLIC (preSLIC) [43], and Linear Spectral Clustering (LSC) [44]) are used to compare with the 6D-SLIC algorithm, as shown in Figure 4, the four methods do not perform better, and the 6D-SLIC algorithm also shows more similar shapes to the ground-truth maps of the buildings.Moreover, the metrics, e.g., standard boundary recall BR and under-segmentation error USE [45], are used to measure the quality of boundaries between building over-segments and the ground-truth.From the visual assessment and the statistical results of two quantitative metrics in Table 1, it can be inferred that the 6D-SLIC algorithm performs better than the SLIC algorithm and other four state-of-the-art methods do due to the additional height information used for superpixel segmentation in the 3D space instead of a 2D image plane space.
Remote Sens. 2019, 11, x FOR PEER REVIEW 8 of 33 Enforcing connectivity.Figure 3 depicts that the boundaries of the superpixels at the building edges obtained from the proposed 6D-SLIC algorithm are closer to the true boundaries of buildings than those obtained from the SLIC algorithm are.Additionally, other four state-of-the-art methods (e.g.Entropy Rate Superpixels (ERS) [41], Superpixels Extracted via Energy-Driven Sampling (SEEDS) [42], preemptive SLIC (preSLIC) [43], and Linear Spectral Clustering (LSC) [44]) are used to compare with the 6D-SLIC algorithm, as shown in Figure 4, the four methods do not perform better, and the 6D-SLIC algorithm also shows more similar shapes to the ground-truth maps of the buildings.Moreover, the metrics, e.g. standard boundary recall BR and under-segmentation error USE [45], are used to measure the quality of boundaries between building over-segments and the ground-truth.From the visual assessment and the statistical results of two quantitative metrics in Table 1, it can be inferred that the 6D-SLIC algorithm performs better than the SLIC algorithm and other four state-of-the-art methods do due to the additional height information used for superpixel segmentation in the 3D space instead of a 2D image plane space.
Vegetation Removal
In this study, height similarity is not immediately used to merge superpixels for generating initial building boundaries after 6D-SLIC segmentation because the vegetation surrounding buildings with similar heights may be classified as part of these buildings.An example is given in Figure 5.The image-derived 3D point clouds show that the tree canopies have approximately equal heights relative to the nearby buildings; therefore, the surrounding 3D vegetation points are the obstacle and noise for building detection.Vegetation removal is used to truncate vegetation superpixels for further processing to improve the robustness and efficiency of building detection.
Vegetation Removal
In this study, height similarity is not immediately used to merge superpixels for generating initial building boundaries after 6D-SLIC segmentation because the vegetation surrounding buildings with similar heights may be classified as part of these buildings.An example is given in Figure 5.The image-derived 3D point clouds show that the tree canopies have approximately equal heights relative to the nearby buildings; therefore, the surrounding 3D vegetation points are the obstacle and noise for building detection.Vegetation removal is used to truncate vegetation superpixels for further processing to improve the robustness and efficiency of building detection.
Vegetation Removal
In this study, height similarity is not immediately used to merge superpixels for generating initial building boundaries after 6D-SLIC segmentation because the vegetation surrounding buildings with similar heights may be classified as part of these buildings.An example is given in Figure 5.The image-derived 3D point clouds show that the tree canopies have approximately equal heights relative to the nearby buildings; therefore, the surrounding 3D vegetation points are the obstacle and noise for building detection.Vegetation removal is used to truncate vegetation superpixels for further processing to improve the robustness and efficiency of building detection.The NDVI is commonly used to detect vegetation on the basis of near-infrared information, but it is unavailable to 3D image-derived point clouds with true color (RGB) in most UAV remotely-sensed imagery.Thus, many vegetation indices based on the RGB system are proposed, and they include the normalized green-red difference index (NGRDI) [46], visible atmospherically resistant index (VARI) [47], green leaf index (GLI) [48], ratio index (RI) [49], and excess green minus excess red (ExG-ExR) [50].Figures 4(d)-(h) show the extracted vegetation information of Figure 5(a) using the five vegetation indices.GLI performs better than NGRDI, VARI, GLI, and ExG-ExR do.A suitable intensity threshold is actually difficult to set to separate vegetation from the results of the vegetation index calculation.In [5], a standard SVM classification and a priori training data were employed to extract vegetation from an MFV, which was integrated by the five vegetation indices.However, the method may not achieve a satisfying result when a priori training data are not representative, and the poor vegetation indices also reduce the performance of vegetation extraction.Therefore, in this study, a GGLI is created to extract vegetation by enhancing vegetation intensity and using a self-adaptive threshold.The GGLI is defined as follows: where γ denotes the gamma value, which is set to 2.5 that is approximately estimated based on the range of 0 to 255 of GGLI value in this study; and R , G , B are the three components of RGB color.The NDVI is commonly used to detect vegetation on the basis of near-infrared information, but it is unavailable to 3D image-derived point clouds with true color (RGB) in most UAV remotely-sensed imagery.Thus, many vegetation indices based on the RGB system are proposed, and they include the normalized green-red difference index (NGRDI) [46], visible atmospherically resistant index (VARI) [47], green leaf index (GLI) [48], ratio index (RI) [49], and excess green minus excess red (ExG-ExR) [50].Figure 4d-h show the extracted vegetation information of Figure 5a using the five vegetation indices.GLI performs better than NGRDI, VARI, GLI, and ExG-ExR do.A suitable intensity threshold is actually difficult to set to separate vegetation from the results of the vegetation index calculation.In [5], a standard SVM classification and a priori training data were employed to extract vegetation from an MFV, which was integrated by the five vegetation indices.However, the method may not achieve a satisfying result when a priori training data are not representative, and the poor vegetation indices also reduce the performance of vegetation extraction.Therefore, in this study, a GGLI is created to extract vegetation by enhancing vegetation intensity and using a self-adaptive threshold.The GGLI is defined as follows: where γ denotes the gamma value, which is set to 2.5 that is approximately estimated based on the range of 0 to 255 of GGLI value in this study; and R, G, B are the three components of RGB color.Figure 5i shows that the proposed GGLI performs better than the other five vegetation indices do.
When the number of pixels belonging to vegetation in the superpixel C k is more than half of the number of pixels in the superpixel C k , then the superpixel C k is considered a vegetation region.The definition satisfies the constraint in Equation ( 9), and the superpixel C k is classified into a vegetation region.
where num denotes the calculation operator of the number of pixels, I i ∈ v denotes the pixel I i belonging to vegetation v, and R C k is the region of the superpixel C k .The GGLI value of a pixel is more than 0.5 times the maximum GGLI value in the entire image, and the pixel is classified into vegetation.Tests using UAV data, including two urban and two rural areas with different vegetation covers, are conducted.( ) ( ) where num denotes the calculation operator of the number of pixels, i I v ∈ denotes the pixel i I belonging to vegetation v , and is the region of the superpixel k C .The GGLI value of a pixel is more than 0.5 times the maximum GGLI value in the entire image, and the pixel is classified into vegetation.Tests using UAV data, including two urban and two rural areas with different vegetation covers, are conducted.Figure 6
Building Detection Using MSCNs
After the removal of vegetation superpixels, there still exist some non-building superpixels that are meaningless for further delineation of building outlines and should thus be eliminated.Building detection is commonly achieved by classification or recognition of ground objects, in which many types of features, such as color, texture, and geometric structure, are used to directly or indirectly represent building characteristics by feature descriptors.However, most manually
Building Detection Using MSCNs
After the removal of vegetation superpixels, there still exist some non-building superpixels that are meaningless for further delineation of building outlines and should thus be eliminated.Building detection is commonly achieved by classification or recognition of ground objects, in which many types of features, such as color, texture, and geometric structure, are used to directly or indirectly represent building characteristics by feature descriptors.However, most manually designed features remain insufficient to extract buildings from UAV images with high-definition details under various complex backgrounds (e.g., shadow, occlusion, and geometric deformation).
In this paper, we present MSCNs used in building recognition as feature representation using a convolutional network can work efficiently under various complex backgrounds.We aim to learn deep convolutional networks that can discriminate building and non-building ground objects by 2D UAV image and height information.In our case, the discriminative training of buildings does not rely on labels of individual ground objects but on pairs of 2D UAV images and their height information.Multiscale Siamese-typed architecture is suitable for achieving this goal due to three reasons.First, MSCNs are capable of learning generic deep features, which are useful for making predictions on unknown non-building class distributions even when few examples are available in these new distributions.Second, MSCNs are easily trained using a standard optimization technique on the basis of pairs sampled from 2D images and 3D height information.Third, the sizes of buildings in UAV images vary from small neighborhoods to large regions containing hundreds of thousands of pixels.The feature maps displayed in Figure 7 indicate that the small local structures of buildings tend to respond to small convolutional filters, whereas the coarse structures tend to be extracted by large filters.Thus, multiscale convolutional architecture is suitable to extract the detailed and coarse structures of buildings.
Remote Sens. 2019, 11, x FOR PEER REVIEW 13 of 33 designed features remain insufficient to extract buildings from UAV images with high-definition details under various complex backgrounds (e.g., shadow, occlusion, and geometric deformation).
In this paper, we present MSCNs used in building recognition as feature representation using a convolutional network can work efficiently under various complex backgrounds.We aim to learn deep convolutional networks that can discriminate building and non-building ground objects by 2D UAV image and height information.In our case, the discriminative training of buildings does not rely on labels of individual ground objects but on pairs of 2D UAV images and their height information.Multiscale Siamese-typed architecture is suitable for achieving this goal due to three reasons.First, MSCNs are capable of learning generic deep features, which are useful for making predictions on unknown non-building class distributions even when few examples are available in these new distributions.Second, MSCNs are easily trained using a standard optimization technique on the basis of pairs sampled from 2D images and 3D height information.Third, the sizes of buildings in UAV images vary from small neighborhoods to large regions containing hundreds of thousands of pixels.The feature maps displayed in Figure 7 indicate that the small local structures of buildings tend to respond to small convolutional filters, whereas the coarse structures tend to be extracted by large filters.Thus, multiscale convolutional architecture is suitable to extract the detailed and coarse structures of buildings.The architecture of the proposed MSCNs is shown in Figure 8, and it includes input, feature learning networks, binary decision networks, and output.In this study, input patches are extracted from the merged superpixels.The feature learning network consists of two streams of convolutional and max-pooling layers, three convolutional layers are arranged for feature extraction in each stream, and two max-pooling layers are inserted in between successive convolutional layers to reduce the number of parameters and the computation in MSCNs.Batch normalization [51] is also inserted into each convolutional layer before the activation of neurons.Three subconvolutional layers arranged for the convolutional layers of Conv_x1, Conv_x2, Conv1, and Conv2 are to extract the feature from multiscale space.The convolutional layers Conv1 and Conv2 in two streams share identical weights, whereas Conv_x1 and Conv_x2 do not because of the different inputs of 1 x and 2 x .The binary decision network consists of two fully connected layers, and the outputs of MSCNs are predicted as 1 and 0 corresponding to building and non-building regions, respectively.The architecture of the proposed MSCNs is shown in Figure 8, and it includes input, feature learning networks, binary decision networks, and output.In this study, input patches are extracted from the merged superpixels.The feature learning network consists of two streams of convolutional and max-pooling layers, three convolutional layers are arranged for feature extraction in each stream, and two max-pooling layers are inserted in between successive convolutional layers to reduce the number of parameters and the computation in MSCNs.Batch normalization [51] is also inserted into each convolutional layer before the activation of neurons.Three subconvolutional layers arranged for the convolutional layers of Conv_x1, Conv_x2, Conv1, and Conv2 are to extract the feature from multiscale space.The convolutional layers Conv1 and Conv2 in two streams share identical weights, whereas Conv_x1 and Conv_x2 do not because of the different inputs of x 1 and x 2 .The binary decision network consists of two fully connected layers, and the outputs of MSCNs are predicted as 1 and 0 corresponding to building and non-building regions, respectively.In the proposed MSCNs, the output l j f of the j th hidden vector in the l th layer via the operators of linear transformation and activation can be expressed as , where 1 l j f − is the i th hidden vector in the ( ) In the proposed MSCNs, the output f l j of the jth hidden vector in the lth layer via the operators of linear transformation and activation can be expressed as where f l−1 j is the ith hidden vector in the (l − 1)th layer; S l−1 is the number of hidden vectors in the (l − 1)th layer; w and b represent the weights (or convolution kernels with size k × k in the convolutional layers) and biases, respectively; * is the dot product (or convolution operator in the convolutional layers); and σ(.) denotes the activation function.ReLU is applied to the feature learning and binary decision networks, and sigmoid is used in the output of MSCNs.In this study, discriminative training is prone to achieve the binary output of building and non-building probabilities, which are restricted between 0 and 1.Hence, sigmoid function (σ(x) = 1 1+e −x ), instead of ReLU, is used to compute the building and non-building probabilities of a ground object, and the global cost function is an alternative function of the hinge-based loss function with regard to sigmoid output.The proposed MSCNs are trained in a supervised manner by minimizing the global cost function L.
where h(x) denotes the predicted results of the output layer; y refers to the expected output values (i.e., 0 and 1 in this study) given in a supervised manner; n and n l are the numbers of trained data and layers, respectively; λ is a weight decay parameter; and S l and S l+1 are the numbers of hidden vectors in layers l and l + 1, respectively.The optimization of the proposed MSCNs is achieved by using the standard back-propagation algorithm based on stochastic gradient descent.The update rule of weights and biases at epoch T can be written as where η is the learning rate and µ is momentum.We let , and the partial derivatives with respect to the weight and bias between the layer l and the successive layer l + 1 can be computed by ∂L(w, b) The residual errors δ n l i and δ l i of the output layer and back propagation in the ith feature map of the lth convolutional layer can be computed as In this study, the two outputs of MSCNs are considered building probability p (b) and non-building probability p (nb) , which are used to define whether a non-vegetation object belongs to a building.The two probabilities satisfy the constraint in Equation (18), and the non-vegetation object is regarded as a building region.
where T 1 and T 2 are two given thresholds.
Building Outline Regularization
Once a building and its initial outline have been determined, the next step is to refine the building outline.An initial outline of a building is shown in Figure 9a.Many points are located in the same line segment, and the building edges are jagged and disturbed by small structures because of pixel-wise segmentation.The initial outline should be optimized by eliminating low-quality vertices and regularizing line segments.For this task, an iterative optimization algorithm, which utilizes the collinear constraint, is applied to regulate the building boundary.This algorithm consists of the following steps: (1) The Douglas-Peucker algorithm [52,53] is used to optimize building outlines by simplifying the curves that are approximated by a few vertices; the simplified outline is shown in Figure 9b.
(2) The consecutive collinear vertex v i , which satisfies the condition that the angle θ = (as shown in Figure 9c) between two adjacent line segments θ ∈ 11π 12 , 13π 12 ∪ 0, π 12 , is determined.Vertex v i is added to a candidate point set S co to be eliminated.
(3) Step ( 2) is repeated by tracking the line segments sequentially from the first vertex to the last vertex until all vertex set V b of the outline is traversed.The vertices of initial outline belonging to the point sets S co are eliminated from the vertex set V b , the vertex set V b is updated, and the candidate point set S co is set as null.
(4) Steps ( 2) and ( 3) are repeated until no more consecutive collinear vertex v i is added to the candidate point set S co .
(5) The vertex set V b is tracked sequentially from the first vertex to the last vertex; two adjacent vertices v i and v i+1 are considered too close if they satisfy the condition that the distance d (as shown in Figure 9c) between v i and v i+1 is less than a given threshold d < T vv (0.5 m).One of v i and v i+1 is eliminated, and the vertex set V b is updated.(6) Step ( 5) is repeated until no more vertex needs to be eliminated, and the outline is reconstructed by the vertex set V b .
utilizes the collinear constraint, is applied to regulate the building boundary.This algorithm consists of the following steps: (1) The Douglas-Peucker algorithm [52,53] is used to optimize building outlines by simplifying the curves that are approximated by a few vertices; the simplified outline is shown in Figure 9(b).
(2) The consecutive collinear vertex i v , which satisfies the condition that the angle , (as shown in Figure 9(c)) between two adjacent line segments 11 13 , 0 , 12 12 12
One of i v and
1 i v + is eliminated, and the vertex set b V is updated.(6) Step ( 5) is repeated until no more vertex needs to be eliminated, and the outline is reconstructed by the vertex set b V .Figure 9d shows that the proposed iterative optimization algorithm can effectively reduce the superfluous vertices while reconstructing a relatively regular building shape.
Data Description
Two datasets for building extraction are collected by a UAV aerial photogrammetry system, which comprises a UAV platform, one digital camera, a global positioning system, and an inertial measurement unit, to evaluate the performance of the proposed method.The digital camera selected to capture low-altitude UAV remotely-sensed imagery is a SONY ILCE-7RM2 35 mm camera.The test datasets were captured over Zunqiao of Jiangxi Province of China (28 • 21 30 N, 117 • 57 39 E) in the summer of 2016, during which the UAV flew upward for approximately 400 m.These study areas include urban and rural areas, which are characterized by different scales, different roofs, dense residential, tree surrounding, and irregular shape buildings.Structure from motion [54] and bundle adjustment are used to yield high-precision relative orientation parameters of all UAV remotely-sensed images and recover 3D structures from 2D UAV images, which are referenced by using ground control points collected from high-precision GPS/RTK equipment.Dense and precise 3D point clouds with an approximately average point spacing of 0.1 m are derived from corresponding UAV images using a multiview matching method [55] and can thus provide a detailed 3D structure description for buildings.These image-derived 3D point clouds are also used to generate high-resolution UAV orthoimages and DSMs.Two subregions of Zunqiao are selected for building extraction with two datasets of 3501 × 3511 and 1651 × 3511 pixels.The experimental datasets are shown in Figure 10.The two selected regions include not only urban and rural buildings of different materials, different spacings, different colors and textures, different heights, and complex roof structures, but also, complex backgrounds (e.g., topographic relief, trees surrounding buildings, shadow next to buildings, and roads that resemble building roofs).
To facilitate the comparison, the proposed method was also evaluated on an open benchmark dataset, the International Society for Photogrammetry and Remote Sensing (ISPRS) 2D semantic labeling contest (Potsdam), which can be downloaded from the ISPRS official website (http://www2.isprs.org/commissions/comm3/wg4/2d-sem-label-potsdam.html).The dataset contains 38 patches (of the same size, i.e., 6000 × 6000 pixels), each consisting of a very high-resolution true orthophoto (TOP) tile that is extracted from a larger TOP mosaic, and the corresponding DSMs were also provided.The ground sampling distance of both, the TOP and the DSM, is 5 cm.And the buildings were labeled in the ground truth.In this study, to be as consistent as possible with the UAV images, and to evaluate the performance of distinguishing building roof from ground, two very high-resolution true orthophoto tiles that are partially similar in texture and spectral characteristics (e.g., cement road and bare land), are selected to evaluate the proposed method, as shown in Figure 11.We provide the referenced building outlines, namely, ground-truth building outlines, that are extracted by manually digitizing all recognizable building outlines using ArcGIS software to verify the accuracy of the proposed method and compare it with other state-of-the-art methods.The boundary of each building is difficult to manually interpret by UAV orthoimage alone; therefore, we digitize the boundaries of buildings by the combination of UAV orthoimage and DSM.The two datasets contain 99 and 34 buildings separately.Figure 10(a) shows many buildings with boundaries that are not rectilinear and not mutually perpendicular or parallel.The ground-truth buildings of the four experimental datasets are given in Figure 12, some buildings with boundaries that are not rectilinear and not mutually perpendicular or parallel are shown in Figure 12(a), (c), and (d).We provide the referenced building outlines, namely, ground-truth building outlines, that are extracted by manually digitizing all recognizable building outlines using ArcGIS software to verify the accuracy of the proposed method and compare it with other state-of-the-art methods.The boundary of each building is difficult to manually interpret by UAV orthoimage alone; therefore, we digitize the boundaries of buildings by the combination of UAV orthoimage and DSM.The two datasets contain 99 and 34 buildings separately.Figure 10a shows many buildings with boundaries that are not rectilinear and not mutually perpendicular or parallel.The ground-truth buildings of the four experimental datasets are given in Figure 12, some buildings with boundaries that are not rectilinear and not mutually perpendicular or parallel are shown in Figure 12a,c,d.White and black denote building and non-building regions, respectively.
Evaluation Criteria of Building Extraction Performance
The results of building extraction using the proposed method and other existing methods are evaluated by overlapping with them with the ground-truth maps on the basis of previous reference maps of buildings.Four indicators are used to evaluate the classification performance of buildings and non-buildings: (1) the number of building regions correctly classified as belonging to buildings (i.e., TP), ( 2) the number of non-building regions incorrectly classified as belonging to buildings (i.e., FP), (3) the number of non-building regions correctly classified as belonging to non-buildings (i.e., TN), and (4) the number of building regions incorrectly classified as belonging to non-buildings (i.e., FN).Three metrics (i.e., completeness, correctness, and quality) are used to assess the results of building detection, which are computed as
Evaluation Criteria of Building Extraction Performance
The results of building extraction using the proposed method and other existing methods are evaluated by overlapping with them with the ground-truth maps on the basis of previous reference maps of buildings.Four indicators are used to evaluate the classification performance of buildings and non-buildings: (1) the number of building regions correctly classified as belonging to buildings (i.e., TP), (2) the number of non-building regions incorrectly classified as belonging to buildings (i.e., FP), (3) the number of non-building regions correctly classified as belonging to non-buildings (i.e., TN), and (4) the number of building regions incorrectly classified as belonging to non-buildings (i.e., FN).Three metrics (i.e., completeness, correctness, and quality) are used to assess the results of building detection, which are computed as [56] Comp = TP TP+FN , Corr = TP TP+FP , Qual = TP TP+FN+FP , (19) where Comp (i.e., completeness) is the proportion of all actual buildings that are correctly identified as buildings, Corr (i.e., correctness) is the proportion of the identified buildings that are actual buildings, and Qual (i.e., quality) is the proportion of the correctly identified buildings in all actual and identified buildings.The identified building or non-building regions are impossible to completely overlap with the corresponding regions in the reference maps.Therefore, we define two rules to judge whether a region is correctly identified to the corresponding category.First, the identified region that overlaps the reference map belongs to the same category.Second, the percentage of the area of the identified region that overlaps the reference map is more than 60% [9].
Although Comp, Corr, and Qual are the popular metrics to assess the results of building detection, these metrics remain insufficient to measure how good the overlap is between an outline of a building and the corresponding outline in the reference map.Hence, we use three other metrics, i.e., Recall, Precision, and intersection over Union (IoU) [57], to quantitatively evaluate the delineation performance of building outline.As shown in Figure 13, A and B are respectively the ground truth and the extracted building area, then Recall, Precision, and IoU can be computed as Remote Sens. 2019, 11, x FOR PEER REVIEW 21 of 33 where Comp (i.e., completeness) is the proportion of all actual buildings that are correctly identified as buildings, Corr (i.e., correctness) is the proportion of the identified buildings that are actual buildings, and Qual (i.e., quality) is the proportion of the correctly identified buildings in all actual and identified buildings.The identified building or non-building regions are impossible to completely overlap with the corresponding regions in the reference maps.Therefore, we define two rules to judge whether a region is correctly identified to the corresponding category.First, the identified region that overlaps the reference map belongs to the same category.Second, the percentage of the area of the identified region that overlaps the reference map is more than 60% [9].Although Comp , Corr , and Qual are the popular metrics to assess the results of building detection, these metrics remain insufficient to measure how good the overlap is between an outline of a building and the corresponding outline in the reference map.Hence, we use three other metrics, i.e., Recall, Precision, and intersection over Union (IoU) [57], to quantitatively evaluate the delineation performance of building outline.As shown in Figure 13, A and B are respectively the ground truth and the extracted building area, then Recall , Precision , and IoU can be computed as )
MSCNs Training
The training datasets of MSCNs are generated from UAV orthoimages and DSMs, which are obtained by photogrammetric techniques.The datasets include buildings of multiscale, different colors and heights, and complex roof structures in urban and rural areas.The datasets also contain patches with complex backgrounds, such as shadows, topographic relief, and trees surrounding buildings.A total of 50,000 pairs of patches (half building and half non-building patches) with a fixed size of 127 × 127 pixels are extracted in a supervised manner from the UAV orthoimages and DSMs that do not include the experimental images.The non-building patch examples are generated by two ways.First, we randomly select patches from non-building areas, which are determined by manually masking building areas.Second, some examples that are easily confused with buildings are specially selected from the regions of roads, viaducts, and railways to supplement non-building patches.Furthermore, 150,000 pairs of patches are extended to avoid overfitting by image rotation (e.g., 90°, 180°, and 270°), Gaussian blur, and affine transformation.Therefore, the total number of patch pairs is 200,000, in which 195,000 and 5,000 pairs of patches are randomly selected as training and test datasets, respectively.
At the training stage of MSCNs, a batch size of 100 is used as the input; hence, 1950 iterations exist in each epoch.The MSCNs are trained in parallel on NVIDIA GPUs, and training is forced to
MSCNs Training
The training datasets of MSCNs are generated from UAV orthoimages and DSMs, which are obtained by photogrammetric techniques.The datasets include buildings of multiscale, different colors and heights, and complex roof structures in urban and rural areas.The datasets also contain patches with complex backgrounds, such as shadows, topographic relief, and trees surrounding buildings.A total of 50,000 pairs of patches (half building and half non-building patches) with a fixed size of 127 × 127 pixels are extracted in a supervised manner from the UAV orthoimages and DSMs that do not include the experimental images.The non-building patch examples are generated by two ways.First, we randomly select patches from non-building areas, which are determined by manually masking building areas.Second, some examples that are easily confused with buildings are specially selected from the regions of roads, viaducts, and railways to supplement non-building patches.Furthermore, 150,000 pairs of patches are extended to avoid overfitting by image rotation (e.g., 90 • , 180 • , and 270 • ), Gaussian blur, and affine transformation.Therefore, the total number of patch pairs is 200,000, in which 195,000 and 5,000 pairs of patches are randomly selected as training and test datasets, respectively.
At the training stage of MSCNs, a batch size of 100 is used as the input; hence, 1950 iterations exist in each epoch.The MSCNs are trained in parallel on NVIDIA GPUs, and training is forced to terminate when the average value of the loss function is less than 0.001 or the epochs are more than 100.The weights of convolutional and fully connected layers are initialized by random Gaussian distributions [58].The momentum and weight decay are fixed at 0.9 and 0.0005, respectively.The initial learning rate is set to 0.01 and then gradually reduced by using a piecewise function [25] to accelerate the training of MSCNs.Another metric, namely, overall accuracy (OA), is used to evaluate the performance of building and non-building classification for quantitatively assessing the training performance of the proposed MSCNs.OA is computed as in which TP, FN, TN, and FP are defined in Section 3.2.We train three Siamese networks, namely, SCNs3, SCNs5, and SCNs7, to evaluate the effects of Siamese networks with and without multiscale.Here, a convolution operator is achieved by using one of the filters with sizes of 3 × 3, 5 × 5, and 7 × 7 in our model.We also evaluate the effect of layer number in our model by adding one convolutional layer to train and test the datasets, namely, MSCNs(layer+).The trained model achieves state-of-the-art results in training and test datasets (Table 2), and Figure 14 shows the changes in OA and the losses with increasing epochs during the training of MSCNs.Our network and the deeper network (layer+) achieve higher accuracies than SCNs3, SCNs5, and SCNs7 do.Although the deeper network (layer+) performs slightly better than MSCNs do, the convergence of MSCNs(layer+) is slower than that of MSCNs.MSCNs(layer+) converge at nearly 24 epochs (4.68 × 10 4 iterations), whereas MSCNs converge at nearly 30 epochs (5.85 × 10 4 iterations).In addition, MSCNs perform better than SCNs3, SCNs5, and SCNs7 do in terms of Completeness, Correctness, and Quality.The experimental results demonstrate the effective performance of MSCNs given the tradeoff between accuracy and network complexity.terminate when the average value of the loss function is less than 0.001 or the epochs are more than 100.The weights of convolutional and fully connected layers are initialized by random Gaussian distributions [58].The momentum and weight decay are fixed at 0.9 and 0.0005, respectively.The initial learning rate is set to 0.01 and then gradually reduced by using a piecewise function [25] to accelerate the training of MSCNs.Another metric, namely, overall accuracy ( OA ), is used to evaluate the performance of building and non-building classification for quantitatively assessing the training performance of the proposed MSCNs.OA is computed as
TP TN OA TP FN TN FP
in which TP , FN , TN , and FP are defined in Section 3.2.We train three Siamese networks, namely, SCNs3, SCNs5, and SCNs7, to evaluate the effects of Siamese networks with and without multiscale.Here, a convolution operator is achieved by using one of the filters with sizes of 3 × 3, 5 × 5, and 7 × 7 in our model.We also evaluate the effect of layer number in our model by adding one convolutional layer to train and test the datasets, namely, MSCNs(layer+).The trained model achieves state-of-the-art results in training and test datasets (Table 2), and Figure 14 shows the changes in OA and the losses with increasing epochs during the training of MSCNs.Our network and the deeper network (layer+) achieve higher accuracies than SCNs3, SCNs5, and SCNs7 do.Although the deeper network (layer+) performs slightly better than MSCNs do, the convergence of MSCNs(layer+) is slower than that of MSCNs.MSCNs(layer+) converge at nearly 24 epochs (
Comparisons of MSCNs and Random Forest Classifier
After vegetation removal and superpixel merging, many non-building regions remain.Postprocessing is needed to further classify building and non-building regions.The identified vegetation and the remaining regions after vegetation removal are shown in Figure 15.A classifier of MSCNs is designed for building detection in this study due to its capability of non-linear estimation and the robustness of object classification under complex backgrounds.Another classifier, named Random Forest, has been proven to perform efficiently in the classification of building and non-building regions in the literature [59], in which an experiment comparing Random Forest with MSCNs was conducted to test the effectiveness of the MSCN classifier.Multiple features were extracted to classify using Random Forest and compared to deep features.Table 3 provides the details of multiple features and the parameters of the Random Forest classifier.The experimental results of the ISPRS dataset are given in Figure 16, Figure 17 shows the confusion matrices of building and non-building classification obtained from the Random Forest classifier and MSCNs in the four experimental datasets.
After vegetation removal and superpixel merging, many non-building regions remain.Postprocessing is needed to further classify building and non-building regions.The identified vegetation and the remaining regions after vegetation removal are shown in Figure 15.A classifier MSCNs is designed for building detection in this study due to its capability of non-linear estimation and the robustness of object classification under complex backgrounds.Another classifier, named Random Forest, has been proven to perform efficiently in the classification of building and non-building regions in the literature [59], in which an experiment comparing Random Forest with MSCNs was conducted to test the effectiveness of the MSCN classifier.Multiple features were extracted to classify using Random Forest and compared to deep features.Table 3 provides the details of multiple features and the parameters of the Random Forest classifier.The experimental results of the ISPRS dataset are given in Figure 16, Figure 17 shows the confusion matrices of building and non-building classification obtained from the Random Forest classifier and MSCNs in the four experimental datasets.Figure 17 shows that the performance of the proposed MSCNs is better than that of the Random Forest classifier that uses the color histogram, bag of SIFT, and Hog in terms of confusion matrices.Almost all buildings in the two experimental datasets are correctly identified by using the proposed MSCNs, whereas the building identification accuracy of the Random Forest classifier based on color histogram and the bag of SIFT is less than 85%, and that based on Hog is less than 90%.This finding is attributed to two reasons.First, height is combined with spectral information for jointly distinguishing building and non-building ground objects.This approach helps determine a clear gap between building and other ground objects that are similar in texture and spectral Figure 17 shows that the performance of the proposed MSCNs is better than that of the Random Forest classifier that uses the color histogram, bag of SIFT, and Hog in terms of confusion matrices.Almost all buildings in the two experimental datasets are correctly identified by using the proposed MSCNs, whereas the building identification accuracy of the Random Forest classifier based on color histogram and the bag of SIFT is less than 85%, and that based on Hog is less than 90%.This finding is attributed to two reasons.First, height is combined with spectral information for jointly distinguishing building and non-building ground objects.This approach helps determine a clear gap between building and other ground objects that are similar in texture and spectral characteristics (e.g., cement road and bare land).Second, deep learning-based networks can extract non-linear and high-level semantic features that are not easily affected by image grayscale variations, and they show higher robustness than the other three low-level manually designed features (color histogram, bag of SIFT, and Hog) do. Figure 18
Comparisons of Building Extraction Using Different Parameters
In the 6D-SLIC-based algorithm, the initial size and compactness of superpixels and the weight of height are the three key parameters that affect the extraction of building boundaries.The metric (i.e., IoU ) are used to evaluate the effects of building extraction.Figure 19 shows the results of segmentation with different initial sizes of superpixels (e.g., 3, 5, 10, and 15 m 2 ; i.e. Figure 19 (a) depicts that 6D-SLIC at 5 m 2 initial size of superpixels performs better than it does at other sizes in terms of IoU .The superpixel merging of the small size (e.g., 3 m 2 ) is susceptible to UAV image-derived poor-quality 3D point clouds at the edge of buildings (as shown in Figures 3 and 4) that result in the shrinkage of building boundaries.By contrast, the superpixel merging of the larger size (e.g., 10 and 15 m 2 ) may be insensitive to building boundary identification because building details are ignored.Therefore, the results of 6D-SLIC at 3, 10, and 15 m 2 initial sizes are worse than those at 5 m 2 initial size.Figure 19(b) shows a trade-off between spatial proximity and pixel similarity of color and height information when the compactness value is set to 20.A good segmentation performance can be achieved when the weight α is set as 0.6 in Figure 19(c), which is also a trade-off of the contribution between lab distance lab d and height difference h d .
Comparisons of the Proposed Method and State-of-the-Art Methods
Our work uses the proposed 6D-SLIC algorithm as the building outline extractor in the image segmentation part as it allows the full use of the spectral and terrain information of UAV remotely-sensed imagery.The proposed MSCNs with nine layers are then used to classify building and non-building areas.The state-of-the-art results have fewer parameters and involve less computation than the results of two of the most popular networks for image segmentation, i.e., FCN [27] and U-Net [29], do.
To testify the superpixel segmentation performance of the proposed 6D-SLIC algorithm for building extraction, ERS, SEEDS, preSLIC, and LSC are used to extract building from the four experimental datasets.For a fair comparison, the segmented subregions are merged on the basis of the height similarity in the neighborhoods, and the optimal segmentations of ERS, SEEDS, preSLIC, and LSC are achieved through many repeated trials.Also, we select three other state-of-the-art methods, namely, UAV data-(i.e., see Dai [5]), FCN-, and U-Net-based methods, for comparison and analysis to evaluate the proposed building extraction method.The open-source code and pretrained weights of FCN and U-Net are respectively collected from the corresponding GitHub to ensure the repeatability of the experiments.The training samples generated from the UAV images are used for the parameter fine tuning of FCN and U-Net.
Table 4 and Table 5 present the comparative results of Recall , Precision , and IoU values using the six superpixel segmentation algorithms (i.e., SLIC, ERS, SEEDS, preSLIC, LSC, and 6D-SLIC) before and after the regularization.6D-SLIC achieves a better performance than the other five algorithms do in terms of the Recall , Precision , and IoU values.The building outlines obtained from 6D-SLIC are closest to the ground-truth maps, whereas the regions at the building edges with similar colors are easily confused in the other five algorithms and result in poor building extraction.From the comparison of before and after the regularization, it can be inferred Figure 19a depicts that 6D-SLIC at 5 m 2 initial size of superpixels performs better than it does at other sizes in terms of IoU.The superpixel merging of the small size (e.g., 3 m 2 ) is susceptible to UAV image-derived poor-quality 3D point clouds at the edge of buildings (as shown in Figures 3 and 4) that result in the shrinkage of building boundaries.By contrast, the superpixel merging of the larger size (e.g., 10 and 15 m 2 ) may be insensitive to building boundary identification because building details are ignored.Therefore, the results of 6D-SLIC at 3, 10, and 15 m 2 initial sizes are worse than those at 5 m 2 initial size.Figure 19b shows a trade-off between spatial proximity and pixel similarity of color and height information when the compactness value is set to 20.A good segmentation performance can be achieved when the weight α is set as 0.6 in Figure 19c, which is also a trade-off of the contribution between lab distance d lab and height difference d h .
Comparisons of the Proposed Method and State-of-the-Art Methods
Our work uses the proposed 6D-SLIC algorithm as the building outline extractor in the image segmentation part as it allows the full use of the spectral and terrain information of UAV remotely-sensed imagery.The proposed MSCNs with nine layers are then used to classify building and non-building areas.The state-of-the-art results have fewer parameters and involve less computation than the results of two of the most popular networks for image segmentation, i.e., FCN [27] and U-Net [29], do.
To testify the superpixel segmentation performance of the proposed 6D-SLIC algorithm for building extraction, ERS, SEEDS, preSLIC, and LSC are used to extract building from the four experimental datasets.For a fair comparison, the segmented subregions are merged on the basis of the height similarity in the neighborhoods, and the optimal segmentations of ERS, SEEDS, preSLIC, and LSC are achieved through many repeated trials.Also, we select three other state-of-the-art methods, namely, UAV data-(i.e., see Dai [5]), FCN-, and U-Net-based methods, for comparison and analysis to evaluate the proposed building extraction method.The open-source code and pretrained weights of FCN and U-Net are respectively collected from the corresponding GitHub to ensure the repeatability of the experiments.The training samples generated from the UAV images are used for the parameter fine tuning of FCN and U-Net.
Tables 4 and 5 present the comparative results of Recall, Precision, and IoU values using the six superpixel segmentation algorithms (i.e., SLIC, ERS, SEEDS, preSLIC, LSC, and 6D-SLIC) before and after the regularization.6D-SLIC achieves a better performance than the other five algorithms do in terms of the Recall, Precision, and IoU values.The building outlines obtained from 6D-SLIC are closest to the ground-truth maps, whereas the regions at the building edges with similar colors are easily confused in the other five algorithms and result in poor building extraction.From the comparison of The experimental results indicate that the proposed framework presents more significant improvements than the other methods do in terms of the effectiveness and efficiency of building extraction, which can be explained by a number of reasons.First, the point clouds provide valuable information for building extraction, the 6D-SLIC algorithm can rapidly cluster pixels into superpixels by utilizing UAV image spectral information and image-derived point clouds; the latter helps accurately delineate the outline of ground objects despite the existence of similar intensity and texture at building edges in Figure 3. Second, the proposed GGLI can significantly remove vegetation and improve the efficiency of building detection.Third, the deep and salient features The experimental results indicate that the proposed framework presents more significant improvements than the other methods do in terms of the effectiveness and efficiency of building extraction, which can be explained by a number of reasons.First, the point clouds provide valuable information for building extraction, the 6D-SLIC algorithm can rapidly cluster pixels into superpixels by utilizing UAV image spectral information and image-derived point clouds; the latter helps accurately delineate the outline of ground objects despite the existence of similar intensity and texture at building edges in Figure 3. Second, the proposed GGLI can significantly remove vegetation and improve the efficiency of building detection.Third, the deep and salient features learned by a Siamese-type network are more useful and stable in classifying building and non-building areas, even in this case of image intensity dramatic variations, in comparison with the manually designed features in Figure 18.Finally, the proposed building outline regularization algorithm integrates the Douglas-Peucker and iterative optimization algorithms that can remove superfluous vertices and small structures, i.e., the pruned processing is useful to improve the precision of building delineation.
In the method of Dai, the height of the off-terrain points is calculated by a certain threshold that is unstable; thus, some buildings that are not in this threshold are incorrectly identified.The assumption that only the geometry of two mutually perpendicular directions exists in buildings, i.e., the building boundary regularization has limitations for accurately delineating non-regular buildings, is referred to.In the FCN-based method, the subsampling and upsampling operations may cause the information loss of input images, and thus, the prediction results of buildings often have blurred and inaccurate boundaries of buildings, as shown in the results of FCN in Figure 20.In the U-Net-based method, despite the skip connections added to achieve superior performance in comparison with the FCN-based method, pixel-wise classification solely relies on the features within a localized receptive field; therefore, it is still insufficient to capture the global shape information of building polygons, and it is sensitive to noisy data.That is, the architectures of FCN and U-Net are not perfect enough, and there are restrictions on performance improvement.As a result, small structures may exist in building boundaries.The experimental results imply that the low-level manually designed features are unsuitable for building detection because of the influences of grayscale variations.FCN-and U-Net-based methods are difficult to use in extracting the regulated boundaries of buildings when noisy data are present.Our method performs better not only because the point clouds provide valuable information but also is much less computational cost in comparison with FCN-and U-Net-based methods.
Conclusions
In this paper, we present a framework to effectively extract building outlines by utilizing a UAV image and its image-derived point clouds.First, a 6D-SLIC algorithm is introduced to improve superpixel generation performance by considering the height information of pixels.Initial ground object outlines are delineated by merging superpixels with approximately equal height.Second, GGLI is used to eliminate vegetation for accelerating building candidate detection.Third, MSCNs are designed to directly learn deep features and building confirmation.Finally, the building boundaries are regulated by jointly using the Douglas-Peucker and iterative optimization algorithms.The statistical and visualization results indicate that our framework can work efficiently for building detection and boundary extraction.The framework also shows higher accuracy for all experimental datasets according to qualitative comparisons performed with some state-of-the-art methods for building segmentation, such as UAV data-based method and two semantic segmentation methods (e.g., FCNand U-Net-based methods).The results prove the high capability of the proposed framework in building extraction from UAV data.
The proposed building extraction framework highly relies on the quality of photogrammetric processing.UAV image-derived poor-quality point clouds at building edges can decrease the accuracy of building boundary extraction.In addition, there are many parameters used in the proposed method, these parameters are referred from literature or determined based on the best trials.
In future studies, we will optimize our framework to achieve the best performance through a collinear constraint and by reducing the dependence on the quality of image-derived point clouds.We will also try to improve the proposed method by reducing the related parameters, and improve the architecture of U-Net to suit for building extraction from RGB bands and the point clouds for further comparing with the proposed method.
Figure 1 .
Figure 1.The proposed framework for building extraction.
Figure 1 .
Figure 1.The proposed framework for building extraction.
Figure 2 .
Figure 2. Comparison of building extraction from UAV images using two classical segmentation methods.Column (a) includes four types of buildings in urban and rural areas.Columns (b) and (c) are the results of quadtree and MRS, respectively; the red lines are the outlines of ground objects.Column (d) is the ground-truth outlines corresponding to (a), with the red regions denoting the buildings.
Figure 2 .
Figure 2. Comparison of building extraction from UAV images using two classical segmentation methods.Column (a) includes four types of buildings in urban and rural areas.Columns (b,c) are the results of quadtree and MRS, respectively; the red lines are the outlines of ground objects.Column (d) is the ground-truth outlines corresponding to (a), with the red regions denoting the buildings.
Figure
Figure3depicts that the boundaries of the superpixels at the building edges obtained from the proposed 6D-SLIC algorithm are closer to the true boundaries of buildings than those obtained from the SLIC algorithm are.Additionally, other four state-of-the-art methods (e.g., Entropy Rate Superpixels (ERS)[41], Superpixels Extracted via Energy-Driven Sampling (SEEDS)[42], preemptive SLIC (preSLIC)[43], and Linear Spectral Clustering (LSC)[44]) are used to compare with the 6D-SLIC algorithm, as shown in Figure4, the four methods do not perform better, and the 6D-SLIC algorithm also shows more similar shapes to the ground-truth maps of the buildings.Moreover, the metrics, e.g., standard boundary recall BR and under-segmentation error USE[45], are used to measure the quality of boundaries between building over-segments and the ground-truth.From the visual assessment and the statistical results of two quantitative metrics in Table1, it can be inferred that the 6D-SLIC algorithm performs better than the SLIC algorithm and other four state-of-the-art methods do due to the additional height information used for superpixel segmentation in the 3D space instead of a 2D image plane space.
Figure 3 .
Figure 3.Comparison of building extraction using SLIC and 6D-SLIC algorithms from four building examples corresponding to Figure 2(a).Columns (a) and (d) are the superpixels obtained from the SLIC and 6D-SLIC algorithms, respectively.Columns (b) and (e) are the initial building areas that are shaped by merging superpixels on the basis of approximately equal heights.Column (c) shows the 3D point clouds of the four building examples.A high segmentation performance can be achieved when the weight α is set to 0.6.
Figure 3 .Figure 4 .
Figure 3.Comparison of building extraction using SLIC and 6D-SLIC algorithms from four building examples corresponding to Figure 2a.Columns (a,d) are the superpixels obtained from the SLIC and 6D-SLIC algorithms, respectively.Columns (b,e) are the initial building areas that are shaped by merging superpixels on the basis of approximately equal heights.Column (c) shows the 3D point clouds of the four building examples.A high segmentation performance can be achieved when the weight α is set to 0.6.
Figure 4 .
Figure 4. Building extraction using ERS, SEEDS, preSLIC, and LSC algorithms from four building examples corresponding to Figure 2(a).(a), (b), (c), and (d) include the superpixels and the corresponding initial building areas obtained from the ERS, SEEDS, preSLIC, and LSC algorithms, respectively.
Figure 4 .
Figure 4. Building extraction using ERS, SEEDS, preSLIC, and LSC algorithms from four building examples corresponding to Figure 2a.(a-d) include the superpixels and the corresponding initial building areas obtained from the ERS, SEEDS, preSLIC, and LSC algorithms, respectively.
Figure 4 .
Figure 4. Building extraction using ERS, SEEDS, preSLIC, and LSC algorithms from four building examples corresponding to Figure 2(a).(a), (b), (c), and (d) include the superpixels and the corresponding initial building areas obtained from the ERS, SEEDS, preSLIC, and LSC algorithms, respectively.
Figure 5 .
Figure 5. Example to illustrate the vegetation surrounding a building with similar heights.(a), (b), and (c) are the orthoimage, 3D point clouds with true color, and 3D point clouds with rendering color, respectively.(d)-(i) are the results of NGRDI, VARI, GLI, RI, ExG-ExR, and GGLI.The red lines denote the boundaries of the superpixels.
Figure 5 (
i) shows that the proposed GGLI performs better than the other five vegetation indices do.When the number of pixels belonging to vegetation in the superpixel k C is more than half of the number of pixels in the superpixel k C , then the superpixel k C is considered a vegetation region.The definition satisfies the constraint in Equation (9), and the superpixel k C is classified into a vegetation region.
Figure 5 .
Figure 5. Example to illustrate the vegetation surrounding a building with similar heights.(a-c) are the orthoimage, 3D point clouds with true color, and 3D point clouds with rendering color, respectively.(d-i) are the results of NGRDI, VARI, GLI, RI, ExG-ExR, and GGLI.The red lines denote the boundaries of the superpixels.
Figure 6 shows the receiver operating characteristics (ROCs) of the five popular indices and the proposed GGLI.The true positive rate TPR = TP/(TP + FN) and false positive rate FPR = FP/(FP + TN) of vegetation are computed on the basis of the number of true positives (TP), true negatives (TN), false positives (FP), and false negatives (FN).Over 92.3% of vegetation can be correctly extracted by the proposed GGLI, and the FPs are mainly caused by roads and bare land.Hence, the proposed GGLI achieves the best performance in vegetation detection among all vegetation indices.The vegetation superpixels can be effectively detected and removed with the proposed GGLI, and non-vegetation ground objects are shaped by merging the superpixels on the basis of height similarity.
Figure 6 .
Figure 6.Examples to illustrate the accuracy of vegetation detection by using different datasets.(a) and (b) are the results of vegetation detection in two urban areas; (c) and (d) are the results of vegetation detection in two rural areas.
Figure 6 .
Figure 6.Examples to illustrate the accuracy of vegetation detection by using different datasets.(a,b) are the results of vegetation detection in two urban areas; (c,d) are the results of vegetation detection in two rural areas.
Figure 7 .
Figure 7. Example to illustrate the feature maps extracted by convolutional filters with three different sizes, which are selected from the first layer of an MSCN model.
Figure 7 .
Figure 7. Example to illustrate the feature maps extracted by convolutional filters with three different sizes, which are selected from the first layer of an MSCN model.
Figure 8 .
Figure 8. Architecture of MSCNs.In (a), C( n , k , m ) denotes the convolutional layer with n filters of spatial size k k × of band number m .Each max-pooling layer with a max filter of size 2 2 × of stride 2 is applied to downsample each feature map.( ) F n denotes a fully connected layer with n output units.ReLU represents the activation functions using the rectified linear unit ( ) ( ) max 0, x x σ = .As shown in (b), 1 x and 2 x with same size denote the true-color RGB ( 3 m = ) and height intensity ( 1 m = ) patches, respectively; the extents of 1x and 2 x are defined on the basis of the external square and buffer of the initial outline of a ground object, and 1x and 2 x are resampled to a fixed size as input, e.g. a fixed size of 127 127 × pixels used in this study.
1 lS
− is the number of hidden vectors in the ( ) 1 l − th layer; w and b represent the weights (or convolution kernels with size k k × in the convolutional layers) and biases, respectively; * is the dot product (or convolution operator in the convolutional layers); and ( ) .σ denotes the activation function.ReLU is applied to the feature learning and binary decision networks, and sigmoid is used in the output of MSCNs.In this study, discriminative training is prone to achieve the binary output of building and non-building probabilities, which are restricted between 0 and 1.Hence, sigmoid function ( ( ) of ReLU, is used to compute the building and non-building probabilities of a ground object, and the global cost function is an alternative function of the hinge-based loss function with regard to sigmoid output.The proposed MSCNs are trained in a supervised manner by minimizing the global cost function L .
Figure 8 .
Figure 8. Architecture of MSCNs.In (a), C(n, k, m) denotes the convolutional layer with n filters of spatial size k × k of band number m.Each max-pooling layer with a max filter of size 2 × 2 of stride 2 is applied to downsample each feature map.F(n) denotes a fully connected layer with n output units.ReLU represents the activation functions using the rectified linear unit σ(x) = max(0, x).As shown in (b), x1 and x2 with same size denote the true-color RGB (m = 3) and height intensity (m = 1) patches, respectively; the extents of x1 and x2 are defined on the basis of the external square and buffer of the initial outline of a ground object, and x1 and x2 are resampled to a fixed size as input, e.g., a fixed size of 127 × 127 pixels used in this study.
( 5 )
added to a candidate point set co S to be eliminated.(3)Step (2) is repeated by tracking the line segments sequentially from the first vertex to the last vertex until all vertex set b V of the outline is traversed.The vertices of initial outline belonging to the point sets co S are eliminated from the vertex set b V , the vertex set b V is updated, and the candidate point set co S is set as null.(4) Steps (2) and (3) are repeated until no more consecutive collinear vertex i v is added to the candidate point set co S .The vertex set b V is tracked sequentially from the first vertex to the last vertex; two adjacent vertices i v and 1 i v + are considered too close if they satisfy the condition that the distance d (as shown in Figure 9(c)) between i v and 1 i v + is less than a given threshold vv d T < (0.5 m).
Figure 9 (Figure 9 .
Figure 9(d) shows that the proposed iterative optimization algorithm can effectively reduce the superfluous vertices while reconstructing a relatively regular building shape.
Figure 9 .
Figure 9. Example to illustrate building outline regularization.(a) is an initial outline of the building, with the red lines denoting the line segments and the green dots denoting the vertices.(b) is the simplified outline of the building using the Douglas-Peucker algorithm.(c) describes the angle of two line segments and the distance of two adjacent vertices.(d) is the regulated outline of building obtained from the proposed iterative optimization algorithm.
Figure 10 .
Figure 10.UAV orthoimages for the test regions (a) and (b) and the corresponding DSMs (c) and (d).Figure 10.UAV orthoimages for the test regions (a,b) and the corresponding DSMs (c,d).
Figure 10 .
Figure 10.UAV orthoimages for the test regions (a) and (b) and the corresponding DSMs (c) and (d).Figure 10.UAV orthoimages for the test regions (a,b) and the corresponding DSMs (c,d).
Figure 11 .
Figure 11.ISPRS true orthophoto tiles for the test regions (a) and (b) and the corresponding DSMs (c) and (d).
Figure 11 .
Figure 11.ISPRS true orthophoto tiles for the test regions (a,b) and the corresponding DSMs (c,d).
Figure 12 .
Figure 12.Ground-truth buildings of the four datasets.(a) and (b) are the ground-truth buildings of two UAV datasets.(c) and (d) are the ground-truth buildings collected from the ISPRS dataset.White and black denote building and non-building regions, respectively.
Figure 12 .
Figure 12.Ground-truth buildings of the four datasets.(a,b) are the ground-truth buildings of two UAV datasets.(c,d) are the ground-truth buildings collected from the ISPRS dataset.White and black denote building and non-building regions, respectively.
Figure 13 .
Figure 13.Overlap of a correctly identified building and the corresponding ground truth.The blue area is the ground truth.Green area is the intersection part of A and B , and the area within the yellow line is the union of A and B .
Figure 13 .
Figure 13.Overlap of a correctly identified building and the corresponding ground truth.The blue area is the ground truth.Green area is the intersection part of A and B, and the area within the yellow line is the union of A and B.
Figure 17 .
Figure 17.Comparison of confusion matrices of building and non-building classification in Random Forest and MSCNs.(a-c) are the confusion matrices of the Random Forest classifier that uses color histogram, bag of SIFT, and Hog, respectively.(d) is the confusion matrix of the proposed MSCNs.
Figure 18 .
Figure 18.Comparison of features of the color histogram, SIFT, Hog, and MSCNs.(a) is an example of a building, and (e) denotes the gray variations (e.g., brightness + 50% and contrast + 50%) corresponding to (a).(b) and (f) are the feature vectors of the color histogram of (a) and (e), respectively.(c) and (g) are the feature vectors of SIFT of (a) and (e), respectively.(d) and (h) are the feature vectors of Hog of (a) and (e), respectively.(i) is the visualization of deep features extracted by MSCNs in the three convolutional layers, i.e., Conv_x, Conv_1, and Conv_2.Only 12 feature maps are provided in each convolutional layer, and (a)→ and (e)→ denote the corresponding rows to the images (a) and (e) that are the feature maps of Conv_x, Conv_1, and Conv_2.
Figure 18 .
Figure 18.Comparison of features of the color histogram, SIFT, Hog, and MSCNs.(a) is an example of a building, and (e) denotes the gray variations (e.g., brightness + 50% and contrast + 50%) corresponding to (a).(b,f) are the feature vectors of the color histogram of (a,e), respectively.(c,g) are the feature vectors of SIFT of (a,e), respectively.(d,h) are the feature vectors of Hog of (a,e), respectively.(i) is the visualization of deep features extracted by MSCNs in the three convolutional layers, i.e., Conv_x, Conv_1, and Conv_2.Only 12 feature maps are provided in each convolutional layer, and (a)→ and (e)→ denote the corresponding rows to the images (a,e) that are the feature maps of Conv_x, Conv_1, and Conv_2.
Figure 19 .
Figure 19.Comparison of the IoU values with different initial sizes, compactness of superpixels, and weight of height.
Figure 19 .
Figure 19.Comparison of the IoU values with different initial sizes, compactness of superpixels, and weight of height.
Figure 20 .
Figure 20.Representative results of single-building-level building extraction from Dai's method, FCN, U-Net, and our method.(a)-(g) are the seven examples that are selected to exhibit the experimental results.The green, red, blue, and white channels in the results respectively represent the TP, FP, FN, and TN of building areas.
Figure 20 .
Figure 20.Representative results of single-building-level building extraction from Dai's method, FCN, U-Net, and our method.(a-g) are the seven examples that are selected to exhibit the experimental results.The green, red, blue, and white channels in the results respectively represent the TP, FP, FN, and TN of building areas.
S is the sum of the lab distance d lab , height difference d h , and the 2D image plane distance d xy normalized by the grid interval S; α represents the weight to emphasize the contribution of d lab and d h , and it is the SLIC distance measure when α is set as 1, the weight α can be determined by selecting several building samples from the segmented data and performing multiple trials to obtain the optimal superpixel segmentation effect; and m is a variable that can be given to control the compactness of a superpixel.The distances of d
Table 1 .
BR and USE values of SLIC, ERS, SEEDS, preSLIC, LSC, and 6D-SLIC in the four images in Figure 2(a).
Table 1 .
BR and USE values of SLIC, ERS, SEEDS, preSLIC, LSC, and 6D-SLIC in the four images in Figure2a.
Table 1 .
BR and USE values of SLIC, ERS, SEEDS, preSLIC, LSC, and 6D-SLIC in the four images in Figure 2(a). | 19,808.6 | 2019-05-01T00:00:00.000 | [
"Computer Science",
"Engineering",
"Environmental Science"
] |
The interaction of excited atoms and few-cycle laser pulses
This work describes the first observations of the ionisation of neon in a metastable atomic state utilising a strong-field, few-cycle light pulse. We compare the observations to theoretical predictions based on the Ammosov-Delone-Krainov (ADK) theory and a solution to the time-dependent Schrödinger equation (TDSE). The TDSE provides better agreement with the experimental data than the ADK theory. We optically pump the target atomic species and measure the ionisation rate as the a function of different steady-state populations in the fine structure of the target state which shows significant ionisation rate dependence on populations of spin-polarised states. The physical mechanism for this effect is unknown.
Recently, there has been much interest in the generation and utilisation of few-cycle light pulses that have a length of three or even less optical cycles. This interest is in no small part due to the possibilities in applications such as lightwave electronics 1,2 , high-order harmonic generation 3 , above-threshold ionisation, and multiple ionisation 4 . Additionally, the precise control of the carrier envelope phase (CEP) of a few-cycle laser pulse in strong laser-matter interactions opens many possibilities [5][6][7] . All these effects share a common starting point, namely, the strong-field ionisation of an atom.
Strong-field atomic ionisation is a highly nonlinear process that has been realised through high laser intensities obtained by tightly focusing a few-cycle pulse of light with a high peak pulse power 8 . The different interaction regimes that few-cycle light-matter interactions can be characterised by depend on the magnitude of the electric field in the interaction region relative to the ionisation potential of the atom. In the first regime, the electric field is strong enough to induce a perturbative non-linearity in the matter, but not strong enough to cause significant ionisation of atoms. In the second regime, the electric field is sufficiently strong to provide a high probability of ionisation in the target material. This is known as the strong-field regime. The Keldysh parameter, γ = I U /2 p p , is used to determine what regime a particular interaction belongs to. Here I p is the ionisation potential of the medium and U p is the ponderomotive energy, i.e., the kinetic energy imparted to an ionised electron by a linearly polarised oscillating electric field 9 . The perturbative regime corresponds to γ > 1 and the strong-field regime to γ < 1 8 .
In the strong-field regime, it is possible to treat the light-matter interaction semi-classically through a three-step model 10 that describes the effects and results of the interaction. The first step corresponds to ionisation by the light pulse as a result of the suppression of the Coulomb atomic potential. The second step involves the acceleration of the electron wavepacket by the electric field of the light pulse. The motion of the ionised electron corresponds to the classical motion of a charge in an oscillating electrical field, which then imparts ponderomotive energy to the ionised electron. The third step may include a recollision of the electron, which results in a variety of interactions with the parent ion.
Inelastic recollision can result in secondary electron promotions within the parent ion, either causing a direct secondary ionisation known as non-sequential double ionisation (NSDI) 4 or exciting another valence electron to a higher energy state. This excitation lowers the effective second ionisation potential of the atom, thereby providing the opportunity for ionisation in the remainder of the laser pulse in a process known as recollision-enhanced secondary ionisation (RESI) 11 . The study of NDSI and RESI provides enlightening information about the electron dynamics of an ionising system. Another possible interaction is the recombination of the wavepacket with the parent ion and the subsequent creation of a photon that has a harmonic frequency of the driving field. This process is known as high-order harmonic generation (HHG) 8 and is being studied as a potential method to create a tabletop XUV laser source. Elastic collisions may also occur, or the trajectory of the returning electron may not intersect with the parent ion which provides above-threshold ionisation (ATI) electrons 12 .
As all these processes depend upon the initial ionisation, it is vital to have a good understanding of this process. The most common theoretical method used to describe the process is based on the work of Ammosov, Delone, and Krainov. It is commonly known as the ADK theory 13 and makes two essential assumptions, namely: 1) Only the initial and final wavepackets of the electron are relevant in the ionisation process. 2) The energy of a single photon is not sufficient to promote the valence electron into the continuum state, nor is the electric field of the peak high enough to suppress the atomic potential barrier sufficiently to release the valence electron to the continuum. The ADK theory is based on an analytical expression for the tunnel ionisation rate that was derived by Perelomov et al. 14 . In atomic units, which are in use throughout this paper except where indicated otherwise, it is given by Here |E(t)| is the electric field of the laser pulse, n * is the effective principle quantum number, l * is the effective orbital angular quantum number, m is the projection of the angular momentum quantum number, I p is the ionisation potential of the target species, = F I 2 p 0 , and ⁎ ⁎ C n l 2 is a dimensionless constant that is unique for the atomic system under consideration. Approximating a solution for ⁎ ⁎ C n l 2 was the purpose of the work done by Ammosov et al. Finally, the term f(l, m) is given by The ADK theory is not valid in the intensity regime for over-the-barrier ionisation (OBI). There have been several attempts to rectify this shortcoming. One method involves correcting the wavefunction of the ejected electron for the Coulomb potential 15 , thereby accounting for the possibility of OBI 3 . Another modification to account for OBI involves examining the ionisation rates across a broad range of atomic species, and then using the data to apply an empirical correction to the ADK formula 16 .
Despite the limitations of ADK-based methods for calculating the ionisation rate, they are attractive to utilise since they are computationally far less expensive than attempting to find solutions of the time-dependent Schrödinger equation (TDSE) for the ionising system. This has made ADK modelling the traditional method until the past decade, when several techniques to obtain approximate solutions of the TDSE were developed (see, for example 17,18 and references therein). These techniques are taking advantage of significant increases in computational power and available resources.
The aim of the present work is to investigate the strong-field ionisation from atoms in an excited state, for which there have been very few experimental investigations to date. Experiments have been conducted to investigate the strong-field ionisation of Li 19 (γ = 0.09 to 0.21). That work, however, focusses on identifying the role of intermediate excited states in the Li atom during the ionisation process, rather than considering ionisation from an initially excited atomic state as will be presented here. Experiments examining the ionisation of metastable xenon have been performed by Huismans et al. 20 using a λ = 7 μm laser capable of providing pulses in the picosecond regime in order to examine holography between directly ionised and rescattered electron wavefunctions (γ = 0.8 to 1.5). Our work uses much higher laser intensities relative to the ionisation potential of the initial state than the work performed in ref. 20 and investigates different ionisation regimes. Recent experiments conducted by the authors demonstrate significant differences in the transverse electron momentum distribution for the OBI regime compared to the tunnelling regime 21 .
Singly excited states of noble-gas atoms have an electron in the valence shell, which leaves a hole in the remaining electron core. The jj angular-momentum coupling scheme describes these states. However, LS coupling notation suitably describes the 2p 5 ( 2 P 3/2 )3s 3 P 2 state of neon (hereafter defined as Ne * ) that we investigate in this work 22 . Ne * is forbidden by selection rules to optically decay via single-photon dipole-allowed transition to the ground state. It has a lifetime of approximately 14 seconds and has been previously used in laser cooling/atom trap experiments [23][24][25][26] , due to an accessible closed cooling transition to the 3 D 3 state at 640.24 nm. Below we present an experimental investigation of strong-field ionisation of Ne * . Note that neon has a second metastable state ( 3 P 0 ) which is not considered in this work.
Investigating the strong-field ionisation of a metastable noble-gas species is interesting for several reasons. Firstly, the ionisation potential of Ne * is only 5.1 eV, and hence it is relatively straight forward to investigate OBI phenomena with laser systems that are routinely used in strong-field physics experiments. Noble-gas species have closed single-photon dipole-allowed transitions that can be used to manipulate the trajectories of the atoms as well as optically pump the target atom. It is therefore possible to investigate the role of the initial atomic state in the strong-field ionisation process. For example, it is possible to spin-polarise the target atom and investigate ionisation dynamics from an oriented atomic system.
Describing strong-field ionisation experiments is also a challenge to theory. The critical field at which the unperturbed atomic energy level lie above the potential barrier and hence OBI becomes possible is given by provides data from a challenging target over a wide range of experimental parameters and facilitates an extensive test of our current theoretical understanding of strong-field physics.
We present a new experimental apparatus that is capable of performing an experimental investigation of the strong-field ionisation of Ne * . We compare the measured ionisation data to predictions from the ADK and the TDSE theories. We also present first results for the ionisation of optically pumped Ne * and investigate the role of the initial atomic state in strong field ionisation.
Results
The experiment was prepared as described in the Methods section. In order to examine the response of spin-averaged Ne * to ionisation intensity a number of data runs were performed at different laser intensities with Keldysh parameters ranging from γ = 0.37 to 2.32. The experimental parameters were as follows. The integration time of the experiment was 120 s. The laser pulses had random CEP and a pulse length of 6.3 ± 0.2 fs, measured as the full width at the half maximum of intensity. The final Ne * ion yield ( ⁎ S Ne ) was determined according to coll off , where S coll−on is the time-of-flight (TOF) measurement with the optical collimator on, and S coll−off is the TOF measurement with the optical collimator off. S coll−off contains ionisation information from all atomic states in the beam, while S coll−on contains information on an atomic beam with an enhanced Ne * flux. This results in ion yield information that is provided solely by the enhanced number of Ne * atoms in the atomic beam. Background contributions in all measured cases were less than 0.6% of the signal.
The theoretical results were obtained as described in the Methods section. In order to compare the predictions to experiment, the theoretical results were scaled to fit the experimental intensity dependence using a Matlab two-parameter spline fitting procedure. The scaling was done for both the ion yield and the laser intensity using the equation y = A × spline(ηx). Here spline is the spline function that is fit to the theoretical predictions, A is the ion yield scaling factor, and η is the laser intensity scaling factor. The method has been used in previous work to compare theory to experiment in the case of atomic hydrogen 27,28 . The uncertainty presented in the experimental section is given by the Poissonian counting error. Uncertainties in the laser intensity calibration include measurement error as well as systematic power measurement to intensity calculation errors. The latter is corrected with the intensity scaling. The experimental results and theoretical comparison are shown in Fig. 1.
It should be noted that there appears to be an outlying data point below the curve at 6.38 × 10 13 W/cm 2 . The five data points at 6.38, 7.76, 7.79, 9.46 and 9.70 × 10 13 W/cm 2 were taken by employing two different experimental techniques for intensity variation; one where the intensity was controlled solely by adjusting the half-wave plate and the germanium plates, and one where the intensity was locked at the germanium plates while flip-in pellicle beamsplitters were used to reduce intensity. This was done to determine the accuracy of overlap between the two experimental techniques. For the point in question it was ascertained that using the half-wave plate for intensity control at this intensity would not effectively maintain the polarisation state of the light and it is likely an outlier caused by a systematic error due to this issue.
The present work also utilised optical pumping of the target atom with another laser beam tuned to the cooling transition in order to spin-polarise the target atom. If the optical pumping laser light is circularly polarised, it acts on a target atom by causing many single-photon absorptions followed by relaxations due to spontaneous emission. The result of this process is that the atomic population is transferred into the largest m j = ± 2 states (+ 2 for σ + left hand circularly polarised light and − 2 for σ − right hand circularly polarised light) after the interaction with the light beam 29 . Atoms with these magnetic projection quantum numbers have the maximum total angular momentum and are spin-polarised. The sublevel transitions and their associated decay probabilities are shown in Fig. 2. An additional laser beam was added after the optical collimator to facilitate the optical pumping. The laser beam interacted perpendicular to the atomic beam and was on resonance with the cooling transition used in the optical collimator. The laser beam was retro-reflected and the laser detuning is set to 0 MHz so that the net scattering force on the atoms in the atomic beam was zero 30 , thus ensuring that the trajectory of the atoms remained unaltered, which avoided a loss in ion yield signal. The polarisation state of this beam was altered using a quarter-wave plate and facilitated a polarisation change which changed the distribution of m j states. The optical pump beam has a measured power of 125 mW, across a collimated beam geometry with a 6.1 mm radius. This gives a pump intensity of 20 times the saturation intensity (4.22 mW/cm 2 ) of the optical transition. We modelled the optical pumping process by numerically evaluating the optical Bloch equations (OBEs) in the rotating-wave approximation (RWA). The OBEs fully describe the evolution of the internal atomic states in the presence of an external field including the atomic state coherences and spontaneous decay. For example, Fig. 2 shows the evolution of a Ne 3 P 2 atoms pumped by σ + light. The system reaches a steady state after approximately 1 μs with 50% of the atoms in the ground 3 P 2 m j = 2 state and 50% of the atoms in the excited 3 D 2 m j = 3 state. A fully polarised state is only reached after a period of relaxation where the system is allowed to evolve without the influence of the pump laser. This second step takes a further 80 ns, after which approximately 99% of the atoms are in the desired 3 P 2 m j = 2 state. On average, an atom was under the influence of the optical pumping beam for 12 μs, which is more than sufficient to fully polarise the atomic beam. Between the optical pumping region and the interaction region (approximately 45 cm), there is a small residual magnetic field from the Earth, which could have induced a small depolarisation of the atoms 31 . However, our results show that the majority of atoms remain well polarised. Figure 3 shows the ion yield when rotating the quarter-wave plate of the optical pump light. The degree of circular polarisation of the optical pump light was measured by measuring the Stokes parameters utilising the classic method involving a linear polariser and a quarter-wave plate as described in ref. 32; in this case the normalised parameter S 3 /S 0 describes the prevalence of σ + circularly polarised light to σ − circularly polarised light. The average maximum absolute value for |S 3 /S 0 | max was measured to be 0.96 ± 0.02, i.e. the maximum degree of circular polarisation is 96% in this experimental setup. Figure 3(b) is a broad function around the point of full circular polarisation and such a change in the degree of circular polarisation will have a negligible effect on the optical pumping with a less than 1% change in the fully spin polarised state. A further consistency check for the ionisaton rate as a function of optical pumping was made by flipping the quarter wave plate so that the opposite handedness for the ionisation rate could be measured with the results consistent with what is presented in Fig. 3(a). Figure 3 shows that as pump light becomes more circularly polarised, there is a corresponding increase These results describe the system reaching steady state as described in the text, with 50% of the atoms in the displayed 3 P 2 m j = − 2 state. The remainder exist in the 3 D 3 m j = − 3 excited state, which is not displayed in the figure. When the atoms leave the pump beam they decay from the excited state into the m j = − 2 state as described in the main text.
in the ionisation rate. There are a number of important observations that can be made about this measurement. The change in the ellipticity of the optical pumping beam changes the atomic state distribution of the Ne * atoms, and we clearly observe an ionisation dependence on the initial state of the Ne * system. The second observation is that the ionisation rate maximises for the fully spin polarised states compared to the mixed state case created by π polarisations which produces a mixed distribution between all m j substates. There also appears to be an asymmetry in the ionisation distribution. These are remarkable features and clearly demonstrates that the tunnel ionisation rate depends on the fine structure population of the excited state with maximum ionisation rates when the atoms are spin polarised.
Discussion
The results exhibited in Fig. 1 are the first using Ne * as a target atom, and the first to examine the strong field ionisation effects of a metastable target. The results are fit with arbitrary scaling. The ADK theoretical predictions for ion yield observe a significant increase at an intensity of 1.5 × 10 13 W/cm 2 . This is due to the focal volume averaging used to determine the total ion yield as described in the methods section. At intensities below the sharp increase in ionisation rate, the probability of ionisation of a single atom is below unity as predicted by ADK theory and as such there is a limited number of ionisation events occurring across the entire focal volume of the laser pulse. In this region, the peak intensity of the laser pulse in the single atom ADK calculations is what limits the maximum calculated ionisation yield. At intensities above 1.5 × 10 13 W/cm 2 , the probability of a single atom ionising is close to, or at, unity. There is a considerable increase in ion yield at this point. As the peak intensity increases, more of the outlying pulse volume contributes to the ionisation rate. In this region, the localised intensities of the laser pulse throughout the focal volume is what limits the maximum calculated ionisation yield. This is demonstrated in the inset of Fig. 1, where the ionisation probability of a single atom is compared to the ADK theoretical results that have been focal volume averaged.
There is poor agreement with the ADK fit below 4.0 × 10 13 W/cm 2 . This is expected as ionisation due to multiphoton processes and OBI are not predicted with ADK theory, both of which may contribute to the total ion yield. This compares favourably to previous results 33,34 , where it was noted that multiphoton processes affect the accuracy of ADK ionisation rates at similar peak intensities. The OBI intensity for our target is below the intensity where ADK theory fails, unlike the targets used in refs 33,34. This indicates that OBI contributes to the difference between ADK and experiment at intensities below 4.0 × 10 13 W/cm 2 , which can be confirmed through the measurement of the transverse electron momentum distribution as shown in ref. 21. As the TDSE solution accounts for both OBI and tunnelling ionisation effects, one might expect to see a better scaled fit at those lower intensities. This is indeed what we observe. At intensities higher than 4.0 × 10 13 W/cm 2 the fit after scaling is similar for both ADK and TDSE theories. This is expected, despite the inability of the ADK approach to model OBI ionisation. At these high peak intensities, the probability of ionisation becomes unity for both theories across a similar and large fraction of the volume of the interaction region, with focal volume averaging effects at the edges of the laser beam volume (where the probability of ionisation is less than unity in the modelled lower electric field amplitudes) causing slight differences in modelled ion yield. Physically this implies that at these high intensities, the exact process of ionisation for determining ion yield is irrelevant, as the ionisation event will always occur. For this reason, more relevant comparisons of theory should be made at intensities below 4.0 × 10 13 W/cm 2 . Figure 3. (a) Measurements of ionisation yield as a function of the angle that the quarter-wave plate makes relative to the polarisation axis defined by a linear polariser when using 640.24 nm optical pumping light. The intensity of the ionising laser is I = 9.2 × 10 13 W/cm 2 . This intensity was chosen as it allows accurate use of ADK modelling of the ion yield for later analysis (see Fig. 1). The pump light is intended to pump the atom beam into an ensemble of different m j states, depending on the alignment of the fast axis of the quarter-wave plate with respect to a linear polariser. There is a significant ion yield difference between the Ne * beam being pumped with σ ± circularly polarised light and being pumped with linearly polarised π light. This indicates an average ionisation potential difference between a spin-polarised atomic ensemble compared to a spin-averaged atomic ensemble. (b) Indicates the expected m j state fraction of the beam at different wave-plate angles. When pumped with π light, the state distribution for all remaining states are approximately 0.02. The modelling was performed for the experimental pump beam parameters by numerically solving the OBEs and is provided as a guide for the eye.
Scientific RepoRts | 6:34101 | DOI: 10.1038/srep34101 The mechanism for the modulation in the ion yield as the quarter wave plate is rotated, and hence the fine structure population distribution in the target atom state changes, as displayed in Fig. 3 is unknown. However, it may be a result of the magnetic field of the strong field pulse inducing a spin flip in the metastable state and facilitating a decay to the neutral ground state of the neon atom. In this case the ground state has a significantly larger ionisation potential and hence a change in the ionisation rate would be expected. This is the first demonstration of the effect of the fine structure on tunnel ionisation rates and this system provides a new challenge for modelling tunnel ionisation for atomic systems.
We have performed the first strong-field ionisation experiment with excited-state neon atoms and measured the complete ion yield from the ionisation of Ne * atoms using a COLTRIMS setup. Our work showed that solving the TDSE, even with the necessary approximations to make the problem computationally tractable, provides better agreement with experiment than the ADK theory. This is likely the result of applying the theories to an atom with such a low ionization potential, where the basic assumptions for ADK become invalid. A maximum difference of 16% in the ion yield was experimentally demonstrated between atoms pumped to the stretched m j states compared to atoms pumped into a mixture of m j states using π polarised light.
Methods
Experimental setup. Few-cycle light pulses were provided by a commercially available chirped pulse amplification system (Femtopower Compact Pro CE Phase). The final laser output in typical operating conditions was a 1 kHz train of pulses 6 fs long, with a pulse energy of approximately 450 μJ.
The pulses from the laser system passed through a half-wave plate and a pair of germanium plates at Brewster's angle in order to provide variable intensity from 150 mW down to 8 mW. In order to preserve the polarisation state, a series of flip-in pellicle beamsplitters were used to reduce the laser intensity further. For intensity calibration purposes, a removable quarter-wave plate was also placed in the beam path. The few-cycle pulses were then focussed into the interaction region of the detection system. The intensity of the focussed light beam in the interaction region was determined for a number of measured input powers, utilising the approach outlined in the work of Alnaser et al. 35 . This method provided an absolute intensity accurate to within 50%. These data are used to create a calibration curve that maps the measured power to effective intensity. In addition, this calibration curve allowed for the calculation of the beam waist at the focus, assuming a Gaussian beam propagation. The calculated beam waist diameter is 14 ± 1 μm, with an associated Rayleigh range of 810 ± 120 μm. The random shot-to-shot uncertainity of the laser intensity is dependent upon the uncertainity of the Thorlabs S310C power meter used to measure pulse power. This was estimated to be 11% based on manufacturer specifications.
The detection system was a cold target recoil ion momentum spectroscopy (COLTRIMS) device. This is an ultrahigh vacuum (UHV) system that utilises electric fields to separate the products of a light-atom interaction based on charge polarity 36 . The charged products are first guided onto multichannel plates to amplify the signal, and then onto delay-line detectors that record the time and location of the ion strikes on the detector. Electron momentum spectroscopy was available, but not required for this experiment. Mass spectroscopy of the product ions was performed by correlating TOF data from the delay line detectors. This was used to obtain ion counts from the interaction with the ionising laser. Position data can be used to determine ion momentum but was not utilised for this experiment.
A DC discharge source was used to generate the Ne * atoms. This type of source is common for generating metastable noble-gas atoms and was repurposed from previous experiments 37,38 . Neon gas was fed at a pressure of 1.1 Torr past a cathode tip and through a liquid nitrogen cooled 250 μm diameter nozzle into the evacuated (≈ 10 −6 Torr) source chamber. The gas expands supersonically towards an anode skimmer, which provides collimation to the atomic beam downstream. The application of a high voltage across the two electrodes created a DC discharge in the region where the neon is expanding into the vacuum system. Electron collisions with neon atoms generate several products, including Ne * at approximately 0.01% efficiency 39 .
Immediately following the skimmer was an optical collimator 31,40 which was utilised in order to increase the Ne * flux. The collimator consists of two pairs of elongated mirrors at right angles to each other that are placed near parallel to the direction of travel of the atomic beam. These mirrors were tilted slightly from parallel such that four incident laser beams frequency-locked close to the cooling transition for the 3 P 2 state create an angle frequency detuned two dimensional (2D) optical molasses along the path of the atomic beam. This 2D optical molasses reduces the transverse velocity component of only the 3 P 2 neon atoms and can be viewed as a collimation matter lens for the atomic beam.
Following the collimator, two chambers separated by two 1.5 mm apertures were used to create a differential pumping section in order to match the vacuum pressure to the COLTRIMS UHV. The first chamber contained electron deflector plates to remove charged particles from the atomic beam created by the discharge. The second chamber contained a Faraday cup that is used to measure the beam flux and assisted in aligning the Ne * source. A pneumatic gate valve separated the Ne * beamline from the COLTRIMS chamber. Also on this chamber were a pair of optical viewports which allowed for the atomic beam to be illuminated perpendicular to the atomic beam by two retro-reflecting laser beams at 640.24 nm, which are produced by a dye laser frequency locked and on resonance with the cooling transition. A linear polariser and two quarter-wave plates were used to alter the ellipticity of the pump beam in order to pump the atoms into various m j states. When the atomic beam rached the interaction region of the COLTRIMS device, it had a diameter of 1.5 ± 0.3 mm, as measured by scanning the strong-field laser beam focus across the atomic beam and observing the change in ion yield. See Fig. 4 for a schematic of the experiment.
Modelling the ion yield. In order to provide comparison to theory, a 3D focal-volume-averaged model was created and implemented through Matlab. It is important to correctly model the interaction region, since the low ionisation potential of metastable neon causes the ionisation probability to quickly reach unity at the centre of the pulse at relatively low intensities. This implies that, as the pulse intensity increases, the outer areas in the interaction region significantly contribute to the total ion yield when compared to the ionisation of ground-state neon. The model made the assumptions that the laser pulse was Gaussian, the divergence of the atomic beam was Only one pair of mirrors for the optical collimator is shown, whereas two pairs are employed in the actual experiment to collimate in two directions. The optical pump laser is propagating in the same direction as the electric field of the ionising laser, which defines the quantisation axis. The magnetic sublevel optical pump apparatus was not used for the results displayed in Fig. 1. The atomic beam is travelling in the plane made with the z-axis and the θ = 0 angular coordinate. As the system is solved symmetrically in θ, the axis along the θ = 0 coordinate is labelled the r axis as the solution requires knowledge of the displacement along the radial coordinate. The laser beam is propagating in the z direction. Part (b) is a modelled 2D ionisation yield map for Ne * interacting with a laser pulse with the following parameters: I pk = 9.6 × 10 13 W/cm 2 ; w 0 = 7.25 μm; T pul = 6.3 fs; atomic beam width = 1.5 mm; average atomic beam speed = 1000 m/s; atomic beam flux = 1.4 × 10 14 atoms/sr/s. These parameters, with the exception of I pk , were held constant throughout the modelling.
Scientific RepoRts | 6:34101 | DOI: 10.1038/srep34101 negligible over the interaction region, the laser pulse was completely linearly polarised, and all ions generated by the interaction were detected by the COLTRIMS. Smoothing functions based on the work of Kielpinski et al. 28 were employed. A representation of the interaction region is displayed in Fig. 5, with axes labelled according to a cylindrical coordinate system.
In order to perform the focal-volume averaging, the cylindrical symmetry of the region was exploited by flattening the interaction region onto a 2D area, as shown in Fig. 5. The total ion yield for a single pulse is obtained by integrating the ion yield map displaying in Fig. 5(b), which is then multiplied by the total pulse number to give a final ion yield result.
In order to generate a curve of ion yield as a function of intensity, a batch script was designed that creates a number of input peak laser intensity I pk values. The script ran the ion yield script for each value of I pk and generated a plot when the batch script was completed. Two theoretical ion yields as a function of intensity plots were created for Ne + ions. One curve is generated by utilising ADK theory to provide the ionisation probability as provided in Eq. (1). Values for ⁎ ⁎ C n l were calculated by determining the wavefunction, Ψ m , and the orbital energy of the Ne 3s atom 41 , before fitting to the expression 42 . Here F l (r) is the wavefunction in the asymptotic region where tunneling occurs, and Y lm are spherical harmonics.
Theoretical predictions for ionisation based on solving the TDSE are processed in the same manner. The ionisation probabilities of the Ne 3s orbital were calculated by solving the TDSE under the single-active electron approximation with the second-order split-operator method in the energy representation 17,43 . The model potential 44 was calculated by using density functional theory with a self-interaction correction 41 . The calculated atomic ionisation potentials were in good agreement with the measured ones. The numerical convergence was cross-checked by comparing the ionisation probabilities obtained from the integration of the ATI spectra and the survival probability of the 3s orbital as well as the excitation to other bound states. The two results agree within a few percent. | 7,943.6 | 2016-01-15T00:00:00.000 | [
"Physics"
] |
Bridge Structural Deformation Monitoring Using Digital Camera
Burgeoning off-the-selves Digital Single Lens Reflector (DSLR) cameras have been gaining attentions as a fast and affordable tool for conducting deformation monitoring of man-made engineering structures. When a sub millimetre of accuracy is sought, deliberate concerns of their usage must be considered since lingering systematic errors in the imaging process plaque such non metric cameras. This paper discusses a close range photogrammetric method to conduct structure deformation monitoring of the bridge using the digital DSLR camera. The bridge is located in Malang Municipality, East Java province, Indonesia. There are more than 100 images of the bridge’s concrete pillars were photographed using convergent photogrammetric network at distance variations between 5m to 30m long on each epoch. Then, the coordinates of around 550 captured retro-reflective markers attached on the pillars facade are calculated using self-calibrating bundle adjustment method. The coordinate differences of the markers from the two consecutive epochs are detected with a magnitude between 0.03 mm to 6 mm with a sub-millimetre precision measurement level. However, by using global congruency testing and a localization of deformation testing, it is confirmed that the bridge pillar’s structures are remain stable between those epochs.
Introduction
Deformation monitoring of the bridge's structures has been disseminated in wide range multi discipline literatures [1][2][3]. A state of the art of spatially driven information in localizing deformations of manmade bridge structures is categorized into two approaches namely: contact-based and non-contact-based methods [4]. The contact-based method is achieved by utilizing a single or multi sensor of measurement tools attached on the bridge [5,6]. For examples, Global Navigation Satellite Systems (GNSS) technology has been employed to monitor bridge deformation [7,8]. Albeit it offers some advantages such as weather proof continuous operability and a provision of instantaneous 3D absolute displacements [7], but its high observation noise limits an attainable precision displacement extraction [8]. Furthermore, multipath effects could downgrade precision since the GNSS receivers are stationed along the bridge [9].
On the other hand, the non-contact based method provides more advantages [10] such that it cannot destruct the bridge surface by equipment [11], it has high precision, high efficient and high flexibility characteristics [12], and it can be operated in real time [13]. The non-contact method usually utilizes optical centric devices such as laser beam [14], radar [15,16], acoustic [17], thermal model [18], and image-based measurements [19,20]. Furthermore, the image-based methods are mainly grouped into two approaches: computer vision approach [21] and photogrammetric restitution approach [22]. This paper discusses the close-range photogrammetric restitution approach for processing images to calculate the coordinates of observation points of retro reflective markers. Any 3D structure displacements can be analyzed through coordinates differences of the markers from different epochs of image acquisition. A workflow of the restitution starts from image registration process and followed by self-calibrating bundle adjustment process to produce 3D coordinates of the markers. Then, a set statistical tests are conducted to ascertain stability of some or all markers points by utilizing congruency testing and deformation localization testing. This procedures are elaborated as follows. Figure 1 depicts a general methodology to deformation monitoring of the bridge using two epoch analysis. The method is generally separate into two stages. The first stage is an image acquisition processes which aims to determine the object points coordinates. The next one is the deformation analysis itself which aims to test a stability of the point network. Those methods are elaborated as follows.
Self-Calibrating Bundle Adjustment
The photogrammetric restitution begins with by selecting two arbitrary overlapped images to determine its relative orientation parameters [23] and datum of a reference frame coordinate. Then, estimated orientation parameters of each processed images using a sequence of resection [24,25] and intersection [26] methods iteratively. Once the approximate values of each image's exterior orientation parameters and each marker's 3D coordinates of the chosen datum are obtained, these parameters are entered into the least squares adjustment process which known as self-calibrating bundle adjustment method rooted from photogrammetric collinearity condition [27]. The method generates a refined values of aforementioned parameters as well as the camera lens distortions parameters. Equation (1) compactly illustrates the method.
Equation (1) is a hyper matrix of the method's normal equation. Subscripts of i, j and p represent information pertaining to the i th image of m images and j th point of n object points (i.e. markers), while p contains the number of lens distortion parameters. The matrix P is formed by inversing the covariance matrix of the measured image points. The ̇,̈, ⃛ submatrices are symmetric, block diagonal, with each block on the diagonal referring to the particular exterior orientation parameters in ̇, the object point coordinates in ̈, and lens distortion parameters in ⃛ respectively. These matrices are formed by a summation process as illustrated in equation (2a).
Since the image measurements are assumed to be independent of each other, the contributions to the normal equations from each set of the collinearity equation can be summed. The total ̇ matrix is block diagonal, with 6 by 6 blocks on the diagonal, each referring to a separate image. Each ̇ is the sum of the ̇ submatrices, formed by the A1ij and Pij matrices from each set of the collinearity equations that refer to the image i. Also, the ̈ has 3 by 3 blocks on the diagonal, each referring to the coordinates of the individual point marker. Each ̈ is formed from the A2ij and Pij of the collinearity equations referring to the point marker j. The ̅ , ̃, ̂ submatrices in equation (2b) are generated based upon a point by point basis, not a summations. Their compositions are determined by which point marker occurs on which images.
In the application of deformation analysis, each epoch of image acquisition is adjusted separately as a free network bundle adjustment for obtaining markers' 3D coordinates as well as their covariant matrices. Since our prime focus is to identify and discern displacements of suspected point markers with highly confidence, a removal systematic image errors is deemed necessary. A viable solution until now is to utilizing the self-calibrating bundle adjustment method. Additional parameters p are introduced into the bundle adjustment method to model the behavior of the systematic error in the form of ⃛ submatrix. The estimation and solution of the additional parameters are determined from equation (1). In the last iteration, the covariance matrix of the solution ( = 0 2 − ) and the adjusted markers coordinates are then used to analyze the occurrence of possible point displacements.
Deformation analysis
Deformation analysis aims to detect the smallest possible displacements which are of the same order of magnitude as the precision of the measurement from which they are derived. The analysis process involve identification and quantification of the displacements, as well as ensuring that the measured IOP Publishing doi:10.1088/1755-1315/1051/1/012009 4 displacements were indeed not the result of random or systematic observations errors. Statistical testing of estimated displacements between two epochs is necessary to analyze whether significant movements have occurred. An acceptance of the test indicates that no significant displacement was occurred, otherwise the point movements were implied. The deformation analysis in this research is consisted of two interrelated phases: congruency test of the photogrammetric network between two epochs and localization of deformations test in Euclidian space and time.
Congruency Testing
The congruency test detects a stability and consistency of networks of a set of point markers between any two epochs. The set of points can either be all common points (i.e. a global congruency test) or few selected common points (i.e. a partial congruency test) suitable for datum definitions [28]. The testing procedure was initiated by performing the global congruency test. When the significant movements were indicated, the localization test is conducted then followed by some more partial congruency tests using reduced common points. These processes were repeated until the congruency test is pass and the remaining points were set as stable datum points. The global congruency test examines null hypothesis 0 (i.e. no significant displacements) of all points of markers over two epochs which can be formulated as: Where x1 , x2 are the vector of 3D coordinates of common point markers in both epochs in the same datum, d is a displacement vector with its cofactor matrix: Where Qx1 and Qx2 are the cofactor matrix of computed coordinates of x1 and x2 respectively. The test value is expressed as [29]: Where h is a rank of the cofactor matrix of of coordinate differences, i.e. (3n -7) for a 3D spatial network of n number of point markers. The common variance factor of ŝ0 2 is estimated from ̂0 2 = ( 1̂01 2 + 2̂02 2 )⁄ ; and = 1 + 2 Where r1 and r2 being the degrees of freedom, together with their corresponding variance factor in the estimation of x1 and x2. The test of is against the Fisher's distribution ℎ, ,1−∝ , and usual significant level chosen for the test is ∝= 0.05. If the is less than this critical value, the null hypothesis 0 is accepted. It means that the points of network at the second epoch must be congruent (i.e. same shapes) with that at the first one. On the other hand, if the null hypothesis of global congruency is rejected, it indicates a significant change of movements. Also, the + is the Moore-Penrose pseudo inverse of together with its inner constraint matrix such that [28]: = [ However, in the photogrammetric network whose coordinate points of x1 , x2 are calculated using a free network adjustments, the congruency test can be simplified into [30]: The next step is to identify point or points in the network of point markers whose displacements cause a change in shape.
Localization of Deformation Test
When the congruency test fails, it indicates significant displacement. A non-congruency of the network between the two epochs is encoded in the quadratic form of which possible to measure the contribution of each point displacement di of each Ω . The point which has highest value of Ω is likely to be a significant displacement, and it needs to be removed from the network by using partitioning method [30]: Where di is the vector of eliminated point and dr are the retain datum points. S is implied similarity transformation when equation (9) is used to perform congruency test. Once the localization test was conducted, a verification of each stable point is confirmed using: If is less than 3, ,1−∝ , point i is considered as stable. The next section will discuss a process and result of the aforementioned general methodology.
Results and Discussion
A two series of photogrammetric campaigns were conducted to monitor a bridge located in Pandansari village, Malang Municipality, East Java province, Indonesia. The retro reflective markers attached on the bridge's concrete pillars facades were photographed by using a DSLR camera as seen in figure 2. Approximately, more than 500 markers were observed as object points of the deformation monitoring network ( figure 3). The self-calibrating bundle adjustment outlined in equation (1) The three parameters of p are interior orientation parameters which consist of calibrated focal length (c), and the camera's coordinates of principal point (xp, yp). The next three parameters in table 1 are the lens radial distortion parameters (K1, K2, K3), and followed by the lens decentering distortion parameters (P1, P2) and the sensor camera's affinity (B1, B2). It can be noticed that a relatively insignificant perturbations of theses parameters between epochs still could degrade precisions of the obtained 3D coordinate of point markers. The values of the 2 parameters comprise 555 point markers computed using free network datum on each epoch. Coordinates of these points and their cofactor matrices of 1 and 2 in equation (4) on each epoch are generated using the self-calibrating bundle adjustment outlined in equation (1). Rigorous statistical testing were conducted on each epoch to ensure that all measurements are free of systematic errors and meet reliability criteria for deformation measurements. Some of the point coordinates as well as its variance components presented in standard deviations are illustrated in table 2 and table 3. The sign of (⋮ ) that appear in all tables is indicated that not all data are presented. For a clarity of the discussion only few data are selected as an illustration purpose. The differences of points of coordinates between two epochs of d as illustrated in figure 4 are not necessarily indicated as displacements. In order to check the integrity of the network between epochs, the congruency test was conducted using the Fisher's distribution with the significant level of ∝ = 0.05, and it gives the value of 2.61 at the maximum boundary. Table 5 shows the result of the test which implies that the value in equation (9) of each point displacement are none surpass the threshold. It indicated that there were no significant movements occurred between measurements. Hence, the localization of deformation test was not necessarily conducted. Although the averaged movement is about 0.534 mm with a magnitude between 0.026 mm -5.867 mm, the congruency of the network shape is still valid in all epochs. Table 5. Global congruency test using Fisher's distribution according to equation (9). The sign of (⋮ ) means that not all data are presented. | 3,094 | 2022-07-01T00:00:00.000 | [
"Materials Science"
] |
Porphyry Body And Geological Structure Identification As Control Of Low Sulphidation Epithermal System In Sangon, Kokap Sub-District, Kulonprogo Regency, Special Region Of Yogyakarta, Indonesia
There is gravity measurement that is supported by magnetic measurement in Sangon to identify porphyry body and geological structure as low sulfidation epithermal system control. The survey area is 6.4 × 5.6 km for gravity method and 2.5× 1.2 km for magnetic method. The value of gravity anomaly after flat plane reduction processing is 122-142 mGal which is positive anomaly located in north-eastern area and negative anomaly to 82102 mGal located in south-western area. Whereas the magnetic residual anomaly is 800-1300nT. Conducted 2.5 D modelling of gravity method that is based on local anomaly slice. The result of 2.5D modelling show that an intrusion body interpreted as Dacite intrusion as host rock which plays a role as heat source of mineralization system. The density of Dacite is 2.70 gr/cm3. The result of gravity modelling has correlation with the result of magnetic modelling. Based on magnetic modelling, the intrusion body is located in south-west.
I. Introduction
Sangon Area, Kulonprogo District has an alteration zone that brings potential low sulfidation type of gold mineralization. This has been proved by the presence of locally managed traditional mines. This mineralization system is controlled by the presence of structures and intrusions of porphyry bodies carrying economical minerals. Intrusion of igneous rocks generally have the characteristics of closed closures on the surface forming a puncture that signifies the occurrence of magma intrusion into the surface thus lifting the area around which it is penetrated. Magma that rise to the surface has a lower density of the surrounding area so it can rise to the surface.
The main targets of intrusionary structures and bodies as control agent of mineralization can be identified by geophysical methods such as gravity and magnetic methods. The main target evidence is identified by the method is further reinforced by the results of Geophysics Expedition 2015 which resulted a low value of gravity with closed closures in the southeast as an indication of mineralization control intrusion. But because the measurement point was still too at least, the results could not be interpreted further. The integration of Magnetic and Gravity Methods on FieldCamp 2018 are expected to further demonstrate the condition of mineralized controllers in Sangon, Kulonprogo better.
A. Gravity Anomaly
The expected result from measurement of gravity data is obtain gravity field anomaly. The basic principle of measuring gravity data is the theory of universal gravity, which is the attraction force (F) between two mass particles at a certain distance. The earth's gravity field (g) has a vertical direction Figure 1: Schematic theory of universal gravitation, two particles of mass at a certain distance perpendicular to the equipotential plane, whereas the gravity field due to anomalous body existence (local mass distribution) has a varying direction toward the vertical direction and is affected by its position on the anomaly. Changes in the earth's gravity field due to the existence of anomalies are called gravity anomalies (∆g). [1] used the term gravity effect (∆g) to describe the gravity field changes due to the anomaly whose value is much smaller than the earth's gravity field. In measurement, the anomalous gravity field and the earth's gravity field are measured in the vertical axis (z). Since the gravity effect is measured in the g (vertical) and ∆g << g direction g direction is not affected by the existence of the anomaly.
An anomaly of any given point on the horizontal plane can be written down, ∆g(x, y) is an anomaly of the function x(longitude) and y(latitude) obtained through surface measurements due to the subsurface mass distribution at z(+). While σ(x, y) is the surface density at z = 0. The gravity anomaly on the functions of x and y is proportional to the density of the surface area on the functions of x and y anyway, so that the measured gravity anomaly value ∆g(x, y) can be represented and extrapolated into the density distribution of the area σ(x, y) on the surface with the same contour pattern and different values between the contours of gravity anomaly and surface density contours.
B. Gravity Reduction
Mathematically it can be defined that gravity field anomaly in topography or in position (x, y, z) is the difference from the observed gravity field in topography to the theoretical gravity field (g(ϕ)) in topography, free air corrected gravity (g F A ), bouger anomaly (g b ), and terrain correction (T ).
Mathematically, gravity field anomalies in topography can be expressed in terms of the following equations: where, ∆g(x, y, z) = Gravity field anomaly in topography
Reading Scale Conversion
Reading scale conversion is used to convert the reading value in gravimeter (mV) into mGal. The reading scale conversion is varying, depending on the type of equipment used. Conversion scale reading into mGal for Lacoste & Romberg G-1118 gravymeter without feedback is as follows.
where g ukur = Observed − gravitational f ield (mGal) V im = V alue in miligal unit on CR limit CR = Counter Reading (f rom the equipment) SB = Reading scale in gravitymeter F F I = F actor f or interval (f rom the equipment)
Feedback Correction
Feedback is a nonius scale of the reading scale that serves to keep the beam gravitymeter fixed on the reading line.
Instrument height correction
This means, that each height of one meter affects the gravitational field value of 0.3085672 mgal. Gravity value with instrument height correction is expressed by the following equation: ,where The following equation (eq.5) means that every meter effects the value of gravity field 0.3085672 mGal. Then the value of instrument height-corrected gravity (g T A ) is: Tidal Correction Tidal correction aims to eliminate the effects that arise due to the celestial bodies, especially the moon and the sun.
The effect of maximum gravity due to the Tidal Effect is 0.33 mGal in 1 day of measurement [2] or about 3 g.u = 0.3 mgal [3] with a portion one thirds of the sun and two thirds of the month. The influence of gravity due to tidal effects on the vertical direction by [4] approached by [5] is as follows thus the value of tidal-corrected gravity (g ps ) is
Drift Correction
In the gravity instrument, drift is an exhaustion factor of the instrument that will affect the measured gravity value. Drift is affected by time and temperature Effect of drift is linier over time. Where the longer the measurement time the greater the influence of drift on the gravity reading. To overcome the effect of drift on the measurement time, we collect gravity data with closed loop The drift correction of the measurement can be expressed by the following equation: thus the value of the drift-corrected gravity (g d ) is Observed Gravity Observed gravity (g obs ) is the true value of gravity at the measuring point, obtained by binding the relative gravity value to the tied gravity point and the unnecessary reduction of gravity data. The tied gravity point is the known point of its absolute gravity. Gravity observation can be calculated through the following equation, , where g 0 = absolute gravity value in tie point g d = drif t − corrected gravity value in view point g d0 = drif t − corrected gravity in tie point(base) g obs value from the eq.12 is in mGal unit and in topography.
Latitude Correction
A normal gravity field located on the datum plane (at z = 0) as the reference point of geodesy. The normal gravity field formula in the field of datum has been established by the International Association of Geodesy (IAG) and the National Imagery and Mapping Agency (NIMA), namely: g(ϕ)(x, y, 0)7 = 978032.700 , where In the latitude or normal gravity field correction, the position of the measurement point affects the calculation. From the equation it is seen that the higher the location of latitude the greater the acceleration of gravity. So the gravitational field of the earth tends to grow larger toward the poles.
Free Air Correction
The normal gravity field g(ϕ) lies in the plane of datum (z = 0) or in the spheroidal plane, whereas g obs (x, y, z) is on topography. Thus, the normal gravitational field trait g(ϕ) to the topography is required to be corrected with g obs (x, y, z). Bring the normal gravity field to topography by performing free air correction (mgal/m). Mathematically free air correction is described as follows.
Free-air correction only calculates the elevation between the topography surface (observation points) and the reference spheroid by ignoring the mass between them.
Bouger Correction
In the calculation of free air gravity field anomaly, the mass that lies between the datum and the topography surface is not calculated, whereas this mass greatly affects the anomalous price of the gravitational field. Then the free air anomaly will be more perfect if the mass is also calculated. Bouger correction using infinity horizontal slab approach calculation as follows With ρ is the mass density of the bouger (topographic mass) and h is the measurement point height of the datum. In this research, determination of bouger density uses Parasnis method. Parasnis is done by using measurement data as same as Nettleton is. In this determination, used simple equation from complete Bouger anomaly and then linear regression is made. In the determination of Bouger density by [6] can be expressed by the following equation: , as ∆F AA is free air anomaly between base point and point of i as y-axis, k∆h − ∆T C ρ0 as x-axis, and gradient is obtained m = ρ as the result of Bouger density calculation.
Terrain Correction
There is mass above the Bouguer plane and a part of the lost mass below the Bouguer plane which in fact represents the existence of hills and valleys. The effect of this mass is called terrain effect. The existence of the valley will reduce the value of the gravitational field value at the point of observation, as well as the presence of the hill resulted in the reduction of the gravitational field value at the point of observation. The hill mass results in the presence of an upwardly opposite force component with the gravitational component. So the existence of valleys and hills around the observation point will reduce the value of the actual gravity field at that point, so that the calculated field correction is always positive.
Plane Reduction
Plane reduction is a process to reduce data distortion on topography caused by differences of mass distance from survey points. This process will make clearer interpretation and model building. Dampney reduces anomaly object to a mass equivalent point then projected the anomaly to a plane eith equal elevation [7] C. Magnetic Anomaly Magnetic force is force that is caused by the interaction of two magnetic poles that is separated by r distance. The force can be attractive if the poles have the same sign and repulsive if the poles have opposite sign [2]. According to Systeme International (SI), magnetic force theory is formulated using the analogy that magnetic poles can be considered as an electric charge, so that the force ( − → F ) that is formed by q 1 and q 2 poles interaction that is separated by r can be formulated using Coulumb's Law: Where − → F is a force that acts in q 1 and q 2 in Newton, µ 0 is magnetic permeability in vacuum (µ 0 = 4π × 10 −7 H/m), and r is the distance between the two magnetic poles q 1 and q 2 [3] Magnetic Field Strength Magnetic field is a force in a point with a distance of r that is caused by magnetic pole q 2 . From classical theory, it can be defined that magnetic field is magnetic force per unit pole q 1 . Magnetic field can be formulated mathematically: Where magnetic field is in Ampere/m [3] Magnetic Intensity or Magnetization Magnetic intensity can be defined as magnetic dipole moment ( − → m) per unit volume (V ).
Earth's Magnetic Field Earth's magnetic field is generated by three main sources. Those three sources are earth main magnetic field, external magnetic field, and spatial variations of magnetic field or magnetic field anomaly where earth's main magnetic field is the dominant one. In geomagnetic field measurement, the measured field is the resultant of those three above.
Earth's Main Magnetic Field
Recent theory states that earth's main field is formed by convection current in outer core fluids that is rich in nickel and iron that rotates as the earth rotates in its axis. Rotation from conductive outer core liquids and solid inner core produces magnetic field, the mechanism is similar to that dynamo mechanism. Around 90% of earth total field is from this main field.
External Magnetic Field
External magnetic field is formed by the sources that are located outside the earth. This field has low value compared to that main field and vary rapidly in time. This field mainly can be caused by atmosphere conductivity changes, sun activity effect which periodically changes in 24 h within a range of 30 nT, diurnal variation from moon's activity which has range of 2 nT, and sun storm activity that is randomly occur and can give value within range of 1000 nT.
Magnetic Field Anomaly
Magnetic field anomaly usually can exist by the effect of magnetic materials that are distributed in rocks. Remanent, induction, or demagnetization can give different effect in the anomaly field. This variation is mainly caused by different in magnetic characteristic between one rock to another or specifically is the susceptibility of rocks.
III. Methodology
The first gravity data retrieval is to determine the absolute value of gravity by bonding the gravity value at the base with an absolute gravity. Furthermore, gravity data retrieval is done daily using the Gravitymeter LaCoste & Romberg G-1118 Model, which is daily carried out the daily target data collection by starting from the measurement at the base point in the morning, before taking measurements for the points survey targets, then ends by re-measuring the base point at night, after taking measurements at the last point of the day. Based on the data retrieval time, it is necessary to correct drift and tidal correction. Then, at the data collection each point of measurement, taken data three times to get the average scale reading.
While taking GPS data using Trimble 4600LS to determine the precise position is to use the method of connective point. The system of this method is to tie the gravity / rover data retrieval point at the known base point of fixed positioning, so that at the point of reference the gravity data can be identified (referenced positioning).
The gravity data processing begins by converting the reading scale listed on the tool during measurement and technical corrections are made to determine the value of gravity observation. The correction is a instrument height correction, tidal, and drift and then added to the absolute value of gravity that was known at the beginning of the survey. After that, correction is done to determine theoretical gravity value. The correction is the correction of latitude (normal gravity), free air, Bouguer, and terrain. Then, to get the value of gravity anomaly is to reduce the value of observed gravity (Gobs) with theoretical gravity value. The value of gravity anomaly is called complete bouger anomaly (ABL).
ABL value still presents at the height according to their respective topography. Therefore, a flat field reduction is carried out by bringing all the measurement data points at the same elevation point. After that, the upward continuation and residual filtering are done. And at the end of the research is to do 2.5 D modelling as the final result of final interpretation.
IV. Result and Discussion
One of the main objective in Fieldcamp 2018 is to identify the existence of intrusion (porphyry body) and existence control agent of mineralization zone in Sangon. Hydrothermal alteration in the research area is the result of the change event of rock minerals that is caused by hydrothermal fluid interaction with rock around. The fluid that brings metal liquid is from igneous rock involves control from geological structure, like fault zone. Mineralization potential in the research area is the result of precious mineral gets into rock and creates ore deposit.
According to [8], in general the process of mineralization is effected by some control factors, including: • Hydrothermal liquid that functions as mineral carrier liquid, • Weak zone that functions as channel for hydrothermal liquid to pass, • Availability space for hydrothermal liquid deposition, • Chemical reaction event from host rock with hydrothermal liquid that is possible to happen mineral ore deposition, • Concentrate liquid that is fair high to deposit mineral ore. Magmatic activity as heat source produces hydrothermal fluid which is the main control agent of the creation of gold deposit. Hydrothermal activity creates gold deposit in economic scale also needs heat source for enough time period. Heat source is commonly known as magma. Basaltic magma or ultra-basalt commonly creates magma body in small dimension, so that quickly turns into cold. Whereas, in Sangon, estimated the magma is acid and tends to create magma body to big dimension. Therefore, geological condition is potential to create gold in economic scale in the area of the presesence of acid igneous rock. To know the anomaly response that is caused by intrusion beneath the surface, conducted gravity measurement with large area 6.4 × 5.6 km. After processing data by reducing some effects that affects gravity value from complete bouger anomaly (ABL), but ABL is still affected by topography where point measurement is, so that ABL needs to be reduced to flat plane. After that, then the anomaly pattern becomes clearer, which is positive anomaly pattern relatives to eastern in the research area with the value is 122-142 mGal and negative anomaly pattern relatives to south-western in the research area with the value is 82-102 mGal. After reducing to flat plane is done, then the anomaly is separated Figure 4: Complete Bouguer Anomaly Map in Equivalent Stratum shows highly positive anomaly at North-East direction by upward continuation filter, so that we have local anomaly to slice for making model. Modelling is done by slicing research area that is suspected as shallow anomaly source. From the local anomaly map is known that positive anomaly value is in SE and in NW is the result of intrusion that becomes control agent of low sulfidation in the epithermal system of research area. The 2.5 D gravity modelling results as existence of intrusion rock which is suspected as host rock and control agent of mineralization in Sangon, also response from Dacite intrusion with density 2.72 gr/cc which intrudes another older intrusion, Andesite with density 2.5 gr/cc. Two processes of these intrusions make partial damaged of mineralization, so that in some areas can't be found fresh mineral ore (not altered) in mineralization zone. It can be interpreted that intrusion radius is around 1000 m. Then, the gravity modelling correlates with magnetic modelling which suspects existence of intrusion in SW research area. Besides of heat source in the epithermal system, control agent system in mineralization zone has spatial relation between major structure and mineralization process itself. Regionally, a structure system in magmatic arc will form intrusions in which fills fracture areas exist although new fracture. So that, in the major structure area will happen some activities relate to mineral traps. Magnetic data interpretation suspects there is geological structure, fault. That fault is also can be seen from river straightness and close map contour. This fault accommodates the existence a fracture zone that is filled by hydrothermal liquid that can create vein as sulfide mineral deposited. From total magnetic anomaly we can see that anomaly range values from around -300 to 1300 nT. Total anomaly inclination in the amount of −32.39 0 that will make dipole pattern with negative value in southern area and positive value in northern area. But from total magnetic anomaly map is known that in the southern anomaly has positive value, whereas in the northern area has negative value, so that it can be guessed that dipole is not a set dipole in the area.
From upward continuation anomaly 500 m is known that high regional anomaly is in SW area and low anomaly is in NE area. The interpretation is according to residual anomaly map. Residual anomaly map (local anomaly) is the result of total magnetic anomaly map reduction to regonal anomaly map. Residual anomaly map has residual anomaly values around -800 to 1300 nT. Residual anomaly map shows there is low anomaly along which is suspected as structure.
In the epithermal deposit of low sulfidation can be alteration will be created around extensional geological structure. From residual magnetic anomaly map that has been reduced to pole, we can tell that the faults will be seen in low anomaly as the effect from debris zone and demagnetization as the intrusion outcome. Reference says that fractured fault on the surface can be delineated some adds of structure control agent SE-NW oriented.
Another important feature is there is another control agent as intrusion that is showed by high anomaly. In this research, we can find some Andesite instrusion, confirmed from Andesite mine found in the measurement point. This intrusion also can function as control agent of demagnetization in surrounded area that is symbolized by blue color and have low anomaly as the cause of demagnetization zone by hot fluid.
V. Conclusion
• There is high gravity anomaly with closed closure pattern and North-South oriented. In the eastern of research area is suspected as intrusion body response. • After gravity and magnetic modelling by slicing both gravity and magnetic residual map show the same intrusion of Dacite body intrusion with 1000 m diameter. It is suspected as control agent of low sulfidation of epithermal system. • Strike-slip fault can't be seen in gravity data, but it can be seen in magnetic data. It is estimated in NE-SW oriented of research area.
VI. Acknowledgements
Authors | 5,173 | 2020-04-27T00:00:00.000 | [
"Geology"
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Prognostic value of canine pancreatic lipase immunoreactivity and lipase activity in dogs with gastric dilatation-volvulus
This study evaluated the association between a selection of candidate predictor variables, including the elevation of specific pancreatic enzymes, and outcome in dogs with gastric dilatation-volvulus (GDV). Twenty-two dogs with gastric dilatation-volvulus were included, being classified as survivors or non-survivors based on the final outcome. Dogs with intestinal obstruction (n = 16) were selected for comparison. Blood samples were collected upon admission (T0) and after 24 hours (T1). Serum lipase activity, canine pancreatic lipase immunoreactivity (cPLI) and other variables (plasma lactate concentration and C- reactive protein -CRP- in particular) were evaluated as predictive variables. T0 cPLI and serum lipase activity were not found to differ significantly between dogs with gastric dilatation-volvulus or intestinal obstruction. Canine pancreatic lipase immunoreactivity values above 400 μg/L were detected in 6/22 dogs with gastric dilatation-volvulus and 4/16 with intestinal obstruction. However, lactate concentration was significantly higher and CRP significantly lower in GDV as compared to IO dogs, and in the GDV group, lipase, cPLI and CRP measured upon admission were significantly associated with a negative outcome. No differences in lipase activity and canine pancreatic lipase immunoreactivity values were detected between T0 and T1. Presurgical cPLI and lipase activity were frequently increased during gastric dilatation-volvulus and were suggestive of the presence of pancreatic damage; while more extensive studies are required, based on this pilot analysis, cPLI has the potential to be a useful predictive variable for outcome in GDV. Further to this, serum CRP was able to predict outcome in this population of dogs with GDV, while blood lactate was not.
The aim of the present study was to better understand pancreatic involvement and its association with outcome in dogs with GDV. The main hypothesis was that increased cPLI concentration was associated with poor outcome in GDV and could be used as a prognostic marker; as no data regarding cPLI in GDV are currently available to perform a sample size analysis, this will be a pilot study. A secondary hypothesis that other candidate variables, such as lipase activity, plasma lactate and C-reactive protein concentration, might have predictive value was also evaluated. Finally, a comparison between GDV dogs and dogs presented with intestinal obstruction was introduced, in order to examine serum lipase activity and cPLI in animals with a different gastrointestinal tract disease and determine whether any differences were specifically caused by GDV, or were common findings in abdominal surgical diseases.
Materials and methods
Ethical committee approval for this study was obtained at the University of Bologna, in accordance with DL 26/2014 (Project ID 581).
Presurgical data included signalment, history, clinical signs at presentation, and any administered treatment or any presurgical procedure performed at the Veterinary Teaching Hospital (VTH). Surgical medical records were used to determine: the type of surgery, the condition of the abdominal organs during the exploratory celiotomy and any complications when present. Postsurgical data included animal condition during hospitalization, the administered treatments and the final outcome. Animals receiving any medical treatment before their arrival, animals affected by pre-existing pancreatic diseases, and dogs euthanized for non-ethical reasons were excluded from this study.
GDV dogs were grouped according to their outcome: dogs that survived until discharge were classified as survivors, while those euthanized or that died spontaneously were classified as non-survivors. Euthanasia was performed in some cases with extensive gastric wall necrosis.
A control group of dogs presenting non-neoplastic intestinal obstruction (IO; n = 16) was selected. These animals were diagnosed with IO at the VTH during the same study period.
Clinicopathological evaluation
Complete laboratory tests were performed for all the GDV dogs on admission. The serum chemistry profile (AU 480; Olympus/Beckman-Coulter) was evaluated for all patients. Blood lactate was immediately assessed using a portable lactate analyzer (Lactate Scout +, EKF diagnostics, Cardiff, UK). Blood samples were collected before starting fluid resuscitation (T0) and after 24 hours (T1) in dogs surviving to that point. Within 30 minutes after collection, these samples underwent centrifugation at 4˚C, 3000 x g. After this procedure, they were immediately analyzed or stored at -80˚C until the assay. Serum lipase activity (Lipase, OSR 6130, Olympus/Beckman-Coulter) was measured using the 1,2-diglyceride (1,2DiG) method (reference range in normal dogs: 70-700U/L); cPLI (cPLI, IDEXX Laboratories) was evaluated as well, considering values < 200 μg/L as normal, > 400 μg/L as indicative of pancreatitis, and concentrations between 200 and 400 μg/L as suspicious for pancreatitis [12]. IO dogs followed the same protocol of clinicopathological evaluation as reported for GDV dogs.
The GDV group was submitted to gastric decompression through an oral gastric tube and/ or through trocarization with 18-gauge needle.
All dogs were postoperatively admitted to the intensive care unit and monitored for 3-5 days after surgery.
Statistical analysis
Data were expressed by standard descriptive statistics. Normality was tested graphically and using the D'Agostino Pearson test. Because of the non-normal distribution of most variables, non-parametric testing was adopted for all analyses and reported as median and (range). The Mann Whitney test was used to evaluate differences between groups. The Wilcoxon signedrank test and Friedman test were conducted for comparing differences between T0 and T1. Logistic regression analyses (using univariate models) were performed to evaluate outcome prediction (stepwise approach). Variables were screened for collinearity before introduction into the regression model. Results were presented as the odds ratios (OR) and their 95% confidence intervals (CI). Overall model fit was assessed by the percentage of outcome correctly classified by the receiver operator characteristic (ROC) curve analysis and by the Hosmer & Lemeshow test (p > .05). The results of all statistics were considered significant if p .05. A sample size and power analysis was performed using the Altman's normogram in order to determine the power of our pilot study and the number of dogs that must be included in future studies as a statistical sample to reach a minimum power of 80%. This was made on the basis of the mean values and standard deviation of cPLI, calculated as previously reported [15] in survivors and non-survivors in GDV group of this study. Statistical analyses were completed using MedCalc Statistical Software version 17.9.7 (MedCalc Software bvba, Ostend, Belgium; http://www.medcalc.org; 2017).
Signalment
Twenty-two dogs with GDV were included in the study. The median age was 8 years (2-17) and the median body weight was 35 kg . Seventeen dogs were males (three neutered) and five were females (one spayed). Large and giant dogs predominated, accounting for 18/22 cases (seven German Shepherd Dogs or German Shepherd Dog crossbreds, four Dobermanns, two Labradors, two Bull Mastiffs, one Great Dane, one Rhodesian Ridgeback, one Neapolitan Mastiff), although 4/22 medium-sized dogs (one German Shorthaired Pointer, one Basset Hound, one French Bulldog, one Dalmatian dog) were also included.
Outcome, surgical results, complications and hospitalization
Sixteen of 22 dogs (73%) with GDV survived to discharge, while 6/22 (27%) did not survive; four of them were euthanized intraoperatively due to massive gastric wall necrosis. The other two non-surviving dogs died spontaneously during the surgical procedure or a few hours later. The median age of survivors and non-surviving dogs was 8 years (3-14) and 9 years (2-17), respectively. The median body weight of survivors was 36.5 kg (18-55) while for non-survivors was 30.5 kg (24-54). Among the non-survivors, two were females and four males (one neutered).
All GDV dogs had a complete splenectomy and an incisional right gastropexy; only one of them underwent gastrotomy for the presence of a concomitant gastric acuminate foreign body that could not be removed by endoscopic procedure.
Among the IO dogs, 2/16 (12.5%) did not survive to discharge. One of them died spontaneously during a revision surgical procedure performed two days after the original enterectomy, due to extensive intestinal necrosis; while the second dog died spontaneously few hours after surgery. One of them was a neutered male and the other was a female. Their median age was 8.5 years (5-12) and their median body weight was 25 Kg (18-32). The median age and the median body weight of the surviving dogs with IO was 8.5 years (range, 1-14 years) and 14 Kg (range, 5-36.5 Kg). Eight dogs out of 16 underwent enterotomy and 3/16 dogs received enterectomy to remove intestinal foreign bodies. Two dogs out of 16 presented intestinal intussusceptions and one dog had an obstruction secondary to adhesions; in these three cases the obstruction was resolved during explorative laparotomy without any intestinal dieresis. The remaining 2/16 dogs did not need a surgical procedure as they presented a duodenal foreign body that could be removed by an endoscopic procedure.
Laboratory results
The clinicopathological results of the GDV and IO groups at T0 are reported in Tables 1 and 2. Median cPLI concentration and lipase activity were not significantly different between GDV and IO. cPLI concentrations of survivors and non-survivors in the two groups are reported in Fig 1. Median serum lactate concentration was significantly higher in GDV group; of these 19/ 20 had increased serum lactate concentration (RI = 0,5-2,0 mmol/L). CRP was significantly lower in GDV dogs.
In GDV group, lipase, cPLI and CRP were significantly associated with a negative outcome, while lactate concentration was not; Logistic regression analysis results were reported in Table 3.
Based on ROC curve analysis, cPLI had poor accuracy for predicting outcome. Instead CRP, with a cutoff of 2,02 mg/dL, had 100% sensitivity and 80% specificity for prediction of outcome (AUC = 0,850). No differences in cPLI values were detected between T0 and T1 in the GDV dogs (p = 0.95), with a median value less than the lower threshold for both. cPLI values did not differ between GDV and IO dogs both at T0 (p = 0.7) and at T1 (p = 0.85).
Furthermore, neither the cPLI values (p = 0.6 for IO), nor lipase activity differed significantly between T0 and T1 in the two pathological groups (p = 0.4 and p = 0.6 for IO and GDV respectively).
Finally, considering the absolute difference of 294 μg/L of the mean values between survivors and non-survivors in our sample of 22 GDV dogs, this study appears to have a 40% power to detect that difference with statistical significance.
In order to achieve a minimum of 80% power in a future assessment of cPLI as an outcome predictor in GDV, we calculate that a sample of at least 78 dogs is required assuming a similar mortality rate.
Discussion
The high mortality rate related to GDV motivates the investigation of biomarkers that could provide a prognostic aid to the veterinary surgeon. Our results showed that cPLI concentration Table 2
Survivors (n = 16) Non-survivors (n = 6) Survivors (n = 14) Non-survivors (n = 2)
Lactate (mmol/L) 5 was higher in non-surviving GDV dogs (median 716 μg/L) than in survivors (median 67 μg/ L), although this difference was not significant (p = 0.08). Previously, the myoglobin level at the time of GDV diagnosis (Mbt0) has been found to predict outcome, but with only moderate sensitivity. Adamik et al. reported that 90% of dogs presenting a Mbt0 < 168 ng/mL (considered the cutoff value) survived, while 50% of dogs with Mbt0 > 168 ng/mL did not survive [16]. Similarly, presurgical serum pepsinogen-A concentration was significantly associated with gastric wall lesion severity, but it turned out to be only a moderate prognostic factor [17]. Coagulation parameters and inflammatory markers do not seem to have significant prognostic value in GDV dogs [17,18]; on the contrary, in this study, an increase in CRP concentration was significantly associated with a worse outcome. This discrepancy indicates the need for further studies with larger sample populations in order to understand the real importance of acute-phase proteins as an outcome-specific predictor. Plasma lactate concentration and plasma lactate clearance during resuscitation are the most studied and commonly used parameters in clinical practice [6,10,19,20], although their usefulness is not completely understood. Israeli et al. argued that lactate concentration is mostly affected by the severity of systemic hypoperfusion, acidosis and shock, and that it is only indirectly associated with the presence and extent of gastric wall necrosis [17]. Zacher et al. and Green et al. reported that there was no significant correlation between hyperlactatemia at presentation and gastric wall necrosis or outcome [6,10]; this is consistent with the results of the present study, in which most of the dogs presented hyperlactatemia but blood lactate concentrations did not appear to be associated with outcome.
Our decision to investigate lipase and cPLI serum concentrations as prognostic factors came from the study of the results of previous works evaluating these parameters before and after surgery [17,21]. Pancreatitis is a possible complication in dogs with GDV: it seems to derive from gastric and splenic displacement [17,21] or from the decreased venous return which could cause hypoperfusion, resulting in pancreas inflammation [22].
Lipase is considered to have low/moderate accuracy and specificity (60%) for diagnosing pancreatitis in dogs [11, 23,24]. Simpson et al. demonstrated the presence of serum lipase activity in pancreatectomized dogs [25], while dogs presenting exocrine pancreatitis but with serum lipase concentrations within the reference range were reported by Steiner et al. [26]. Moreover, it has been found that non-pancreatic pathologies (i.e. renal failure, intestinal diseases, hepatic diseases) could cause alterations in lipase activity [27,28], while 47.6% of 70 dogs with fatal pancreatitis presented normal values of lipase serum concentration [29].
In contrast, cPLI is synthesized and released only by pancreatic acinar cells, and its immunoreactivity is pancreas-specific [12]. In the veterinary literature, cPLI values higher than the threshold of 400 μg/L are considered to have a very high specificity for the diagnosis of pancreatitis (ranging between 97.5 and 100%). [12,30] Israeli et al. reported an increased serum cPLI value of over 200 μg/L in 58% of dogs with GDV included in their study, with 18% of these animals recording a cPLI concentration higher than 400 μg/L [17]. In the present study approximately 36% of dogs had an increased cPLI concentration, and dogs with cPLI values above the cutoff value of 400 μg/L accounted for 27% of the study population.
A previous study investigated the role of cPLI as a prognostic factor in dogs affected by inflammatory bowel disease, highlighting that there is a negative correlation between cPLI values and outcome [11]. Our results could indicate that the pancreas is likely to be affected by inflammation during gastrointestinal tract pathologies, with consequent cPLI alterations, without a specific correlation with GDV (lipase activity and cPLI values did not differ significantly between GDV and IO dogs both at T0 and at T1).
Another hypothesis that supported indirect secondary pancreatic activation was proposed by Li et al. in 2013 and investigated through experiments on rats. The authors observed a noteworthy level of "neural intimacy" between the pancreas and duodenum [31]. This finding was a direct effect of an indirect vagal pathway that is common to most upper gastrointestinal organs and suggests that an acute lesion to one of these organs could lead to indirect stimulation of others [31]. If this finding was replicated in dogs, it would provide an easy explanation of the increased cPLI in dogs with GDV, without macroscopic pancreatic disease or alteration.
An interesting result of the present study is that lipase activity and cPLI values were correlated with outcomes in GDV dogs, confirming our main hypothesis. As already stated, the involvement of an organ different from pancreas could cause an increase in lipase activity and this extended organ damage could explain its association with outcome. However, the correlation between cPLI and outcome was borderline significant (p = 0.05): dogs with a higher concentration of cPLI were more likely to have a bad outcome, a result that encourages further studies of this relationship in a larger sample of GDV dogs.
GDV dogs included in the present study demonstrated neither classical clinical signs of pancreatitis, nor macroscopic signs of inflammation on direct visual examination of the pancreas during surgery, or during the ultrasound examinations. This is in line with the study by Israeli et al., in which only one dog presented clinical signs of pancreatitis postoperatively, recording the highest serum cPLI concentration among the dogs included in that cohort (3380 μg/L) [17]. These findings indicate that pancreatic damage may occur during GDV, but without impacting the clinical condition of the dogs. However, it is also possible that the symptoms of pancreatitis were masked by the postoperative treatment of GDV, which is almost identical to the management of pancreatitis.
A further point of note is that, in a recent study, a high agreement was found between cPLI and lipase activity measured using a 2-o-dilauryl-rac-glycero-3-glutaricacid-(6 0 -methylresorufin) ester (DGGR) assay [32]. In the present work, a 1,2 DiG method was used for the lipase measurements, but evaluation of lipase activity via DGGR in dogs presenting GDV has never been performed and could provide useful additional results.
This study had several limitations. A small number of GDV and IO dogs were included, limiting the strength of the statistical analyses as indicated by the performed power analysis. Moreover, pancreatic biopsies were not performed and so histological data, the gold standard for diagnosis of pancreatitis, were not available to compare to lipase and cPLI values.
In conclusion, in this population of dogs with GDV, serum CRP was able to predict outcome while blood lactate was not. Presurgical cPLI concentration and lipase activity are frequently increased in abdominal surgical diseases, and particularly in GDV. Based on our pilot analysis, cPLI has the potential to be a useful predictive variable for outcome in GDV. To confirm this in a potential future prospective study, assuming the same mortality risk, a sample size of at least 78 dogs would be recommended. | 4,103.4 | 2018-09-18T00:00:00.000 | [
"Biology",
"Medicine"
] |
Numerical investigation of enhanced femtosecond supercontinuum via a weak seed in noble gases
Numerical simulations are employed to elucidate the physics underlying the enhanced femtosecond supercontinuum generation previously observed during optical filamentation in noble gases and in the presence of a weak seed pulse. Simulations based on the metastable electronic state approach are shown not only to capture the qualitative features of the experiment, but also reveal the relation of the observed enhancement to recent developments in the area of sub-cycle engineering of filaments. © 2016 Optical Society of America OCIS codes: (320.6629) Supercontinuum generation; (190.5940) Self-action effects. References and links 1. For a comprehensive overview see, D. Faccio, A. Couairion, and P. Di Trapani, Conical Waves, Filaments and Nonlinear Filamentation Optics (Aracne Editrice Rome, 2007). 2. M. Kolesik, E. M. Wright, and J. V. Moloney, “Interpretation of the spectrally resolved far field of femtosecond pulses propagating in bulk nonlinear dispersive media,” Opt. Express 13, 10729–10741 (2005). 3. M. Kolesik, and J. V. Moloney, “Perturbative and non-perturbative aspects of optical filamentation in bulk dielectric media,” Opt. Express 16, 2971–2988 (2008). 4. P. Béjot, G. Karras, F. Billard, E. Hertz, B. Lavorel, E. Cormier, and O. Faucher, “Harmonic generation and nonlinear propagation: When secondary radiations have primary consequences,” Phys. Rev. Lett. 112, 203902 (2014). 5. P. Béjot, G. Karras, F. Billard, J. Doussot, E. Hertz, B. Lavorel, and O. Faucher, “Sub-cycle engineering of laser filamentation in gas by harmonic seeding,” Phys. Rev. A 92, 053417 (2015). 6. J. Doussot, P. Béjot, G. Karras, F. Billard, and O. Faucher, “Phase control of two-color filamentation,” J. Phys. B: Atom. Mol. Opt. Phys. 48, 184005 (2015). 7. J. Doussot, P. Béjot, and O. Faucher, “Impact of third-harmonic generation on the filamentation process,” Phys. Rev. A 93, 033857 (2016). 8. E. E. Serebryannikov and A. M. Zheltikov, “Strong-field photoionization as excited state tunneling,” Phys. Rev. Lett. 116, 123901 (2016). 9. M. Kolesik, J. M. Brown, A. Teleki, P. Jakobsen, J. V. Moloney, and E. M. Wright, “Metastable electronic states and nonlinear response for high-intensity optical pulses,” Optica 1, 323–331 (2014). 10. J. M. Brown, C. Shanor, E. M. Wright, and M. Kolesik, “Carrier-wave shape effects in optical filamentation,” Opt. Lett. 41, 859 (2016). 11. T. R. Ensley, D. A. Fishman, S. Webster, L. A. Padilha, D. J. Hagan, and E. W. Van Stryland, “Energy and spectral enhancement of femtosecond supercontinuum in a noble gas using a weak seed,” Opt. Express 19(2), 757–763 (2011). 12. T. R. Ensley, “White light continuum for broadband nonlinear spectroscopy,” Ph.D. thesis, CREOL, The College of Optics and Photonics (2015). #264346 Received 29 Apr 2016; revised 16 Jun 2016; accepted 17 Jun 2016; published 24 Jun 2016 © 2016 OSA 27 Jun 2016 | Vol. 24, No. 13 | DOI:10.1364/OE.24.015110 | OPTICS EXPRESS 15110 13. F. Théberge, N. Aközbek, W. Liu, A. Becker, and S.L. Chin, “Tunable ultrashort laser pulses generated through filamentation in gases,” Phys. Rev. Lett. 97, 023904 (2006). 14. X. M. Tong and C. D. Lin, “Empirical formula for static field ionization rates of atoms and molecules by lasers in the barrier-suppression regime,” J. Phys. B. 38, 2593 (2005). 15. H. J. Lehmeir, W. Leupacher, and A. Penzkofer, “Nonresonant third order hyperpolarizability of rare gases and N2 determined by third harmonic generation,” Opt. Commun. 56, 67 (1985). 16. M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations”, Phys. Rev. E. 70 036604 (2004). 17. J. Andreasen, and M. Kolesik, “Nonlinear propagation of light in structured media: Generalized unidirectional pulse propagation equations”, Phys. Rev. E 86, 036706 (2012). 18. http://acms.arizona.edu/FemtoTheory/MK personal/guppelab/
Introduction
The theory and accompanying experiments regarding the phenomenon of weak radiation generation during the optical filamentation of ultrashort pulses in atomic gases are now well documented [1].In the effective three-wave mixing picture [2] of this phenomenon the optical filament is viewed as an optical wave-packet localized in space and time, formed by the complex interplay between diffraction, group-velocity dispersion, nonlinear self-focusing, and plasma generation and defocusing.This resulting near solitary wave describing the filament in turn produces a moving refractive-index perturbation from which weak waves can scatter, giving rise to the growth of weak radiation according to phase-matching conditions dependent on the detailed dispersion landscape for the medium.The weak radiation generated in this manner is responsible for the detailed features of a range of phenomena in atomic gases and condensed media alike, including supercontinuum (SC) or white light continuum (WLC) generation, and conical waves such as X-waves and O-waves [3].
A series of recent theoretical and experimental works have shown that the interaction between an optical filament and an externally applied weak seed, a variant of the situation discussed above, can give rise to sub-cycle engineering of the filament [4][5][6][7].In particular, it was shown that adding a weak third-harmonic seed pulse can be used to alter the propagation characteristics, SC generation, and plasma generation for optical filaments that are orders of magnitude stronger.Using numerical solutions of the time-dependent Schrödinger equation, Bejot et.al [5] traced this enhancement to interference between ionization channels involving different color photons, highlighting that this is a quantum coherent effect rooted in the extreme nature of the off-resonant light-matter interaction, see also the recent Ref. [8].In subsequent work some of the present authors (CS,EMW,MK) showed that the enhancement could also be explained in the framework of the Metastable Electronic State Approach (MESA) [9], in which the atomic state is represented in terms of the metastable, or resonance, states for the atom in the off-resonant field [10].The MESA view highlights the relation of the enhancement to the carrier-wave shape, and the occurrence of local temporal peaks, which depends critically on the relative phase between the carrier waves of the filament and weak seed pulse.
In the present paper we examine an earlier set of experiments by some of the present authors (TRE,DJH,EVS) that reported enhanced SC generation in noble gases, but for seed wavelengths closer to the filament, see Refs.[11,12] for details.More specifically, Fig. 1 shows experimental SC spectra for the case of Krypton gas, a filament of center wavelength 780 nm, and seed wavelengths of 600 nm (left plot) and 1300 nm (right plot).The filament or pump energy was 0.4 mJ and the seed energy 1 μJ, and the pump and seed pulses were overlapped spatially and temporally in the noble gas chamber.The experimental SC spectra extended up to 1400 nm and was limited to greater than 300 nm by the notch filter employed.Furthermore there are gaps in the experimental data appearing in the vicinity of the pump (750 − 810 nm) and the seed (550 − 650 nm for the 600 nm seed and 1240 − 1340 nm for the 1300 nm seed), these being indicated by the gray areas.Each plot shows the angle integrated SC energy density in nJ/nm versus wavelength both with (red data points) and without (black data points) the seed present.Key features that have remained without detailed explanation are why the enhancement occurs at all in this experiment, the spectral distribution of the SC, and why it occurs for the 600 nm seed but not for the 1300 nm seed.The authors of Ref. [11] stressed the critical role played by four-wavemixing (FWM) and we shall elucidate on this here.Earlier simulations of the above experiment by B. Shim, S. E. Schrauth, and Alex Gaeta of Cornell University, also alluded to the role of FWM in the SC generation process.These simulations are reported in the thesis of Ref. [12] but have not been published in an archival journal.A somewhat similar role was played by FWM in the experiment reported in [13], which demonstrated efficient, filament-aided conversion of mid-infrared radiation into the visible.The features that distinguish the physics discussed here are that the seed energies are exceedingly small, and that the supercontinuum enhancement extends well beyond the discrete frequencies dictated by the FWM process.Fig. 1.Angle integrated SC energy density in nJ/nm versus wavelength both with (red data points) and without (black data points) the seed applied.The left plot is for a seed wavelength of 600 nm and the right plot for 1300 nm.The gray regions indicate gaps in the experimental data in the vicinity of the pump and seed pulses.The data is adapted from that given in Fig. 2 of Ref. [11].
This experiment predates the enhancement experiments described in the second paragraph above, and attracts particular attention due to the potential as an alternative to conventional sources of radiation for applications such a nonlinear spectroscopy.Here using numerical simulations based on MESA we demonstrate that we can capture the qualitative features of the SC spectra for this experiment, in particular the relevance of the seed wavelength to the enhancement.Furthermore, we find that the enhancement is sensitive to the carrier-wave shape offering the possibility that the white-light spectral power can be optimized in a given wavelength interval.This observation may be important for future applications.Finally we allude to the applicability of our findings to other noble gases.
Supercontinuum spectra for Krypton gas
We employ numerical simulations of optical filamentation with a two-color pulse comprising both pump and seed with full spatial and temporal resolution.More specifically, for the atomic model we employ a quasi-static approximation based on the single-state MESA (ssMESA) [9], and employing Single Active Electron (SAE) models of noble gas atoms utilizing the SAE potentials given in [14].This procedure yields the nonlinear polarization, related to the change in refractive-index, and the ionization rate, both as functions of the electric field strength.This approach is microscopically self-consistent in the sense that the derived nonlinear polarizations and ionization rates are automatically in correct proportion.To complete the specification of the optical properties the linear data are incorporated using the known dispersion relation for noble gases [15].The carrier resolved field propagation is then performed using the gUPPEcore [16,17] pulse propagation solver [18] coupled to the ssMESA data.
Before discussing the results, we remark that we also performed extensive simulations with the classical model for optical filamentation, in which the nonlinear polarization is proportional to E 3 (t), and the nonlinear response due to ionization is parameterized by a power-law rate, with the free electrons giving rise to a Drude current.This classical filamentation model is also capable of reproducing some of the experimental results discussed here.Indeed the simulations by B. Shim, S. E. Schrauth, and A. Gaeta reported in the thesis of Ref. [12], but not published, allude to such agreement.However, we found that the classical approach requires parameter fine-tuning (the nonlinear Kerr coefficient, the order and coefficient for multi-photon ionization etc.) and even for optimal parameter sets some of the features and connections to the experiment are less robust.In particular, we found that the dependence of the SC enhancement on the seed energy is significantly underestimated in the classical model.The classical model therefore requires quite higher seed energies to mirror the experimental data at small seed intensities, while in the experiment the signal first grows faster with increasing seed energy and only later saturates (see Section 3).
In contrast, the ssMESA is free from the parameter uncertainties associated with the classical model.While it is fair to say that it is still not a quantitative theory, the fact that all qualitative features of the SC enhancement experiment can be reproduced with no parameters to adjust indicates that it as a suitable tool to explore the underlying physics of the SC enhancement.Because our focus here is not a comparative study of the two models, only the results obtained from the ssMESA based simulations will be discussed in what follows.
We focus attention in this Section on the case of SC generation in Krypton gas as that was the gas used in the experiment reported in Ref. [11].In particular we have incorporated the parameters from that experiment, as documented in Ref. [12], into our simulations.Specifically, the pump pulse entering the gas chamber was chosen as Gaussian with spot size w p = 1300 μm, duration t p = 150 fs, energy 0.4 mJ, and center wavelength 780 nm.The seed pulse was selected to overlap the pump pulse spatially and temporally half-way along the simulated chamber length of 40 cm held at a pressure of 3.7 atm, the seed energy being 1 μJ.This yields an optical filament of approximately L f il ∼ 5 cm length starting around z = 28 cm as inferred from the simulations (see Sec. 4 for a discussion), and the SC generation is assessed at the end of the chamber.Figure 2 shows the profiles of the angle-integrated SC spectra versus wavelength for the 600 nm seed (left plot) and the seed centered at 1300 nm (right plot).(As is usual we focus on the profile of the SC spectrum as opposed to the absolute yield as the latter is very sensitive to the detailed parameters.)For each case the black line indicates the SC spectrum without the seed present.As opposed to the experimental results shown in Fig. 1 the SC spectrum is shown on a log scale: This allows us to visualize the pump, seed, and SC on the same spectral plot, and also to look beyond the wavelength limit of the experiment, where the notch filtered limited observations to wavelengths greater than 300 nm.The experimental gaps around the pump (710 − 850 nm) and seed (550 − 650 nm for the 600 nm seed and 1240 − 1340 nm for the 1300 nm seed) are indicated by gray regions in each plot.
The results in Fig. 2 show reasonable qualitative agreement with the experimental results displayed in Fig. 1.First, it is clear that once one accounts for the experimental pump and seed gaps there is little enhancement of the SC generation due to the presence of the seed for the 1300 nm wavelength in comparison to the 600 nm seed.Second, for the 600 nm case there are oscillations in the enhanced spectrum in the presence of the seed for wavelengths shorter than the gap around the seed, and a peak appearing for wavelengths larger than the pump gap.The simulations therefore capture two key qualitative features of the Krypton experiment [11].Fig. 2. Simulated angle-integrated SC spectra versus wavelength for the 600 nm seed (left plot) and the seed centered at 1300 nm (right plot).The gray regions indicate the experimental gaps around the pump (710 − 850 nm) and seed pulses (550 − 650 nm for the 600 nm seed and 1240 − 1340 nm for the 1300 nm seed).
Spectral enhancement
We next look at the spectral enhancement in more detail for the Krypton simulations in comparison to the experiment.The coarsest measure of the enhancement is to look at the ratio of the wavelength integrated SC generation both with and without the seed present, removing the experimental gaps to conform to the experimental situation.This was measured in the experiment as a function of the seed wavelength and is tabulated in the last column of Table 1 of Ref. [11] for a seed energy of 1 μJ.This enhancement is plotted versus seed wavelength in Fig. 3(a) as the red line, with a peak enhancement of around 3 for a seed wavelength of around 650 nm.The blue line in Fig. 3(a) is the corresponding result from the simulations obtained using the previous parameters, and this shows a peak enhancement of around 5.4 for a seed wavelength of around 650 nm.The simulations are therefore in reasonable qualitative agreement with the experiment: The larger enhancement from the simulations is not surprising given that deviations from exact beam alignment etc. could easily reduce the observed enhancement.We note that both the experiment and simulations show negligible enhancement for the 1300 nm seed.[11] for the enhancement as a function of seed wavelength with a peak enhancement of around 3 for a seed wavelength of around 650 nm.The blue line shows the corresponding result from the simulations, and shows a peak enhancement of around 5.4 for a seed wavelength of around 650 nm.b) Enhancement versus seed energy for a wavelength of 600 nm.For both cases the seed energy is 1 μ J.The inset shows the experimental data from Ref. [11] (see text for details).
As a further study Fig. 3(b) shows the enhancement obtained in the same manner as above but versus seed energy for a wavelength of 600 nm.This figure is reminiscent of the experimental Fig. 5 of Ref. [11], for which the corresponding data set is reproduced in the inset.It, too, shows output energy versus seed energy, but with an important difference: In Fig. 5 the energy collected is in the narrow spectral region 532 ± 4 nm [11], whereas for Fig. 3(b) the energy is assessed over all the full wavelength range minus the experimental gaps.Indeed we could not reproduce Fig. 5 of Ref. [11] with our simulations, but rather saw oscillations in output energy with seed pulse energy over the 8 nm window of the experiment.
The reason for our inability to reproduce Fig. 5 of Ref. [11] is actually an important finding from our simulations.So far we have tacitly assumed a fixed relative phase φ between the carrier waves of the pump and seed waves, cos(k Pump z − ω Pump t) and cos(k Seed z − ω Seed t + φ ), respectively: Note that this does not imply a fixed phase relationship between the pump and seed, and the instantaneous phase between the pump and seed waves changes with time and also evolves during the propagation.Figure 4(a) shows the angle integrated spectra versus wavelength obtained for φ = 0, π/5, π/2, as well as the unseeded case, and plot (b) shows the corresponding integrated energy in the small range 535 ± 5 nm, normalized to the value for φ = 0, versus the relative phase.Here we clearly see that the energy so calculated depends on the relative phase.(In contrast the results in Fig. 3 are relatively insensitive to the relative phases as they are integrated over a large spectral window.)Now, in the experiment the pump and seed waves are spatially and temporally overlapped in terms of their envelopes, but no effort was made to control this at the level of the relative phase of the carrier waves.Furthermore, the experimental spectra are averaged over many shots, so it is reasonable that the results in Fig. 5 of Ref. [11] are an ensemble average over the relative phase of the carrier waves.We remark that we obtain results similar to Figure 4(a) if the relative phase remains fixed but the pump energy is varied by a small amount.The key point is that the experimental results are an ensemble average over realizations, whereas our simulations are single shot.We have refrained from performing the ensemble average numerically due to the lack of detailed knowledge of the pump and seed pulse fluctuations and also the prohibitive computational time required (tens to hundreds of realizations would be needed each taking many hours).The sensitivity of the SC spectra to the relative phase between the carrier waves of the pump and seed is a signature that the carrier-wave shape is playing a role in the propagation characteristics and plasma generation of the optical filament, leading to enhanced SC generation.Depending on the relative phase between the constituent waves with different wavelengths, the local electric field maximum of the composite carrier wave can become more peaked or flat.The resulting change in the local field modifies both the electronic Kerr response, and the local ionization rate.Both effects can accumulate and influence the pulse propagation despite the fact that the local field changes are relatively small.This is analogous to the recently studied case where the weak seed was at the third-harmonic, enabling systematic diagnostics to be performed on the plasma generation and SC enhancement [5].In that work it was argued that the phase sensitivity will survive under propagation if the filament length L f il reph is much shorter than the rephasing length between the pump and seed given by so that the pump and seed remain in relative phase over the filament length.On the contrary if L f il reph the phase sensitivity will be washed out under propagation.For the experiment under consideration we find L f ill ∼ 5 cm (see Sec. 4), and using the dispersion data for Krypton [15] gives reph ∼ 5.2 cm for the 600 nm seed, and reph ∼ 12.6 cm for the 1300 nm seed.Thus the current experiment is in the intermediate regime with L f il ∼ reph so that some level of sensitivity to the relative phase can survive as demonstrated by the simulations.
In the present case it is clear from Fig. 4(b) that the relative phase φ between the carrier waves could be used as a control knob to optimize SC generation within a spectral window a few nanometers wide.Thus control of the relative phase and subsequent SC modification presents an opportunity to increase the enhancement seen in the experiment of Ref. [11] if sufficient control could be exacted over the pump and seed pulses.Importantly, the relative pump-seed phase can be utilized to tune-up the generated white-light power by up to 100%-200% in a given target wavelength interval.This may increase the potential of this system as an alternative to conventional sources of radiation for applications such a nonlinear spectroscopy.
Role of four-wave mixing
Next we address the issue of why enhanced SC generation appears for the 600 nm seed and not the 1300 nm seed, as reflected in Figs.1-3.In particular Fig. 3(a) shows that both experimentally and theoretically the enhancement maximizes at around a seed wavelength of 650 nm and falls off with increasing seed wavelength.What is a priori clear is that in our simulations the distinction between the two seed wavelengths cannot be rooted in some extreme light-matter interaction: The ssMESA model employed gives the nonlinearity as a function of the instantaneous electric field, so that within the quasi-static approximation the lightmatter interaction is nearly blind to the photon colors involved.Post-adiabatic correction can improve the MESA-based model to account for delayed interactions and wavelength-dependent ionization, but they are not included here in the single-state treatment; This is why we can conclude that the physics is mainly driven by the local electric field intensity changes due to seeding, and not by some complex interplay between different-color fields.
Here we demonstrate numerically that the distinction between the two seed wavelengths lies in the process of four-wave-mixing (FWM) and associated phase-matching.If we denote the pump and signal wavelengths by λ Pump = 780 nm and λ Seed , then FWM involving two pump photons and one seed photon can yield a FWM signal with wavelength λ FW M determined by Seed .For a collinear interaction of the waves the phase-matching condition is Δk = 2k Pump − k Seed − k FW M = 0, where k μ = 2πn μ /λ μ , μ =Pump, Seed, FWM, n μ being the refractive-index for the wavelength λ μ .Using the known dispersion relation for Krypton it is found that collinear phase-matching of the FWM is not possible [15].However, non-collinear phase-matching can occur, and using the law of cosines the required angle θ between the pump and seed wavevectors is given by cos For the case of Krypton with λ Seed = 600 nm we find λ FW M = 1114 nm and θ 600 = 0.0022 rad, whereas for λ Seed = 1300 nm we find λ FW M = 557 nm and θ 1300 = 0.0062 rad, a three-fold increase in the required angle between the pump and seed wavevectors for phase-matching.The geometry for the two different seed wavelengths is illustrated in Fig. 5, for (a) 600 nm, and (b) 1300 nm, and highlights the larger angle required for the 1300 nm seed wavelength.Note that since this non-collinear FWM is phase-matched the corresponding coherence length is infinite, and this underpins why the rephasing length in Eq. ( 1) is the relevant spatial scale.Fig. 5. Non-collinear phase-matching of the FWM for seed wavelengths of (a) 600 nm, and (b) 1300 nm.For purposes of illustration the angles θ 600 and θ 1300 between the pump and probe are exaggerated.
The above analysis is for plane-waves whereas the experiment involves a filament of width w ∼ 50 μm (diameter 100 μm) as determined from the simulations.The angular spread of the optical filament is therefore of the order of θ f il ∼ λ Pump πw ∼ 0.005.To assess the relevance of FWM this angular spread is compared with θ from above: Then for the 600 nm seed the angular spread of the propagating fields can easily accommodate that needed for the FWM process θ 600 = 0.002 < θ f il , and we expect non-collinear phase-matched FWM to occur: This will lead to both on-axis and off-axis FWM as the pump and seed beams have a spread of angles.In contrast, for the 1300 nm seed θ 1300 = 0.006 ∼ θ f il , so we expect FWM to play a relatively minor role.
We contend that the above phase-matching picture explains the presence (600 nm seed) or absence (1300 nm seed) of enhanced SC generation compared to the unseeded case.First, for the 1300 nm seed we argue that FWM does not play a role so we expect that the SC generation to be the same as the unseeded case.Second, for the 600 nm seed case the FWM can grow during propagation prior to filamentation and prolific SC generation, producing new frequencies via cascading over and above the pump and seed, and this acts as a catalyst that boosts the SC generation once it starts.To demonstrate this numerically Fig. 6 contains Visualization 1 of the angularly resolved logarithmic power spectrum log |E(k ⊥ , ω, z)| 2 as the propagation distance z is varied, obtained by Fourier transforming the propagating field along the chamber length into the transverse wavenumber k ⊥ and angular frequency ω, for the unseeded case (left), 600 nm seed (center), and the 1300 nm seed (right).The angularly resolved power spectrum is a very useful diagnostic tool that not only displays the frequency content of the propagating field but also the associated transverse wavevectors k ⊥ that correlate with on-axis (k ⊥ = 0) and offaxis emission directions in the far field.The stills shown in Fig. 6 are the angularly resolved spectra at the exit of the chamber: In all cases the pump has frequency ω Pump = 2.4 × 10 15 rad/s, whereas the seed frequency is ω Seed = 3.14 × 10 15 rad/s for seed wavelength 600 nm and ω Seed = 1.45 × 10 15 rad/s for 1300 nm.First we note the clear similarity between the unseeded case (left) and the 1300 nm seed case (right), and viewing the animation shows that the SC generation proceeds in much the same way in both cases: Concentrating on the unseeded animation, the angularly resolved spectrum consists of waves centered around the pump (ω Pump = 2.4 × 10 15 rad/s) and third harmonic (7.2 × 10 15 rad/s) up to a propagation distance of around 28 cm.Past this point the spectrum starts to become rapidly populated between the pump and third harmonic, a process of prolific SC generation that persists until around 33 cm.Since SC generation is intimately tied to optical filamentation for propagation in bulk gases, we identify the start of the filament at around 28 cm, and the terminus at around 33 cm, yielding an estimate of the filament length as L f il ∼ 5 cm.We note that this estimate of the filament length would vary some depending on the criterion, for example, the length of the induced plasma channel, but this qualitative picture will suffice for our purposes.
In contrast, for the 600 nm seed case, even for the still, there is clear evidence of several on-axis peaks along k ⊥ = 0, and these arise from FWM.The structure revealed in the angularly resolved spectrum is called a 'fish-wave' as it displays a fish bone-like structure due to the on-axis and off-axis FWM that is noticeably absent from the unseeded case [1].This is clearly seen by viewing the animation for this case (center): At the start the pump (ω Pump = 2.4 × 10 15 rad/s) and seed (ω Seed = 1.45 × 10 15 rad/s) are present, but as the propagation proceeds the first FWM peak (ω FW M = 1.7 × 10 15 rad/s) appears, along with some third-harmonic (7.2 × 10 15 rad/s), followed by cascaded FWM, and then the SC generation kicks in around 28 cm and is clearly influenced, indeed enhanced.These simulations elucidate the role played by FWM in the enhanced SC generation, as conjectured in Ref. [11].
Other noble gases
To finish we demonstrate that the enhanced SC generation captured by our simulations for Krypton also appears for other noble gases.Experiments were carried out for Argon and Xenon, but the parameters needed for detailed simulations were not as extensively documented in this case [12], so we satisfy ourselves by showing some generic SC spectra for these gases.Figure 7 shows the simulated SC spectra for both Argon (left plot) and Xenon (right plot) for seeds with wavelengths of 650 nm and 680 nm, respectively.In each case the unseeded case is shown for comparison, and we see features very similar to Fig. 2 for Krypton.We emphasize that while our simulation results can not be considered for quantitative comparisons against the experiment, the fact that the model does not rely on any adjustable parameters (note that each gas is fully characterized by its frequency-dependent susceptibility plus a single-active-electron potential) underlines the universal nature of the SC enhancement effect across the noble gases.The success of the model in explaining the most important qualitative features also indicates that the physics included in the model is indeed sufficient.We therefore conclude that the supercontinuum generation increase can be interpreted in terms of the local electric-field enhancement mediated by the seed, combined with the off-axis FWM phase-matching picture.
Summary and conclusions
In conclusion, using numerical simulations based on the metastable electronic state approach we have revealed the physics underlying the enhanced SC generation previously observed for optical filament propagation in noble gases in the presence of a weak seed.The simulations were shown to be in good qualitative agreement with the experiments, and examination of the angularly resolved spectrum clarified the role played by four-wave mixing in selecting an effective seed wavelength to produce enhancement.We also found that the SC spectrum was sensitive to the relative phase between the pump and seed carrier waves: This observation is a key finding of this paper and establishes the relation between the physics underlying the SC enhancement observed in Ref. [11] to recent developments in sub-cycle engineering of optical filaments.In finishing we mention that if this relative phase can be controlled this may provide a means to further improve the capability of this system as an alternative to conventional tunable sources for nonlinear spectroscopy.
Fig. 3 .
Fig. 3. Enhancement of the SC generation.a) The red line shows the experimental results from Ref.[11] for the enhancement as a function of seed wavelength with a peak enhancement of around 3 for a seed wavelength of around 650 nm.The blue line shows the corresponding result from the simulations, and shows a peak enhancement of around 5.4 for a seed wavelength of around 650 nm.b) Enhancement versus seed energy for a wavelength of 600 nm.For both cases the seed energy is 1 μ J.The inset shows the experimental data from Ref.[11] (see text for details).
Fig. 6 .
Fig. 6.Visualization 1. Animation of the evolution of the angularly resolved power spectrum |E(k ⊥ , ω, z)| 2 (on log scale), obtained by Fourier transforming the propagating field along the chamber length into the transverse wavenumber k ⊥ and angular frequency ω, for the unseeded case (left), 600 nm seed (center), and the 1300 nm seed (right).The stills are for the case at the exit of the noble gas chamber.
Fig. 7 .
Fig.7.Simulated spectra show a roughly order of magnitude enhancement of the supercontinuum radiation for Argon (left plot) and Xenon (right plot) for seeds with wavelengths of 650 nm and 680 nm, respectively. | 7,484.4 | 2016-06-27T00:00:00.000 | [
"Physics"
] |
Does the Digital Age Require New Models of Democracy ? – Lasswell ’ s Policy Scientist of Democracy vs . Liquid Democracy
Introduction The world is changing ever since. Due to new information and communication technologies (ICTs), this change is happening a lot faster than ever before though. The era the world is in at the moment is often described as the digital age. It is characterised by the shift from traditional industry to an economy based on information: “Like the steam engine during the First Industrial Revolution, the ICT has completely changed the way society organizes its economic activity” (Humbert, 2007, p. 2). However, this change does not only affect the economy, but nearly all spheres of people’s lives including society and politics. Democracy, or rather plebiscitary democracy is nowadays the most common form of government in the world. Plebiscitary democracy describes a mixture of indirect democracy with little parts of direct democracy (Schallehn & Haun, 2013). Yet, the acceptance of democracy is declining worldwide. As the non-profit organisation Freedom House describes in their latest report, democracy as a form of government is at its lowest level since 1989. The developments in 2014 show that nearly twice as many countries suffered declines in democracy as registered gains, 61 to 33 (Aghekyan et al., 2015). Within the field of political science, but also emerging from other fields and civil society itself, there is a groundswell of people calling for new models of democracy. Their biggest argument is that the form of plebiscitary democracy most countries are executing nowadays routes in the circumstances of the ancient Greece which means it is not fully applicable anymore nowadays (Jochmann, 2012). This results in, for instance, decreasing voter turnouts and political apathy. Thus, with the possibilities of the digital age, also new models for democracy are required. First and foremost, in order to put this essay and the two chosen democracy models (Lasswell’s policy scientist of democracy and liquid democracy) into the right frame, the term democracy should be explained and an elaboration on the democracy spectrum is needed. A very simple definition of democracy could be: rule by the people (Clawson & Oxley, 2012). Becker and Raveloson (2008) explain that democracy in a nutshell consists out of certain key elements, namely fundamental freedom and rights, elections, rule of law, separation of powers, a parliament, democratic pluralism, a government and an opposition, public opinion, and freedom of the media. Larry Diamond (2004), Senior Fellow at Stanford University adds that next to elections and the rule of law, also active participation of citizens in politics and the civic life and the protection of human rights are crucial in a democracy. However, democracies can look very different from each other. First of all, there is the distinction between direct and indirect democracy. Direct democracy is an umbrella ARTICLE
Introduction
The world is changing ever since.Due to new information and communication technologies (ICTs), this change is happening a lot faster than ever before though.The era the world is in at the moment is often described as the digital age.It is characterised by the shift from traditional industry to an economy based on information: "Like the steam engine during the First Industrial Revolution, the ICT has completely changed the way society organizes its economic activity" (Humbert, 2007, p. 2).
However, this change does not only affect the economy, but nearly all spheres of people's lives including society and politics.Democracy, or rather plebiscitary democracy is nowadays the most common form of government in the world.Plebiscitary democracy describes a mixture of indirect democracy with little parts of direct democracy (Schallehn & Haun, 2013).Yet, the acceptance of democracy is declining worldwide.As the non-profit organisation Freedom House describes in their latest report, democracy as a form of government is at its lowest level since 1989.The developments in 2014 show that nearly twice as many countries suffered declines in democracy as registered gains, 61 to 33 (Aghekyan et al., 2015).
Within the field of political science, but also emerging from other fields and civil society itself, there is a groundswell of people calling for new models of democracy.Their biggest argument is that the form of plebiscitary democracy most countries are executing nowadays routes in the circumstances of the ancient Greece which means it is not fully applicable anymore nowadays (Jochmann, 2012).This results in, for instance, decreasing voter turnouts and political apathy.Thus, with the possibilities of the digital age, also new models for democracy are required.
First and foremost, in order to put this essay and the two chosen democracy models (Lasswell's policy scientist of democracy and liquid democracy) into the right frame, the term democracy should be explained and an elaboration on the democracy spectrum is needed.A very simple definition of democracy could be: rule by the people (Clawson & Oxley, 2012).Becker and Raveloson (2008) explain that democracy in a nutshell consists out of certain key elements, namely fundamental freedom and rights, elections, rule of law, separation of powers, a parliament, democratic pluralism, a government and an opposition, public opinion, and freedom of the media.Larry Diamond (2004), Senior Fellow at Stanford University adds that next to elections and the rule of law, also active participation of citizens in politics and the civic life and the protection of human rights are crucial in a democracy.
However, democracies can look very different from each other.First of all, there is the distinction between direct and indirect democracy.Direct democracy is an umbrella This essay provides a debate about Lasswell's policy scientist of democracy (PSOD, 1948) in comparison to the model of liquid democracy (21 st century) based on the question if the digital age requires new models of democracy.The PSOD of Lasswell, a disciplinary persona, is in favour of an elitist approach to democracy including elite decision-making, as well as the values of wealth and power.Liquid democracy, on the other hand, emerged from the notion that the Internet provides a vast amount of possibilities for a mix between direct and representative democratic aspects.The term liquid democracy describes a more "fluid and responsive participation of citizens in the democratic process through the use of both online and offline networks" (david, 2013).In general, one can say that both models have their drawbacks and benefits.Since there are new technologies available in the digital age, we should make use of them for the public good, but in order to not exclude anyone, there should be a mix between traditional and technology-based methods with regard to democracy.
term covering a variety of political processes which allow citizens to vote directly on laws rather than candidates for office.Forms of direct democracy can include town meetings, ballot measures, propositions, referenda, or legislative measures (Matsusaka, 2005).Indirect democracy, or more often called representative democracy, whereas, is the government by representatives of the people (Lijphart, 2012).
Moreover, one can distinguish between three theories, namely elitist, pluralist, and participatory (Clawson & Oxley, 2012).Democratic elitists see elections as the primary mechanism with which citizens can express their preferences.The elected officials or political elites can be held accountable to the public via periodical (re-)elections.Hence, the representatives have an incentive to truly represent the will of the citizens which will be reflected, to some degree, in governmental decisions."Yet the daily decisions are made by the elites, who, by their knowledge and expertise, are better able to make these decisions", as Clawson and Oxley (2012, p. 7) explain.
Likewise, pluralists see elections as an important mechanism for accountability.However, they emphasise the role of interest groups as intermediaries between the public and the elites in representative democracies.Those interest groups are supposed to represent certain segments of the public including their issues and concerns.Consequently, they attempt to influence elected officials and other governmental decision makers (Clawson & Oxley, 2012).
The newest among those three theories is participatory democracy.This theory emphasises political participation of citizens on a nation-wide level.This is the case especially in order to address issues such as inequality.According to Clawson and Oxley (2012), participatory democracy evolved during the US protest movements of the 1960s and "represented dissatisfaction with the democratic elitist and pluralist models that were dominant at that time" (Clawson & Oxley, 2012, p. 11).This links to Hajer's (2003) claim that nation states are weaker than ever and that it is far less obvious that governments are the only ones to agree on policies which will be further elaborated on during this essay.
This essay provides a debate about Lasswell's policy scientist of democracy (1948) in comparison to the model of liquid democracy (21 st century) based on the question if the digital age requires new models of democracy.These two models were chosen because when looking at them from a broader angle, they allow an extensive comparison between, on the one hand the democratic elitist view and, on the other hand, the democratic pluralist view.In comparison to Lasswell's model which is purely based within representative democracy, liquid democracy shifts between direct and representative democracy.Moreover, unlike Lasswell's PSOD, liquid democracy can not only be applied to a democracy itself but also within organisational and institutional structures.
Harold D. Lasswell
Harold Dwight Lasswell was born in 1902 and was a US-American political and communication scientist mainly interested in sociology, mass communication, and propaganda.He was one of the most influential political scientist before 1945 and a pioneer in his field (Farr, Hacker & Kazee, 2006).His research into propaganda like the formation of public opinion, the roles of political leaders, or the content analysis of mass media became highly politicised over the course of time (Graham, 2007;Rogers, 1997).
Lasswell belonged to the Chicago School which had a deep influence on US-American as well as international political science.When the US took a leading role in world politics, many political scientists, like for instance Lasswell, followed this path (Berndtson, 1987).Farr, Hacker, and Kazee (2006) describe Lasswell as "a giant within political science" (p.580).He was surrounded by chosen young political scientists that formed a famous and promising group.During his life time, there was much at stake within politics like the Second World War and the Cold War.Hence, Lasswell was of the opinion that political scientists or experts should advice policy makers which was one of the reasons he developed the Policy Scientist of Democracy (PSOD).He was definitely not a theorist only sitting behind his desk.He was rather convinced that political science is "the policy science, par excellence" (Lasswell, as cited in Farr, Hacker & Kazee, 2006).
Lasswell's Policy Scientist of Democracy
According to Farr, Hacker, and Kazee (2006), the PSOD, a disciplinary persona, emerged during the 1940s based on Lasswell's own concrete life experiences and was first mentioned in "Power and Personality" in 1948.It is a model which knows all about the process of elite decision-making, advises those in power, and strives for the individual's dignity.The PSOD can be seen as an expert that is intelligent, comfortable in and around power, and prepared for struggle.Moreover, he is strategic, innovative, forward looking, and especially relevant to governance in the times of crises.Threats to the PSOD are characterised as communism, tyranny, and its propaganda (Farr, Hacker & Kazee, 2006).
Lasswell himself commented on the PSOD and his strategic plan to it as follows: "My ultimate objective in the field of science is far from modest.I propose to contribute to the systematic theory of the political sciences" (Lasswell as cited in Farr, Hacker & Kazee, 2006).According to Berndtson (1987), Lasswell wanted to turn political science into the science of democracy.This is consistent with the questions that arose in connection to the PSOD: "What is the role of the political scientist in a democratic society?Do political scientists have any obligation to inform or shape policy?"(Farr, Hacker & Kazee, 2006, p. 586).
After publishing the model of the PSOD, Lasswell was exposed to a lot of criticism by fellow scholars.Many described his approach as being unrealistic and difficult (Farr, Hacker & Kazee, 2006).Consequently, Lasswell altered his model, including functions of the decisionmaking process, intellectual tasks, and eight goal values of policy of the PSOD.Those goal values are: "wealth, power, respect, rectitude, skill, well-being, enlightenment, and affection" (Farr, Hacker & Kazee, 2006, p. 584).When looking at those eight goal values of policy, it becomes clear why Lasswell's approach stands in sharp contrast to the later in this paper explained model of liquid democracy.Many have criticised Lasswell for his elitism and the use of experts, which neglects the aspirations of democratic citizens (Hajer, 2003).Yet, Lasswell did not deny that, describing the model himself as being "elitist", although grading it down to "realist" later in time (Farr, Hacker & Kazee, 2006, p. 587).
Another point at issue is the lacking explanation for applications of the PSOD by Lasswell.How should a PSOD look like in real life?Apparently, Lasswell thought of policy scientists being those experts.But who exactly are those policy scientists and how can they be fostered and trained to fulfil the tasks and goals of the PSOD?Eventually, Farr, Hacker, and Kazee ( 2006) come to the conclusion that Lasswell's vision of the PSOD is far too heroic to be acceptable.
Liquid Democracy
The other side of the democracy spectrum is represented by liquid democracy.Basically, liquid democracy is a collective term to describe a more "fluid and responsive participation of citizens in the democratic process through the use of both online and offline networks" (david, 2013).As Norris ( 2004) explains, political communication in general is about the transmission of information among politicians, media, and the public.This process operates either top-down (from governing institutions to the public), horizontally, or bottom-up (from the public towards governing institutions).The original influence on liquid democracy stems from the aspiration to replace the top-down chain of command within the political system.Consequently, what all the different approaches calling themselves liquid democracy have in common is the concept of delegating your vote for certain subject areas or topics.Hence, it is possible to actively participate in one topic while delegating one's vote to someone else for others (vprotest, 2012).It is this fluid rotation between direct and indirect democracy that characterises the model of liquid democracy (Jochmann, 2012).
In order to understand why some people claim a new form of democracy in the digital age, one has to take a look at the context in which modern democracy was developed.According to Jochmann (2012), in ancient Greece all men came together on a designated hill in order to discuss current issues and create policy solutions.The word on the street was transformed into politics.Nowadays, in modern nation states there is no possibility for the common public to regularly meet somewhere.Additionally, today's problems are a lot more complex than those of the ancient Greeks.This especially has to do with globalisation: Globalisation is the ongoing process that is linking people, neighbourhoods, cities, regions and countries much more closely together than they have ever been before.This has resulted in our lives being intertwined with people in all parts of the world via the food we eat, the clothing we wear, the music we listen to, the information we get and the ideas we hold.(UNESCO, 2010, para.2) That may be part of the reason why many people today feel that they do not have the adequate expert knowledge about the issues at stake anymore in order to contribute to the political sphere (Jochmann, 2012).However, it must be acknowledged that next to critical and engaged citizens, there is also a big group of people who consider themselves to be powerless, marginalised, and disenchanted about politics (Christensen, n.d.).Therefore, most modern democracies have designated representatives who devote all their time to be professional politicians.The public is informed on the issues being in dispute by mass media, as well as social media and other sources of information, but only the appointed people are in the position to shape the political arena (Jochmann, 2012).
The technological progress of the last few decades has made global communication a lot easier and faster.Liquid democracy focuses on a dilemma that more and more citizens face -they are actively involved with organisations and networks of all kinds, personally as well as professionally, but at the same time, many people have the feeling that they lack the opportunity to effectively influence and campaign for their stance on a higher level (vprotest, 2012).
Paetsch and Reichert (2012) distinguish three different dimensions of liquid democracy.First, the field of application, which could be for instance an institution or organisation initiating a liquid democracy process.Second, the specific objectives to be achieved with the help of liquid democracy, like for example agenda setting, consultation, or participation.Third, the participants included in the specific liquid democracy process, which could be certain organisation members or the general public.
In order to include liquid democracy into an organisation or institution, there are a lot of different tools with numerous advantages and disadvantages.As claimed by vprotest (2012), there are many approaches that work relatively well in small groups such as wikis, forums, or just face-to-face meetings, but as soon as it comes to larger groups these come to a limit.This might lead to situations where either only a few participate or where the transparency of the process begins to decrease (vprotest, 2012).
A form of organisation that many organisations involved in liquid democracy use is adhocracy.It is defined as an organisation with barely any structure being flexible, adaptable, and informally operating in an opposing manner to bureaucracy.It was first mentioned by the US-American writer and futurist Alvin Toffler in 1970 (Travica, 1999).Mintzberg (1989) describes it as a complex and dynamic organisational form.It is, for example, utilised by the Federal Government of Germany for their online platform "www.enquetebeteiligung.de" (translation by the author: survey participation) which was launched on February 24, 2011.On this website, for the first time, the public is being provided with information and documents not yet agreed on by the commission as a whole.The aim of the website is to incorporate citizens' suggestions in the national decision-making process with the purpose of making public participation possible on equal terms (Bundestag, 2011).The maybe most famous example within Germany for an organisation using liquid democracy is the German Pirate Party.It was founded in September 2006 and is part of the international movement of pirate parties.Simon Weiss, former member of the parliament of the federal state of Berlin for the Pirate Party, argues that the structure of the Pirate Party had to adapt with the further expansion of the party.The system of liquid democracy is in jeopardy in the context of much larger memberships."They [the systems] were designed to fit fifty people, not thousands" (Weiss as cited in Meyer, 2012).
As stated by Meyer ( 2012), the platform used by the German Pirate Party is called Liquid Feedback.It builds around the concept of liquid democracy and could be described as an advanced version of adhocracy.To put it into a nutshell: it is about competition and decision-making.Since the software is openly accessible for any of the more than 29,000 members of the German Pirate Party (reading 2014), anybody can use it and propose a policy.In the ideal case different people work on the same topic proposing different policies so that a healthy competition is created in which the best will win the poll.Hence, people stay involved in the topic (Meyer, 2012).
As formerly mentioned, every member has one vote which can be delegated for everything, for certain topics, specific proposals, or not at all, to someone else.In order to avoid votes being passed up the leading to a person obtaining most of the votes and consequently a lot of power, every delegated vote can be reclaimed at any time.It is a trust-based approach as explained by Bormuth (as cited in Meyer, 2012): "We want effective people to be powerful and do their work, but we want [the grassroots] to be able to control them" (para.16).
However, some questions and issues at stake are just too complex and important to be only a decision on Liquid Feedback according to Weiss (as cited in Meyer, 2012).Sometimes, there is a decision needed at a conference by an elected group of people.He gives the example of implementing a basic income or not."You can't have a system that maps the whole discourse that has to happen for this kind of democracy.But you can have quantified feedback that shows you where the majority lies on a given point" (Weiss, as cited in Meyer, 2012, para. 19).Liquid Feedback, thus, makes it easily possible for public representatives of the party to present in only a couple of seconds where the opinion of the party concerning a given topic lies (given a significant number of party members participates in an opinion poll).Imagine how long it would take any other of the traditional parties to do so.
Discussion
In general terms, Lasswell's PSOD could be described as being top-down and the model of liquid democracy as working bottom-up.Lasswell wants experts, namely political scientists to advise policy makers and liquid democracy aims at asking basically everyone.There is no denying the fact that involving everyone in a nation's decision-making process is more desirable than only letting a few being behind the wheel, is it not?Already in the 1990s Jonathan Rauch (2008) coined the term demosclerosis which is the "post-war democratic government's progressive loss of the ability to adapt" (p.125).For him, it is the most important governmental phenomenon of our time describing the decreasing capability of governments to deal with problems and consequently decisions that become more and more complex in our widely globalised world.According to Rauch (2008), many people think that demosclerosis is treatable with political reforms, but it may be inherent and irreversible, nonetheless manageable.Consequently, does it not make more sense to let someone like the PSOD guide us through these convoluted times instead of a public that might not be educated enough to make far-reaching decisions concerning millions or even billions of people?
No it does not because the speed of decision-making is not the only aspect that matters.Rauch ( 2008) may be right about the fact that many issues require faster decisions nowadays, but that is no justification for excluding the majority of people.Marcus, van Dam, Medhurst, and Perdeck (2012) describe both the speed of decisionmaking, as well as the acceptance of a decision on a scale where authority and unanimous decisions mark the far extremes.They come to the conclusion that an authority's speed (e.g.Lasswell's PSOD) is much faster than a unanimous decision (e.g.liquid democracy) regarding decisionmaking, but that the acceptance of a decision is much larger in the latter case than under an authority.
Also Hajer (2003) thought about the PSOD and whether or not there is a need for new democracy models nowadays or not.He is of the opinion that nation states are weaker than ever when it comes to (decision-making) powers and it is far less obvious that governments are the only actors to agree on policies.To his mind, persistent problems cannot be solved within the boundaries of sovereign states only because established institutions often lack the power to truly affect a vast amount of people.Thus, transnational, polycentric networks of governance in which power is dispersed become more important."The weakening of the state here goes hand in hand with the international growth of civil society, the emergence of new citizen-actors and new forms of mobilization" (Hajer, 2003, p. 175). Dryzek (as cited in Farr, Hacker & Kazee, 2006) goes into the same direction.In 1989 he already mentioned that there needs to be "a policy science of participatory democracy" (p.585) meaning greater citizen involvement including public discussions.Providing a space for more citizen involvement on a global scale is exactly what liquid democracy wants to convey.
What Hajer (2003) predicted and analysed more than ten years ago, is indeed happening on a global scale.Sriskandarajah (2015) explains that global civil society has flourished in recent years which is also recognised by the UN who are facilitating civil society participation.However, Sriskandarajah (2015) also claims that civic space is shrinking in all parts of the world due to repressive actions.The organisation Freedom House agrees."For the ninth consecutive year, Freedom in the World, Freedom House's annual report on the condition of global political rights and civil liberties, showed an overall decline" (Aghekyan et al., 2015, p. 1).
Among the worst affected categories of democratic indicators is civil society (Aghekyan et al., 2015).
If a global civil society is the aim, than another case in point has to be social exclusion.Lasswell only takes academics into account which obviously excludes people without a university degree.Moreover, his theory is based upon political scientists excluding cross-disciplinary fields with relevance to political change.Liquid democracy, whereas, excludes media illiterate people.Castells (2003) describes this term as people who are excluded by no or only limited access to the Internet, as well as those unable to use it effectively.This leads to a global digital divide which increases "the gap between the promise of the digital age and its bleak reality for many people around the world" (Castells, 2003, p. 247).
The digital divide often also reflects the inequality within a nation.Castells (2003) supports that with data from the US where in August 2000, 70.1 percent of people earning 75,000 dollars and above had Internet access compared to 18.9 percent for those with less than 15,000 dollars.The same data gives evidence to the fact that also ethnical inequality is reflected in the access to Internet.Worldwide 40 percent of the people access the Internet.Yet, this number shrinks to 26.5 percent when looking at Africa only (Internet World Stats, 2014).
Social exclusion is widely discussed among scholars and bloggers.In order to overcome social exclusion, Paetsch and Reichert (2012) propose to connect online possibilities such as Liquid Feedback to already existing offline participation methods.Bödecker (2012) adds that especially people with a high educational level and high income make use of political participation possibilities.Consequently, Ertelt (2012) claims that participation is an educational process and not primarily a matter of software.Thus, from nursery school on constructive participation needs to be trained so that everyone can take part in the development and design of our world.
However, liquid democracy might collide with political apathy because it cannot be assumed that every media literate person is also politically engaged.Thompson (2013) alleges that one can distinguish between four types of citizens: inactive apathetic citizens, inactive latent citizens, active critical citizens, and active engaged citizens.The group of apathetic citizens is characterised by being much less active than any other group, even in comparison to the inactive latent citizens (Thompson, 2013).Christensen (n.d.) adds that there is a difference between critical and disenchanted citizens.The first are critical towards authorities, but nonetheless are interested in political matters and believe that they can make a difference.The latter, on the other hand, has given up on politics and lost faith in the authorities.
This definitely needs to be taken into account when talking about democratic models.On the one hand, the PSOD requires citizens to cast their vote only once every four to five years, which might correspond better to inactive citizens.On the other hand, disenchanted citizens might not react to any form of democratic participation.Thus, political apathy needs to be taken seriously within the whole democracy debate.Yet, this needs to be discussed separately.
Conclusion
Concluding, one can say that both Lasswell's PSOD and liquid democracy have their drawbacks and benefits.Admitting more direct democracy tools within representative democracy, like liquid democracy does, can help providing people with more spaces for participation and decision-making.Furthermore, it can help to better represent the will of the people especially in issues of topicality.There are also fewer opportunities for abuse of power, corruption, and lobbyism.On the other hand, there might occur organisational or technical problems which might jeopardise the efficiency of the political system due to the fact that liquid democracy tools still need to be tested on bigger scales.Moreover, minorities could be deprived of their rights by the vote of the majority and the media obtains more power which leaves room for manipulation (Schallehn & Haun, 2013).These arguments are in favour of a model like Lasswell's PSOD which is led by political experts who are able to grasp the complexity of our world probably to a higher degree than the ordinary population is able to.
Nevertheless, this should not be an argument to withdraw the model of liquid democracy.Since there are new technologies available in the digital age, we should make use of them for the public good.But in order to not exclude anyone, there should be a mix between traditional and technology-based methods.Eventually, media literacy has to be ensured from children's earliest days, so that everyone has the same chances in becoming heard keeping in mind the topic of general political apathy.Thus, there might not be a need to overthrow all the existing models of democracy, but there should be space created for an amendment bearing in mind new developments and technologies, as well as the changing needs of citizens.
ARTICLE
Does the Digital Age Require New Models of Democracy?-Lasswell's Policy Scientist of Democracy vs. Liquid Democracy Jelena Gregorius * | 6,727 | 2015-06-21T00:00:00.000 | [
"Political Science",
"Philosophy"
] |
PROTECTIVE ROLE OF ARTEMISIA AFRA AQUEOUS EXTRACT ON TISSUE ANTIOXIDANT DEFENSE SYSTEMS IN STREPTOZOTOCIN-INDUCED DIABETIC RATS *
Changes in antioxidant capacity in the body as a result of oxidative stress play an important role in the development of diabetic complications. The aim of this study was to evaluate the effect of aqueous extract of Artemisia afra Jacq. ex Willd. on antioxidant defense systems in the liver and kidney of streptozotocin–induced diabetic rats. Administration of the extract to diabetic rats for 21 days significantly reduced blood glucose levels and increased body weight. The diabetic animals exhibited decreased levels of glutathione reductase (GR), glutathione peroxidase (GPx), superoxide dismutase (SOD) and reduced glutathione (GSH) in the liver and kidney, which were restored to near normal levels following treatment with the herb. The increased levels of lipid peroxidation observed in the tissues of diabetic rats were also reverted back to near normalcy after administering the extract. These findings revealed the protective role of A. afra on tissues by reducing oxidative stress which could be attributed to its flavonoids content. The efficacy of the plant compared favourably well with glibenclamide, a standard hypoglycemic drug.
Introduction
Diabetes is a metabolic disorder characterized by chronic hyperglycaemia leading to various dysfunctions in the body.Free radical generation is currently suggested to play an important role in the causation and complications of the disease (Senthilkumar and Subramanian, 2007).These radicals are continually produced in the body as a result of normal metabolic processes and interaction with environmental stimuli.In healthy individuals, the generation of free radical appears to be approximately in balance with the antioxidant defense system comprising both enzymatic and non-enzymatic antioxidants.In diabetes however, there are alterations in the endogenous free radical scavenging mechanisms which may lead to the production of reactive oxygen species, resulting in oxidative damage and tissue injury (Oberley, 1988).Implication of oxidative stress in the pathogenesis of diabetes is suggested not only by oxygen-free radicals but also due to non-enzymatic protein glycosylation and auto-oxidation of glucose (Mullarkey et al., 1990); alterations in antioxidant enzymes (Strain, 1991) as well as formation of lipid peroxides (Baynes, 1991).Enhanced oxidative stress and changes in antioxidant capacity, observed in both clinical and experimental diabetes, are thought to be the etiology of diabetic complications (Baynes, 1991).
The management of diabetes is considered a global problem and there is no successful and definite therapy yet.A few chemotherapeutic drugs have been in use to manage the disease since the accidental discovery of the hypoglycemic action of sulfonamides (Robinson and Johnston, 1997).The thrust of such management measures is to achieve an effective blood glucose control or utilization, with a view to delaying or averting the onset of complications.The application of these measures is however limited due to their high cost and associated side effects (Upadhyay et al., 1996;Reynolds, 1997).Recently, attention is being focused on the identification of natural antioxidants from plants to replace synthetic ones.Findings from scientific reports have shown that plants contain various substances that possess antioxidant activity (Chanwitheesuk et al., 2005).
The present study was undertaken to evaluate the antioxidant activity of aqueous leaf extract of Artemisia afra on the liver and kidney of streptozotocin-induced diabetic rats and the efficacy was compared with glibenclamide, a standard hypoglycemic drug.
Chemicals
Streptozotocin was procured from Sigma Chemical Co., St. Louis, MO, USA while the assay kits used for biochemical analyses were products of Randox Laboratories Limited, Ardmore, Co Antrim, United Kingdom.All other chemicals and reagents used were of analytical grade.
Plant material and preparation of extract
Fresh and mature leaves of A. afra were collected around the University of Fort Hare, Alice (Eastern Cape Province, South Africa).The plant was authenticated by Prof DS Grierson of Botany Department and a voucher specimen was prepared and deposited in the University herbarium.An aqueous extract of the plant was prepared as previously described by Sunmonu and Afolayan (2010).The dried plant material recovered was reconstituted in distilled water to give the required doses of 50 and 100 mg/kg body weight used in the experiment.
Animals
Male albino rats of Wistar strain with a mean weight of 154 ± 4.20 g were used for the experiment.The animals were obtained and reared as described by Sunmonu and Afolayan (2011), after seeking approval from the Ethical Committee on the Use and Care of Animals of the University of Fort Hare, South Africa.
Induction of diabetes
Diabetes was induced in the rats according to the procedure described by Sunmonu and Afolayan (2010).The animals were allowed to drink 5% glucose solution overnight to overcome streptozotocin-induced hypoglycemia.Control rats were injected with citrate buffer alone.After 48 h, fasting blood glucose levels were estimated and levels above 250 mg/dl in streptozotocin-treated rats confirmed diabetes in the animals.
Animal grouping and extract administration
Thirty male rats were randomized into five groups of six animals and were orally administered appropriately for 21 days.Group 1 (normal control) and Group 2 (diabetic control) received distilled water.Groups 3 and 4 are diabetic rats treated with 50 and 100 mg/kg body weight/day of A. afra extract respectively while Group 5 comprised diabetic rats administered with glibenclamide (600 µg/kg body weight/day).The body weights of the animals were determined at the beginning and end of the experimental period.
Collection of blood and preparation of tissue homogenate
Twenty four hours after the last dose, blood sample was collected from the tail vein of the animals for estimation of glucose level after which the rats were humanely sacrificed by ether anaesthetization.After dissecting the animals, the liver and kidney were excised carefully and rinsed immediately in ice cold physiological saline.Known weights of the tissues were homogenized in Tris-HCl buffer (pH 7.4) and the resulting homogenates were used for analyses.
Biochemical assays
Tissue protein was estimated according to the method of Lowry et al. (1951) using bovine serum albumin as standard.Superoxide dismutase (SOD) activity was determined by the method of Marklund and Marklund (1974).Glutathione reductase (GR) activity in the tissues was measured according to the method of Goldberg and Spooner (1983) while glutathione peroxidase (GPx) was assayed using the method of Paglia and Valentine (1967).Lipid peroxidation (LPO) was determined by the formation of malondialdehyde (MDA)-thiobarbituric acid reactive substances (TBARS) adduct according to the method of Ledwozyw et al. (1986).The released malondialdehyde served as the index of lipid peroxidation.Reduced glutathione was estimated by the method of Ellman (1959).
Statistical analysis
Data were expressed as mean ± SD for six animals in each group and were subjected to one way analysis of variance (ANOVA) followed by Duncan multiple range test to determine significant differences in all the parameters.p values of less than 0.05 were considered statistically significant.
Effect of A. afra on hyperglycemia and body weight
Table 1 summarizes blood glucose levels and body weight in the control and experimental groups of animals.The diabetic rats showed significant increase in serum glucose levels and significant decrease in body weight compared to the normal control.Administration of aqueous extract of A. afra restored glucose levels and body weight to near normal range.
Effect of A. afra on lipid peroxidation and GSH content
As reported in Table 2, there was a significant elevation in MDA and a significant decrease in GSH levels in the liver and kidney of diabetic rats.Treatment with the herb resulted in a marked improvement in these indices at the end of the experiment as they were reverted back to normalcy after 21 days.
Effect of A. afra on the activities of antioxidant enzymes
Tables 3 and 4 show the activities of enzymic antioxidants (GPx, GR and SOD) in the liver and kidney respectively.Significantly decreased activities of these enzymes were observed in the tissues of diabetic rats.However, these activities were significantly improved following administration of the extract for 21 days.Generally, the effect of the extract compared favourably well with glibenclamide, a standard hypoglycemic drug.
Discussion
Many of the complications of diabetes have been linked to oxidative stress and antioxidants have been considered as treatments (Reaven et al., 1995;Cunningham, 1998).Hence, it could be suggested that antioxidant action may be an important property of plant medicines associated with diabetes.The present study has clearly demonstrated that aqueous extract of Artemisia afra has antioxidant activity; and the efficacy is comparable to glibenclamide, a standard hypoglycemic drug.Increase in blood glucose level is an important characteristic feature of diabetic state.The extract from A. afra produced significant hypoglycemic effect in diabetic rats and by day 21, the glucose levels tended towards normalcy as found in the control.Microchemical analyses of the plant have indicated the presence of saponins (Silbernagel et al., 1990) which had been reported to possess hypoglycemic activity in diabetic rabbits (Abdel-Hassan et al., 2000).Therefore, the hypoglycemic activity of A. afra observed in this study could be attributed to the presence of saponin.
The reduction in body weight observed in diabetic rats could be attributed to excessive breakdown of tissue proteins (Chatterjea and Shinde, 2002).The improvement in body weight in the A. afra treated rats could be due to increase in metabolic activity.This clearly indicates that the plant extract increased glucose metabolism and thus enhanced body weight in diabetic rats.Similar observation was reported by Ravi et al. (2004a).According to these authors, Eugenia jambolana seed kernels enhanced body weight of diabetic rats.
Most tissue damages are mediated by free radicals which attack membranes through peroxidation of unsaturated fatty acids (Stringer et al., 1989).Diabetes induction with streptozotocin in rats results in an increase in lipid peroxidation, which is an evidence of intensified free radical production (Maritim et al., 2003).In this study, the levels of malondialdehyde (MDA) were increased in the liver and kidney of diabetic rats which is an indication of increased free radical generation leading to oxidative stress in the tissues.Administration of the extract significantly reduced MDA level, which suggests that the extract might possess antioxidant activity.This is an indication that the herb has a protective effect by ameliorating tissue oxidative stress.Similar observation was reported by Ravi et al. (2004b) using E. jambolana seed kernel in STZ treated rats.The evidence presented in this study suggests that the antioxidative role of A. afra could be attributed to its flavonoids content which act as strong free radical scavengers.
Glutathione is an important antioxidant which plays the role of an intracellular radical scavenger and is a substrate for many xenobiotic elimination reactions (Gregus et al., 1996).Decreased levels of reduced glutathione (GSH) observed in the liver and kidney of diabetic rats may be a result of increased oxidative stress.GSH has the ability to manage oxidative stress with adaptional changes in enzymes regulating GSH metabolism (Arulselvan and Subramanian, 2007).The treatment of the rats with A. afra extract significantly increased the GSH levels in their tissues and consequently improved the antioxidant status.This increase may, in turn, activate GSH dependent enzymes such as glutathione peroxidase and glutathione reductase.
Increased concentrations of ROS have been implicated in many of diabetic complications (Halliwell and Gutteridge, 1989).The present findings indicate significantly reduced tissue antioxidant enzymic activities in diabetic rats and its attenuation by A. afra treatment.GPx is involved in the reduction of hydrogen peroxide to water by using glutathione as a hydrogen donor (Sies, 1993).Reduced activity of this enzyme in the liver and kidney of diabetic rats has been observed in the current study.Our result is consistent with Ravi et al. (2004b) who reported a reduction in the activity of tissue antioxidant enzymes in diabetic rats.The reduced activity of GPx may result in accumulation of toxic products due to oxidative damage; and its recovery following treatment with A. afra extract indicates the protective effect of the herb on antioxidants.
The decreased activities of SOD and GR in both liver and kidney during diabetes as observed in this study may be due to increased production of reactive oxygen radicals which are capable of reducing the activities of these enzymes (Wohaieb and Godin, 1987).SOD is an important defense enzyme which catalyses the dismutation of superoxide radicals while GR is required for the conversion of oxidized (GSSG) to reduced glutathione (GSH).Oral administration of A. afra increased the activities of these enzymes which may help to scavenge the free radicals generated during diabetes.This is indicative of the protective role of the herb on antioxidant enzymes in the tissues.Generally, the effect of the treatment with A. afra compared favourably with the effect of glibenclamide, a known standard drug for diabetes.
Conclusion
Aside its hypoglycemic action, findings from the present study clearly revealed antioxidant property of aqueous extract of A. afra which could protect tissues from oxidative damage.This is an indication that the extract could be a very useful therapeutic agent for treating radical-related pathological damages.
Table 1 :
Effect of A. afra on blood glucose levels and body weight in diabetic rats (n = 6, X ± SD)
Table 2 :
Effect of A. afra on malondialdehyde and reduced glutathione levels in the liver and kidney of diabetic rats (n = 6, X ±
Table 3 :
Effect of A. afra on the activities of antioxidant enzymes in the liver of diabetic rats (n = 6, X ± SD)
Table 4 :
Effect of A. afra on the activities of antioxidant enzymes in the kidney of diabetic rats (n = 6, X ± SD) | 3,047.8 | 2012-10-01T00:00:00.000 | [
"Biology"
] |
Particles in Relativistic MHD Jets. I. Role of Jet Dynamics in Particle Acceleration
Relativistic jets from (supermassive) black holes are typically observed in nonthermal emission, caused by highly relativistic electrons. Here, we study the interrelation between three-dimensional (special) relativistic magnetohydrodynamics, and particle acceleration in these jets. We inject Lagrangian particles into the jet that are accelerated through diffusive shock acceleration and radiate energy via synchrotron and inverse Compton processes. We investigate the impact of different injection nozzles on the jet dynamics, propagation, and the spectral energy distribution of relativistic particles. We consider three different injection nozzles—injecting steady, variable, and precessing jets. These jets evolve with substantially different dynamics, driving different levels of turbulence and shock structures. The steady jet shows a strong, stationary shock feature, resulting from a head-on collision with an inner back-flow along the jet axis—a jet inside a jet. This shock represents a site for highly efficient particle acceleration for electrons up to a few tens of TeV and should be visible in emission as a jet knot. Overall, we find that the total number of shocks is more essential for particle acceleration than the strength of the shocks. The precessing jet is most efficient in accelerating electrons to high energies reaching even few hundred TeVs, with power-law index ranging from 2.3 to 3.1. We compare different outflow components, such as the jet and the entrained material concerning particle acceleration. For the precessing nozzle, the particle acceleration in the entrained material is as efficient as that in the jet stream. This is due to the higher level of turbulence induced by the precession motion.
INTRODUCTION
Astrophysical jets are often observed as relativistic, well-collimated outflows of plasma and fields originating in a region near a compact object accreting matter.These jets are present in a number of astrophysical systems on various scales including Active Galactic Nuclei (AGNs), high mass X-ray binaries or microquasars, gamma-ray bursts (GRBs) and young stellar objects (YSOs).Jets originate from a deep gravitational potential well and from sources hosting strong magnetic fields and an accretion disk (Hawley et al. 2015).
AGN jets travel long distances, reaching hundreds of kpc from the supermassive black hole.The parent galaxies of these sources (called radio galaxies), can be categodubey@mpia.de,fendt<EMAIL_ADDRESS>* Fellow of the International Max Planck Research School for Astronomy & Cosmic Physics at the University of Heidelberg rized into two classes (Fanaroff & Riley 1974) depending on their radio jet kinetic power and morphology.
Although the processes responsible for formation and launching of these jets are not yet completely understood, the power released from the rotational energy of the black hole (Blandford & Znajek 1977) or the accretion flow (Blandford & Payne 1982) are thought to be the sources of jet energy.This power is ultimately transferred from the gravitational energy to the jet kinetic energy via the magnetic field.The magnetic field can be deduced from observations of power-law spectra, polarization spectral distribution and polarisation.The magnitude of the magnetic field is typically obtained from the cutoff in power-law spectra, whereas the direction is determined via polarisation of these systems, (Meisenheimer et al. 1997;Carilli et al. 1999;Heavens & Meisenheimer 1987;Brunetti et al. 2003) that is due to non-thermal particles that undergo synchrotron and inverse Compton losses.
AGN jets are typically super-(magneto)sonic, and hence produce strong shocks leading to a turbulent magnetic field and velocity component.This makes these sources an ideal site for accelerating particles to high energies (Hargrave & Ryle 1974).Strong shocks, through diffusive shock acceleration, play a vital role in accelerating particles (Krymskii et al. 1978;Blandford & Ostriker 1978;Bell 1978a,b).Additionally, various other mechanisms of particle acceleration are also at play in these sources.These include second-order Fermi acceleration (Fermi 1949;Kundu et al. 2021) particularly in the radio lobes, magnetic reconnection in highly magnetized jet regions (Giannios et al. 2009) and shear acceleration (Rieger et al. 2007;Sironi et al. 2021).
The dynamics of the jet seems to plays an essential role in the emission and subsequently, in studying the shock structure and particle acceleration.In particular, jets that undergo a time-dependent injection of material (and magnetic field), such as intermittent jets and precessing jets, are able to drive a high excess of turbulence or instabilities in the jet flow.This leads to more shocks, and hence, more sites of particle acceleration, and also to an increased efficiency of particle acceleration.(Yates et al. 2018;Giri et al. 2022).
The AGN jet sources are also thought to be one of the sites for production of ultrahigh energy cosmic rays (Pierre Auger Collaboration et al. 2017;Aab et al. 2018;Matthews et al. 2018).Although several studies have pointed out the ineffectiveness of highly relativistic shocks to accelerate particles to such high energies (Reville & Bell 2014;Bell et al. 2018), other investigations have shown that non-relativistic or mildly relativistic shocks can accelerate particles to high energies (Kirk & Duffy 1999;Marcowith et al. 2016;Matthews et al. 2019;Marcowith et al. 2020;Araudo et al. 2021;Ortuño-Macías et al. 2022).Such shocks are capable of accelerating both protons and electrons.In particular, existence of high energy protons is crucial for understanding the origin of neutrino emission associated with blazar jets (Mannheim 1993).Even at large scales, these accelerated particles play a crucial role in governing the heating due to feedback.Simulations of jet inflated bubbles in presence of cosmic ray transport have shown the dominant role of cosmic ray mediated heating at large cluster scales (Ehlert et al. 2018).
As the propagation of astrophysical jets is highly dynamical due to the various non-linear physical processes at work, numerical simulations play an essential role for studying jets.A number of numerical simulations have been performed to study various aspects of jet propagation (for relativistic jets see e.g.Leismann et al. 2005;Mizuno et al. 2007;Keppens et al. 2008;Rossi et al. 2008;Meliani & Keppens 2009;Mignone et al. 2010).In particular, shock diagnostics and particle acceleration in the jet are studied in Mukherjee et al. (2021) for a straight jet with small velocity perturbations to induce turbulence through three-dimensional (3D) relativistic magnetohydrodynamical (RMHD) simulations.
In our paper, we present 3D (special) RMHD simulations of jets injected into a uniform ambient medium.We inject Lagrangian macro-particles into the propagating jet that are advected along with the flow, each of them representing an ensemble of electrons.We then look how these particles are accelerated along the jet flow by internal and external shocks (Vaidya et al. 2018).We study different kinds of time-dependent injection nozzles and investigate how injection from these nozzles affects the dynamics of the jets -its turbulence, shock structure, symmetry -and, as a result, how particle acceleration varies for these nozzles.More specifically, we use three different nozzles -injecting (i) a straight jet, (ii) a precessing jet and (iii) an intermittent jet into the ambient medium.
The different nozzles we apply are thought to be generated by different jet launching conditions at the jet origin.Jet launching itself -the transition from accretion to ejection -is not further considered in our simulations.We may distinguish between jets being launched from resistive accretion disks, as modeled in the non-relativistic case in axisymmetry (see e.g.Casse & Keppens 2002;Zanni et al. 2007;Sheikhnezami et al. 2012;Stepanovs & Fendt 2016).Fully 3D simulations e.g. for binary systems in a Roche potential (Sheikhnezami & Fendt 2015) indicate on precession effects on the accretion disk and thus the jet launched from that disk.
Jet launching from the black hole ergosphere (the BZ process) has been numerically modeled since two decades, mostly applying the evolution from an initial torus surrounding the black hole (McKinney & Gammie 2004;Tchekhovskoy et al. 2011).More recent work applying resistive GR-MHD has been able to consider in addition the evolution of disk winds and jets from thin accretion disks and comparing them to the central spine jet (Qian et al. 2018;Vourellis et al. 2019;Dihingia et al. 2021), even including a disk dynamo (Vourellis & Fendt 2021).We note that the kinematics of the BZ jets obtained in these simulations is biased by the floor model for density and pressure that needs to be considered.
The observation of jet knots hints to a time-dependent mechanism behind their origin, probably a timedependent injection (nozzle).Some recent observations indeed provide indication for precessing AGN jets (see e.g.Britzen et al. 2018;von Fellenberg et al. 2023), and their connection to binary black holes (see e.g.Kharb et al. 2017;Krause et al. 2019).
Our paper is structured as follows.In section 2 we detail our model approach and the numerical methods.In section 3 we discuss the dynamical evolution of the different jets, their energetics and turbulence level.In section 4 we finally present energy spectra of particles moving with the jet and being accelerated by shocks arising in the turbulent jet motion.We conclude with a summary in section 5.
Here, D is the laboratory density, m is the momentum, B is the magnetic field in the lab frame, E t is the total energy density, v is the velocity, γ f is the Lorentz factor of the fluid, and Ī is the diagonal tensor.The magnetic field can be represented by the 4-vector with the magnetic energy density the momentum vector m i = w t γ f v i −b 0 b i , the relativistic total enthalpy w t = ρh + b 2 , and the total pressure of the fluid p t = p + (b 2 /2) where p is the gas pressure (Del Zanna et al. 2003;Mignone & McKinney 2007).Further, the specific enthalpy h is related to the internal energy ε of the gas as where ρ = D/γ f is the density in the fluid frame and p is the gas pressure.
In order to close the aforementioned equations, an equation of state relating h with ρ is further needed (which we discuss in Section 2.1).With this, the total energy density in the lab frame is given as (5) (Mignone & McKinney 2007), where the first two terms represent the kinetic, thermal and the rest mass energy density while the last two terms represent the electromagnetic energy density.Specifically, the third term represents the magnetic energy density, whereas the last term represents the electric energy density as a result of an electric field E = −v×B (Keppens et al. 2008), altogether considering the contribution by Poynting flux.
To study the particle acceleration, we use the Lagrangian particle module of the PLUTO code (Vaidya et al. 2018), which uses passive Lagrangian particles moving in an Eulerian grid to model the non-thermal spectral signatures from relativistic jets.Essentially, we consider particle acceleration due to diffusive shock acceleration (DSA; or first-order Fermi acceleration) following the sub-grid approach developed in Vaidya et al. (2018); Mukherjee et al. (2021).The Lagrangian macroparticle, in this approach, represents an ensemble of particles (electrons) following the fluid, initially distributed as following a power-law energy spectrum.This initial spectrum subsequently evolves for each macro-particle in time and momentum space, taking into account acceleration due to DSA and cooling as a result of adiabatic expansion, synchrotron radiation processes, and inverse Compton (IC) scattering of particle in a background of cosmic microwave background (CMB) photons.For this purpose, the particle code solves the relativistic transport equation for cosmic rays in scattering medium (Webb 1989) which we discuss in Section 2.4.
Equation of State
In order to solve the RMHD equations mentioned above, we need a proper closure provided by an additional equation, that is the equation of state (e.o.s.), relating two thermodynamic parameters (e.g.density and internal energy).
For a perfect gas, this relationship is derived using the relativistic theory (Synge 1957).However, applying this general relationship in a numerical code is too time-consuming and for saving computational resources, a constant-Γ e.o.s. is often used.We apply an approximate e.o.s. which follows a simple analytical form and is fast and suitable to be adopted for numerical studies, (Mathews 1971;Mignone et al. 2005) where Θ = p/ρ is the temperature.This e.o.s., widely denoted as Taub-Mathews (TM) e.o.s., differs from the theoretical Synge e.o.s.only by a few percent, and provides thermo-dynamical variables that are very similar to the constant-Γ e.o.s. in the limit of a cold gas (Γ = 5/3, Θ → 0) and a hot gas (Γ = 4/3, Θ → ∞).For intermediate temperatures, the respective values vary smoothly between the two limiting cases.For the TM e.o.s., the adiabatic index is Γ = (h − 1)/(h − 1 − Θ), whereas the sound speed relative to the fluid c s is defined as Applying c s we define the (ordinary) relativistic sonic Mach number in the lab frame M s = v/c s and the proper sonic Mach number with the proper speed of the fluid u and the proper sound speed u s relative to the fluid (and similarly for the Lorentz factors γ f and γ fs , respectively).Here we follow the arguments by Konigl (1980) and others stating that the proper sonic Mach number M s is the relativistic generalization of the Newtonian Mach number.
Similarly, the Alfvén velocity c a , the magnetisation σ and the plasma β are defined as and similarly for the related Alfvén Mach numbers M a and M a (Mizuno et al. 2014).
As extractable energy E x of the fluid in the lab frame, we define the total energy E t (Equation 5) subtracted by the rest mass energy density Dc 2 .Substituting the specific enthalpy h for the TM e.o.s we obtain where the first and second terms on the right hand side represent the kinetic energy density E kin and the thermal energy density E th , respectively, and the last two terms represent the electromagnetic energy density E em .
The extractable power of the jet P x at time t is calculated by integrating the extractable energy density E x over the volume V and dividing by the time t.Thus, is the (volume-weighted) mean extractable energy density over the outflow volume V (considering cells, where v > 0).We have thoroughly tested both ideal and TM (implemented in PLUTO as Taub e.o.s.) e.o.s. in our simulations in order to compare their effects on the flow dynamics and internal structure.We came to the conclusion that the TM e.o.s. is a much better approach when treating (relativistic) gases of different temperature, such as the low-density, hot gas in the jet, and the high-density, cool gas of the ambient medium.The TM approach is particularly interesting when it comes to the dynamics of the jet cocoon or back-flow material consisting of shocked and entrained gas, thus a mixture of jet gas and ambient gas.
Numerical Specifics
Applying a 3D Cartesian grid, we model magnetized, rotating, one-sided relativistic jets injected from different injection nozzles.
In order to be able to study the turbulence and shock properties properly, it is necessary to resolve small-scale motions as good as possible.We have thus performed a resolution study by modeling and comparing the evolution and structure of the jet at different grid resolution (see Appendix B) applying the same input profiles and parameters values as specified for the steady, straight jet setup in the next section.For the resolution study we have compared simulations with a resolution of 5, 10, 15, 20, 25, and 30 cells per jet radius r j .We find that while the jet dynamical variables as well as particle energy spectrum are sufficiently converged for a resolution of 25 grid cells per jet radius.
We use divergence cleaning to implement the solenoidal condition for the magnetic field ∇•B = 0. We adopt a multidimensional shock flattening algorithm, a second order Runge-Kutta time-stepping, a Courant-Friedrichs-Levy number of 0.25, and a HLL Riemann solver with linear reconstruction that is second order accurate in space.
While the MHD simulations are basically scale-free and could be applied to a variety of sources of different size and energy output, the treatment of radiation as well as of particles requires a proper astrophysical scaling, thus adapted to individual sources of interest.Radiation effects, such as particle acceleration and cooling as well as determining emissivities and intensities, depend on actual density, pressure (temperature) or magnetic field strength.For the present paper, since we are mostly interested in the dynamics and the particle acceleration, we work in dimensionless code units for most of the time (except where we explicitly mention the physical units).In order to convert from code units to astrophysical units, a suitable scaling factor must be applied.However, the synchrotron cooling modeled in our simulations depends on the physical value of the magnetic field.In order to deal with that, we have chosen one set of such normalization units in our simulations (see Table 1).The different variables evolved in our code are normalized based on the choice of three basic Note-Conversion factors from code units to physical scales.Shown for the three basic parameters: length l0, speed v0 and density ρ0 along with the derived normalization factors for time t0, magnetic field B0, pressure p0, temperature T0, and power P0.
unit parameter, the unit length l 0 = r j , the unit speed v 0 = c and the unit density ρ 0 .Other variables or the normalized accordingly as where t 0 , B 0 , p 0 and T 0 represent the unit time, the unit magnetic field, the unit pressure and temperature, respectively, while m u , µ and k B denote the atomic mass unit, the mean molecular weight and the Boltzmann constant, respectively1 .The unit for the power is then defined as P 0 = l 3 0 ρ 0 v 2 0 /t 0 .
Initial Conditions
We employ a constant density profile across the domain except within a cylindrical region inside the domain, with a radius r j = 1, a height z j = 1, centered at x = y = z = 0.This is the injection nozzle.Initially, the ambient medium is defined as the region outside the injection nozzle with a density ρ a = 1000, and being at rest, v a = 0.The initial gas pressure p = 0.1 is constant throughout the domain (including the injection nozzle).
The magnetic field in the ambient medium is purely vertical, B z,a = 0.176, thus B r,a = B φ,a = 0. Here, B r,a , B φ,a and B z,a are the components of the magnetic field in the ambient medium in cylindrical coordinates r, φ and z, respectively.
Boundary Conditions -Steady Jet Equilibrium
We investigate three different injection nozzles -a steady injection, and two nozzles with time-dependent injections giving -a jet with a variable velocity and a precessing jet.Here, we first describe the boundary con-ditions for the steady jet injection.A time variation of these will be applied for the other two nozzles (see next sub-section).
In all our simulations, we inject an under-dense jet with density ρ j = 1 from an injection nozzle of radius r j = 1 and height z j = 1, centered at x = y = z = 0.The nozzle is prescribed by a PLUTO user-defined internal boundary condition.
We have implemented outflow boundary condition at all other boundaries of the domain for all setups, applying a zero-gradient condition for all variables.Through this, we make sure that the material at the boundary can leave the domain freely.Note that using such boundary condition may give rise to an inward Lorentz force in case of sub-fast magnetosonic flows, resulting in artificial collimation of the jet (Porth & Fendt 2010).To avoid this, we restrict the outflow boundaries sufficiently far from the jet stream, not allowing the jet material to leave the domain during the simulation.
Since our main goal is to investigate how the physics and geometry of the nozzle impacts the jet propagation and subsequent high energy particle acceleration, we find it essential to apply a verified equilibrium solution for the gas and the magnetic field that is injected through the nozzle.Any internal instability of the injected gas may lead to an (artificial) modification of the internal equilibrium.
As a proper equilibrium condition for the jet injection we apply the equilibrium solution derived by Bodo et al. (2019) inside the jet injection nozzle.For convenience of the reader, we show the corresponding equations for the leading variables (e.g.velocity, magnetic field) along with plots of the injection profiles in Appendix A. Applying these profiles for our simulations, we obtain a stable jet injection with the bulk motion in the selected injection direction (z-axis) and a rotation around the jet axis.We refer to this simulation setup with steady injection as std throughout the text.
Boundary Conditions -Time Variation
We now describe the time-dependent nozzles for a straight jet with a time-variable injection and a precessing jet.For the time-variable injection, we choose to vary the velocity of the jet in the z−direction, applying a sinusoidal variation above a floor velocity, where v z,flr is a floor velocity (comparable to the other two setups), v 0 is the amplitude of the variable component of v z , and ω var is the frequency of the variation.
Here, we set v z,flr and v 0 at a value of 80 and 20 percent of v z , the velocity of the steady jet in z−direction, respectively.The maximum velocity (in z−direction) of the injected jet in variable nozzle setup is then same as that of the steady nozzle setup, corresponding to a Lorentz factor γ f = 10 at the jet axis.Through this we get a straight jet with a velocity varying sinusoidally with a period P var = 2π/ω var = 5 in the z−direction.
We refer to this simulation setup with variable injection as var throughout the text.
The setup for the precessing nozzle is more complex as we need to change that vector components of velocity and magnetic field periodically, while maintaining the equilibrium solution across the nozzle.We thus need to introduce additional terms in the velocity vector of the rotating jet described in previous section.We do this by using transformation matrices T x , which represents a rotation by an angle ψ about the x−axis, and T z , which represents a time dependent rotation at an angular velocity ω prc about the z−axis.Using these transformation matrices, we get the precessing velocity vector with and Here, the un-primed velocity components correspond to the non-precessing jet described in the previous section and t is time.Multiplying this unprimed velocity vector gives us a jet with a velocity vector having the same magnitude as the unprimed velocity vector, but now inclined by an angle ψ from the z−axis.Subsequently multiplying this resultant tilted velocity vector by T z , we rotate this velocity vector with an angular velocity ω prc in the x − y plane.Hence, we get a rotating jet which is precessing at a precession angle ψ = 10 o about the z−axis with a precession period P prc = 2π/ω prc = 5.We refer to this simulation setup with precessing injection as prc throughout the text.Note that the angular frequency of ω var corresponds to a sinusoidal variation of velocity in a particular direction i.e the jet axis.On the other hand ω prc refers to a precessional motion of the injected velocity vector.We present the input values of selected parameters which we have chosen for jet profiles as mentioned in Appendix A, along with other initial values for some jet parameters applied in the jet nozzle at t = 0, as well as the initial parameters for particle injection (discussed in the next section) in Table 2.Note that these values are common to all three injection nozzles as we prescribe the same initial boundary conditions for all the nozzles.
Particle Injection
So far we have discussed how we numerically govern the dynamics of the jet propagation.Here, we present how we implement particles into the jet, how we follow them in a Lagrangian approach, and how we accelerate them.
Overall, we apply the particle module for PLUTO invented by Vaidya et al. (2018).From the jet nozzle, along with the fluid material, we also inject Lagrangian macro-particles into our simulation domain, which, at each spatial point, always have the same velocity as the fluid.
These macro-particles should be understood as ensembles of micro-particles (electrons) that evolve and flow with the jet material and subsequently distribute over the jet volume.The energy distribution of these micro particles establishes the energy spectrum of the macroparticle.
In order to avoid ambiguity in notation, from now on in this paper we denote the macro-particle (the ensemble of micro-particles as particle and the constituent microparticles as electrons. For the particle injection we define a region of circular cross-section with radius r j and at a height of one pixel above the injection nozzle.This cross-section is divided into a cylindrical grid with 25 uniformly distributed radial divisions (along r) and 36 randomly distributed angular divisions (along φ) with 0 < φ < 2π, that are fixed in time.Here r and φ are usual cylindrical coordinates.Hence, we get a collection of 25 × 36 randomly distributed points from which we inject Lagrangian macro-particles.This injection is done after every two (numerical) time steps so that for a simulation run lasting 50 physical time steps, we get 10 6 such particles injected into the domain, ensuring a proper sampling of the jet material.
Each macro-particle represents an ensemble of nonthermal electrons with an energy distribution following a power-law with a chosen initial power-law index α = 6.We apply initially a power-law cut off at γ min = 10 2 and γ max = 10 8 .Obviously, when the jet evolves, particle acceleration and non-thermal cooling will affect the cutoff energies as well as the particle distribution evolves Note-Input parameters for all three injection nozzles (in code units).Note that for t = 0 these are identical, while for the time-varying nozzles the boundary conditions change over time.Shown in columns 2-8 are the input values of jet density ρj, ambient density ρa, gas pressure p, the magnetic field z-component Bzc, the magnetic field pitch angle δc, the angular velocity Ωc, and the jet Lorentz factor γc.The subscript c denotes the respective values at the z-axis, thus i.e. at r = 0. Also shown are (columns 9-14) the initial values of selected physical parameters (averaged over the nozzle), such as the proper sonic Mach number Ms, the proper Alfveénic Mach number Ma, the magnetization σ, the plasma β parameter, and the extractable power Px.Further, we show the total densities of kinetic energy E kin , the magnetic energy Emag, and the thermal energy E th .Columns 18-21 show the initial particle parameters such as the initial power-law index α, minimum and maximum energy cutoffs γmin and γmax, respectively, and the equipartition deviation factor concerning magnetic energy and particle energy.
away from the initial power law.With that, N (γ) measures the number of particles per unit volume with a Lorentz factor γ, while N 0 is defined by the number density of electrons N e as γmax γmin With a chosen normalization of m e c 2 = 1, the Lorentz factor of the electron γ then gives us the energy of the electron, where m e is the mass of the electron.Hence, in order to convert the particle energy into physical scales, the Lorentz factor of the electron γ must be multiplied with m e c 2 = 0.511 MeV.Finally, we quantify N e by using assumption of equipartition of energy density between magnetic field and radiating electron giving where U e is the energy density of electron and B eq represents the magnetic field corresponding to the equipartition.The magnetic field B dyn in our simulation, varies from B eq by a factor , which can be used to vary the ratio of the energy density between the magnetic field and the radiating electrons in our simulations.The value of N e can now be calculated by substituting Equation 15and Equation 16in Equation 17as Since the magnetic field in the jet injection nozzle varies following the profiles mentioned in Appendix A, we define B dyn as the average total field strength in the injection nozzle, giving B dyn = 6.27.With a choice of 2 = 8 × 10 −5 in our simulations, such that the particle energy is initially in sub-equipartition with the energy in the magnetic field, we get N e ∼ 0.29 and N 0 ∼ 1.46 × 10 10 .
Subsequently, these particles are advected along with the flow and fill the outflow volume.
Particle Acceleration & Evolution
After being injected at the jet base with an initial energy distribution, the particles evolve in the time and momentum space following a Lagrangian approach in which the particles follow the fluid velocity streamlines.As a result, the position of the particle r p is updated with time t according to the equation dr p /dt = v p = v f , where v p is the velocity of the particle and v f is the velocity of the fluid interpolated from the underlying Eulerian grid at the position of the particle.It must be noted that the particles here do not have any feedback on the fluid i.e. they do not change the fluid properties (e.g.density and velocity).
This procedure takes into account the acceleration of the particle through diffusive shock acceleration.Additionally, we take into account energy losses due to the adiabatic expansion of the jet, the synchrotron cooling of the particles by acceleration in the jet magnetic field, and IC scattering of CMB photons by the particles.
The DSA is often invoked to explain the presence of non-thermal particles in astrophysical systems.It results from repeated scattering of a particle off a coherent in-homogeneous magnetic field e.g. at a shock.To model DSA, we follow the novel approach developed in Vaidya et al. (2018).Here, the Lagrangian particles are flagged when entering a shocked region, defined as the area of cells with negative velocity divergence, together with a pressure gradient ∇p/p above some (normalized) threshold of 2. Following these conditions, the shocks in PLUTO are resolved with 3 grid cells.
Particles are followed carefully as they travel through the shocked region, and the pre-shock and post-shock states are defined as the states with the minimum and maximum value of pressure, respectively.Based on these states, we calculate the orientation of the magnetic field with respect to the shock normal and the strength of the shock, which is quantified by calculating the compression ratio in the shock rest frame for relativistic case (for a detailed discussion see Guess 1960;Lichnerowicz 1976).
Here, the subscripts 'u' and 'd' denote the upstream and downstream values, respectively.Using these parameters, the post-shock distribution of particles is updated as per the theory of DSA (see Vaidya et al. (2018) and references therein).
Radiative losses in our simulations occur due to synchrotron process, as well as up-scattering of the surrounding CMB radiation through the IC process.These processes are implemented in the particle module of PLUTO by solving the time-dependent particle transport equation (Webb 1989;Vaidya et al. 2018) where τ is the proper time, the first term inside the round bracket represents the losses from adiabatic expansion, γl represents radiative loss due to synchrotron and IC processes, and u f is the proper fluid velocity.The above equation is solved for each macro-particle advecting spatially with the fluid considering that the spectral distribution N (γ) of constituent micro-particles (i.e., electrons) is evolved at every step accounting for the above loss and shock acceleration processes based on local conditions interpolated from the fluid grid at particle's position.
JET DYNAMICS AND ENERGETICS
We first discuss general features of the jet evolution before we compare specifics of how the different jet nozzles affect the structure of the propagating jet.
General Jet Evolution
In Figure 1, we show the evolution of the dynamical structure of the jet for the different approaches of a time-independent injection (steady nozzle, std) in the top panel, a time-variable injection (var) in the middle panel, and a precessing nozzle (prc) in the bottom panel.We display 2D slices of the 3D density distribution superimposed by (projected) magnetic field lines in the x − z plane at y = 0 at dynamical times t = 20, 30, 40, and 50 (from left to right).
Following the injection from the nozzle, the steady jet (std) propagates at high speed in z−direction, filling the domain with low-density jet material before terminating at the jet head with a termination shock.Subsequently, the jet inflates a low-density cocoon, thereby forming shocks as a result of interaction with ambient medium and also due to interaction within the jet.The steady jet also encounters re-collimation shocks as it evolves.
Note, however, that the strength and even the existence of these re-collimation shocks depends critically on the numerical resolution applied (see Appendix B), which emphasizes the need of high-resolution simulations.The turbulent nature of the jet is evident from the small-scale fluctuations of magnetic field in the jet as compared to a smoother structure around the jet.Despite of its turbulent structure, the jet remains rather symmetric about the z-axis (but see our discussion in Section 3.2 concerning the lateral outflow structure).
We may distinguish four dynamically distinct regions in the simulation domain.First is the high velocity jet, producing strong shocks.Then there is the back-flow of shocked jet gas around the jet that also carries gas entrained from the ambient medium.Further out comes a cocoon structure with shocked ambient gas.All this is enclosed by the original ambient gas that is not yet affected by the jet flow and remains at rest.
An interesting feature, again a feature that is not seen in low-resolution runs, is the existence of a sharp discontinuity at z ∼ 15 in the jet.We call this feature the steady internal shock.This shock surface starts to develop around time t 30 and does not evolve much with time.Along the jet axis, this steady internal shock is located at z = 14.8 at t = 50.Essentially, it does not propagate much, as long as the termination shock at the jet head is within the computational domain.We understand this as resulting from the interaction between the jet beam flowing forward and the presence of an inner back-flow2 .To understand quantitatively the kinematics of the steady internal shock, we find that between time t = 40 and 50, the jet head advances from z = 26.5 to z = 32.5 i.e. a distance 6 (in code units).In the same time interval, the steady internal shock advances from z = 13.9 to z = 14.8, a distance of 0.9 (in code units).
Our explanation is supported by the observation that when running the simulation for longer times, such that the termination shock at the jet head leaves the domain, there is no material deflected from the jet head into the original jet beam.As a result, the steady internal shock surface starts to evolve with time and fades away.An interesting manifestation of this strong, steady internal shock feature could be the formation of a knot in the emission map.Prime observational examples of such a steady knot feature is HST-1 in M87 (Biretta et al. 1999;Harris et al. 2006), and other knot-like features in AGNs discussed in Hervet et al. (2016); Lister et al. (2021).A detailed investigation of this feature will be presented in a subsequent study.
The jet with a variable velocity (var) forms a number of bow-shocks as it propagates, resulting in a skeletonlike appearance.These bow-shocks can be important for particle acceleration in the jet as we will investigate in further sections.This jet remains more collimated than the jet with steady injection, but shows a similar linear extent along the propagation direction.
The precessing jet (prc) is, obviously, highly asymmetric.Essentially, it shows a smaller linear extent in the propagation direction as compared to the steady jet at the same time, a natural consequence of the smaller momentum in this direction.We note, however, that the magnitude of the total velocity in both cases (precessing and steady jet) is same and hence, we inject same total kinetic energy density ρv 2 in the two cases.As a result of precessing velocity vector of the injected material, we see multiple finger-like extensions of the jet head.Note that this is a truly 3D feature, while the figures show slices of the 3D structure.This can also result in enhanced interaction with the ambient medium, which can result in more shocks and turbulence as we discuss in the next section.
We already mentioned the high degree of symmetry we observe in the jets injected without precession.This symmetry shows up despite the 3D treatment of the simulation and also despite the application of Cartesian coordinates, altogether demonstrating the quality of our numerical setup.Note however, that there are locations around the jet where the axial symmetry is partly broke (see discussion in next section).
Lateral Jet Structure
We further investigate the lateral structure of the jet by showing slices of the density distribution across the jet thus in the x−y plane along different distances along the jet and also for a chosen time t = 50 (see Fig. 2).
When we look at the full extent of the outflow structure at z = 15 (left panel), wee see a low-density (in blue) structure in the center -the high velocity jetsurrounded by a structure of intermediate density (yellow), that is moving with lower (and negative) speed, which we interpret as back-flow of shocked jet material.Both are surrounded by a high density and low velocity (in arbitrary direction) cocoon (in red) that contains shocked material from the ambient medium.Outside the cocoon we find the uniform ambient medium (in orange) -still in its initial state.
The cocoon shows a perfectly circular shape, implying that we have sufficient resolution to avoid instabilities generated as a result of injecting a cylindrical jet in a Cartesian grid.The other panels show a zoomed-in version of the density distribution at different values of z, all at the same time.These panels resolve the innermost jet structure close to the jet axis.
At z = 5, thus close to the injection nozzle, we see features resulting from active mixing of jet material with the back flow material.At the very center we see the original jet beam with density ρ = 1 (i.e.log ρ = 0).This is surrounded by a denser region formed as a result of shocks at the contact discontinuity at the jet beam boundary and the back-flowing jet material.
Note the elliptical region of small substructures that has a factor ten time higher density as compared to the jet beam .Interestingly the orientation of this ellipse is not aligned with the numerical grid.Also the number of these features is six, and not four as maybe expected from the Cartesian grid.We may understand this substructure as braids.Just outside these elliptically aligned braids we see two features ("red") that belong to a spiral structure.Indeed, further out the lower density material (greenish) seems also aligned in a spiral shape.Even further out, at r 3, again six features appear, in similar order as the inner braids.The physical reason of this ordered substructure is yet unknown to us.In principle, however, we may think about this as longitudinal re-collimation shock forming a braided structure.The exact origin of this ordered substructure may also be related on the profiles of variables injected from the nozzle, in particular from the profile of the jet rotation.However, we note that these braids are located outside of the jet stream (even at the location of the re-collimation shock), where there can hardly be shear between the jet rotation and the surrounding gas.Interestingly, while these braids break the toroidal symmetry of the outflow, their alignment in φ-direction shows still a degree of symmetry.Furthermore, further downstream, the jet flow recovers again a good degree of axisymmetry.
Further downstream, we show the zoomed-in version of the first plot of Figure 2 at z = 15.We see a denser region in the center, implying that we have captured the shocked area just above the sharp gradient in density and pressure at the steady internal shock.The substructure of two times six braids has disappeared, the jet forms a ring-like structure of rings of different density, with the central jet being densest.
Even further downstream from the nozzle, at z = 25, the jet approaches the jet head where we observe a high density due to the presence of the termination shock.
Further Jet Diagnostics
In order to see how the other dynamical properties of the jet vary over the domain, we show 2D slices of various jet variables at time t = 50, again concentrating on the steady jet nozzle, simulation std (see Fig 3).The pressure distribution shows, like the density distribution, a number of re-collimation shocks in the jet, as well as the strong steady internal shock feature at z ∼ 15, and the termination shock near the jet head.
These features are also visible in the plasma β = 2p/B 2 , the temperature T , and the proper sonic Mach number M s .We show the toroidal components of velocity and magnetic field, by plotting the y−component of v φ and B φ .Through this, we can visualize v φ and B φ coming out (in blue), and going in (red) the x − z plane.We note that by this we also see the axisymmetric nature of the fields demonstrated, strongly indicating that we have applied a proper resolution when injecting a cylindrical jet into a Cartesian domain.We also note the opposite signs of toroidal velocity and magnetic fields in the injection profiles (Equation A1).This reversal of sign is a typical consequence of jet launching and acceleration models (Blandford & Payne 1982;Ferreira & Pelletier 1995;Zanni et al. 2007).
The diagram for the vertical velocity v z shows an interesting feature of jet dynamics.As the jet develops, it expands and eventually undergoes a bifurcation at z ∼ 15.This results from the interaction with backflowing material that was reflected by the jet head.Subsequently, the propagating jet material flows around this inner back-flowing material.Note that the existence of such a feature is not straightforward, as the backflowing material can be expected to bypass the jet material around the jet.Here, the jet reflection is so strong, and of such a reflection angle that it comes back right towards the jet flow.We believe that the reason for this flow structure is the re-collimation shock right behind the jet head, leading to a reflection along the jet axis.
After all, this particular flow feature leads to the formation of the strong steady internal shock structure that we see in the distribution of various physical variables.The essential condition for this steady internal shock to form, we think is the existence of the strong shock at the jet head.In fact, if we let the jet head move out of our computational domain, such that there is no jet head to reflect the jet material (and hence, no back-flow), the strong steady internal shock fades away.
The strong head-on collision between the jet material and the inner back flow does not only provide a site for strong particle acceleration (see below), but also for neutrino production (see e.g.Britzen et al. 2019 for an observationally motivated scenario).From our modeling we indeed expect hadronic material to be entrained into the strong inner back-flow, as it carries shocked material.
Additionally, we show the distribution of a tracer for the origin of the material, where a value of unity tracks the material that originates from the jet nozzle, and a value of zero for material that does not belong to the jet, rather to the initial ambient medium.This enables us in principle to disentangle the jet material from the ambient gas.The intermediate values of the tracer, 0 < tr < 1, basically quantify the mixing state of two media.We see that as the jet propagates, it is expanding, also as a result of encountering the inner back-flowing material at z ∼ 15.Note that the back-flowing material (with negative velocity v z ) is indeed a mixture of jet material and ambient gas and and hence has a tracer value < 1.
Jet Nozzles
Before we compare the particle acceleration and nonthermal cooling processes in our simulations applying different jet nozzles, here we first investigate the differences in the dynamical features of jet propagation that are governed by the nozzle physics.Eventually, the jet dynamics will directly determine the acceleration and radiation properties of the jet.
To this end, we consider the contribution of various dynamical parameters only from the jet-cocoon structure and ignore the ambient medium.For this purpose, we define the jet-cocoon region as being composed by the grid cells where the speed v > 0.Then, the value of a certain parameter at a particular time is calculated by summing up the contribution from all the grid cells in the jet-cocoon region at that time.In Figure 4 we show for all the three nozzles, the time evolution of total energy density in different energy channels, viz the kinetic energy density E kin , the thermal energy density E th and the electromagnetic energy density E em , each defined as in equation 10.
We first see that the outflow dynamics produced by the std and prc setup nozzles show similar kinetic energy density, whereas the var setup nozzle evolves the outflow into a state of somewhat lower kinetic energy density.This is expected as the kinetic energy density we inject depends on the velocity (or Lorentz factor) injection of the jet, that is on average lower in the variable injection nozzle var as compared to the other two nozzles, which have the same velocity injection.Comparing the injection nozzles std and prc, both of which have the same kinetic energy density at initial times, we find that the precessing outflow has a higher kinetic energy at later times.Here, the jet is constantly changing its direction, and the interaction with the ambient medium is weaker.As a result, less of kinetic energy is converted to other energy channels for the case of the precessing outflow.
For the magnetic energy density we find that the steady jet approach leads to the highest level, followed by the variable and the precessing jet.This is a consequence of our injection profiles, as the magnetic field which is injected along the jet depends on the jet velocity (see Equation A1).Thus, the variable jet outflow is expected to be less magnetically energized than the steady jet.The precessing jet on the other hand, produces and contains jetlets 3 moving in different directions.These jetlets, on interacting, may lead to (numerical) reconnection of magnetic field.This is interesting from the point of energetics, as this will also lead to (numerical) heating of the jet.Due to the high resolution we apply, numerical diffusion and reconnection does play a minor role only.However, this energy will have in principle implications on the particle acceleration in such jets.In our approach of ideal MHD we cannot not model physical magnetic reconnection.
Another interesting point to note here is that although the steady and the variable jet are in equipartition with respect to the kinetic, thermal and electromagnetic energy densities, the precessing jet with similar injection as the steady jet is less magnetically dominant than the other jets we discuss.
Outflow Turbulence Level
In the approach of the present paper, acceleration of particles is achieved by shocks.Shocks are typically generated by a misaligned velocity field.Such velocity fields are a typical signature of turbulence.From Figure 1, we (literally) see that the level of turbulence looks different for the different jet nozzles we apply.We thus expect that the various nozzles we consider in this work drive turbulence in the domain differently based on their dynamics.We now want to quantify the level of turbulence generated by the various injection nozzles.
3 With jetlets we denote the jet portions that are injected from the nozzle at each time.These jetlets can also be understood as small volumes of material traveling together with the same bulk velocity.
In this context, we define the level of turbulence in a variable X at a certain grid cell 'i' located at (x, y, z) as where X i is the mean value of the variable X over all grid cells inside a cube of 20 3 grid cells, centered at (x, y, z).
Note that for calculating the local turbulence level δX T i , we only consider grid cells i where the tracer tr > 0.1.So, we do not take into account the grid cells that are in the ambient medium for calculating turbulence as well as for averaging.Also, we consider grid cells only above z = 2, thus above the injection nozzle only.As a measure of the total level of turbulence of the jet we then sum over all local measures of turbulence X T = Σ i δX T i (independently for all components x, y, z if X represents a vector field).
We can now compare the turbulence level in the velocity and the magnetic field for the different jet nozzles by calculating spatial averages of v T /v and B T /B, respectively.We find that both, the variable jet nozzle and the precessing jet, drive a higher level of turbulence in the velocity with an average v T /v 0.21, while for the steady jet we find average v T /v 0.15.Similarly, for the turbulence level in magnetic field we find B T /B 0.10, 0.17, 0.33 for the steady, variable, and precessing jet, respectively.
Another way of quantifying the level of turbulence is to compare the different energy channels viz the kinetic, thermal and electromagnetic energy densities E T kin , E T th , and E T em , respectively, as defined in equation 10.We show the exact values of these terms in Table 3.These can then be compared to the corresponding (integrated) energy terms (see Equation 10), which we also show in Table 3, providing the fraction of the total energy trans-formed into turbulent energy.After all, we expect that different nozzles govern a different fraction of the injected energy that is turned into turbulent energy.
Computing these fractions we find that 1.12% of the injected kinetic energy is turned into turbulent kinetic energy for the std nozzle setup.Similarly, the var and prc nozzles turn 1.81% and 1.12% of the injected kinetic energy into the turbulent kinetic energy, respectively.On the other hand, the std, var and prc nozzle convert 1.62%, 0.89% and 1.71% of their injected magnetic energy into the turbulent magnetic energy, and 0.23%, 0.22% and 1.26% of the injected thermal energy into the turbulent thermal energy, respectively.From this comparison, we conclude that the time-variation of the jet injection, in particular the precessing jet, leads to enhanced level of turbulence in the domain.
As a turbulent jet will lead to the formation of more number of shocks, turbulence has an implication on the acceleration of particles as well.Thus, from investigating the outflow turbulence levels we predict that the precessing jet will be most efficient in accelerating particles.
We show values of some characteristic dynamical output parameters at time t = 50 for the different injection setups, along with the parameters connected to particle acceleration (see next section) in Table 3.
PARTICLE ACCELERATION
In our simulations we inject Lagrangian macroparticles at the base of the jet which follow the flow of the fluid.
Propagation of Particles
In Fig. 5 we show the distribution of these particles in the jet for the simulation run std at time t = 50.All the particles injected are projected on the x − z plane, but in reality follow a 3D distribution.In addition, we color code these particles denoting the compression ratio η they have experienced (in the left panel) and the shock velocity in z−direction at that location (in the middle panel).
As can be seen, particles just below the strong steady internal shock at z = 15 have a high compression ratio η, suggesting the presence of very strong shocks at this position.The distribution of the vertical velocity v z for the particles follows exactly that for the jet material.Obviously this is expected for Lagrangian particles.Hence, we see a forward going jet with positive v z (in red) along with the back-flow where particles have a negative v z (in blue).
Figure 5 shows also the trajectories of few selected particles in the jet.We may follow their path from injection evolving over time.It can be seen that after injection at the jet base, the particles interact with the local fluid at their present location.Depending on the interaction, a particle may traverse over the whole jet length or may end up in the jet back flow or cocoon upon reflecting off a shock.
When a particle enters a shock, the strength of the shock is given by its compression ratio η as calculated by Equation 19.When a particle leaves the shock, this value of η is retained by the particle until it meets another shock with a different compression ratio.
Figure 6 shows the statistics of the compression ratio η at time t = 50 over the whole numerical domain for simulations applying different injection nozzles.Note that we detect compression ratios beyond the theoretical limit of 4 for RMHD shocks.We note here that this classical limit of 4 for MHD shocks is enhanced by the Lorentz factor in case of RMHD shocks and can have large values (Blandford & McKee 1976).However, the compression ratio η calculated in the shock rest frame, as is done in our study for a particular shock rest frame (Normal Incidence Frame), is limited by a values of 4 (Guess 1960;Appl & Camenzind 1988;Kirk & Duffy 1999;Summerlin & Baring 2012).
The number of shocks with compression ratio η > 4 in our simulations is low (<10%) and primarily arises due to numerical artifact when the macro-particle passes through a complex network of turbulent/interacting shocks in a short time and is unable to resolve multiple shocks.As the fraction of such particles is much less than those that sample the shocks accurately, such an update will have no effect on the quantitative comparison of compression ratio of shocked particles from different nozzles as described below.
We see that the variable jet nozzle var produces more strong shocks, compared to the precessing nozzle prc, which is similar to var concerning strong shocks.This can be explained as being the result of different dynamics of two injection nozzle setups.In the var nozzle setup, the slow moving jet material injected at an earlier time is repeatedly hit by the fast moving material injected at later time during various jet injection cycles.As a result, there are more number of such back-on collisions in the var setup as compared to the prc setup, where the injected jet continuously changes the direction of its motion.This results in more of the stronger shocks being formed in the var setup.On the other hand, the standard injection std simulation has shocks comparatively weaker than for the other two nozzles as a result of its time-independent injection.However, note that the number of shocks N shk a particle has encountered along its path is not represented by the compression ra- Note-Output parameters of simulation runs for the steady outflow setup std, the variable outflow setup var and the precessing outflow setup prc(in code units) at t = 50.Shown are the average values for the proper sonic Mach number Ms, the proper Alfvénic Mach number Ma, the magnetization σ, the plasma β, and the jet Lorentz factor γ.This is followed by the extractable power Px ≡ ExV /t, the outflow volume V (for cells where v > 0), the total energy density E V tot over the whole outflow volume, the integrated values of the kinetic energy density E kin , the thermal energy density E th , the electromagnetic energy density Eem, and the turbulent kinetic, thermal and electromagnetic energy densities E kin , E th , and Eem, respectively.The averaging and the integration is done for the cells where the tracer tr > 0.1.We also show for all the particles in the domain their total effective energy E ef p (i.e. total particle energy above γ = 10 3 ), their minimum Lorentz factor γmin, and their maximum Lorentz factor γmax. tio η, but by the number of times the η has changed its value.
In Figure 6 we show the histogram of the number of shocks the particles have encountered.We see that although the precessing nozzle prc leads to somewhat weaker shocks than the variable nozzle var, the overall number of shocks is substantially larger.In fact, the total number of shocked particles in the var setup is even lower than for the std setup.
Since both, the strength of the shock and also the number of shocked particles, are crucial in regard to the energetics of the particles, it is interesting to study which of these two is dominant.This can be investigated by comparing the particle spectra in different jets, as we will discuss in the next section.
Particle Energetics
The Lagrangian macro-particles (ensemble of electrons) which are injected at the jet base follow a powerlaw spectrum for the constituent electrons given by Equation 15.As the particles evolve with time (along their path), they may encounter shocks and become ac- celerated depending on the compression ratio they experience and the orientation of magnetic field with respect to the shock normal (see Vaidya et al. 2018).It should be noted that spectra of particles with compression ratio beyond a value of 4 (< 10% of all particles) is updated assuming an asymptotic limit of the power-law index α = 2.23 for ultra-relativistic shocks (see e.g.Kirk et al. 2000;Huang et al. 2023).
In addition to being accelerated while crossing shocks, the particles cool down due to various processes discussed in section 2.4.As a result, the overall spectrum of injected particles changes over time, from the initial steep power law to an energy spectrum indicating particle energy beyond and below the initial cut-off energies and with varying slope.
In Figure 7 we show the spectrum of one example particle (labeled P3 in the right panel of Fig. 5) for some simulation time steps.A good presentation of the energy spectra is to plot the particle energy density distribution N (γ)γ 2 as a function of particle energy γ.
When the particle is injected at time t 15, it has the initial spectral slope α = 6 and a maximum (thermal) Lorentz factor γ max = 10 8 .Note that the jet bulk motion (in z-direction) injected has a (maximum) Lorentz factor γ f of 10.
As the particle evolves, following the fluid, it cools down -with higher energy electrons of the macro particle cooling faster than the lower energy electrons.As a result, we see the high-energy tail of initial spectrum decaying and a subsequent decrease of γ max during t = 20.Before t 22, the particle encounters4 a shock leading to a change in the slope of the spectrum and an increase in γ max showing acceleration.The particle again enters a shock region at t 28 and 45, again modifying the spectral slope.However, as a consequence of rapid cooling of high-energy electrons, overall we see a decrease in the maximum Lorentz factor γ max .Finally, at t 50, The blue and green dashed lines show the slope of spectra with power-law index α = 2.6 and 3.1, respectively, for comparison with the particle spectra.The magenta dashed line shows the asymptotic limit of α = 2.23 for ultra-relativistic shocks.
the particle encounters a strong shock resulting in a flat spectrum and a sudden increase in γ max .Now we can compare the effect of the different injection nozzles on the particle population in the different jets they generate.A first point of view is to study the full spectrum of the jets from the different nozzles.We thus plot the combined spectrum of all the particles in the domain.This is done by adding the contributions of each of the particles to an overall spectrum.In Fig. 8 we compare the result for all three nozzles.
For comparison, we also show the initial spectrum (black dashed line) on the same plot.This is normalized by taking the initial spectrum of one particle and multiplying it with the total number of particles at t = 50.Hence, we have a one to one comparison between the initial and final spectrum for the different nozzles.
Essentially, we see that compared to the initially injected spectrum, the spectrum for all three nozzles has a significantly larger contribution from higher energies.Some particles are accelerated to such high energies going even above the initially defined γ max = 10 8 .The shape of the spectrum is represented by a broken powerlaw for the three nozzles, featuring a major peak at γ 100.This peak is a relic from the initial γ min = 100.
For all three nozzles, the spectrum falls for energies below the initial minimum cut-off energy γ min .We emphasize that we do not inject particles at these energies and, thus, the presence of particles at these low energies is a result of physical cooling that is implemented in our treatment.Interestingly, from the peak at γ = 100 till γ 10 3.5 , we see the spectrum declining following a power-law with a slope of 6.This part of the spectrum is indeed similar to the initial spectrum, which follows a power-law with an index of 6 as well.We note that particle are continuously being injected from the jet nozzle.So, the particles found following the initial spectrum at later times are newly injected particles, that are not yet accelerated or cooled down.Note that the cooling time for those low energy particles is long, and, seemingly, longer than their current age since injection.
In general, beyond γ 10 3.5 the spectrum flattens, following an ankle into another power-law.The deviation from the injection spectrum is resulting from a number of reasons.On the the pure increase in number of particles that are accelerated or have cooled.However, we see that this deviation is also different for the different injection nozzles, thus, strongly indicating that the overall particle acceleration indeed depends on the jet injection mechanism.
Beyond γ 10 3.5 , the spectrum for setup prc flattens the most, following a power-law with index α 2.3 till γ 10 4.5 where it steepens, forming a knee, and another power-law with α 3. The subsequent power law again steepens after passing a second knee at γ 10 8.5 , again followed by rapid steepening of the spectrum.
The spectrum for setup std, on the other hand, after flattening at γ 10 3.5 , follows a power-law with index α 2.6 till γ 10 7.5 , followed by a subsequent decline in the spectra.
Finally, the setup var follows a power-law with α 3 between γ 10 3.5−6 .Beyond this, the spectrum flattens till a γ 10 8 , and a subsequent rapid steepening.
Of the three injection nozzles we consider in this study, the precession setup prc is clearly the most efficient in accelerating particles, with γ going up to values even beyond ∼ 10 9 , corresponding to a physical energy reaching few hundreds of TeV.This is followed by he steady injection std, while the variable jet setup var seems the least efficient of the three (apart from a narrow range of energies around γ 10 8 , where it is more efficient than the std setup).
After all, and after having in particular compared the energy evolution in various channels for the dynamical evolution in the previous section, the interesting question remains about what the energy that is deposited in the particles.We thus now compare the total energy of all the particles in the domain for different injection nozzles setups for a certain point in time, t = 50.
For this purpose, we define the energy of a single (macro-) particle i as E p,i = γmax,i γmin,i N (γ i )γ i dγ i , where γ max,i and γ min,i denote the upper and lower energy cutoffs for that particle, respectively, and γ i is the Lorentz factor of the electrons of the particle i.Then, the total energy of all the particles is E p = Σ i E p,i .We find that for the precessing nozzle the particle energy is largest, E p 5.9 × 10 6 (in code units), followed by the variable nozzle with E p 5.5 × 10 6 , and the steady nozzle with E p 4.1 × 10 5 .
Note at this point that the total particle energy is not only the energy gained by the particles through shocks but also contains a portion of the injected particle energy which the particle has to start with.In addition, after the particle is injected, the high-energy end of its spectrum decays rapidly as the cooling time for higher energies is very small as compared to the dynamical timescales.Cooling, of course, also happens to the particles that become shock accelerated, thus a part of the gained energy is lost as well.
Overall, the injected energy of the particles, as well as the gained energy by shocks, can be quickly lost as a result of cooling, except at the low-energy regime that have a cooling time larger than the age of the jet (i.e.t = 50).This can be seen e.g. in the total particle energy spectra shown in Figure 8, which are dominated by the injected energy spectrum for energies lower than γ 10 3 .
Hence, to quantify the level of total energy gained by the particles, we define an effective total particle energy E ef p similar to the total particle energy E p , but taking into account only the energy contribution above a threshold of γ = 10 3 .Thus, we neglect the injected particle energy and only consider the contribution from the energy regime where the particles were re-energized by shocks.With that find that the prc nozzle simulation leads to the highest effective particle energy E ef p 8.93×10 3 , while the nozzles var and std lead to effective particle energies E ef p 0.95 × 10 3 and 1.44 × 10 3 , respectively.
Note that these values are only snapshots in time, and a thorough energetics of the particle energy must include considerations of cooling and re-acceleration along the particle path, involving some time integration of the relevant processes.We will come back to this issue in our follow-up paper.
Spectra of Jet Components
Astrophysical jets appear as structured beams of material, however, we don't know yet how these structures form.We don't know either whether the observed jet sub-structures indicate some radiation pattern or actual Here, the particles in the jet and the entrained material are defined by having a tracer value > 0.8 and < 0.8, respectively.
material substructure.Sub-structure observed in motion could thus be pattern motion or material motion.One way to disentangle the structure formation process is to study the emission processes of the material.Here, we compare the particle spectra of the different outflow components.
In order to investigate the role of the different jet components for the acceleration of particles, we have therefore studied the spectrum from these regions.
Along the length of the jet, we are interested in the spectrum near the jet base, the jet head, and at some intermediary region in the jet.Note that comparing spatially different areas along the jet also corresponds to investigate a time evolution of these features, as, due to the jet propagation, these areas have evolved for different periods of time after injection.Of particular interest is steady internal shock feature we have observed in simulation run std, where we can as well study its effect on the particle acceleration and spectrum.
In addition to substructures along the jet, we want to compare substructures across the jet.We thus distinguish between the particles in the jet and in the entrained material (a mix of the ambient and jet material), and investigate particle acceleration in these areas.In this regard, we define the jet and entrained material as the regions where the value of tracer is ≥ 0.8 or < 0.8, respectively.We show the spectral energy distribution for the particles in the jet and entrained material for all three nozzles in Figure 9.
For the steady injection nozzle, the jet is dominant in accelerating particles as compared to the entrained material at all particle energies.This is also true for the nozzle with variable injection.However, we find that the material entrained by the steady nozzle setup std is much more efficient than that in the var nozzle setup in order to accelerate particles to energies beyond γ 10 4 .
In contrast, the entrained material in the precessing jet is a much more efficient accelerator.Here the spectra from particles located in the entrained material have a contribution comparable to those located in the jet for the energy range γ = 10 3.5 to 10 6 .At the highest particle energies, γ ≥ 8.5, for the setup with the precessing nozzle the acceleration in the entrained material surpasses even that in the corresponding jet.This is ultimately a consequence of the dynamics of the precessing nozzle.The gas in the entrained material in this setup is being constantly hit and perturbed by the jet material, generating many shocks, and subsequent enhanced shock acceleration in the entrained material.
To study the effect of strong steady internal shock feature in the steady nozzle setup std, we analyze the spectra from the area blocks of region above, below and enclosing the steady internal shock.These blocks are essentially cylindrical slices with radius spanning the whole domain 5 and a height of ∆z = 1, centered at z = 2 (below the steady internal shock region, at the jet base), z = 14 (in the steady internal shock region), and z = 20 (above the steady internal shock region).Hence, the average spectrum from a block is the sum of spectra from each of the particles inside the block normalized to the number of particles in the block.Additionally, we also analyze the spectrum from the jet head which we define as the region where z > 32.
We expect a stronger acceleration for particles in the block located at z = 14 due to the presence of the strong shock around that location.We expect the same for the particles in the jet head, owing to the presence of a termination shock there.This is precisely what we see in Figure 10 where we show the spectra from these four blocks.We clearly see a larger contribution to the spectrum for energies beyond γ 10 4 from the blocks at z = 14 and z > 32 as compared to the two other blocks.
Interestingly, the steady internal shock is capable of accelerating particles to energies higher than γ 10 8 5 Although the size of the blocks span the whole domain, it should be noted that the particles are concentrated just in the jet and the cocoon and there are no particles in the ambient medium.(corresponding to electrons with energies of few tens of TeV), surpassing the efficiency of the termination shock as well.Since this shock at z = 14.8 is (i) steady and (ii) filled with high energetic particles, we expect to see a stationary knot-like feature in the emission map (which we will explore in a subsequent paper) at this location.
As discussed above, comparing spatially different areas along the jet also corresponds to study the timeevolution of the jet spectrum.This is also evident in Figure 10.At z = 2, we are in the close vicinity of the jet base from where the new particles are being continuously injected.As a result, the spectrum at that location closely resemble the initially injected spectrum with a peak at γ 100, a consequence of the initial minimum cutoff γ = 100.Beyond this, the spectrum follows a power-law with slope 6, same as the initially injected power-law index α = 6.As we move downstream along the jet, the particles enter the steady internal shock and are accelerated to high energies, as discussed.Further downstream, at z = 20, the particles have cooled down after leaving the strong shock to lower energies, decreasing both the upper and lower energy cutoffs.At last, particles meet the termination shock and are accelerated again to high energies.
CONCLUSIONS
We have applied the PLUTO code (Mignone et al. 2007) to perform 3D relativistic MHD simulations in combination with a hybrid module (Vaidya et al. 2018) that is capable of following Lagrangian macro-particles with the fluid.The injected Lagrangian macro-particles constitute ensembles of electrons that are close in space.Their initially defined energy distribution changes as they evolve in time, considering diffusive shock acceleration and cooling due to synchrotron radiation, inverse Compton processes and adiabatic expansion of the jet.
We investigate how physically different jet injection nozzles affect the particle spectrum that is generated as a consequence of the underlying jet dynamics.We have considered three different nozzle setups, a standard steady jet injection into an unstratified ambient gas, a time-dependent jet injection, and a jet nozzle undergoing precession.We adopt jet injection profiles applying an equilibrium solution from Bodo et al. (2019).This is essential in order to avoid artificial instabilities that mimic turbulence and, hence, lead to unphysical particle acceleration.We adopt a Taub-Matthews equation of state, as we consider a relativistic gas embedded in a non-relativistic ambient medium.
Considering our resolution study, we apply a resolution of 25 cells per jet radius, more than ever applied in 3D MHD jet simulations.This resolution is needed for both, resolving dynamically interesting features, as well as capturing the structure and strength of the shocks that are involved in acceleration.
While our simulations are run in code units and are applicable to any relativistic jet source, from the prescribed injection Lorentz factor of 10, the corresponding astrophysical scaling of our simulations would be that of a pc-scale AGN jet, with a size of our simulation domain of 10 × 10 × 20 pc.Naturally, micro-quasars with a similar initial speed can also be described, however, the physical magnetic field strength we have to assume for particle cooling, is chosen for AGN-like conditions.
Our results are as follows.
(i) For all nozzle geometries investigated the interaction of injected jet material with the ambient gas and with the previously injected gas leads to the formation of strong shocks.Essentially, the location and the properties of these shocks vary for the different nozzles.
(ii) The steadily injected jet forms a well known jetcocoon structure.In this simulation we find a special shock feature -a strong and stationary shock resulting from head on collision of jet and a back-flow along the jet axis inside the jet.The location and structure of this feature converges only for sufficiently high numerical resolution, i.e. 25 cells per jet radius.
(iii) The jet with variable injection evolves into a narrower cocoon, resulting in an overall structure more collimated than the steady jet.This jet forms multiple bow shocks as a result of various episodes of time-dependent activity, leading to a skeletal appearance.
(iv) The dynamics of the precessing jet is more turbulent as compared to the other nozzles we consider.As the jet axis change over time, multiple shocks are observed at the positions where the (multiple) jet heads interact with the ambient medium and with the jet.
(v) We quantify the level of turbulence mainly by the fluctuations of the energy density.We compare the energy budget involved in turbulent motions with the mean fluid motion and other energy channels.We find that about 1% of the bulk energies is turned into the turbulent energy channels.
(vi) On encountering a shock, the injected Lagrangian macro-particles change their spectral energy distribution depending on the shock compression ratio they experience.We find that the variable jet injection nozzle produces the strongest shocks (with more of the highest compression ratios), followed by the precessing jet and the steady jet.On the other hand, the total number of shocks is largest for the precessing jet, followed by the steady and the variable jet.The overall particle acceleration depends on the interplay between the available shock strength and the number of shocks they experience.
(vii) The macro-particles cool down due to synchrotron, inverse Compton and expansion losses.While particle acceleration happens instantaneously when a macro-particle crosses a shock, cooling depends on magnetic field strength and particle energy.For the chosen magnetic field strength, the cooling time for the high energy tail of the particle energy spectrum is well below the dynamical time scale of our jet simulations.
(viii) The total energy spectral distribution induced by the different nozzles shows a significant increase in the number of high-energy particles over time.The precessing jet leads to the formation of comparatively more shocks that are most efficient in accelerating particles, followed by the steady jet, while the shocks in the variable jet are the least efficient of the three.In the precessing jet electron are accelerated up to a few hundreds TeV with a power-law index of α 2.3 to 3.1.For the steady and the variable jets electron energies are up to a few tens of TeV, with spectra of similar but somewhat steeper slopes.From this we find that particle acceleration is governed more by the total number of shocks available than by the strength of the shocks.
(ix) We have compared various regions of the jet concerning their particle energy distribution.Compared to the jet-entrained ambient material the jet plays a dominant role for the particle acceleration for the steady nozzle and the variable injection nozzle.For the variable nozzle, the particle acceleration in the entrained structure is highly suppressed for higher electron ener-gies.For the precessing jet, entrained material and jet are comparable in particle acceleration efficiency, except at the very high-energy end, where the entrained material is even more dominant than the jet for acceleration.Here, particles in the entrained material are being reenergized through shocks continuously -a result of the highly turbulent jet dynamics.Hence, we expect precessing AGN jets to be the best sites for highly efficient particle acceleration.
(x) The total energy of accelerated particles in the precessing and variable jet is higher than the steady jet as a result of more shocks available due to the turbulent motion induced by the time-dependent injection.The energy the particles have gained till the end of the simulation can be up to 5% of the turbulent energy, i.e. below 1% of the injected jet energy.
(xi) We have studied the effect of the strong, stationary shock feature that we have discovered, on the particle spectrum.Like the jet termination shock, this strong stationary shock is a particular site where electrons are accelerated to very high energies of few tens of TeV.As these highly energized particles cool rapidly, we expect that this dynamical feature can be observed as a stationary knot of enhanced intensity in emission.The similarity to the famous HST-1 knot seems intriguing.
To summarize we have demonstrated and quantified how different jet nozzles convert the injected jet power to different levels of turbulence, which in turn leads to the generation of shocks that can accelerate electrons to energies up to tens and even hundreds of TeV.The resulting particle energies are about 10% of the turbulent energy and below 1% of the available jet energy.
In a subsequent paper, we will apply our results presenting synthetic emission maps of these jets.This will require a specific choice of the physical scaling for densities and pressure, and can be applied for different relativistic jet sources, such as AGN or micro quasars, as well as for different viewing angles.
ACKNOWLEDGMENTS
This project is financed through grant DFG-FOR5195 of the German Science Foundation DFG.B.V. acknowledges funding by the Max Planck Partner Group located at IIT Indore.R.D. acknowledges travel funds by the International Max Planck Research School for Astronomy & Cosmic Physics at the University of Heidelberg.We thank Andrea Mignone for providing and sustaining the PLUTO code.We acknowledge enlightening discussions with Karl Mannheim and John Kirk.All simulations were performed at the MPCDF computing center of the Max Planck Society in Garching (utilizing the compute clusters Vera, Raven & Cobra).We are grateful to an unknown referee for a detailed and helpful report that considerably improved the clarity of the paper.
A. JET INJECTION PROFILES
In our study, we adopt the equilibrium solution derived by Bodo et al. (2019), who solved for the radial component of the momentum equation for constant gas pressure p.
In cylindrical coordinates (r, φ, z) they find where One may define a pitch angle of the magnetic field, δ = rB z /B φ , the Lorentz factor in z−direction, γ z (r) = 1 + γ c − 1 cosh (r/r j ) 6 , the azimuthal velocity, and the function Here, r is the radial coordinate in the cylindrical coordinate system, γ c is the Lorentz factor at r = 0, r j = 1.0 is the radius of the injection nozzle, a = 0.6 is commonly denoted as the magnetization radius at which the magnetization of the jet nozzle has its maximum value, and Ω c is the angular velocity.Choosing a magnetization radius a less than the jet radius r j , we make sure that we do not have an infinite Lorentz force or a strong shear acting at the jet edges.Note that a subscript c denotes the value of a parameter at r = 0.This gives the following injection profiles within the cylindrical injection nozzle (see Bodo et al. 2019 for detailed derivation) where The parameter ζ governs the strength of rotation and E is the error function.Note that not all combinations of input parameters lead to a physical solution.In general, it must be required that B 2 z and B 2 φ are positive everywhere.
Overall, with these equations we can define a rotating, magnetized, relativistic jet of density ρ j and pressure p, launched from the injection nozzle, which is propagating along the z−direction and is governed by the choice of the parameters ρ j , γ c , Ω c , B zc , δ c and p.Our choice of these parameters for our simulations is summarized in Table 2.We show the profiles of the z− and φ−components of the velocity and magnetic field injected through the steady jet nozzle setup as a function of radius R, following the aforementioned equations in
B. RESOLUTION STUDY
A resolution study is essential for numerical simulation work.It is important for our study in particular as we are not only interested in the gross dynamical behavior of the jet flow, but also in its small-scale structure that is eventually responsible for particle acceleration.Thus, it is necessary to avoid (artificial) numerical effects in our study and achieve a sufficient resolution of turbulent structures.
We have performed a number of simulation runs with different numerical resolution applying the setup with the steady jet nozzle.To this end, defining the resolution as the number of grid cells inside the jet radius r j , we run simulations with a resolution of 10, 15, 20, 25 and 30 pixels per r j .In Fig B .1 we show 2D slices of the density distribution in the x − z plane (at y = 0) at time t = 50 for various resolutions for the simulation setup std, in order to compare the effect of resolution on the dynamics of the jet.
We see that with a low resolution of 10 grid cells per jet radius, we miss a lot of small-scale structure of the jet which could be essential for particle acceleration.Also, we do not see the formation of the strong steady internal shock structure, which is a very efficient site of particle acceleration as we discussed.The formation of the strong steady internal shock can be detected as we move to a higher resolution of 15 grid cells per jet radius.Still the position of the strong, steady internal shock still depends on resolution, which converges only even higher resolution.As we go on from a resolution of 15 to a resolution of 20 cells per r j , we see additional shocks near the the jet head seen as an over-dense region of filamentary structure.In addition we see an upstream shifting of the strong, steady internal shock.
These differences to the lower resolution study are even more visible as we move to a resolution of 25 cells per r j .Here, we see the formation of two finger-like (crab-like?) structures near the base of the jet, which is not present at lower resolutions.We also see the location of the strong steady internal shock further upstream, although now the difference in position is smaller than between the lower resolutions.We thus think that we have rule out simulation runs applying a resolution of less than 25 cells per r j .On the other hand, runs with a resolution of 25 and 30 cells per r j look really similar, suggesting a convergence with regards to the resolution.
We also investigated convergence beyond the dynamical jet structure.In particular, we are interested in studying how the particle acceleration is affected, for example by effects that remain invisible by a comparison of the pure dynamical structure.In Fig. B.2 we show the histograms of the shock compression ratio η the particles have experienced until t = 50 for the simulation setup std for the different resolutions of 20, 25, and 30 grid cells per jet radius .We clearly see that the difference in the statistics between the runs with resolution 25 and 30 grid cells per jet radius is lower than that between the runs with resolution of 20 and 25 grid cells per jet radius.
We conclude that for both, the dynamical evolution and the particle evolution, the simulations with resolution 25 grid cells per jet radius are sufficiently converged compared to the resolution of 30 grid cells per jet radius, which justifies the use of a resolution of 25 grid cells per jet radius.
Figure 1 .
Figure 1.Distribution of density (in log scale) in the domain at a time (left to right) t = 20, 30, 40 and 50 (in code units) in the x − z plane for the simulation run std (upper panel), var (middle panel) and prc (lower panel).Magnetic field lines projected onto the plane are also shown (black lines).
Figure 2 .
Figure 2. Cross section of the jet density distribution (in log scale) at t = 50 in the x − y plane at z = 5, 15, 25 (see panel title) for the simulation run std.Note the different sizes and different color bars of the first and the other three panels.
Figure 3 .
Figure 3. Top: Distribution of (left to right) pressure (in log scale), plasma β (in log scale), temperature Θ (in log scale), and proper sonic Mach number Ms (in log scale) in the domain at a time t = 50 (in code units) in the x − z plane for the simulation run std.Bottom: Distribution of (left to right) vz, the y−component of v φ , the y−component of B φ , and the passive tracer tr in the domain at a time t = 50 (in code units) in the x − z plane for the simulation run std.
Figure 4 .
Figure 4. Time-evolution of global outflow energetics.Shown are integrated values of the kinetic energy density E kin , the thermal energy density E th , and the electromagnetic energy density Eem (from left to right).We consider computational values beyond t = 1 and integrated from above z = 2.
Figure 5 .
Figure 5. Distribution of particles with different compression ratio (left) and shock speed (vz−component) (middle) at a time t = 50.Right panel shows example trajectories of five representative particles from injection till t = 50, with the background showing the density distribution for better visualization.The colored dots on the trajectories represent the locations where the particle encounters shock.
Figure 6 .
Figure 6.Histograms of number of particles N with different compression ratio η (left) and total number of shocks N shk (right) for the simulation run std (green), var (blue) and prc (red) at a time t = 50 (in code units).
Figure 7 .
Figure 7. Energy spectrum of a particle (labeled P3 in the right panel of Fig. 5) at different times (as mentioned in code units) for simulation run std.
Figure 8 .
Figure 8. Energy spectrum of all particles in the domain for the simulation run std, var and prc at t = 50.The injected spectrum for each particle normalized to the total number of particles at t = 50 is shown by the black dashed line.The blue and green dashed lines show the slope of spectra with power-law index α = 2.6 and 3.1, respectively, for comparison with the particle spectra.The magenta dashed line shows the asymptotic limit of α = 2.23 for ultra-relativistic shocks.
Figure 9 .
Figure9.Energy spectra considering all the particles in the jet structure (solid line) and the surrounding entrained material (dashed line) for the simulation runs std (blue), var (orange) and prc (green) at a time t = 50 (in code units).Here, the particles in the jet and the entrained material are defined by having a tracer value > 0.8 and < 0.8, respectively.
Figure 10 .
Figure 10.Average energy spectra of all the particles in the cylindrical slices of height 1 (in code units) centered at z = 6 (below the steady internal shock region), z = 14 (in the steady internal shock region), and z = 20 (above the steady internal shock region).
Figure A. 1 .
Figure A.1.Variation of the z− and φ−components of the velocity and magnetic field in the steady injection nozzle as a function of radius R.
Figure B. 1 .
Figure B.1.Distribution of density (in log scale) in the domain at a time t = 50 (in code units) in the x − z plane (for y = 0) for the simulation run std at a resolution of (from left to right) 10, 15, 20, 25 and 30 cells per jet radius.
Figure B. 2 .
Figure B.2. Histogram of compression ratios η.Shown is the number of particles N in a specific range of η, normalized by the total number of particles in the domain Ntot (in log scale) for different compression ratio for the simulation run std at a resolution of 20 (green), 25 (blue) and 30 (red) at time t = 50.
Table 2 .
Input and Initial Parameters
Table 3 .
Output Characteristic Values | 21,004.2 | 2023-06-19T00:00:00.000 | [
"Physics"
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Diversity of Dominant Peripheral T Cell Receptor Clone and Soluble Immune Checkpoint Proteins Associated With Clinical Outcomes Following Immune Checkpoint Inhibitor Treatment in Advanced Cancers
Dynamic changes of the peripheral T cell receptor (TCR) and soluble receptors and ligands (sRLs) have the potential to be used as biomarkers to monitor the evolution of the immune system in tumor patients undergoing immunotherapy. These functional biomarkers could be used to predict immune response to treatment with immune checkpoint inhibitors (ICIs) and to provide high-value information on the immune function status of cancer patients, thereby helping physicians to make effective clinical decisions. We collected paired pre- and post-treatment peripheral blood samples from 31 solid tumor patients treated with ICIs. TCR and sRL status were investigated using next-generation sequencing and magnetic bead panels. We found that the diversity of the dominant TCR clone at baseline was correlated with durable clinical benefit in patients receiving single-agent treatment. The D50 index, the diversity from the cumulative 50% of the total complementary determinant region 3, was obtained during treatment. A significant difference in progression-free survival was demonstrated between the D50 high and D50 low groups. This result was validated in an independent cohort. A signature including soluble immune checkpoint proteins (sICPs) was identified. Upregulation of the signature during treatment was correlated with durable clinical benefit. All these results indicate that a novel biomarker based on peripheral TCR and sICPs has the potential to be used in prognostic prediction and for rapid determination of therapeutic outcomes in patients treated with immune checkpoint inhibitors.
INTRODUCTION
In recent years, immune checkpoint inhibitors (ICIs) that target cytotoxic T lymphocyte-associated antigen (CTLA-4), programmed cell death receptor-1 (PD-1), and programmed death ligand-1 (PD-L1) have led to revolutionary advances in tumor immunotherapy (1). However, only a minority of patients achieve clinical benefit from ICI therapy, and there remain many challenges when using current biomarkers to predict the efficacy of ICI therapy. Although certain biomarkers have been approved by the Food and Drug Administration for various tumors, the quantity and quality of biopsies are not consistent. Moreover, biomarkers for in-treatment evaluation are useful, especially those obtained from non-invasive material such as peripheral blood. Biomarkers from peripheral blood can provide real-time information about the patient's immune system.
The peripheral T cell receptor (TCR) repertoire reflects the immunological status of all functional T cells in an individual's circulatory system at a given time. Each unique T cell has a unique TCR, which varies among individuals within a population. The complementary determinant region 3 (CDR3), encoded by random rearrangements and junctions of variable, diversity, and joining [V(D)J] sequences, plays an important part in the recognition of tumor antigens (2) and contributes to the diversity of the TCR. The diversity of the TCR determines the immune effects against pathogens. Currently, next-generation sequencing-based technologies are widely employed for highthroughput analysis of the immune cell repertoire. The development of biomarkers based on TCR-CDR3 sequencing will be meaningful for cancer therapeutic decision-making (3).
Soluble receptors and ligands (sRLs) are important components of immune regulation. Their expression levels in serum can be detected. Some sRLs have already been used when assessing clinical severity and prognosis in cancer patients (4,5). Soluble cytokine receptors (sCKR) include proteolytic cleaved cell-surface receptors, extracellular release of membrane-bound receptors, and alternative gene-generated cytokine-binding proteins. They are key regulators of inflammation and immune responses (6,7). Immune checkpoints regulate immune response and the proteins expressed by immune cells or tumor cells. They have an important role in preventing excessive immune response and maintaining normal immune homeostasis, and can also help tumor cells to escape attack by T cells. The application of soluble immune checkpoint proteins (sICPs) has been studied for its potential to predict the immunotherapy response.
In this study, we performed peripheral TCR sequencing and sRL magnetic bead panel testing using samples from tumor patients who had been treated with PD-1 or PD-L1 ICIs. A novel biomarker was discovered and validated in clinical cohorts. The biomarker shows promise for use in clinical practice owing to its rapid and non-invasive application.
Patients and Sample Collection
A total of 31 patients with advanced solid tumors who were treated in the Oncology Department of the General Hospital of the Chinese People's Liberation Army from January 2016 to September 2018 and received ICIs were enrolled in this research. Informed consent forms were obtained from all participants. All patients with solid tumors received intravenous injections of either PD-1 or PD-L1 inhibitors, including nivolumab, pembrolizumab, atezolizumab, durvalumab, and sintilimab. Patients were treated with or without combined chemotherapy or targeted therapies until the tumor progressed or intolerable adverse reactions occurred. Clinical hematology, bone marrow cell morphology, histochemical staining, immunology, molecular biology examination, and the FAB collaborative group diagnostic criteria were used to confirm that the patients did not have any infectious disease, autoimmune disease, or other immune-related diseases. Blood samples were obtained at baseline before treatment with anti-PD-1/PD-L1; one additional blood sample was obtained after treatment to assess dynamic changes in 24 patients. Peripheral blood mononuclear cells (PBMCs) were isolated, added to a protective solution, and immediately stored at -80°C until further processing. Patients' clinical data were collected prospectively. Disease progression was evaluated based on version 1.1 of the RECIST criteria. The study was conducted according to the Helsinki guidelines and was approved by the Ethics Committee of the General Hospital of the People's Liberation Army (S2016-097-01); written informed patient consent was obtained.
High-Throughput Sequencing of TCR
PBMCs were isolated by standard Ficoll gradient separation from whole blood within 4 h of collection. Lamina propria mononuclear cells were isolated from endoscopic biopsies. Total RNA was extracted using TRIzol reagent (Invitrogen, USA) according to the manufacturer's instructions, and the final concentration was determined using a NanoDrop 2000 spectrophotometer (Life Technologies). Then, 1 µg of total RNA was used for cDNA synthesis with random hexamers using a Qiagen One-step RT PCR kit (Qiagen, USA). The CDR3 region of the TCR b chain was amplified using the iRepertoire multiplex primer set (iRepertoire, Inc.). A set of nested primers specific to various V and constant (C) elements of the TCR b chain were used in the first amplification cycles, followed by amplification using communal primers based on the manufacturer's protocol. Libraries were purified by agarose gel electrophoresis, cut between 200-400 bp (predicted amplicon size 210-310 bp), extracted (Qiagen), and sequenced (Illumina 4000, Illumina Inc.). The read length of sequencing was 150 bp. The sequencing technology platform used in our study was proven to be feasible and repeatable by a technical duplicate test.
TCR Sequence Analysis
Sequence reads were de-multiplexed according to barcode sequences at the 5′ ends of reads from the TCR b constant region. Reads were then trimmed according to their base quality to remove low-quality 3′ ends [FastX-toolkit (8), Cutadapt, SOAPnuke (9)]. Trimmed pair-end reads were joined together through overlapping alignment with a modified Needleman-Wunsch algorithm. If paired forward and reverse reads in the overlapping region were not perfectly matched, both forward and reverse reads were discarded without further consideration. The merged reads were mapped by use of an edited version of MiXCR (10) to identify V and J genes across the germline V, D, J, and C reference sequences downloaded from the IMGT (11) website. To define the CDR3 region, the positions of CDR3 boundaries of reference sequences from the IMGT database were migrated onto reads through mapping results, and the resulting CDR3 regions were extracted and translated into amino acid sequences. Then, aligned reads were aggregated into clonotypes based on the CDR3 nucleotide sequence and the same IGH V(D)J gene segment using open source software VDJtools (https://github. com/mikessh/vdjtools ) version 1.1.1. A frequency-based correction was performed with default parameters. Corrected samples were stored as clonotype abundance tables for subsequent analyses. Figures including heatmaps and plots of V gene usage frequencies were generated using the programming language R. The Shannon-Wiener index (12) was used to identify the diversity of the TCR receptor. The D50 index was used as a measure of the diversity from the cumulative 50% of the total CDR3 counted in the sample (13).
Statistical Analysis
All statistical analyses were performed using R software. The significance of differences between groups was estimated by paired, two-tailed student's t-test, Fisher's exact test, or Mann-Whitney test, as appropriate; p-values less than 0.05 were considered to indicate statistical significance.
Correlation Between TCR Repertoire and Clinical Efficacy at Baseline
The Shannon-Wiener index (12) is widely used to measure TCR receptor diversity. Previous studies have reported that clones with high frequency are associated with response to immunotherapy at baseline (14). Therefore, we calculated the Shannon-Wiener index in TCR clones with frequency higher than 0.1% and 1%. Association analysis showed that the Shannon-Wiener index of clones with frequency higher than 0.1% was associated with durable response only in the patient group treated with singleagent anti-PD-1/PD-L1 ( Figure 1A). The median Shannon-Wiener index in the DCB group was 33.37, which was 2.78 times that in the NDB group (p = 0.0040). It is noteworthy that no significant difference was found in the combination group. This was probably because the mechanism of combination therapy was more complex, enabling it to improve the microenvironment of tumors through various mechanisms and change the diversity of T cells more in the course of treatment so as to benefit clinically. Therefore, the diversity of TCR at the baseline level cannot effectively reflect the clinical efficacy of combination therapy. Another notable thing is that the diversity measurement was only found significant in the TCR clone with frequency higher than 0.1%. These indicated that the dominant clone rather than the global clone accounted for the response of anti-PD-1/PD-L1. We then used the D10, D20, D50 indexes (13), which are defined as the minimum percentage of distinct CDR3s accounting for at least 10%, 20%, or 50% of the total CDR3s in a population of T cells to measure diversity, because these indexes focused on the diversity calculation of dominant unique clones. Significant differences in the D50 index were found between the DCB and NDB groups: the D50 index was 4.69 times higher in the DCB group than in the NDB group (p = 0.022, Figure 1B and Supplementary Figures 1A, B). Comparative analysis of Vb, Jb, and Vb-Jb paired gene usage in TCR repertoires at baseline between the DCB and NDB groups was performed to further investigate the preferential usage of anti-PD-1/PD-L1 treatment. As shown in Supplementary Figures 1C, D, the usage of the V gene and J gene had relatively similar frequency between the two groups, but only three fragments were significantly differentially expressed between the two groups. TRBV15 fragments had higher frequency in the DCB than the NDB group (p < 0.05), whereas TRJ1-3 fragments in the J gene had lower frequency (p < 0.05). These three significantly differentially expressed fragments were abundantly expressed in tumor patients, and their differential expression indicated that the two clinical benefit groups had different preferential usage of the TCR Vb and Jb genes.
Dynamic Change of the TCR Repertoire Is Correlated With Clinical Characteristics
In order to investigate whether treatment with ICIs caused global T cell expansion and/or loss of T cell clonotype diversity in patients, and whether the dynamic changes of the TCR receptor could be used as a marker for predicting clinical efficacy, we collected one additional blood sample from each patient after treatment. A total of 24 samples were collected and prepared for TCR sequencing. The additional time point during therapy was at a median of nine weeks (from 3 to 36 weeks). Pearson's correlation coefficient was used to define the similarity of the diversity of the TCR receptor pre-and post-treatment. The similarity was found to be related to time and therapy ( Supplementary Figures 2A, B). The longer the therapy time, the lower the similarity, and the greater the change in TCR diversity (p = 0.0076). The correlation coefficient was higher for single-agent than for combination therapy (p = 0.043), confirming the previous hypothesis that combination therapy might lead to greater changes in the global TCR repertoire.
Considering that the TCR repertoire of samples changed greatly with the time of treatment, we used blood samples taken within nine weeks from the start of treatment to analyze the correlation with clinical efficacy. The Jaccard index (14), which was used to define the similarity of TCR clones, was significantly different between the DCB and NDB groups (p = 0.031); the lower the Jaccard index, the better the clinical efficacy, especially in the combined therapy sample (Supplementary Figure 2C). The Jaccard index was used to compare TCR similarity by determining which clones were present in both pre-and post-treatment samples. Thus, the results suggest that anti-PD-1/PD-L1 treatment affected the changes to the TCR repertoire, and that the degree of TCR change reflected the clinical response.
To assess whether the dynamic changes of the Shannon-Wiener index between pre-and post-treatment were related to clinical outcomes, we performed a correlation analysis. In the combination group, the Shannon-Wiener index was significantly increased in DCB patients, with an average increase of 20.44% ( Figure 1C, p = 0.031), whereas there was no significant change in NDB patients. This suggests that upregulation of TCR diversity by 20.44% would indicate DCB. To understand which type of TCR clones were changed, we first focused on the top 10 high-expressed TCR clones (15). The expression abundance of high-frequency TCR clones in baseline and post-treatment samples decreased significantly in the NDB group ( Figure 1D, p < 0.001) but not in the clinical benefit group. This indicates that the high-frequency expression of TCR clones was maintained in the clinical benefit group.
We inferred that the diversity of high-frequency TCR expression in post-treatment samples might be related to clinical efficacy. Therefore, we expanded the dominant T cell clones that accounted for the cumulative 50% of the total CDR3 counted in the sample and used the D50 index to measure the diversity of samples after treatment. Significant correlation between the D50 index and DCB after treatment was found only in the combined therapy group (Figure 2A, p = 0.012). The D50 index was also associated with response in both the combined therapy group ( Figure 2B, p = 0.0020) and the all patients group ( Figure 2B, p = 0.00021). The higher the D50 index, the more likely patients were to show response. The D50 index was also higher in responders than non-responders in the single-agent group, but this difference did not reach statistical significance. The area under the curve (AUC) of the receiver operating characteristic (ROC) curve was 0.952 when predicting the response of objective response rate (ORR) ( Figure 3A). The sensitivity and specificity of the response using a D50 of 3.09 as a cut-off point were 100% and 83.30%, respectively. Patients were divided into D50 high and low groups based on the Youden index (16) (the maximum sensitivity and the best specificity under the ROC curve). A significant difference in progression-free survival (PFS) rate was identified between the D50 high and D50 low groups ( Figure 3B, p = 0.098). Overall survival was also longer in D50 high patients than in D50 low patients ( Figure 3C, p = 0.068).
To validate the potential of the D50 index for prognostic prediction, an additional validation cohort of 11 NSCLC patients treated with anti-PD-1/PD-L1 was established (Supplementary Table 3). The D50 index was higher in DCB patients ( Figure 3D), and the PFS rate was significantly greater in D50 high patients (log-rank p = 0.029) ( Figure 3E). We further analyzed at which time points the D50 index could predict response. By comparing the D50 index at different blood collection points with the clinical benefit group, we observed that the D50 index could significantly differentiate DCB patients at six weeks (Supplementary Figure 3A, p = 0.0088).
We continued to identify TCR clones with significant differences at baseline and post-treatment. Briefly, Fisher's exact test was used to generate a p-value for every T cell clone, and p-values were adjusted using a positive false discovery rate method to identify significantly expanded T cell clones. Similarly, the number of differentially expressed TCR clones was correlated with clinical efficacy. The number of differentially expressed TCR clones in the clinical benefit group was higher than that in the non-clinical benefit group (median 27 versus 18, p = 0.038, Supplementary Figures 3B, C). We focused on clonal expansion of TCR clones at baseline and found three shared TCR clones (Supplementary Table 2). These clones were expanded in at least two samples, and most in DCB groups, suggesting that they indicated an immune-selective response. Harnessing these T cells could provide practical strategies to improve the shared antigenspecific response to cancer.
We first evaluated differentially expressed sRLs in baseline samples. As shown in Figure 4A, there were significant differences in the expression of sIL-2Ra and sCD27 between the DCB group and the NDB group (p < 0.05). Expression levels of sIL-2Ra and sCD27 were more than 5.04% and 11.52% higher in the DCB group than in the NDB group, respectively.
In order to better understand the dynamic changes between baseline and post-treatment, we performed a fold-change comparison for all sRLs between baseline and post-treatment. When considering single sCKRs or sICPs, as shown in Figure 4B, sRAGE and sCD27 showed significant fold changes before and after immunotherapy (p < 0.05); both were upregulated in post-treatment samples. We then analyzed whether signatures of fold change were associated with clinical efficacy. The correlation results for the fold changes of each sRL are shown in Figure 4C. Three fold change signatures were identified. Notably, Signature-1 included sCD27, sBTLA, sCD28, sCD40, sGITR, sLAG-3, sTLR-2, sGITRL, sPD-1, sCTLA4, sCD80, sCD86, sPD-L1, sICOS, sTNFRI, sIL-1RI, and sHVEM, that is, most of the immune checkpoint proteins. We normalized the signatures by taking the average expression levels of the signature genes for each patient, and then analyzed the relationship between the signatures and clinical benefit. As shown in Figure 4D, Signature-1 was significantly upregulated in the NDB group compared with the DCB group (p < 0.05). Signature-1 mostly contained immunological checkpoint proteins. We further subdivided the Signature-1 genes into a co-inhibitory protein group and a co-stimulatory protein group. There were significant differences in co-stimulatory proteins and co-inhibitory proteins between the DCB and NDB groups, with higher levels of co-stimulatory and co-repressor proteins in the NDB group. These results indicate that upregulation of sICP might have adverse clinical effects.
We divided the patients into two groups according to upregulation and downregulation of Signature-1 genes, and compared the TCR diversity between the two groups. Patients with upregulation of Signature-1 showed more downregulation of TCR clones from baseline to post-treatment (p = 0.0085, Supplementary Figure 4A), indicating a correlation with TCR diversity. Finally, we analyzed the association of D50 with sCKRs and sICPs, and found that the D50 index was significantly associated with sCD30 (p = 0.000032, Figure 4E).
To further validate the association of the sICP signature with clinical efficacy, we used RNA sequencing data of immunotherapy cohorts from Prat et al. (17), Riaz et al. (18), and Liu et al. (19), and calculated Signature-1 scores based on RNA expression. Signature-1 scores were significantly higher in the DCB group than in the NDB group in the Prat, Riaz Ipi-prog (ipilimumab-progressed), and Liu cohorts (p = 0.024, p = 0.0071, and p = 0.019, respectively, Figure 5A). In order to explore the correlation between Signature-1 and the intratumoral immune compartment, we used Riaz's tumor RNA data to evaluate the (Figures 5B, C). The fractions of CD8+ and CD4+ T cells and PD-L1 in the Signature-1 upregulated group were increased significantly ( Figure 5D). These results further validate the prediction ability of the gene set from Signature-1.
We also performed a correlation analysis between TCR diversity and immune cells. The results were similar to those described above: TCR diversity was more correlated with CD8 and CD4 T cells. There was also a certain correlation with the expression level of PD-L1 (Supplementary Figure 5).
DISCUSSION
It is not easy to obtain tumor tissues from patients with advanced disease in order to dynamically monitor the efficacy of immunotherapy. Therefore, it is of great value to develop peripheral blood biomarkers to predict the clinical benefit of anti-PD-1/PD-L1 therapy. In this study, 31 patients with baseline data were enrolled; for 24 patients, paired blood samples were also collected during treatment to explore clinical biomarkers. This is the first systematic exploration of peripheral blood markers in patients treated with ICIs. The TCR repertoire, sCKRs, and sICPs in peripheral blood were analyzed at the same time.
We first observed that the diversity of the TCR dominant clone at baseline was associated with DCB in patients receiving single-agent therapy. The greater the diversity, the more likely the patients were to show durable benefit. However, we did not observe any such correlation in patients receiving combination therapies. Most of the patients in our study were treated with anti-PD-1/PD-L1 combined with chemotherapy. Chemotherapy can induce immunogenic death of tumor cells, release tumor antigens, and activate more T cells that recognize tumors. This was confirmed by the comparison analysis of the dynamic changes of TCR for the two therapies. That is, the changes in TCR clones were greater in patients treated with combination therapy. Therefore, TCR diversity at baseline was not correlated with durable benefits in the combination cohort. Furthermore, we found that the dominant clone (that occupying >0.1% of the repertoire) was associated with DCB. The dominant clone was also found to be significantly associated with ICI response in a recent study of metastatic melanoma (20). When comparing dynamic changes of TCR diversity between pre-and post-treatment samples, we found that changes in TCR diversity were related to treatment time and treatment method. The diversity in DCB patients with combination therapy increased significantly (i.e., the Shannon-Weiner index increased by 20.44%), but that in NDB patients did not. This indicates that the diversity of TCR generally increased in the DCB group. We then analyzed which aspect of TCR clone abundance was beneficial with respect to DCB. The results showed that the highly expressed TCR clone remained highly expressed in the clinical benefit group but was significantly decreased in the non-clinical benefit group. The diversity of TCR clones with high abundance contributing to 50% of the samples was also related to clinical efficacy. The higher the D50 index, the more likely the patients were to show durable benefit. A significant difference in PFS rate was identified between the D50 high and D50 low groups. We validated this result in an independent cohort of NSCLC patients treated with anti-PD-1/ PD-L1 (N = 11). At a time point of six weeks, the D50 index could differentiate patients with durable benefit. D50 at baseline was also found to be associated with survival and response in patients treated with anti-PD-1 in previously published studies (21)(22)(23). From the above findings, we can conclude that the diversity of TCR during treatment, especially the diversity of high-abundance TCR, could be used to dynamically monitor whether patients will show durable benefit in the future. Moreover, the D50 index is a potential marker that could predict durable clinical benefit and PFS. The Shannon-Weiner index of the TCR clone with frequency higher than 0.1% at baseline and the D50 index during therapy together proved that only the dominant TCR clone accounts for clinical outcomes.
The sRLs are regulators of over-inflammation and immune response, indicating their potential role as therapeutic markers of immunotherapy. Therefore, we further explored the role of sRLs in peripheral blood combined with the TCR repertoire in predicting the efficacy of ICIs. Expression of sCD27 in peripheral blood at baseline and its changes during treatment were both found to be related to the efficacy of ICIs. CD27 acts as a co-stimulatory molecule involved in the activation and proliferation of T cells and plays an important part in the function of T cells (24). Initial CD4+ and CD8+ T cell activation upregulates CD27 expression, which leads to the release of CD27 from the surfaces of activated T cells, resulting in circulating soluble CD27 (sCD27) (25). However, persistent triggering of CD27, such as that caused by the constitutive expression of CD70 in transgenic mice, leads to progressive and ultimately fatal defects of T cells, natural killer cells, and B cells, caused by direct exhaustion and activationinduced cell death or IFN-g-mediated indirect depletion. Therefore, CD27 signaling can either improve the function of effector T cells or enhance their exhaustion and death. In this study, patients with higher expression of sCD27 showed higher DCB rates, whereas those with significantly upregulated sCD27 during treatment had lower DCB rates. A combination of anti-PD-1/PD-L1 and an anti-CD27 agonist was recently examined in clinical trials. To obtain the best clinical results with such a combination, it may be necessary to consider the intensity, timing, and duration of treatment.
The role of these tumor immune-related factors in tumor immune regulation remains to be further studied. Analysis of sRLs revealed that cytokines with similar functions showed similar expression trends. In this study, we introduced the concept of a signature and found different fold-change expression patterns of sRL signatures between baseline and post-treatment samples. Signature-1 could serve as a negative predictive factor, as its expression was significantly higher in the NDB group than in the DCB group. Interestingly, Signature-1 mainly contained immune checkpoint proteins. After subdivision into co-inhibition and co-stimulation protein groups, the two subgroups of proteins also showed significant differences between the NDB and DCB groups. We validated the clinical prediction efficacy of Signature-1 in three independent cohorts from previous studies. We also found that Signature-1 was associated with intratumoral immune compartments, including CD4+ and CD8+ T cells and PD-L1 expression. These results indicate that the signature, as a global indicator of integration of multiple functionally similar molecules, is better able to predict ICI efficacy than a single molecule.
Owing to the limited sample size, some of our results did not reach statistical significance and lacked validation. We tried to use a combination of the TCR D50 index and sRL signature to predict DCB and PFS. The DCB rate was significantly higher in the D50 high and signature low groups (Fisher's exact test, p = 0.0089), whereas the PFS rate did not show a significant difference (Supplementary Figure 4B). However, these results are meaningful as preliminary findings. Besides, our cohort did not include patients receiving dual-immune combination treatment, such as nivolumab plus ipilimumab, so it was not possible to directly evaluate the association between dualimmune combination treatment and the newly discovered blood biomarkers. Therefore, in our next study, we will collect more samples and consider more treatments to evaluate and explore the mechanisms underlying the existing findings. Another limitation was that the T cells sequenced in this study were unsorted. Some previous studies used sorted TCRs from CD8+ T cells (20) or CD8+PD-1+TCR (26) to evaluate diversity and found that TCR diversity had predictive value. Unsorted TCR information may be affected by other non-tumor-related TCRs, resulting in biased results. We will use sorted CD8+ T cells in the future.
In conclusion, this study revealed the dynamic changes of peripheral blood biomarkers-the TCR b-chain repertoire and sRLs-before and during treatment, in patients with solid tumors treated with anti-PD-1/PD-L1. We found that diversity of the TCR dominant clone was correlated with DCB. Patients with DCB had increased overall TCR diversity and maintained the expression of the top 10 high-abundance TCRs. The D50 index of the sample during treatment could reflect the patient's response (or lack of response), indicating that it might be useful for prognostic prediction. Upregulation of the sICP signature during treatment might serve as a negative biomarker for prediction of DCB. Moreover, sCD27 may have different roles in different DCB groups. In addition, the diversity of the TCR repertoire was correlated with the expression of sICPs, which might be directly or indirectly related to the immune changes induced by anti-PD-1/PD-L1 therapy. Further integration of the peripheral blood TCR repertoire and sICPs might improve our ability to predict the efficacy of anti-PD-1/PD-L1 therapy.
DATA AVAILABILITY STATEMENT
The original contributions presented in the study are included in the article/Supplementary Material. Further inquiries can be directed to the corresponding authors.
ETHICS STATEMENT
The studies involving human participants were reviewed and approved by The Ethics Committee of the General Hospital of the People's Liberation Army. The patients/participants provided their written informed consent to participate in this study
AUTHOR CONTRIBUTIONS
YL and JW contribute equally to this work. YL and JW designed and performed experiments and manuscript preparation. SJ and SS were responsible for the provision of study resources, materials, and patient access. LW and XZ performed the experiments. GZ collected samples and clinical information. JW and XL analyzed the sequencing data. YL and JW wrote the manuscript. JW, SX and XL revised the manuscript. All authors contributed to the article and approved the submitted version. | 6,713 | 2021-06-07T00:00:00.000 | [
"Medicine",
"Biology"
] |
In vitro effect of hyperthermic Ag and Au Fe3O4 nanoparticles in cancer cells
Methods: HEK293, HCT116, 4T1 and HUH7 human cell lines and 4T1 musculus mammary gland cell line were incubated with Fe3O4 core Ag(Au) shell nanoparticles (NPs) prior to a hyperthermia session. MTT assay was performed to estimate the cytotoxic effects of these NPs. RNA extraction and cDNA synthesis followed so as to quantify mRNA fold change of hsp-70, p53, bcl-2 and casp-3 via qRT-PCR. Results: Fe3O4 core Au shell (concentrations of 400 and 600μg/mL) produced the greatest reduction of viability on HCT116 and 4T1 cells while Fe3O4 core Ag shell (200, 400 and 600μg/mL) reduce viability on HUH7 cells. Hsp-70, p53 and casp-3 were up-regulated while bcl-2 was downregulated in most cases.
Introduction
Hyperthermia refers to the type of treatment in which body tissue is exposed to high temperature in order to damage and kill cancer cells or make them more sensitive to radiation and anticancer drugs [1,2]. Different tools have been suggested to induce hyperthermia; ionizing radiation, laser and microwaves to heat up malignant tissues. Radiotherapy and chemotherapy have been widely used in tumour regions but leading to harmful effects on healthy tissues [2,3].
Nanotechnology introduced non-invasive techniques using different nanoparticles (NPs) as heat-ing mediators. Gold and silver NPs can be applied on their own or in combination with other molecules (i.e., polymers, surfactants, organic dyes) for targeting, imaging and therapeutics [4]. Hyperthermic NPs are a promising tool in cancer therapy. In magnetic hyperthermia, NPs like Fe 3 O 4 NPs, absorb energy and convert it into heat (>41.5°C). Magnetic NPs have been successfully used in many studies and even progressed in clinical trials [5,6]. However, in order to succeed a specific anti-tumour effect to the tumour site, the construction of targeted NPs seems compulsory. This work by JBUON is licensed under a Creative Commons Attribution 4.0 International License.
Previously, we estimated the nanotoxicity of colloidal mono-and bimetallic silver/gold NPs stabilized with tryptophan (Trp), in three cell lines 4T1, a breast cancer cell line, HCT116, a colon cancer cell line and HEK293, embryonic kidney cells [7]. We found that the NP toxicity was lower in non-cancer cells, making them promising tools for cancer treatment approaches [7,8]. In this study we investigated the effect of hyperthermic Fe 3 O 4 core Αg(Au) shell NPs in cancer cell cultures. Our initial hypothesis was that cancer cell lines exposed to hyperthermic NPs will suffer thermal damage which will lead to cellular death. In order to test this hypothesis, we included a fourth cell line, HUH7, a well-differentiated hepatocyte derived cellular carcinoma and we approached the underlying molecular mechanism in vitro, in cancer cells. We estimated the expression of genes involved in programmed cell death (casp-3, p53, bcl-2) and hsp-70, a gene for cellular responses to environmental stressors including hyperthermia [9]. These NPs are stabilized with Trp as an effective way in attenuating potential hepatotoxicity and nephrotoxicity of NPs during their future in vivo application [10].
Fe 3 O 4 core Ag(Au) shell NPs synthesis
Colloidal solutions of nanocomposites containing iron oxide core and noble metal shell Fe 3 O 4 core Αg(Au) shell were obtained via chemical reduction of metal ions (AgNO3, HAuCl4, Merck, Germany) by amino acid tryptophan (Trp, SC12-20120713, China) in the presence of magnetic fluid -suspension of iron oxide Fe 3 O 4 in sodium oleate. The synthetic procedure was similar to the previously described [7]. Initial solution of Trp was adjusted to high pH and heated to boiling. Then, magnetite was injected followed by silver nitrate (tetrachlorauric acid). The components molar ratio was ν(Trp): ν(M): ν(Fe 3 O 4 ) = 2:1:0,5. Colloid was stirred and heated continuously.
Cell culture
HEK293, HCT116, 4T1 and HUH7 cell lines were grown in DMEM high glucose culture medium (BioSera, Nuaille, France) containing 10% fetal bovine serum (FBS), 2 mmol/L glutamine, 100 U/ml penicillin and 100 g/ml streptomycin at 37°C. The medium was changed every 48 h and cells were passaged once weekly using standard trypsin-EDTA concentrations. Beginning at 38, 32, 41 and 36 cell passages respectively, cells were cultured continuously. Cells were frozen in freezing medium containing FBS, 5% DMSO. All cell lines used were adherent. HEK293 cell line was used as control group (non-cancer cell line) in our experiments.
MTT assay
The MTT cell viability assay measures alterations in cell viability; when metabolic events lead to apoptosis or necrosis, the cell viability is decreased. As a general protocol, 50.000 cells/well were seeded in 24well plates (Corning-Costar, Corning, NY) and cultured overnight. Positive, negative and background controls were used throughout the study. Positive control had cells with culture medium but not exposed to NPs. Negative control had NPs without cells. Background control had culture medium without cells. The cell lines used were treated with 200, 400 and 600 μg/mL of Fe 3 O 4 core Ag shell , Fe 3 O 4 core Au shell and Fe 3 O 4 alone for 1 h and then ionized for 15 min. Subsequently, the cells were rinsed once and incubated in 37°C with 100μL of serum-free medium containing 0.5 mg/mL MTT. After 1.5h, 100μL of SDS-HCl were added to each well, mixed thoroughly and incubated for 1 h at 37°C. Optical densities (OD) were read at 570 nm (reference filter was set at 690 nm), using a microplate spectrophotometer (SPECTROstarNano, BMG LABTECH, Ortenber, Germany). Absorbances were normalized with respect to the untreated control cultures to calculate changes in cell viability.
Hyperthermia
The hyperthermia session was performed using a water loaded circular waveguide applicator (7 cm diameter) with an effective aperture of 7 cm [11]. HEK293, HCT116, 4T1 and HUH7 cells were incubated for 20 min at 43°C. The hyperthermia device operated as a 433 MHz microwave heating. The device had an omitted power of 100 Watts RMS. However, the transmitted power in our case was at the level of 15-20 Watts for 4 min [12].
RNA extraction and quantitative real-time RT-PCR
Total RNA extraction (for all three NPs used and for concentration of 400μg/mL) was performed using TRIzol reagent (Thermo Fisher Scientific), according to the manufacturer's instructions. Reverse transcription was performed using the PrimeScript First Strand cDNA Synthesis Kit (TAKARA). The reaction conditions were as follows: 37°C for 30min and 85°C for 5s. The reaction was performed on Thermal Cycler (Kyratec Super Cycler). Assessment of casp-3, bcl-2, p53 and hsp-70 mRNA levels was performed for HCT116, 4T1, HUH7 and HEK293; 4T1 cells are p53 null [13] and as such expression of p53 was not investigated.
Quantitative real-time RT-PCR was conducted on an ABI Prism 7000 apparatus (Applied Biosystems, Foster City, CA, USA). Each cDNA sample was mixed with specific primer sets and PCR master mix (KAPA SYBR FAST qPCR Kit). The levels of genes expression were normalized by subtracting the Ct value of the GAPDH RNA internal control from that of the GOI (gene of interest) (ΔCt=-|CtGOI-CtGAPDH|). To determine the relative expression of GOI in cancer cells compared to non-cancer cells the 2ΔΔCt model was used, where ΔΔCt=ΔCtGOI-ΔCtGAPDH.
Statistics
All statistical analyses were performed using GraphPad version 3.00 (GraphPad Software, San Diego, CA). P<0.05 was considered statistically significant.
Characterization of magnetic NPs
Prepared colloidal solutions of magnetic NPs containing iron oxide core and noble metal shell had a bright yellow and red colour inherent to NPs of silver and gold respectively.
A specific colour is a distinguishing feature of noble metal NPs and is caused by the phenomenon of localized surface plasmon resonance (LSPR) that appears as absorption in the visible range of the spectrum. The maxima of LSPR absorption bands of Fe 3 O 4 core Αg shell and Fe 3 O 4 core Au shell colloids were localized at 420 and 527 nm (Figure 1), indicating the formation of continuous shell around the magnetite particles. The obtained NPs, with both silver and gold shell, were of spherical shape with the average size of 10-20 nm according to data obtained by transmission electron microscopy (TEM) and dynamic light scattering (DLS) methods ( Figure 1). Both colloids carried neutral pH, namely 7.2 for Fe 3 O 4 core Au shell and 7.7 for Fe 3 O 4 core Αg shell . cells (400 μg/mL and 600 μg/mL of Fe 3 O 4 core Au shell NPs reduced viability at 40 and 55% respectively). Fe 3 O 4 core Au shell NPs appeared highly toxic for 4T1 cells. Non-ionized 4T1 cells showed a low, doseindependent toxicity (approximately 80% viability), while ionized cells showed a decrease of viability by 58 and 65% (for concentrations 400 μg/mL and 600 μg/mL). In HUH7 cells, there was 30% difference of viability between ionized and non-ionized cells incubated with Fe 3 O 4 core Ag shell . (200, 400 and 600 μg/mL). Interestingly, in 400 and 600 μg/mL of hyperthermic Fe 3 O 4 core Au shell and in 200 and 400 μg/mL with Fe 3 O 4 core Ag shell the toxic effects of these NPs were reduced in non-cancer cells HEK293 (Figure 2a).
Discussion
According to our results, the NPs exhibit a toxic effect against cancer cells after ionization. (Figures 2b,c). Specifically, nonionized HCT116 show no toxicity in concentrations 400 and 600 μg/ml of Fe 3 O 4 (~5% toxicity), while in 200 μg/ml of Fe 3 O 4 the toxicity is ~30%. On the other hand, ionized HCT116 in concentrations 400 and 600 μg/ml of Fe 3 O 4 showed ionization-dependent toxicity (40% and 55% respectively). In 200 μg/ ml of Fe 3 O 4 the toxicity is no ionization-dependent.
Regarding non-ionized 4T1, they show maximum 20% toxicity in the three concentrations tested, opposed to ionized 4T1 that in the concentrations 400 and 600 μg/ml of Fe 3 O 4 show high toxicity (~58% and 65% respectively), indicating ionizationdependent toxicity. Fe 3 O 4 core Ag shell NPs because of the toxic effect of Ag NPs on their own, compared to Au NPs that are considered to be the less toxic metal NPs for in vivo applications, do not seem to act as heating mediators [7,14]. Fe 3 O 4 core Ag shell NPs show no ionization-dependent toxicity in both cell lines. Interestingly, in the same concentrations the toxic effect of hyperthermic Fe 3 O 4 core Au shell NPs is minimized in non-cancer cells HEK293 (Figure 2a) VS ~55% viability in cancer cells with 400μg/ml and 45% viability with 600μg/ml) (Figures 2 a-c).
On the contrary, it is Fe 3 O 4 core Ag shell NPs that show a decrease of viability in HUH7 cells, serving as hyperthermia-inducing agents whereas both Fe 3 O 4 core Au shell and Fe 3 O 4 have a lower cytotoxic effect. Ag NPs show a dose-independent toxicity with almost 30% difference between ionized and non-ionized cells in all three concentrations tested. Thus, it seems that there is not a single hyperthermic NPs suitable for all cancer cell types but different hyperthermic NPs are cytotoxic for different cancer cells. Furthermore, as already mentioned, Ag NPs have an endogenous toxicity that Au NPs lack. This finding suggests that hyperthermia and Ag could have a synergistic effect on HUH cells; neither non-ionized HUH7 cells incubated with Fe 3 O 4 core Ag shell nor bare Fe 3 O 4 on ionized HUH7 show similar toxicity. Therefore, these results indicate that HUH7 could be hyperthermia-resistant, requiring the action of Ag for toxicity to be induced. Indeed, increased resistance to hyperthermia has already been described in a study [15] in which integrin-linked kinase was associated with poor response to hyperthermia. However, the molecular basis of this phenomenon remains unclear.
We also examined the expression of hsp-70 and apoptosis-related genes (p53, casp-3 and bcl-2). Hsp-70 is a protein family induced under environmental stress, heat shock included, and assists the cell to cope with denaturated proteins and prevents ionized HEK293 (a), HCT116 (b), 4T1 (c) and HUH7 (d) cells with 400μg/mL of Fe3O4 core Αg shell, Fe3O4 core Αu shell and Fe3O4 nanoparticles. a b c d apoptosis. Considered as the hallmark of hyperthermia, its up-regulation in exposed cells is found in several studies [16,17]. Hsp-70 serves as a danger signal by triggering immunological responsiveness against cancer cells and increasing tumour tissue infiltration by eosinophil granulocytes [18]. Tsang et al [19], reported that administration of both hsp-70 and dendritic cells at irradiated cancer tissue triggers a more potent anti-cancer response than dendritic cells alone. In our study, except Fe 3 O 4 core Au shell NPs, ionized HEK293 showed almost no fold change in hsp-70 expression, suggesting a lower intake of hyperthermic NPs. On the other hand, HUH7 had a mild up-regulation of hsp-70. Combined with the MTT results, this finding supports the synergistic hypothesis (hyperthermia combined with Ag result in increased toxicity); hyperthermia alone mildly affected the viability of HUH7 cells. HCT116 and 4T1 cells showed the highest up-regulation of hsp-70 in all four cell lines and also showed a high decrease in viability (ionized HCT116 and 4T1 using Fe 3 O 4 core Au shell NPs, 400μg/mL).
Following the study of hsp-70 fold change, our next goal was to approach the molecular pathway that leads to cancer cell death. Apoptosis is of crucial importance for cell fate since pro-and anti-survival signals determine tumour initiation and progression. However, cancer cells are apoptosis-resistant while many chemotherapeutic drugs function by triggering apoptotic mechanisms [20]. P53 is a tumour suppressing gene that guards genome and inhibits tumorigenesis since it promotes DNA repair and cell death [21]. Bcl-2 is anti-apoptotic gene, targeted by p53 transcription factor and promotes cell survival by binding cytochrome C residues. Casp-3 also has a key-role in apoptosis by catalysing the cleavage of several important intracellular proteins [22][23][24].
In our study, p53 and casp-3 were found up-regulated, except HEK293 cells where they remained almost unchanged for all NPs used. On the contrary, bcl-2 was found down-regulated in every cell line except Fe 3 O 4 core Ag shell in HEK293 and Fe 3 O 4 core Au shell and Fe 3 O 4 HUH7 cells. These results are consistent with the MTT results; HEK293 had the mildest viability reduction and also showed the mildest fold change in gene expression. All the cancer cell lines which had an increased toxicity also showed an analogous fold change in gene expression. These results reveal that cancer cells treated with the hyperthermic NPs used in this study showed anti-cancer potency via the caspase cascade and the p53/bcl-2 apoptotic pathway. However, 4T1 cells are p53-null. Thus, the cellular death mechanism is triggered by a p53 independent pathway. Yerlikaya et al [13], showed that a proteasome inhibitor leads to a p53 independent apoptosis in 4T1 p53-null cells. Despite the different stimuli (hyperthermia vs proteasome inhibition) the cellular response was the same: caspase-3 was up-regulated. The latter highlights that p53-deficient cell can also lead to apoptosis via caspase-3. However, further research in the underlying mechanisms involved is crucial since in some cancer types p53 is found mutated up to 50% [25]. Additionally, studies have shown contradicting results about the role of pro-apoptotic genes involved in p53-independent apoptosis [13].
Our results are in agreement with other studies in which hyperthermia (not mediated by NPs) results in apoptotic death of cancer cells [26,27], while two more studies using NP-mediated hyperthermia also support this conclusion [28,29]. Furthermore, one study using hyperthermia on p53-deficient H1299 lung cancer cells also showed that the underlying mechanism of cellular death is apoptosis [30].
Based on our findings, the NPs we used seem to have specificity against cancer cells. We deemed that is has to do with the use of tryptophan (Trp) as a stabilizer and reducing agent. Trp is demonstrated to have rather a positive effect on both cell lines compared to the positive control, especially on cancer cells (data not shown). Thus, the increased metabolism of Trp by cancer cells specifically may be beneficial in order to increase the anti-tumour effect of NPs [31]. However, further research is required to elucidate the p53-independent apoptosis triggered by hyperthermic NPs and to predict the vulnerability of cancer cell types towards a particular hyperthermic NP (Fe 3 O 4 core Au shell or Fe 3 O 4 core Ag shell ). | 3,770.2 | 2019-09-09T00:00:00.000 | [
"Medicine",
"Materials Science"
] |
Maximising the number of solutions to a linear equation in a set of integers
Given a linear equation of the form $a_1x_1 + a_2x_2 + a_3x_3 = 0$ with integer coefficients $a_i$, we are interested in maximising the number of solutions to this equation in a set $S \subseteq \mathbb{Z}$, for sets $S$ of a given size. We prove that, for any choice of constants $a_1, a_2$ and $a_3$, the maximum number of solutions is at least $\left(\frac{1}{12} + o(1)\right)|S|^2$. Furthermore, we show that this is optimal, in the following sense. For any $\varepsilon>0,$ there are choices of $a_1, a_2$ and $a_3,$ for which any large set $S$ of integers has at most $\left(\frac{1}{12} + \varepsilon\right)|S|^2$ solutions. For equations in $k \geq 3$ variables, we also show an analogous result. Set $\sigma_k = \int_{-\infty}^{\infty} (\frac{\sin \pi x}{\pi x})^k dx.$ Then, for any choice of constants $a_1, \dots, a_k$, there are sets $S$ with at least $(\frac{\sigma_k}{k^{k-1}} + o(1))|S|^{k-1}$ solutions to $a_1x_1 + \dots + a_kx_k = 0$. Moreover, there are choices of coefficients $a_1, \dots, a_k$ for which any large set $S$ must have no more than $(\frac{\sigma_k}{k^{k-1}} + \varepsilon)|S|^{k-1}$ solutions, for any $\varepsilon>0$.
Introduction
Let a 1 , a 2 and a 3 be fixed coprime integers, none of which is zero. We will consider the linear equation a 1 x 1 + a 2 x 2 + a 3 x 3 = 0. (1.1) In this paper, we are interested in the problem of finding sets with as many solutions to (1.1) as possible. This leads to the following definition.
The trivial upper bound on T (S) is T (S) |S| 2 . This is because, for any choice of x 1 and x 2 , there is at most one choice of x 3 such that a 1 x 1 + a 2 x 2 + a 3 x 3 = 0, namely x 3 = −a1x1−a2x2 a3 . We are interested in making T (S) as large as possible, for a fixed size |S|.
For some choices of coefficients a 1 , a 2 and a 3 , the exact maximal value of T (S) is known. For example, consider the case a 1 = a 2 = a 3 = 1. Then, work of Hardy and Littlewood [8] and Gabriel [5] shows that, when |S| is odd, T (S) is maximised when S is an interval centred about 0. This was extended to even |S| by Lev in [10]. In fact, their arguments show that if S ⊆ Z is a set, and S is an interval centred about 0 of the same size, then T a1,a2,a3 (S) T 1,1,1 (S ). The ideas behind their approaches involve rearrangement inequalites, which are discussed in detail in [9,Chapter 10], and which inspire some of the arguments in this paper.
The set of solutions to x 1 − 2x 2 + x 3 = 0 is precisely the set of three-term arithmetic progressions; that is, the set of affine shifts of the set {0, 1, 2}. By analogy with this, Bhattacharya, Ganguly, Shao and Zhao considered longer arithmetic progressions; in [2,Theorem 2.4], they proved that the number of k term arithmetic progressions in a set S of n integers is maximised when S is an interval.
Ganguly (in a personal communication) asked about other affine patterns; in particular, finding sets S with as many affine copies of {0, 1, 3}, or solutions to x + 2y = 3z, as possible. In this case, such a result would necessarily be less clean; for instance, there are more solutions to x + 2y = 3z in {0, 1, 3} than in {0, 1, 2}.
Indeed, in general, much less is known. For a lower bound on the maximal value of T (S), a fairly good bound is given by the following example. Proof. The idea behind the construction is to split S into three pieces S 1 , S 2 and S 3 , of roughly equal size, for which there are many solutions to a 1 x 1 + a 2 x 2 + a 3 x 3 = 0 with each x i taken from S i . Let M be a large integer, which we assume to be divisible by 6. We will define However, we may find a large collection of triples (x 1 , x 2 , x 3 ) by choosing x 1 ∈ S 1 and x 2 ∈ S 2 arbitrarily, and selecting those for which x 3 = −a1x1−a2x2 a3 is in S 3 . If x 1 = a 2 a 3 x 1 and x 2 = a 1 a 3 x 2 , then we have x 3 = −a 1 a 2 (x 1 + x 2 ). Therefore, a pair (x 1 , x 2 ) will give rise to a solution precisely when |x 1 + x 2 | M/6.
We may compute the number of such pairs (x 1 , x 2 ) as the sum M/6 Thus, the number of triples is at least 1 12 Given this, it is natural to define the following quantity: where S runs over subsets of Z.
Thus, the assertion that 1 12 γ a1,a2,a3 holds for all a 1 , a 2 and a 3 follows from Proposition 1.2 and the work of Hardy and Littlewood in [8].
As far as the author is aware, exact values for γ a1,a2,a3 are only known in cases for which |a 1 a 2 a 3 | 2 (this includes the cases previously discussed). In particular, we have Theorem 2]. The same holds in the third non-equivalent case with |a 1 a 2 a 3 | = 2, namely γ 1,2,1 = 1 2 . Even the value of γ 1,2,−3 is not known, although the author conjectures that it is 1 3 , which is the value calculated for S = [−M/2, M/2]. The main theorem of this paper is a converse, of sorts, to Proposition 1.2. In particular, we will prove the following.
Theorem 1.4. The constant 1 12 in the statement of Proposition 1.2 is optimal, in the following sense. For any ε > 0, there exists a choice of a 1 , a 2 and a 3 for which γ a1,a2,a3 In view of this theorem, (1.2) gives the best possible bounds on γ a1,a2,a3 that are independent of the coefficients a i .
The plan for this paper is as follows. In Section 2, we will record some additive combinatorial lemmas that we will need in order to establish Theorem 1.4. In Section 3, we will use these lemmas to prove Theorem 1.4.
One might also ask about generalising Theorem 1.4 to other settings. For instance, given a system of m linear equations in k variables (where we assume that m k − 2), can we prove an analogue of Theorem 1.4?
If m = 1, then an analogue of Proposition 1.2 holds for any value of k 3. Set Then, for any choice of coefficients a 1 , . . . , a k , there are sets S with at least σ k k k−1 |S| k−1 + O(|S| k−2 ) solutions to a 1 x 1 + · · · + a k x k = 0. We will discuss (1.5) further in Section 4.
Furthermore, the corresponding analogue of Theorem 1.4 holds. For any ε > 0, there are choices of coefficients a 1 , . . . , a k for which any large set S must have no more than ( σ k k k−1 + ε)|S| k−1 solutions. For instance, for any small positive ε, we can find coefficients a 1 , a 2 , a 3 and a 4 with the property that T (S) ( 1 96 + ε)|S| 3 , where T (S) counts the number of solutions to a 1 x 1 + a 2 x 2 + a 3 x 3 + a 4 x 4 = 0. We will discuss this in Section 4.
On the other hand, the opposite is true in the case that m > 1. Indeed, it is possible to show that there is no constant c > 0, such that for any system of 2 equations in 4 variables, there are large sets S with at least c|S| 2 solutions to the system. We will prove this fact in Section 5.
Notation
As we have already noted, T (S) will be the number of solutions to a 1 x 1 + a 2 x 2 + a 3 x 3 in S. We can extend this by defining T (S 1 , S 2 , S 3 ) to be the number of solutions to a 1 x 1 + a 2 x 2 + a 3 x 3 , where x i ∈ S i . We will use the notation a · S to denote the set {ax, x ∈ S}.
We will also make frequent use of the Vinogradov notation f g to mean that f = O(g). When the is subscripted, we allow the implicit constant to depend on the subscripts. This version of the paper replaces a previous version [1]. The argument used to prove Theorem 1.4 is replaced with a new argument which avoids appealing to the arithmetic regularity lemma (and can handle a wider class of equations), and the results of Section 5 are new to this version.
Additive combinatorial lemmas
In this section, we will collect some lemmas that will be necessary for the proof of Theorem 1.4.
For any set A ⊆ Z, let δ[A] be its growth under the differencing operator, |A−A| |A| . If A and B are two sets of integers, let the additive energy between A and B, E(A, B) be defined by It is easy to see that this satisfies the following inequalities: the third of which follows immediately from the first two.
We will require the following lemma, which states that, when two sets A and B have δ[A] and δ [B] small, and if E(A, B) is large, then |A − B| is also small.
We will also require a weak form of a structure theorem due to Green and Sisask.
The quantity T (S 1 , S 2 , S 3 ) is related to the additive energy via the following lemma.
Proof. For any t ∈ Z, let μ(t) denote the number of ways of writing t = a 1 x 1 + a 2 x 2 , for x i ∈ S i . Thus, by definition, Now, we see that the inequality following from Cauchy-Schwarz. This completes the proof of Lemma 2.3.
The following two facts are standard results in additive combinatorics.
Lemma 2.6. Suppose that S 1 , S 2 , S 3 ⊆ Z are sets with sizes s 1 , s 2 and s 3 , respectively. Then, we have the bound Proof. We will first prove Lemma 2.6 in the case that a 1 , a 2 and a 3 are all 1. Without loss of generality, assume s 1 s 2 s 3 . Suppose first that s 3 s 1 + s 2 . In that case, we have . The first line follows from the trivial observation that for each pair of x ∈ S 1 and y ∈ S 2 , there can be at most one solution to x + y + z = 0 with z ∈ S 3 . The third line follows from our assumption on s 3 . Thus, (2.2) follows in this case. Now, suppose s 3 < s 1 + s 2 . In this case, we may apply [11, Lemma 2], which states that 2) follows in this case via an easy application of the Cauchy-Schwarz inequality. Finally, for arbitrary coefficients a 1 , a 2 and a 3 , observe that . This completes the proof of Lemma 2.6.
Finally, we will require the following theorem of Bukh: Given two coprime integers λ 1 and λ 2 , we have that for any S ⊆ Z, 3. Proof of Theorem 1.4 In this section, we will use the lemmas of Section 2 to prove Theorem 1.4. We must prove that, given a suitable choice of a 1 , a 2 and a 3 , all sufficiently large sets S have T (S) ( 1 12 + ε)|S| 2 .
Let ε > 0. Given our choice of ε, we must choose the values of the coefficients a 1 , a 2 and a 3 ; we will do so later. Suppose that S is a sufficiently large set. We will immediately apply the structure theorem, Theorem 2.2, to S, with ε 1 = ( ε 6 ) 4 . This gives us a decomposition S = S 1 · · · S n S 0 . We will start by showing that the contribution to T (S) from solutions a 1 x 1 + a 2 x 2 + a 3 x 3 = 0, with at least one of the x i taken from S 0 , is small.
Proof. The number of such solutions may be upper bounded by and so it suffices to show that each term is no greater than ε 6 |S| 2 . Applying Lemmas 2.3 and 2.5, we have At this point, we must bound the number of solutions to a 1 x 1 + a 2 x 2 + a 3 x 3 = 0, where each of x 1 , x 2 and x 3 is taken from an S i with i 1. To do this, we will start by restricting which triples (i, j, k) can have the property that there are many solutions with x 1 ∈ S i , x 2 ∈ S j and x 3 ∈ S k . For instance, the fact that δ[S 1 ] is small, together with an assumption that a 1 and a 2 are coprime and |a 1 + a 2 | is large, will imply that there cannot be too many solutions with x 1 , x 2 and x 3 all in S 1 .
In particular, this will give us a fairly rigid structure on the collection of triples S i , S j , S k such that T (S i , S j , S k ) can give a non-trivial contribution to T (S, S, S). In order to quantify this structure, we will draw a labelled digraph G whose vertices correspond to the S i with i 1. We will draw an edge from S i to S j with label a1 a2 if and only if T where K 1 is as in the statement of Theorem 2.2. Similarly, we will draw an edge with label a3 |S| 2 , and similarly for the other four possible labels.
In particular, observe that if there is an edge from S i to S j with label x, then there will be an edge from S j to S i with label x −1 . Our definition of G does not necessarily preclude the existence of multiple edges between S i and S j (with different labels), or edges from S i to S i . However, as part of the proof, we will show that this cannot happen, provided that we assume a suitable hypothesis on a 1 , a 2 and a 3 .
First, we will show that G captures almost all of the solutions to a 1 x 1 + a 2 x 2 + a 3 x 3 = 0. Then, the total number of solutions to a 1 x 1 + a 2 x 2 + a 3 x 3 = 0 among all of the bad triples is at most ε 4 |S| 2 .
Proof. There are six ways a triple (S i , S j , S k ) can be bad. One such way is if there is no edge from S i to S j with label a1 a2 .
Let us count the total number of solutions among triples for which the a1 a2 edge is missing. That is, since the number of pairs S i , S j is bounded by K 2 1 . Summing this over the six possible ways for a triple to be bad completes the proof of Lemma 3.2.
In view of Lemmas 3.1 and 3.2, it remains to show that the number of solutions among the good triples is at most ( 1 12 + ε 4 )|S| 2 , for a suitable choice of the coefficients a 1 , a 2 and a 3 . The values we will choose are a 1 = 1, a 2 = M and a 3 = M + 1, where We can now prove the following lemma: With the values of a 1 , a 2 and a 3 that we have chosen, the product of the labels along any cycle in G must be 1.
Remark. This immediately tells us that G has no loops (edges from a vertex to itself). In view of the fact that an edge from S i to S j with label x is accompanied by an edge from S j to S i with label x −1 , this also tells us that there can be at most one edge from S i to S j .
Remark. We have chosen particular values of the a i for simplicity; indeed, we only need a single choice of coefficients to work in order to establish Theorem 1.4. However, the same argument is able to establish Lemma 3.3, and thus also Theorem 1.4, for a much wider class of equations. For example, whenever a 1 , a 2 and a 3 are coprime, and at least two of the three coefficients are large enough, then the analogue of Lemma 3.3 holds, and thus γ a1,a2,a3 < 1/12 + ε.
Conversely, it does not suffice for just one of the a i to be large. For example, if a 1 = a 2 = 1, then it can be shown that, for S a slightly modified version of the set in Proposition 1.2, T 1,1,a3 (S) > 1 5 |S| 2 for any a 3 .
Proof of Lemma 3.3. Suppose there is a cycle whose label product is not 1; consider a shortest such cycle. By minimality, such a cycle may have no repeated vertices, and thus must have at most K 1 vertices. Thus, without loss of generality the cycle is S 1 , S 2 , . . . , S k , S 1 , where S i → S i+1 has label t i (with S k+1 = S 1 ), and k K 1 .
By Lemma 2.3, we deduce that for each i, Now, let us apply Lemma 2.1 to S i and S i+1 . We have that and so we deduce that Now, we can prove, by inductively applying Lemma 2.4, that Thus, setting i = k, we learn that since k K 1 . By hypothesis, t 1 t 2 . . . t k = 1. However, we know that t 1 t 2 . . . t k can be written in the form M e1 (M + 1) e2 for some integers e i not both zero. Suppose that e 1 is non-zero; the argument is similar if e 2 is non-zero.
Write t 1 t 2 . . . t k = r s for coprime integers r and s; our hypothesis tells us that M must divide r or s. Therefore, , as a consequence of (3.1). Thus, we have shown that |r · S 1 − s · S 1 | ( But, if S 1 is sufficiently large, this contradicts Theorem 2.7, which states that whenever |S 1 | is sufficiently large. This contradiction completes the proof of Lemma 3.3. To complete the proof of Theorem 1.4, we just need to bound the number of solutions to a 1 x 1 + a 2 x 2 + a 3 x 3 = 0, with x 1 , x 2 , x 3 taken from a good triple. The following lemma will achieve this. Then, the number of solutions to a 1 x 1 + a 2 x 2 + a 3 x 3 = 0 taken from good triples is bounded above by ( 1 12 + ε 4 )|S| 2 , whenever |S| is large enough.
Proof. We will start by defining a function with the property that if S i → S j has label t, then d(j) = td(i).
One way we can do this is as follows. For each connected component G of G, choose the smallest value of i such that S i is in G , and set d(i) = 1. Then, for any other j with S j in G , d(j) is determined by the product of the labels on any path from S i to S j . Lemma 3.3 guarantees that this value does not depend on the path chosen. Now, for each d, let R d = ∪ i:d(i)=d S i . Suppose that S i , S j , S k is a good triple, in that order (so, for example, the label on S i → S j is a 2 /a 1 ). Then, setting d = a 1 d(i), we have that Therefore, all of the solutions coming from the good triple S i , S j , S k will be counted in T (R d/a1 , R d/a2 , R d/a3 ), and so an upper bound for the total number of solutions coming from good triples is where the sum is taken over all d such that all three of the R i exist (in particular, there can be no more than n terms in the sum).
We may apply Lemma 2.6 to give an upper bound for this.
where the sum on the second line is over unordered pairs d 1 , d 2 such that d 1 /d 2 is equal to the ratio between two of the a i . The second inequality follows because if d 1 ∼ d 2 , then there is exactly one ratio a i /a j such that d 1 /d 2 = a i /a j . Thus, the term |R d1 ||R d2 | appears in at most one of the sums on the right-hand side of the first line. Finally, for i = 0, 1 and 2, define the quantity X i by By our construction of d, each |R d | appears as a term in exactly one of the X i . Furthermore, d 1 ∼ d 2 only if R d1 and R d2 are in different sums X i , and any term |R d1 ||R d2 | appears at most once in (3.6). Consequently, we have the upper bound the latter inequality following from an easy application of Cauchy-Schwarz, since X 0 + X 1 + X 2 |S|. This completes the proof of Lemma 3.4.
We have now essentially proven Theorem 1.4. Indeed, any solution to a 1 x 1 + a 2 x 2 + a 3 x 3 = 0 must either have some x i in S 0 , or must come from a bad triple, or must come from a good triple. Combining Lemmas 3.1, 3.2 and 3.4 gives the result if |S| is large enough.
Equations in more than 3 variables
A fairly natural extension of Theorem 1.4 is to ask if a similar result holds for k-variable equations a 1 x 1 + · · · + a k x k = 0. (4.1) As before, let T (S) be the number of solutions to (4.1) in S. Similarly, let T (S 1 , . . . , S k ) denote the number of solutions with x i taken from S i . We have a trivial upper bound for T (S), namely that T (S) |S| k−1 . Before presenting our analogous example to Proposition 1.2, we require some notation and definitions. Let I x : R → R denote the indicator function of a (real) interval of length x centred at the origin, so I x (y) = 1 if and only if |y| x 2 , and I x (y) = 0 otherwise. Remark. In the introduction, we gave the following formula for σ k : The equivalence of these forms follows from taking a Fourier transform and applying the convolution identity; the details can be seen in [3]. See also [12], where it can be shown that σ 2h is the leading coefficient of the polynomial Ψ h (n).
Remark. σ k obeys a simple asymptotic (see, for example, [13], or [6] for more terms): as k → ∞. We may interpret σ k combinatorially. If f k is the probability density function of a sum of k independent random variables distributed uniformly on [−1/2, 1/2], then σ k = f k (0). Thus, the form of the asymptotic for σ k is not surprising, in view of the Central Limit theorem. In particular, σ k = Φ k (1, . . . , 1).
Remark. There is an explicit formula for Φ. In general, we have (4.4) where ω(ε) = i ε i and ε · t = i ε i t i and sgn denotes the sign function. This is established in [3]. For k = 3, we can write (for t 1 t 2 t 3 ) otherwise. (4.5) In analogy with Proposition 1.2, we have the following.
The proof of Proposition 4.3 will rely on the following fact, which states that, when the coefficients a i are all 1, long progressions behave somewhat like real intervals. Then, the number of solutions to Proof. We may assume without loss of generality that the progressions S i have common difference 1. To prove Proposition 4.4, it suffices to use the following observation.
Up to an error which is at most O k ((s 1 + · · · + s k ) k−2 ), this can be written as an integral The two implications above allow us to show that, up to acceptable error, this is equal to which is equal to Φ(s 1 , . . . , s k ); we omit the details.
We are now ready to prove Proposition 4.3.
Proof of Proposition 4.3. As in Proposition 1.2, we will consider S as the union of k sets S 1 , . . . , S k , with the property that T (S 1 , . . . , S k ) is large.
The way we will do this is as follows. Let M be a large integer, which we assume to be divisible by 2k. Define Perhaps unsurprisingly, Theorem 1.4 also generalises to this setting.
Theorem 4.5. Let ε > 0. Then, there exist coefficients a 1 , . . . , a k with the property that, for any suitably large set S, The proof of Theorem 4.5 is broadly similar to the proof of Theorem 1.4. There are two main places in which the argument slightly differs. Firstly, we must generalise Lemma 2.3 to give a bound for T (S 1 , . . . , S k ) in terms of E(S 1 , S 2 ): Lemma 4.6. Suppose that S 1 , . . . , S k ⊆ Z are finite sets. Then, Proof. For any t ∈ Z, let μ(t) denote the number of ways of writing t = a 1 x 1 + a 2 x 2 , for x i ∈ S i . Thus, by definition, Define ν(t) to be the number of ways of writing t = −a 3 x 3 − · · · − a k x k , for x i ∈ S i . Thus, we see that Finally, we observe that t ν(t) 2 represents the number of solutions to the equation and so we can bound it by (|S 3 | . . . |S k |) 2− 1 k−2 , by the same argument used in (2.1) to bound the energy.
Secondly, we will have to apply a k variable analogue of Lemma 2.6. The analogue of this is the following: Remark. This lemma is actually weaker than Lemma 2.6, where the error term was O(1). The weaker error term here comes from our reduction to the real case using Proposition 4.4; an inductive proof would likely give an O( s i ) k−3 error term. However, the O( s i ) k−2 error term is sufficient for our purpose.
Remark. If k is even, we can actually deduce a stronger version of (4.7) by using Hölder's inequality. We have where the second line used Hölder's inequality along with the fact that k is even. This is stronger than (4.7) via an application of the AM-GM inequality. It is unclear whether the stronger version holds in the case that k is odd; indeed, it is not too hard to establish for k = 3 by using (4.5). However, this stronger form is not necessary, so we only prove the version we need.
Proof of Lemma 4.7. First, observe that the statement of the lemma is unchanged if we assume without loss of generality that each a i is 1, since we may replace S i with a i · S i . The first step in the proof is to apply [10, Theorem 1], which says that we may take each S i to be an interval of length s i , roughly centred at the origin (depending on the parity of s i ), in order to maximise T (S 1 , . . . , S k ). We may immediately apply Proposition 4.4, which says that Thus, it suffices to prove that This will follow if we can prove that, for positive real numbers t 1 , . . . , t k , To prove (4.8), first observe that equality holds in the case that all of the t i are equal. Indeed, when t i = 1 the relation follows from the definition of σ, and for other constant values of t i the equality follows by homogeneity. Set To prove that Θ(t 1 , . . . , t k ) achieves its maximum value (with t 1 + · · · + t k fixed) when all of the t i are equal, observe that it will suffice to prove the following claim. Claim 1. If t 1 + t 2 is fixed (as well as each of t 3 , . . . , t k ), then Θ(t 1 , . . . , t k ) achieves its maximum when t 1 = t 2 .
To see that this claim is sufficient, observe that we may repeatedly replace the largest and smallest of the t i with their average. In doing so, max t i − min t i will tend to 0, and we can use the continuity of Θ to obtain the result.
To prove Claim 1, recall the expression for Θ(t 1 , . . . , t k ): . Now, observe that g may be written as a combination of intervals in the following sense: for some function h : R >0 → R >0 with bounded support. (The exception is when k = 3, in which case g is just a single interval. But that will not affect the remainder of the proof of Claim 1.) To see why this is the case, we may use induction. If k = 4, then suppose without loss of generality that t 3 t 4 . Then, we take h(r) = t 3 t 4 if , and 0 otherwise. For k > 4, it is easiest to apply the induction hypothesis to I t −1 3 * · · · * I t −1 k−1 , and then use a similar decomposition to the one we used for the k = 4 case. We omit the details.
In view of this decomposition, proving Claim 1 may be reduced to the following claim: Then, for any choice of t, we have that t 1 t 2 (I t −1 In fact, the easiest way to prove Claim 2 is via the following explicit formula for (I a * I b * I c )(0): assuming that c a, b without loss of generality. Given (4.9), we can prove that Θ(a, b, c) is a concave function. If, for instance, c −1 > a −1 + b −1 , then Θ(a, b, c) = c which is clearly concave. When a −1 , b −1 and c −1 satisfy the triangle inequality, then We may prove that this is concave by computing the Hessian matrix and showing that it is non-positive-definite everywhere; for instance, by using Sylvester's Rule. We omit the details. In particular, tΘ(t 1 , t 2 , t −1 ) = t 1 t 2 (I t −1 is concave as a function of t 1 and t 2 . Therefore, which is exactly the statement of Claim 2. This completes the proof of Claim 1, and thus Lemma 4.7.
Armed with our more general Lemmas 4.6 and 4.7, we may use an argument similar to the proof of Theorem 1.4 in Section 3 in order to prove Theorem 4.5.
To see why, observe that if X i + X j is kept fixed, moving X i and X j closer together increases the value of the left-hand side without changing the right-hand side. Thus, the left-hand side is maximised when the X i are all the same, at which point equality occurs.
Putting all of this together, we learn that which gives the bound in the statement of Theorem 4.5 when |S| is large enough.
Systems of more than one equation
Another way in which one might wish to extend Theorem 1.4 is to ask if a similar result holds for systems of m equations in k variables. One might imagine that a result of the following form ought to hold.
Question. Suppose k m + 2 and m 1. Does there exist an explicit positive constant σ m,k with the following properties. • For any ε > 0, there are systems such that the number of k-tuples satisfying A in any large S ⊆ Z is no more than (σ m,k + ε)|S| k−m .
Thus, Theorems 1.4 and 4.5 tell us that σ m,k exists whenever m = 1, and that σ 1,k = σ k . However, it turns out that when m > 1, not even the first of these has a positive answer, in the following sense.
Theorem 5.1. Let ε > 0. Then, there exists a non-degenerate system of two equations in four variables with the property that for any large enough S, there are no more than ε|S| 2 solutions to the system in S.
Remark. It is easy to see that Theorem 5.1 implies the analogous result for any choice of k, m with k m + 2 and m > 1.
The goal of this section is to prove Theorem 5.1.
Proof. We will prove Theorem 5.1 for the following system: where M is a sufficiently large constant (in terms of ε) to be chosen later. We will start by borrowing the following lemma, which appears as part of the proof of the Balog-Szemerédi-Gowers theorem.
Lemma 5.2 [14,Corollary 6.20]. Let G be a bipartite graph with vertex sets A and B and edge set E ⊆ A × B. Suppose |E| ε|A||B|, for some ε > 0. Then, we can find subsets A ⊆ A and B ⊆ B, with |A | ε |A| and |B | ε |B|, such that, whenever a ∈ A and b ∈ B , there are ε |A||B| paths of length 3 from a to b in G.
Let S be a sufficiently large set (in terms of M and ε), and suppose that there are more than ε|S| 2 solutions to (5.1) in S. Consider the bipartite graph on vertex set A B, where A = B = S; that is, both parts of G are S. Draw an edge from a to b if and only if there is a solution to (5.1) with x = a and y = b; in other words, if a + b and a + Mb are both in S. In particular, G has at least ε|S| 2 edges.
We may immediately apply Lemma 5.2 to G. This gives us sets A ⊆ A and B ⊆ B such that, for any a ∈ A and b ∈ B , there are ε |S| 2 paths of length 3 in G from a to b.
Claim. These sets A and B satisfy |A + B | ε |S| and |A + M · B | ε |S|.
Proof of Claim. To prove this claim, we can use an argument similar to that used in the proof of the Balog-Szemerédi-Gowers theorem. Showing that |A + B | ε |S| and |A + M · B | ε |S| are similar, so we will only do the former.
Let X denote the set of triples (x, y, z) of elements of (A + B) ∩ S, for which x − y + z ∈ A + B . We may trivially upper bound |X|; indeed, |(A + B) ∩ S| |S|, so |X| |S| 3 .
For a lower bound on |X|, consider an element a + b of A + B . By definition, there are ε |S| 2 paths of length 3 from a to b in G. Each such path may be written a ∼ b , a ∼ b , a ∼ b for some a ∈ A, b ∈ B. In other words, a + b , a + b and a + b are all in S. Now, (a + b ) − (a + b ) + (a + b) = (a + b), so we have located a triple x, y, z ∈ (A + B) ∩ S with x − y + z = a + b. These triples will be different for different paths, and so there must be ε |S| 2 such triples.
There are |A + B | elements of A + B , each of which gives ε |S| 2 triples x, y, z. Thus, we have that |A + B ||S| 2 ε |S| 3 , and thus |A + B | ε |S|, as required.
Let us now see how we may use this claim to complete the proof of Theorem 5.1. Lemma 2.4 immediately tells us that |B − M · B | ε |S|, and thus that |B − M · B | ε |B |. This contradicts Theorem 2.7, provided that M is sufficiently large. | 9,214.8 | 2018-01-22T00:00:00.000 | [
"Mathematics"
] |
Leishmania braziliensis isolated from disseminated leishmaniasis patients downmodulate neutrophil function
Summary Aims The polymorphism observed in Leishmania braziliensis is associated with different clinical forms of leishmaniasis. Neutrophils (PMNs) participate in the pathogenesis of leishmania infection, and here, we evaluate neutrophil function after infection with isolates of L. braziliensis from cutaneous leishmaniasis (CL) or disseminated leishmaniasis (DL) patients. Methods and results Neutrophils from 30 healthy subjects (HS) were infected with isolates of L. (V.) braziliensis obtained from three CL and three DL patients. They were infected at the ratio of 3:1 parasites per neutrophil, and leishmania uptake was evaluated by microscopy. The neutrophil activation markers and oxidative burst by expression of dihidrorhodamine (DHR) were evaluated by flow cytometry and cytokine production by ELISA. The frequency of infected cells and the number of amastigotes were higher in neutrophils infected with CL isolates compared to DL isolates (P < 0.05). The DHR and CD66b expression after infection with DL isolate was lower than with CL isolates. There was no difference regarding chemokine production. Conclusion The L. (V.) braziliensis isolates of DL induced lower respiratory burst and neutrophils activation markers compared with CL isolates which may contribute to parasite survival and dissemination in DL patients.
| INTRODUC TI ON
The American tegumentary leishmaniasis (ATL) is caused predominantly by L. (V.) braziliensis, a parasite that is associated with different clinical forms of the disease as cutaneous, mucosal and disseminated cutaneous leishmaniasis (DL). 1,2 The cutaneous leishmaniasis (CL) is the most common presentation of the disease occurring in over 90% of the cases and is characterized by a well-limited skin ulcer with raised borders. Approximately 3% of CL patients develop concomitantly or months and sometimes years after the cutaneous disease, mucosal leishmaniasis (ML) that affect primarily the nasal mucosa. 3 DL is an emerging clinical form of ATL defined by the presence of ten up to more than 1000 acneiform, papular and ulcerated lesions in at least two parts of the body. 4 In the majority of the cases, DL patients present initially as a typical CL ulcer, and after 1 or 2 weeks or sometimes even during antimony therapy, patients suddenly develop multiple lesions over the body. There are several indicators of the relevance to study this atypical presentation of ATL. DL is an emergent form of leishmaniasis as its prevalence increased 20-fold from 1986 to 2012, 5 up to 40% of DL patients have ML 4,6 and the disease is associated with a high hate of failure to antimony therapy. 7 The pathogenesis of DL is not fully understood. Initial studies showed that DL patients have more negative leishmania skin delayed type hypersensitivity test (LST) and an impairment in lymphocyte proliferation and in the production of interferon-γ and TNF in supernatants of mononuclear cells stimulated with soluble leishmania antigen (SLA) as compared to CL patients. 8 However, more recently, we document that cell-mediated immune response at the lesion site of DL patients is similar to what is observed in CL ulcers. 6,9 We believe that there is no impairment in T-cell response in DL patients and raised the hypothesis that the poor T-cell response observed in cells from peripheral blood was due to the migration of the majority of to the antigen reactive cells to the great number of lesions observed in DL patients. 6 Moreover, these data suggest that parasite, more than host factors, may be involved in the pathogenesis of DL.
It is known that L. (V.) braziliensis is polymorphic and genotypic differences intraspecies of L. (V.) braziliensis are associated with different clinical forms of ATL. 10,11 Specifically, it has been shown that there are six haplotypes presented in four loci of the chromosome 28 of L. (V.) braziliensis that are associated with DL. 10 It has been also documented that some haplotypes in the chromosome 28 are also associated with failure to antimony therapy, indicating the importance of differences intraspecies not only in the presentation of the disease, but also in failure to therapy. 12,13 However, there is a lack of data about the biological behaviour of isolates from DL on phagocytic cells. Neutrophils migrate quickly to the sites of infection and are the main phagocytic cells in the initial phase of L. (V.) braziliensis infection. 14 Studies in experimental models of leishmaniasis have shown that interaction of neutrophils with macrophage may determine the control or progression of leishmania infection. 15 In humans, we have previously shown that neutrophils from CL produce higher levels of reactive oxygen species and pro-inflammatory cytokines than healthy subjects neutrophils upon L. (V.) braziliensis infection. 16 To determine whether the behaviour of L. (V.) braziliensis isolated from patients with DL differs from that observed with parasites from CL patients, we evaluate in the present study the ability of L. (V.) braziliensis isolates from DL and CL patients to penetrate or be up-taken by neutrophils from healthy subjects, as well as whether the genotypic differences among these isolates would influence the neutrophil activation and leishmania killing.
| Subjects
Venous blood was obtained from 30 healthy volunteers from a nonendemic area of leishmaniasis. They denied previous history of leishmaniasis, and none of them have a scar of CL. The group was composed of 17 males and 13 females, and the mean age was 27 ± 12 years. The participants did not have previous contact with Leishmania, and they did not present other infectious diseases and denied symptoms of viral infections and fever at the time of peripheral blood sample collection. The study was approved by Institutional Review Boards (IRBs) of the Federal University of Bahia (Ethical Committee), and informed consent was obtained from all participants.
| Isolation of human peripheral blood neutrophils
Peripheral blood was collected in EDTA, and cells were isolated
| Neutrophils infection
The isolates of 03 CL and 03 DL patients were used to infect PMNs
| Assessment of respiratory burst of neutrophils
The production of reactive oxygen species (
| Evaluation of CXCL8 and CXCL9 production
The supernatants of uninfected neutrophils, cells infected with different L. (V.) braziliensis isolates or stimulated with ionomycin/ PMA were obtained after 90 minutes and frozen at −20°C. The production of CXCL8 and CXCL9 was measured by enzymatic immune assay (ELISA) (R&D Systems, Minneapolis, MN, USA) according to the manufacturer's instructions.
| Statistical analysis
The Friedman's test was used to analyse the frequency of infected neutrophils as well as the parasite burden, obtained by count of two independent blind analysers. The frequency of cells expressing activation molecules (CD62L and CD66b) and the mean fluorescence intensity (MFI) were analysed by Kruskal-Wallis followed by Dunn's post-test. These tests were also used to evaluate the expression of DHR on CD15 + cells and IL-8 production. Analyses were performed using Prism GraphPad software. The P-value of <0.05 was considered significant.
| Frequency of infected Neutrophils and parasite load after infection with different isolates of L. (V.) braziliensis
The Figure 1A
| Reactive oxidants production by infected neutrophils with different L. (V.) braziliensis isolates
We also evaluated the capacity of different isolates of L. (V.) braziliensis to trigger oxidant production in neutrophils.
Fluorescence of DHR-123, an indicator of the abundance of cellular reactive oxidants, was measured by flow cytometry. The Figure 2 presents the MIF of CD15 + DHR + uninfected cells (medium) and
| Neutrophils activation induced by L. (V.) braziliensis infection
The CD62L and CD66b expressions are widely used to detect neutrophil activation. CD62L is an integrin shed from neutrophil Figure 2A shows the MIF of CD62L on uninfected and infected neutrophils. Ionomycin plus PMA was used as positive control. There was no difference in the intensity of fluorescence expression of CD62L between neutrophils infected with DL isolate or CL isolate ( Figure 2B). However, the frequency of CD15 + CD62L + cells was higher on neutrophils infected with DL isolate (38 ± 16%) than that observed with CL isolates (19 ± 14%), P ≤ 0.05.
CD66b is neutrophil granule membrane proteins that migrate in the surface membrane upon granule exocytosis. 22 Neutrophils infected with DL isolates expressed less CD66b on cells surface than neutrophils infected with CL isolate, P ≤ 0.001 ( Figure 3C).
| IL-8 and CXCL9 production by PMNs after infection with different L. (V.) braziliensis isolates
The DL or CL patients (P > 0.05). Production of CXCL-9 was lower than IL-8 but follows the same pattern with no difference in supernatants of cells infected with DL or CL isolates (data not shown). There was no difference between IL-8 ( Figure 4A) and CXCL-9 ( Figure 4B) production in cultures infected with CL or DL isolates production of these cytokines were high and similar was observed in cells stimulated with Ion/PMA.
| D ISCUSS I ON
DL is an emerging and severe form of L. (V.) braziliensis infection associated with a high rate of ML and failure to antimony therapy. 4,7 Substantial variability among the leishmania at the subgenus level has been described, and there are evidences that genotypic differences intraspecies may influence the presentation of the disease 10 and response to therapy. 13 The phagocyted microbes are destroyed by oxidative and nonoxidative mechanisms inside the neutrophils cytoplasm. The uptake of microbes induces the oxidative burst, increases reactive oxygen species (ROS) production and this leads to parasites clearance. 27,28 Monocytes produce ROS after exposure to L. (V.) braziliensis, and in this cell, ROS contribute to control parasite multiplication. 29,30 In contrast to monocytes, the ROS generated by infected neutrophils prevents parasite multiplication but did not decrease the number of intracellular amastigotes. 16 This may explain why despite the previous study showed that the use of EDTA rather than heparin or citrate decreases neutrophil activation after stimulation with PMA. 31 However, as in all experiments of our study, EDTA was used the differences observed were related in the source of L. braziliensis isolates rather than methodological aspects.
Following infection or exposure to PMA neutrophils increases the CD66b expression and decreases CD62L expression, surface markers indicative of an activated phenotype. 19,20 The CD66b expression indicates exocytosis from specific granules, and the decreased expression of CD62L is indicative of an increased ability of the cell to migrate out of the circulation. 21 We have previously shown that neutrophils from both CL and HS infected with an isolate of L. (V.) braziliensis obtained from a CL patient are similarly activated. 16 Here, we showed that neutrophils infected with a DL isolate expressed less CD66b than cells infected with CL isolates.
While we cannot ruled out that the lower number of intracellular parasites observed in neutrophils infected with DL isolates may have influenced a decreasing in the expression of neutrophils activation markers and in the oxidative burst, these data clearly indicate that genotypic differences among L. (V.) braziliensis isolates modify neutrophil function.
The CD66b is endogenous in specific granules, and its increased appearance on the neutrophils surface indicates exocytosis from specific granules. 19 The release of proteolytic enzymes, defences and myeloperoxidase from intracellular granules into phagosomes independently cooperates with neutrophil function to enhance microbicidal activity. 14,32 Our observation that isolates from DL induced less CD66b expression on PMN than isolates from CL indicates that parasites from DL decrease the release of granules decreasing neutrophil function. The CD62L is a homing receptor that is cleaved from neutrophils surface upon activation, and its loss facilitates cell migration out of the circulation. 21 Neutrophils are the first cell to arrive in the leish- Neutrophils produce a variety of cytokines and chemokines including IL-12, CXCL-8, CXCL-9, CXCL-10, CCL-3, CCL-4, IL-23 and IFN-γ. 33 We have previously shown that neutrophils from CL patients upon L. (V.) braziliensis infection produce more CXCL-8 and CXCL-9 than neutrophils from HS. 16 Here using HS neutrophil, we observed that IL-8 and CXCL-9 production did not differ in super- show that isolates from DL behaved differently than CL isolates in neutrophils. This find gives support to the hypothesis that genotypically different isolates of the same leishmania species induce different immune responses which may influence disease expression.
ACK N OWLED G M ENTS
We thank Dr. Ricardo Oliveira and Dr. Luciana Cardoso for their support in the development of this work, and Cristiano Franco for his assistance in the preparation of the manuscript.
D I SCLOS U R E S
All authors of this manuscript deny any conflict of interest.
DATA AVA I L A B I L I T Y
The data that support the findings of this study are openly available | 2,895.2 | 2019-04-14T00:00:00.000 | [
"Medicine",
"Biology"
] |
Workshop on challenges, insights, and future directions for mouse and humanized models in cancer immunology and immunotherapy: a report from the associated programs of the 2016 annual meeting for the Society for Immunotherapy of cancer
Understanding how murine models can elucidate the mechanisms underlying antitumor immune responses and advance immune-based drug development is essential to advancing the field of cancer immunotherapy. The Society for Immunotherapy of Cancer (SITC) convened a workshop titled, “Challenges, Insights, and Future Directions for Mouse and Humanized Models in Cancer Immunology and Immunotherapy” as part of the SITC 31st Annual Meeting and Associated Programs on November 10, 2016 in National Harbor, MD. The workshop focused on key issues in optimizing models for cancer immunotherapy research, with discussions on the strengths and weaknesses of current models, approaches to improve the predictive value of mouse models, and advances in cancer modeling that are anticipated in the near future. This full-day program provided an introduction to the most common immunocompetent and humanized models used in cancer immunology and immunotherapy research, and addressed the use of models to evaluate immune-targeting therapies. Here, we summarize the workshop presentations and subsequent panel discussion.
Introduction
Translating preclinical findings into meaningful clinical outcomes can be a costly and inefficient process, as evidenced by the fact that approximately 85% of oncology drugs to enter clinical testing fail to gain approval by the U.S. Food and Drug Administration (FDA) [1]. There is a pressing need to develop preclinical models that will accurately predict efficacy and toxicity prior to inhuman clinical testing. In order to advance understanding of the current status and future directions of mouse and humanized models used in cancer immunology and immunotherapy research, SITC held a workshop as a part of the SITC 31st Annual Meeting and Associated Programs on November 10, 2016. This workshop provided an overview of current models used in the field, with a focus on accurately modeling the tumor microenvironment (TME), as well as the use of murine models to evaluate the efficacy and toxicities of immunetargeting therapies. The program concluded with an open panel discussion driven by questions from the audience.
Meeting report
Introduction to models of immunotherapy Major questions related to immunotherapies that require models to address Mario Sznol, MD (Yale School of Medicine) opened the session with a presentation on clinical issues with immune-based approaches that will require preclinical models to address. In his presentation, Dr. Sznol summarized the factors that contribute to development of cancer and can later determine the response to therapy, including host genetics, lifetime environmental exposures, T cell receptor (TCR) repertoire, carcinogenesis, and evolution of the tumor and tumor-host immune relationship.
Inhibition of the PD-1/PD-L1 pathway has shown broad clinical activity across a variety of malignancies. However, only a portion of patients respond to anti-PD-1/L1 therapies, and appropriate animal models are needed to identify additional targets in order to increase response rates. The need to better understand the biology of response and the effect of the TME is evident in the large number of trials recently initiated to test combination approaches in unselected patient populations. Dr. Sznol highlighted areas for future investigation, including the need to identify the antigens recognized by antitumor T cells, understand mechanisms governing T cell infiltration into tumors, define the influence of tumor biology on antitumor immune response, and determine whether other immune cells (e.g., natural killer [NK] cells, NK T cells, B cells, etc.), inhibitory pathways, or antibodies are capable of eliciting an antitumor response. Dr. Sznol concluded by presenting an ideal scenario in which tumor types would be matched to a specific animal model in order to investigate clinical efficacy and predict the toxicity of novel therapeutic interventions.
Overview of mouse-mouse models Marcus Bosenberg, MD, PhD (Yale School of Medicine) presented an overview of immunocompetent mouse-inmouse models used in cancer immunotherapy research, including genetically engineered mouse models (GEMMs), chemically induced models, and syngeneic graft models. He highlighted the types of currently available models, their utility, the strengths and weaknesses of each model, and ways to improve upon current systems (Table 1). In doing so, Dr. Bosenberg emphasized that models can be used both to understand the basic biology of the immune system and to test novel immunotherapies in predictive models. Both aspects will be important to drive the field forward; however, developing reliable models to predict clinical outcome in humans may be more difficult.
Dr. Bosenberg also highlighted work from his group on the development of a variety of Yale University Mouse Melanoma (YUMM) syngeneic cell lines that exhibit high somatic mutational burden [2], some of which will be available from American Type Culture Collection (ATCC) within the next few months. One of the lines, YUMMER1.7 (YUMM Exposed to Radiation), has been shown to regress after a brief period of growth in a wild type (WT) C57BL/6 background. This regression can be overcome by injecting high numbers of YUMMER1.7 cells, although previously injected mice develop CD4 + − and CD8 + −dependent immunity against higher doses of tumor challenge [3]. Moreover, tumors generated from the YUMMER1.7 line are titratable and respond to immune checkpoint inhibition. Dr. Bosenberg concluded by reviewing pathological features of the melanoma tumors in these models, including early myeloid infiltration, T cell infiltration at day 7, immune mediated killing at day 8, and tumor regression versus escape by days 15-18.
Overview of humanized mice models
Karolina Palucka, MD, PhD (The Jackson Laboratory for Genomic Medicine) began her presentation by providing an overview of the approaches used to generate humanized mice, including adoptive transfer of human immune cells, transplantation of human hematopoietic cells with or without accessory tissues in pre-conditioned immunodeficient hosts, genetic editing of immunodeficient hosts, and genetic editing of immunocompetent mice. Dr. Palucka summarized her group's work on first generation Onco-Humice, in which human T cells were transplanted into NOD/SCID β2-microglobulin-deficient mice. In this model, breast cancer cells grew rapidly despite the presence of tumor infiltrating lymphocytes (TIL). These experiments led to a model describing the tumor-promoting inflammation observed in breast cancer in which Th2 polarization contributes to the inhibition of an antitumor CD8+ T cell response. Dr. Palucka highlighted complications of this model including the eventual development of graft-versus-host disease (GVHD).
Dr. Palucka presented examples of progress in the field utilizing humanized mice with host modifications, including MISTRG mice [4], MISTRG6 [5], NSG with mutant KIT [6], BAFF for antibody immunity [7], NSG-SGM3 with CSF1-tg for macrophages and IL2-tg for NK cells [8], NSG-FcRg knock-out for intravenous IgG therapy [9], and next generation humanized mice from the Jackson Laboratory [10]. She concluded by outlining current challenges, including considerations for modeling the mouse and thymic environment as well as human T cell maturation and selection. Finally, Dr. Palucka identified practical considerations for making autologous humanized mice, sourcing hematopoietic progenitor cells (e.g., bone marrow, blood, cord blood, induced pluripotent stem cells), and finally accommodating for variations in diverse host microbiomes.
Overview of patient-derived Xenograft models
Andrew Zloza, MD, PhD (Rutgers Cancer Institute of New Jersey) concluded the first session with an overview of patient-derived xenograft (PDX) models, which are subsets of humanized mice with patient engraftments that have been used in models of infectious disease, transplant, GVHD models, and cancer. The PDX models used for cancer research are created by transferring dissociated single cells from patient biopsies into immunodeficient mice. Over time, these tumors grow into patient-derived tumors. The advantage of the PDX model system over cell line-derived tumor models is the ability to model diverse tumor types directly from patients and potential retention of non-tumor cells from the human TME [11]. Tumors can also be fragmented instead of dissociated, and surgically transplanted into mice, resulting in rapid tumor growth (vessels will start to infiltrate within 48-72 h). Using this method, realtime testing of therapeutic interventions could be used to inform clinical decisions, although there are advantages and disadvantages when using both fragmentation and dissociation methods to generate PDX models ( Table 2).
Among the benefits of utilizing PDX models is the ability to study metastasis [12,13]. In addition, tumors engrafted in the original PDX models can be expanded and passaged into subsequent generations of mice. However, the resulting tumors lose some aspects of the original patient tumor characteristics with each generation [12,13]. PDX models have also been shown to model patient's disease course with respect to local and distant metastases as well as overall patient outcomes, illustrating the prognostic value of these models [12,14]. Of note, there are a variety of organizations that are offering PDX models commercially [15]. Concluding with the future of PDX models, Dr. Zloza highlighted the potential for creating double-humanized mice by engrafting both the patient's tumor and peripheral blood immune cells.
In studies using this combination approach, these models lead to good immune reconstitution and maintain proportions of immune cell populations that reflect that of the patients from which the models are derived. Thus, this technique offers an exciting avenue to directly model the human immune system and the TME.
Session II: Modeling the tumor microenvironment Evaluation of the tumor microenvironment
The second session of the workshop opened with a presentation by Mark B. Headley, PhD (University of California, San Francisco) that focused on modeling the TME. Dr. Headley began by describing the TME as a complex network of cells (tumor cells, immune cells, fibroblasts, endothelium, etc.) that cross-communicate and modulate the antitumor immune response. Notably, the TME differs by cancer type, patient, lesion, and can even vary within the same lesion. Since immune cells in the TME can support or inhibit tumor growth and survival, an understanding of the TME composition and function of these cells provides important diagnostic and prognostic information. For example, tumor-associated macrophages (TAM) are typically pro-proliferation, proangiogenic, pro-metastatic, and immunosuppressive. In contrast, NK cells, conventional CD103+ DC, and effector CD8+ T cells, which also populate the TME, act in an antitumor capacity to protect the host from cancer. Neutrophils can be viewed as having both pro-and antitumor functions. Dr. Headley then presented an overview focusing on the mechanisms that balance the pro-and antitumoral functions of myeloid cell populations [16]. Investigations of primary murine and human tumors revealed a combination of macrophage and DC populations within the TME that arise from distinct cell lineages [17]. These results were used to identify a high-DC gene signature that correlated with better patient outcomes [17]. Intravital imaging illustrated conventional DC-CD8+ T cell interactions in the metastatic and primary tumor draining lymph nodes (LN), and elimination of conventional DC in murine models resulted in increased tumor growth, metastasis, and reduced survival. In both primary and metastatic tumors, conventional DC (likely CD103+) set an equilibrium with macrophages, restricting overall tumor growth and metastasis through activation of CD8 + T cells [18]. Dr. Headley concluded by emphasizing that the analysis of cell populations within the TME can yield critical knowledge of the functions of these distinct cell populations and provide prognostic insight into human disease.
Factors affecting tumor -Microenvironment interactions
Historically, mesothelioma is chemotherapy resistant and recent therapeutic advancements have demonstrated only modest improvements in OS compared with previous therapies [19]. Highlighting work from her laboratory on the biology of the TME in the setting of mesothelioma, Lisa M. Coussens, PhD (Oregon Health and Sciences University) described the complexity of the TME, which is typically skewed to a Th2-prosurvial, proinflammatory, pro-angiogenic, profibrotic, immunosuppressive microenvironment that can impede drug delivery and limit response to therapy. Investigations into the cellular composition of human mesothelioma have shown that macrophages are the major immune cell infiltrate present, regardless of the type of chemotherapy or type of mesothelioma [20]. Utilizing multiplex immunohistochemistry, it was found that chemotherapy induces infiltration of CD206+ macrophages that are associated with a Th2/M2 phenotype.
Dr. Coussens' group used syngeneic mouse models of mesothelioma to determine whether macrophages are a valid therapeutic target in this setting. In light of the fact that the colony-stimulating factor receptor axis (CSF1/ CSF1R) is predominantly expressed by macrophages and is required for macrophage maturation [21], and that CSFR1 blockade depleted 50% of macrophages in mice with late-stage disease, the group started by inhibiting the CSF1/CSF1R axis. As monotherapy, reductions in macrophages did not decrease tumor burden or increase survival in the mice. Similarly, although the combination of chemotherapy and CSF1R blockade improved cellular apoptosis, led to an influx of CD8+ T cells, and a 50% reduction in primary tumor burden, these effects did not result in increased survival. Instead, lung metastases were resistant to therapy and although the combination successfully depleted macrophages that were recruited to the lungs, there was no recruitment of CD8+ T cells to the metastases. The addition of a PD-L1 inhibitor to the combination controlled the lung metastases and significantly improved survival compared with combination therapy alone. Dr. Coussens concluded by emphasizing that appropriate modeling is essential to the development of rational combination approaches.
Vascular regulation of the tumor microenvironment and immune responses
Amanda Lund, PhD (Oregon Health & Science University) presented work on the role of vascular regulation at the interface of a developing malignancy and the systemic immune response. The vasculature coordinates the trafficking of leukocytes as they become activated and re-enter the site of inflammation to mediate effector functions. However, tumor-associated vasculature is hyperplastic and dysfunctional: it maintains the fluid dynamics of tissue, which can regulate hypoxia, impact drug delivery, and can act as a route of metastasis. These functions are regulated by members of the vascular endothelial growth factor receptor (VEGFR) family that drive the migration, proliferation, and integrity of endothelial cells. Importantly, the endothelial phenotype in T cell inflamed and non-inflamed tumors has been shown to directly inhibit lymphocytes from infiltrating tumors [22]. Thus, reevaluation of the anatomy or the vasculature may provide insights into the barriers encountered by T cell-mediated antitumor immunity, and inspire novel immunotherapeutic approaches to overcome these. Murine models have proved useful in clarifying the role of the vasculature during an immune response, and lymphatic vessels in particular were found to be necessary for de novo antitumor immunity in an implantable murine melanoma model [23,24]. Inhibition of VEGF-C/D and absence of dermal lymphatic vessels impaired inflammatory carcinogenesis [25], whereas VEGF-C overexpression in the TME drove lymphangiogenesis and regional immunosuppression [24]. Thus, while necessary for immunity, lymphatic function may also lead to immune dysfunction and suppression when activated in an aberrant manner. Flow cytometry was used to examine both the blood and lymphatic endothelial cells in order to understand this complex dependency. Using this method, it was found that tumor associated lymphatic vessels respond to the changing immunologic context within tumor microenvironments and express various regulatory and adhesion molecules that may influence CD8+ T cell responses. Interactions between inflamed, cutaneous lymphatic vessels and egressing lymphocytes may represent a novel point of immune control. Targeting these barriers may, in combination with immunotherapy, drive immune cell priming, infiltration, retention, and function.
Components of the tumor microenvironment that modulate tumor immune responses
Kwok-Kin Wong, MD, PhD (Dana-Farber Cancer Institute, Harvard Medical School) presented work using conditional mouse lung cancer models using intranasal Cre recombinase adenovirus to modulate tumor-relevant genes at specific times, resulting in lung cancer induction with almost complete penetrance. He explained that low mutational load and the low-throughput nature represent limitations of this approach. In the EGFR/KRAS model, PD-1 blockade decreases factors in the TME that are immunosuppressive for these EGFR-driven tumors [26]. In addition, long-term PD-1 blockade results in increased progression-free survival and OS in this model. Unlike humans, these mice develop resistance to PD-1 blockade, which provides the opportunity to investigate changes in the TME that influence mechanisms of resistance.
Dr. Wong presented several approaches to increase the mutational load in next generation GEMMs, to increase their utility in studying the antitumor immune response. In the first approach, KRAS/p53-, KRAS/p53/ LKB1-, and EGFR/p53-deficient transplantable cell lines were exposed to irradiation or a carcinogen, or were combined with DNA damage response (DDR) gene inactivation in vitro. These cells were then transplanted orthotopically to study alterations in the immune response. In another technique, an organotypic culture was developed to test combination therapies in a highthroughput fashion [27]. Lung nodules from GEMMs were extracted and seeded into three-dimensional (3D) microfluidics chambers to grow spheres containing malignant cells as well as immune cell populations [28,29]. This technique allows for a variety of parameters to be measured. Once established in culture, light microscopy can be used to track growth, cytokine analyses can be performed, and fluorescence or confocal microscopy can be used to view cellular interactions in real-time. Moreover, this technique can be performed for murinederived as well as patient-derived tumor spheres. These data indicate that organotypic tumor spheroids derived from murine models can be used in a high-throughput manner to study the TME and correlate with treatment outcomes in patients.
Session III: Modeling evaluation of immune therapies Evaluation of immune checkpoint inhibitors in mice
Arlene H. Sharpe, MD, PhD (Harvard Medical School) presented work evaluating immune checkpoint therapies in mouse models. Dr. Sharpe opened her presentation with an overview of the PD-1 pathway, noting that activation of the PD-1 receptor leads to downstream signaling that results in reduced TCR signaling, cytokine production, and target cell lysis [30]. PD-L1 can be expressed on a wide variety of hematopoietic cells, nonhematopoietic cells, and tumor cells in the TME. The function of PD-L1 on tumor cells is not clear; it may reflect an inflamed tumor environment and/or contribute to immunosuppression [31]. To investigate the function of PD-L1 on MC38 tumors, PD-L1 was deleted on MC38 tumor cells and the growth of PD-L1-expressing and PD-L1-deficient tumors was comparable. However, deletion of PD-L1 in MC38 tumors increased susceptibility to clearance. These results were further validated in a mixed competition assay in which PD-L1-sufficient tumor cells were transplanted alongside PD-L1-deficient tumor cells. In these experiments, the tumor cells lacking PD-L1 were selectively eliminated. Thus, PD-L1 on tumor cells has a dominant role in limiting antitumor immunity to MC38 tumors. However, the role of PD-L1 expression on tumors is tumor-dependent. Analogous studies of PD-L1-deleted Brafv600 PTEN-deficient tumors and B16 tumors revealed that PD-L1 expression on host cells has dominant role in limiting immune responses to these tumors. The dominance of PD-L1 on tumors may be influenced in part by the immunogenicity of the tumor.
Re-evaluating the role of IDO1 in brain cancer; humanized Immunocompetent mice take center stage Derek A. Wainwright, PhD (Robert H. Lurie Comprehensive Cancer Center at Northwestern University Feinberg School of Medicine) opened his presentation with an overview of glioblastoma multiforme (GBM), noting that these central nervous system (CNS) tumors are universally fatal and their diffuse nature, heterogeneity, and resistance to cytotoxic monotherapy all contribute to the challenges associated with treatment. Since T cells can infiltrate the CNS, a phenomenon commonly seen in primary glioblastoma [32], Dr. Wainwright's laboratory utilizes murine models to approximate this aspect of the disease. The most common model for glioblastoma is the syngeneic GL261 orthotopic mouse glioblastoma model in which GL261 glioblastoma cells are stereotactically implanted intracranially. In this model, there is a progressive increase in Treg from one to three weeks during tumor development [33]. However, when B16-F10 cells were used in this model, there was no increase in Treg, indicating that tumor-intrinsic mechanisms drive this infiltration [34]. This finding underscores the significance of Treg in glioblastoma and is functionally validated by increased survival in mice with intracranial glioblastoma and neutralized for Treg infiltrates [33]. Indoleamine 2,3 dioxygenase 1 (IDO1) is an IFNinducible enzyme that converts tryptophan to kynurenine and has been shown to suppress effector T cell functions and activate and expand Treg [35][36][37][38][39][40]. The depletion of tryptophan and/or accumulation of kynurenine leads to functional inactivation of CD8+ T cells and/or induction of Treg [41]. In the GL261 model, a substantial increase in survival is seen when mice are intracranially-engrafted GL261 cells stably knocked down for IDO1 expression. This survival advantage is also observed when GL261 cells are injected into mice with a systemic IDO1 deficiency. However, the survival advantage is abrogated when implanted into T celldeficient mice, highlighting the dual importance of tumor cell IDO1 inhibition, in addition to the presence of an intact immune system for eliciting effective tumor rejection [42]. In humans, high IDO1 mRNA levels are prognostic for decreased GBM patient survival. Notably, increased levels of CD3ε/CD8α mRNA correlate with higher IDO mRNA, suggesting that the presence of T cells regulates IDO1 expression. In the syngeneic mouse model using GL261 cells, simultaneous treatment with standard of care radiotherapy, as well as PD-1 and IDO-1 blockade, synergistically increased survival, durably. Extrapolating these findings to the clinical arena, Dr. Wainwright proposes a combinatorial therapy consisting of radiotherapy plus checkpoint blockade and IDO-1 inhibition for the treatment of adults diagnosed with incurable GBM.
Developing new immunotherapies in preclinical models and humans
Elizabeth M. Jaffee, MD (The Sidney Kimmel Comprehensive Cancer Center at Johns Hopkins University) addressed ways to accelerate the development of immunotherapy for resistant or immunologically inert tumors. There are several challenges in treating malignancies that do not respond to current immune checkpoint therapy. First, methods to induce functional effector T cell recruitment must be developed. Each cancer and cancer subtype may have a unique TME, illustrating the need to understand immunosuppressive mechanisms that have a clinical impact. Another characteristic that can indicate a lack of response to immune checkpoint inhibitor therapy is a paucity of effector T cells. In contrast to melanoma, which shows spontaneous infiltration of CD8+ T cells, pancreatic cancers are infiltrated with suppressive Treg and myeloid-derived suppressor cells (MDSC). Combination approaches to address these challenges will require novel trial designs and clinical development pathways to gain regulatory approval by the FDA.
Dr. Jaffee proposed a two-step process for the effective treatment of currently immunotherapy-unresponsive tumors: reprogramming the TME and optimizing the immunotherapeutic modality to generate a lasting antitumor response. Efforts to reprogram the TME should focus on improving tumor antigen presentation and abrogating local immunosuppression [43]. Using work from her group to illustrate these ideas, Dr. Jaffee described a study using the whole tumor cell vaccine, GVAX, in the neoadjuvant and adjuvant setting. In this study, GVAX was given two weeks prior to surgery. Following surgery, the patients went on to receive adjuvant chemotherapy. Two weeks after a single vaccine treatment, biopsies from 85% of patients had peri-and intratumoral lymphoid aggregates with features reminiscent of tertiary lymphoid structures. Upregulation of PD-1 was noted in the macrophage and dendritic cell populations within the lymphoid aggregates, which led to an ongoing trial of neoadjuvant GVAX with or without PD-1 inhibition. The potential for personalized immune checkpoint inhibitor therapy based on individual patient expression of immune checkpoints was also raised.
What information provided by models will inform immune drug development and use?
Philip Gotwals, PhD (Novartis Institutes for BioMedical Research, Inc.) provided an industry perspective on information gained from models that help direct drug development and optimize current therapies. Questions to be addressed through basic and translational research include patient selection based on knowledge of resistance and biomarkers, determining optimal therapeutics for a given cancer type, and defining appropriate dosing, sequencing, and combinations of therapy. According to Dr. Gotwals, all the models discussed in this workshop could answer such questions; the difficulty is that there are too few models specific to cancer immunotherapy, and limited availability compared to the large libraries of patient-derived xenograft (PDX) models developed to test targeted genetic mutations.
Dr. Gotwals went on to present work from a few ongoing Novartis initiatives, including chimeric antigen receptor (CAR)-T cell approaches targeting TIM-3 and exploiting the effects of signaling through the stimulator of interferon genes (STING) pathway. The STING study focused on use of syngeneic models to study the antitumor immune effects of activating dendritic cells using STING agonists. ADU-S100, a potent cyclic dinucleotide STING agonist, has been shown to induce an abscopal effect and establish immunological memory in a dual flank model using B16 melanoma cells [44]. Combination approaches have also been used in this setting to illustrate that the abscopal efficacy of ADU-S100 combined with immune checkpoint inhibition is dependent on CD8+ T cells. Currently in phase I to assess the pharmacodynamic effects of ADU-S100 in injected as well as distal lesions, these clinical trials are designed to inform further testing in syngeneic models.
Session IV: Panel discussion and future directions Future directions for the development and use of cancer immune models The panel discussion, moderated by Dr. Bosenberg, included all Workshop presenters and was driven by questions from the audience. Highlights included a discussion on the need for paired pretreatment and biopsies while patients are on treatment and responding in order to get a better understand of the mechanisms underlying response. The preference for multiple biopsies in clinical trials was expressed; however, multiple biopsies can raise ethical concerns in addition to considerations of patient compliance and safety. As an alternative to multiple tumor biopsies, patient-derived peripheral blood mononuclear cells (PBMC) could be used in PDX models generated from patient's tumors. The use of models to predict the timing and sequencing of combination approaches was also discussed, as limitations initially attributed to models may actually be the result of improper sequencing and/or dosing of therapies. Finally, the panel addressed questions regarding the use of models to develop treatments for immunologically inert tumors in which tumor-specific T cells may be present but non-functional. Models are necessary to determine the underlying mechanisms behind this phenomenon, which will be key to developing therapies to treat these diseases.
Conclusions
Dr. Bosenberg offered concluding remarks and summarized the main themes from the day. Syngeneic models are cost-effective and easy to use; however, GEMM may better approximate the TME and vascular architecture, but tend to have low neoepitope/mutation burden. Advances in humanized mouse models are rapidly progressing, and with time, will hopefully bridge the gap between mouse-in-mouse models and clinical experience. The unique milieu of the TME can have a significant impact on response to therapy via suppressive mechanisms that are not yet entirely understood. Highlighting the diversity and promise of the types of models presented, Dr. Bosenberg emphasized that reliable pre-clinical models will be essential to understanding mechanisms of response as well as resistance to immunotherapy. Although each model has strengths and weaknesses, advances in modeling the dynamic interaction between the immune system and cancer will be critical to advances in the field, particularly in the development of rational combination approaches. | 6,130.6 | 2017-09-19T00:00:00.000 | [
"Biology",
"Medicine"
] |
Thread milling errors
The study shows that thread milling (including internal threads) is one of the most forward-looking technologies that offers max thread cutting performance. The reasons are the shortest cut-in path equal to the thread depth, and the full thread profile machining time equal to the period of one revolution of the workpiece. The paper highlights that thread milling is an efficient, general-purpose machining process. In this study, we solved the thread profile error estimation problem. Thread milling with parallel workpiece and cutter axis was investigated with a milling simulation model. The optimal thread milling tool parameters for internal thread machining were found. The method efficiency was proven by measuring undercuts and overcuts in pipe thread milling. For instance, the thread error (overcuts/undercuts measured flatwise to the thread profile) diametral compensation does not exceed 0.0268 mm while the pipe thread tolerance G1.25`` is 0.36 mm.
Introduction
Thread milling (including internal threads) is one of the most forward-looking technologies that offer max thread cutting performance [1...7].
Standard CNC thread milling cycles can be used. It is preferable to develop an NC program with CCS (an application that estimates the cutting mode and selects the machining strategy.) The study objective is reducing efforts, milling time and cost through investigating the thread milling process and measuring the undercuts and overcuts in special buttress threading on thin-walled pipes for selecting the most suitable cutter.
We used simulation to estimate the undercuts and overcuts.
Research method
The simulation and under-(over-)cuts calculation were made to achieve the aim. Other researchers tried to solve this problem analytically [8]. The solution was two-dimensional, while shaping is a three-dimensional process. It was noted in [10]: "The difference between the 3D part model and the 3D reference model is the undercut (overcut) volume." In this paper, we identified errors of radiator nipple pipe thread milling.
The final stage of the simulation is creating a 3D model of the thread milling errors. The overcuts were generated by subtracting the resulting part model from the reference model (figure 1); for the undercuts, the reference model was subtracted from the resulting part 3D model ( To find the max value of the overcuts or undercuts (the max distance between the resulting thread surface and reference one) we used the "Surface deviation" tool in the CCS software.
With the surface deviation results we traced the max deviation point, then cut a section at this point, and estimated the errors. Then the simulation model was used in a series of experiments to find the most suitable cutter in terms of minimizing the shape errors. Afterwards, we generated a fitting criterion function.
The simulation objective was minimizing the thread geometry errors. The geometric errors have two components: thread profile overcuts and undercuts. In real applications, one error component is sometimes emphasized. We considered all the components. The objective function is the sum of two components: The function arguments are the cutter radius u R and the number of teeth z. Hereinafter, we will denote the variables as follows: where is the f domain, is the max acceptable thread geometry error.
We used a numerical method for finding the multi-valuable function extremum to find the max value of the two-argument function f .
A solution to the problem is generating a sequence ..., , , k , function values are a decreasing convergent sequence.
These sequence generating methods are called 'descent methods' [10]: where k P is the descending vector from In this case, it is impossible to estimate the partial derivatives (there is no analytical relation), so we replaced them with finite differences [3]: The function value is decreased every time the distance increment increases, that is: ( As a result, the iterative process meeting the condition (3) is as follows. Two initial approximations are specified: Table 1.
The distance increment 1 is found. It is constant for subsequent iterations. Eq. (2) is estimated, and the condition (3) is checked at every iteration.
If the condition is met, the same distance increment is used for the following iterations. Otherwise, the increment is decreased until the condition is met. The process stops when the following condition is met: ( The key milling variable is the engagement angle between the cutter and the blank . Refer to Table 2 for the results. The diagrams based on the table are shown in figure 3. Table 3 for the initial data used to find the f error function maximum value. The lateral undercut is 0.29 mm. That is, such cutter dimensions produce unacceptable machining results. Refer to figure 4 for the part model machined as described above.
Discussion
As can be seen from the simulation results presented in In this case, the thread profile has linearity errors. For the simulation, we measured these errors flatwise to the nominal thread profile. Then we found a factor to recalculate the overcut values measured flatwise into the actual thread profile error values. These errors are recalculated by the mean diameter as follows: Refer to figure 5 for the relation between the root faceting, the cutter radius, and the number of teeth. With this relation, one can assess the impact of the cutter radius and the number of teeth on the root facet formation, so the process planner can choose the optimal tool parameters on an ad hoc basis.
Conclusion
The 13 th iteration simulation results (the cutter diameter is 100 mm and the number of teeth is 32) are the best for the pipe thread 25 1, G milling. What we found is: milling simplifies the manufacturing process. Moreover, it requires a fewer number of tools, the machining time is reduced, while the manufacturing becomes more flexible and efficient.
With the presented thread milling simulation, the optimal cutter parameters for the specific thread milling can be found.
With a larger cutter radius, more teeth can be fitted, and it minimizes the errors (to 0.0268 mm if the number of teeth is 32.) The error is within the average diameter tolerance equal to 0.36 mm.
Thread milling is even more efficient for cutting oppositely directed threads like radiator nipples. | 1,444.8 | 2021-01-19T00:00:00.000 | [
"Materials Science"
] |
Resonant passive energy balancing of morphing helicopter blades with bend–twist coupling
With increasing demand for rotor blades in engineering applications, improving the performance of such structures using morphing blades has received considerable attention. Resonant passive energy balancing (RPEB) is a relatively new concept introduced to minimize the required actuation energy. This study investigates RPEB in morphing helicopter blades with lag–twist coupling. The structure of a rotating blade with a moving mass at the tip is considered under aerodynamic loading. To this end, a three-degree-of-freedom (3DOF) reduced-order model is used to analyse and understand the complicated nonlinear aeroelastic behaviour of the structure. This model includes the pitch angle and lagging of the blade, along with the motion of the moving mass. First, the 3DOF model is simplified to a single-degree-of-freedom model for the pitch angle dynamics of the blade to examine the effect of important parameters on the pitch response. The results demonstrate that the coefficient of lag–twist coupling and the direction of aerodynamic moment on the blade are two parameters that play important roles in controlling the pitch angle, particularly the phase. Then, neglecting the aerodynamic forces, the 3DOF system is studied to investigate the sensitivity of its dynamics to changes in the parameters of the system. The results of the structural analysis can be used to tune the parameters of the blade in order to use the resonant energy of the structure and to reduce the required actuation force. A sensitivity analysis is then performed on the dynamics of the 3DOF model in the presence of aerodynamic forces to investigate the controllability of the amplitude and phase of the pitch angle. The results show that the bend–twist coupling and the distance between the aerodynamic centre and the rotation centre (representing the direction and magnitude of aerodynamic moments) play significant roles in determining the pitch dynamics.
effect of important parameters on the pitch response. The results demonstrate that the coefficient of lag-twist coupling and the direction of aerodynamic moment on the blade are two parameters that play important roles in controlling the pitch angle, particularly the phase. Then, neglecting the aerodynamic forces, the 3DOF system is studied to investigate the sensitivity of its dynamics to changes in the parameters of the system. The results of the structural analysis can be used to tune the parameters of the blade in order to use the resonant energy of the structure and to reduce the required actuation force. A sensitivity analysis is then performed on the dynamics of the 3DOF model in the presence of aerodynamic forces to investigate the controllability of the amplitude and phase of the pitch angle. The results show that the bend-twist coupling and the distance between the aerodynamic centre and the rotation centre (representing the direction and magnitude of aerodynamic moments) play significant roles in determining the pitch dynamics.
Introduction
In many aerospace applications, it is required that the vehicle has a good performance in a broad range of conditions. For example, the minimum required power in helicopter rotors at various flight conditions is achieved from different twist distributions [1]. Inducing control on flexible aerostructures helps to optimize the aerodynamic loads and reduce the energy consumption in different flight conditions [2,3]. In addition, energy exchange between different motions of rotor aerostructures such as flapping, lagging, and pitching is a property that has received attention for controlling such structures [4][5][6]. The shape-adapting capability of morphing aircraft gives the ability to control the performance of aerostructures. Indeed, morphing aircraft can be used not only to improve the performance of an aircraft in one specific flight condition and reduce the energy consumption, but also to broaden the range of good performance over different conditions. Ajaj et al. [4] presented a novel classification framework based on the functionality, operation, and the structural layout of morphing technology. A review of the morphing concept in wind turbine blades can be found in [5]. Vos et al. [7] introduced a new flight control mechanism employing piezoelectric bimorph bender actuators to apply control to an unmanned aerial vehicle with a deformable wing structure. The introduced piezoelectric flight control mechanism was applied to a morphing wing and the details of the design, modelling, and experiments were given in [8]. Fincham and Friswell [9] introduced an inner optimization strategy within the main aerodynamic optimization process to take the limitations of the possible morphing structure into account at the early stages of the design. Eguea et al. [10] exploited the genetic algorithm to find the optimum camber morphing winglet in order to minimize the fuel consumption of a business jet. The potential critical speed for a morphing wing with an active camber design was investigated by Zhang et al. [11] using a low-fidelity model. For this purpose, they also utilized both steady and unsteady aerodynamic models to develop an aeroelastic model for the structure under study.
The concept of bend-twist coupling in morphing structures to increase the controllability of flexible aerostructures has received considerable attention [12]. Bend-twist and extension-twist coupling were studied experimentally on a thin-walled composite beam [13]. It was shown by an analytical model [14] that, by using dynamic blade twist, the performance of a helicopter is enhanced and the power required for the rotor blade is reduced. Theoretical and experimental investigations on the bend-twist coupling concept in wind turbine blades were carried out in [15]. Gu et al. [16] utilized the twist morphing concept and designed a novel metamaterial to increase the aerodynamic efficiency of a rotor blade by the passive twist generated by the bendtwist coupling. The designed meta-material was used to propose a concept design of a blade spar with a rectangular cross section to investigate the relation between the cell geometries of the core material and the bendtwist property of the spar.
The application of a lumped mass moving in the spanwise direction to absorb the vibrational energy and mitigate the oscillation of the helicopter rotor was investigated in [17][18][19]. They demonstrated that the stability of the helicopter rotor is influenced by the coupling of the flapwise oscillation and lagwise motion induced by the Coriolis forces. Kang et al. [20] carried out numerical and experimental analysis and demonstrated the improved stability of rotors resulting from the embedded chordwise absorbers. Combining the bend-twist concept with a movable mass at the tip of a morphing blade is a new concept that exploits the bending moment to generate the twist and control the aerodynamic performance of the structure. A morphing blade composed of a composite hingeless rotor blade and a moving lumped mass at the tip was studied by Amoozgar et al. [21]. The lumped mass is subjected to an actuation force and is allowed to move in the chordwise direction. The bending moment induced by the centrifugal force of the moving mass will generate a twist in the blade due to the bend-twist coupling.
In addition to tuning the structures and optimizing the parameters to increase the performance of aerial vehicles, passive energy balancing (PEB) is utilized to passively balance the energy between the aerostructure and the actuator and reduce the required actuation energy. Wang et al. [22] applied a new passive energy balancing mechanism using a spiral pulley to reduce the required actuation force in a morphing structure. Zhang et al. [23] introduced a negative stiffness mechanism for a passive energy balancing concept applied to a morphing wingtip with a linear actuator. Their target was to optimize the passive energy balancing design and minimize the energy consumption and the required actuation force.
A new extension of PEB is resonant passive energy balancing (RPEB). The mechanism of RPEB utilizes the resonant energy of the structure to provide a portion of the energy required to deflect the morphing structure. In this case, the energy can be gained in the vicinity of various resonances of the structure, depending on the properties and operating condition of the structure. These resonances can either be based on the natural frequencies of the blade and their sub-or super-harmonics, or an additional mechanism. However, in spite of the knowledge gained for PEB in morphing aircraft, this concept is still in its infancy. This study is a step forward in applying RPEB to an MDOF structure.
As described above, a recently introduced morphing concept uses a movable mass at the tip of the blade. In contrast to previous works on the dynamic of spanwise morphing beams [24,25], this concept utilizes the bend-twist coupling in the blade to induce a twist angle from the centrifugal force applied to the moving mass. The moving mass is forced by an actuation mechanism to adjust the required amount of induced twist angle. The parameters of the structure and the moving mass are tuned so that the resonant oscillations are used to supply energy to actuate the moving mass. Hence, the RPEB concept can be used to reduce the actuation energy consumption [26].
This study investigates the application of the mechanism of RPEB in morphing blades with a moving mass at the tip. Indeed, the results shown in this study demonstrate how different parameters of a rotating blade affect the dynamic behaviour of the structure. Then, the controllability of the dynamics of rotor blades using bendtwist coupling and the aerodynamic moment is determined in the current study.
This study is focused on the investigation of RPEB for twist morphing helicopter blades, and a better understanding of the system results in a more efficient design. For instance, the nonlinear behaviour due to the structural nonlinearity of the blade and the nonlinear aerodynamic loading makes the prediction of the dynamics of the system complicated [27]. In addition, unwanted dynamical behaviour, such as quasi-periodic and chaotic responses, should be avoided in the design [28]. Therefore, analysing the nonlinear dynamics of the system is required. Thus, a morphing helicopter blade with an actuated moving mass at the tip is modelled using a three-degree-of-freedom (3DOF) discrete system. The pitch response and the lagging motion of the blade, in addition to the displacement of the moving mass, are the 3DOF in the model. The aerodynamic coefficients are estimated using experimental data [29][30][31][32]. A simplified single-degree-of-freedom (SDOF) model is used to demonstrate the effect of important parameters on the dynamics of the pitch response. The structural analysis is carried out on the parameters of the 3DOF model neglecting the effect of aerodynamic loading. The results of the structural analysis can be used to tune the parameters for desired purposes (e.g. locating resonant frequencies in the range of working rotating speed). The stability analysis of the 3DOF model is carried out and the controllability of the pitch response is discussed. Finally, a brief conclusion is provided.
Mathematical modelling
In this section, a reduced-order mathematical model of the structure is described. The schematic of the cross section of the main rotor blade of a helicopter is shown in Fig. 1. The movable mass m 2 is assumed to be moving along the chord of the blade. That is, the flapwise bending moment induced by the centrifugal force of the movable mass is insignificant. Accordingly, there will not be any significant coupling between the flapwise bending moment induced by the movable mass and the blade twist angle. Hence, the structure of Fig. 1 is modelled by a 3DOF discrete system. The lag displacement x 1 and the pitch angle α of the blade are considered as two degrees of freedom of the reduced-order model of the blade, and the motion x 2 of the moving mass m 2 is considered as the third degree of freedom. In the figure, AC and RC denote, respectively, the aerodynamic centre and rotational centre of the aerofoil, and GC is the centre of gravity of the blade with mass of m 1 . l is the chord length of the aerofoil, and d 1 , d 2 , and d ac are, respectively, the distances of GC, the initial position of the moving mass, and AC with respect to RC. c 1 and k 1 are the damping coefficient and the stiffness of the blade in the lag direction. In fact, k 1 is not really physical, but represents the lagwise bending stiffness of the beam. κ is the rotational (torsional) stiffness of the blade in the pitch angle direction. Aerodynamic force F ac is applied to the blade at the aerodynamic centre AC and the moving mass is excited by a harmonic force with amplitude f m and excitation frequency ω m . The aerodynamic moment at AC is neglected in this study. Note that this is a reasonable assumption because many helicopter blade sections are designed with zero coefficient of moment [33,34]. c 2 , k 2 , and k n are, respectively, the linear damping, linear stiffness, and nonlinear cubic stiffness through which the moving mass is connected to the blade. v b represents the velocity of the where ω 0 denotes the rotating velocity of the main rotor, v 0 is the translational velocity of the blade due to rotation and V f is the forward speed of helicopter.
Potential energy of bend-twist coupling deformation
Due to the bend-twist coupling introduced through the composite layup, the lagwise bending moment in the composite spar induces a twist angle in the spar. For the helicopter blade, a twist is induced in the spar due to the bending moment generated by the centrifugal force of the moving mass, as shown in Fig. 2. The distance of the moving mass from RC is a function of the rotating frequency ω 0 , which in turn induces a periodic torsional moment.
where β is the angle between the direction of the centrifugal force of the moving mass and the longitudinal axis of the spar. The coordinate axes x yz are shown in Fig. 2. For the 3DOF discrete system, the second term on the right side of Eq. (2) is eliminated as there is no spatial variable z. The function cos(β) = is approximately 1 considering the dimensions of the blade. Therefore, Then, the twist induced by bend-twist coupling is determined in the form where T b is the torsional torque due to bend-twist coupling, D denotes the coefficient of bend-twist coupling, and κ and α bt are the torsional stiffness and twist angle due to the bend-twist coupling, respectively. The potential energy U bt due to the bend-twist coupling is obtained as
Equations of motion: 3DOF model
To derive the equations of motion of the 3DOF system of Fig. 1, Lagrange's equations are applied to the kinetic energy, potential energy, and non-conservative terms of the system. Displacements of m 1 and m 2 are determined with respect to RC as whereî andĵ are unit vectors in the x and y directions. Considering the velocity v 0 of the tip of the rotating blade, the absolute velocities of m 1 and m 2 with respect to RC are obtained, respectively, aṡ Using the velocitiesẋ 1 a andẋ 2 a , the kinetic energy of the system is written in the form Using the potential U bt of Eq. (5) due to the bendtwist coupling of the blade, the potential energy and non-conservative terms of the 3DOF system are given, respectively, as whereê x 1 ,ê x 2 , andê α are, respectively, unit vectors in the directions of lagging motion x 1 , moving mass displacement x 2 , and the pitch angle α, and F L and F D denote the aerodynamic lift and drag forces, respectively, given by where c L and c D denote the lift and drag coefficients and ρ is the density of air. Applying Lagrange's equations to the kinetic and potential energy, and non-conservative terms of the system, the equations of motion of the system can be derived as Defining the dimensionless parameters as the non-dimensional equations of motion of the 3DOF system are obtained as where and The superscript * is removed for the sake of brevity in the subsequent discussions. The lift c L (α) and drag c D (α) coefficients are functions of the pitch angle of the blade. These functions are estimated according to the experimental data [29][30][31][32] of the Bo-105 blade for the lift and drag coefficients as The coefficients A 1 , A 2 and B 1 , B 2 , B 3 are obtained by fitting a straight line and a quadratic curve to the experimental data for the lift and drag coefficients, respectively. Figure 3 shows the fitted curves to different experimental data for lift and drag coefficients. Table 2 gives the baseline coefficients for c L and c D in Eq. (17). For reliable analysis of the dynamics of the system under study, the values of the non-dimensional parameters should be in a feasible range. Hence, a set of baseline values for the dimensional parameters of the Bo-105 blade is derived from real dimensions and experimental data and given in Table 1. ω ref in Table 1 is the reference rotating speed of the helicopter in forward flight. These data are then used to estimate physically meaningful variations for the non-dimensional parameters of the system of Eq. (14). For example, from Table 1, is obtained for the Bo-105 blade. Based on this, an approximate rotating frequency range of Ω 0 ≈ 0 ∼ 7 is considered for the dynamic analysis of the structure to account for the variabilities of both the lagwise natural frequency and the blade rotating frequency of the aircraft. The baseline values of the non-dimensional parameters of the system are given in Table 2.
SDOF model
In the first step of this study, the dynamic response of a single-degree-of-freedom (SDOF) model of the morphing blade is investigated to examine the effect of important parameters on the dynamic behaviour of the pitch angle. To find the SDOF model, the lagwise motion of the blade is neglected from the equations of motion given by Eq. (14) and the motion of the moving mass is assumed to be harmonic. A linear dashpot with damping ratio ζ α is added to the equation of motion to include the damping effect of blade lagging on the dynamics of the pitch angle. Hence, the equation of motion of the SDOF model is given as where Harmonic behaviour is assumed for the pitch angle. Thus where α 0 and α i denote, respectively, the static deflection and the complex amplitude of the ith harmonic of Table 3 are used as the initial values of the parameters of Eq. (18).
Results and discussion
In this section, the equations of motion of the structure under study are solved using different methods and the obtained results are discussed. To obtain the dynamic response of the system in this study, two different methods are used: direct integration (DI) using the ODE functions in MATLAB, and the complex averaging technique (CXA) [35] along with arc-length continuation. The former is used to find the response of the system in the time domain. However, the obtained response can be transformed into the frequency domain using methods such as the fast Fourier transformation (FFT). The CXA method, on the other hand, is used to find the steady-state dynamics in the frequency domain. Each method has its advantages and disadvantages. To find the time-domain dynamics of the system, either transient or steady state, direct integration (DI) is used. However, using DI is computationally expen- Table 3 sive to obtain the steady-state response in the frequency domain, particularly for a wide range of frequencies.
On the other hand, using the CXA technique reduces the computational cost significantly. The drawback of CXA is that it is very difficult to use for dynamical systems with high frequency content or non-periodic responses, such as those with chaotic responses.
SDOF analysis of RPEB
The steady-state frequency domain response of the system is given in Fig. 4 for the initial parameters given in Table 3. The values of other parameters of the SDOF model of Eq. (18) are given in Table 2. In the figure, α 0 is the static deflection, α i denotes the ith harmonic of the pitch angle, and |α i | and φ α i are, respectively, the amplitude and phase of α i . The static deflection, amplitude-frequency diagram, and phase of the first three harmonics of the steady-state response of the pitch angle are given. The stability analysis on the analytical results obtained from the CXA method has been undertaken using Lyapunov's First Theory of Stability. The red and blue colours in the figure denote the stable and unstable responses, respectively. A bifurcation analysis is carried out on the steady-state dynamic response of the system, and SN represents the saddle-node bifurcation. All of the phase values of the pitch angle in this study are calculated with respect to the aerodynamic force. The results show that the system responds with a hardening nonlinearity. The effects of the variations of key parameters on the dynamics of the SDOF model of Eq. (18) are now investigated. The effect of variation in the parameter d ac on the dynamics of the pitch angle is shown in Fig. 5. The results illustrate that the blade behaves with a softening nonlinearity for d ac < 0, while altering d ac to positive values causes the nonlinearity of the system to change to hardening. This behaviour is due to the nonlinearity in the aerodynamic moment in Eq. (18). The sign of this nonlinear term is directly associated with the sign of d ac , that is the direction of the aerodynamic moment. It is observed in Fig. 5b that changing the sign of d ac leads to a change in the sign of the static deflection. Indeed, the blade will pitch nose up and down, respectively, for positive and negative values of d ac . According to the results, there exists an asymmetry in the static deflection of the pitch angle with respect to the value of d ac . The reason is that, in the presence of x 2 , the aerodynamic force is not the only load applied to the system. Therefore, although the sign of the pitch angle changes with the sign of d ac , the static pitch is not symmetric even for the case of zero bend-twist coupling. As expected, the vibration amplitude of the pitch response reduces when the magnitude of d ac , and con- Figure 5d shows a shift in the phase of the steady-state response of the pitch angle due to changes in the value and sign of d ac . The smaller phase shift takes place for changes in the magnitude of d ac and the larger shifts happen when the sign of d ac varies. Therefore, d ac , or in other words, the value and sign of aerodynamic force/moment is a key parameter in determining the amplitude and phase of the pitch angle. Figure 6 gives the results of the steady-state pitch oscillation in response to variations in the bend-twist coupling D, neglecting the effect of aerodynamic forces by setting d ac to zero. Figure 6a shows that the resonant amplitude of the pitch oscillations has a direct relation to the magnitude of D. The static deflection results in Fig. 6b show a similar behaviour as the deflection increases when the coupling D increases. Furthermore, Fig. 6b and c shows that both the static deflection and the amplitude of steady-state pitch dynamics are symmetric with respect to zero bend-twist coupling, D = 0. In other words, the magnitude of static deflection and the amplitudes of the pitch response for the same magnitude of coupling D but different signs (e.g. D = 1 and −1) are exactly the same. However, the direction of the static deflection varies when the sign of the coupling changes. Indeed, the blade will pitch nose up and down, respectively, for negative and positive values of D. The phase of the pitch response depends only on the sign of D and any change in the magnitude of coupling without altering its sign does not change the phase of the response, as shown in Fig. 6d. Hence, both the magnitude and sign of the bend-twist coupling D are important in determining the static deflection, and the amplitude and phase of the pitch response. Figure 6 shows the pitch dynamics in the absence of aerodynamic loading. However, the aerodynamic forces and moments are vital for the dynamics of the blade and cannot be ignored. Figure 7 shows the effects of the aerodynamics with d ac = 0.25 on the dynamic behaviour of the pitch angle. It can be observed that the amplitude of vibration still varies by changing the coupling D. However, the sensitivity of the pitch oscillation amplitude to the variation of D has been significantly reduced. Also, including the aerodynamic forces removes the symmetry in the static pitch response, as shown in Fig. 7b. In this case, changing the bend-twist coupling from D = −1.5 to D = 1.5 causes the static deflection to reduce, although the change in static deflection is not significant. The symmetry in the phase of the pitch response shown in Fig. 7c is not observed in this case. In fact, both the sign and magnitude of D will affect the phase of the pitch angle.
Structural analysis
In this section, the effects of important parameters of the 3DOF model of the structure of Fig. 1 on the dynamic behaviour are investigated. The main reason for this investigation is to show which structural parameters can be used for tuning the system according to desired purposes. To this end, the effect of aerodynamic loads is neglected, and the steady-state dynamics of the system is obtained in the frequency domain by applying the CXA technique with arc-length continuation to Eq. (14).
The effect of the natural frequency Ω t1 of the pitch angle on the dynamic pitch response is shown in Fig. 8. The results show that increasing Ω t1 reduces the resonant amplitudes of the dynamic pitch response at different resonant frequencies. Indeed, increasing the natural frequency of the pitch angle is equivalent to higher torsional rigidity, and this leads to lower resonant amplitudes. Furthermore, changing the natural frequency Ω t1 moves the locations of the resonant amplitudes associated with the pitch angle natural frequency and its higher harmonics. Figure 8c shows how increasing the pitch natural frequency reduces the pitch resonant amplitudes. In addition, higher values of Ω t1 increase the natural frequency of the moving mass due to the coupling between the pitch motion and the mov-ing mass. Changes in the phase of the pitch angle in response to changes in Ω t1 are illustrated in Fig. 8d.
The steady-state response-frequency diagram of the pitch angle is shown in Fig. 9. The variation of Ω 21 affects not only the resonant amplitudes of the pitch angle, but also the location of the resonant frequencies. It is observed that the pitch response of the blade experiences one resonance for each natural frequency of the pitch angle and the moving mass. There also exist other resonances related to higher harmonics of the pitch angle. The results show that the nonlinear behaviour of the pitch response is stronger for lower values of the natural frequency Ω 21 , as the linear stiffness of the moving mass decreases. By increasing Ω 21 , the resonant amplitudes of the pitch response increases up to Ω 21 = 2.5 and then reduces for further increases in Ω 21 . The coupling between the motion of the moving mass and the pitch angle dynamics, means that for natural frequencies of the moving mass less than the torsional natural frequency (Ω 21 < Ω t1 ) the pitch resonance moves to the right (i.e. Ω t1 actual > Ω t1 ). On the other hand, for Ω 21 > Ω t1 , the actual pitch resonant frequency Ω t1 actual is less than the uncoupled natural frequency Ω t1 . Figure 9b illustrates that increasing the natural frequency Ω 21 results in stiffening of the moving mass, and this consequently leads to less deflection of the moving mass and less static pitch deflection Fig. 9, the parameter Ω 21 provides the ability to tune the structure so that the rotating (excitation) frequency can be located at, or in the vicinity of, either the moving mass natural frequency or the pitch resonant frequency. Therefore, the structure can use the energy arising from the resonant oscillations. However, the resonant amplitude may be dangerous for the structure, particularly if it is a linear resonant amplitude. To deal with this problem, the parameters of the system are tuned so that the operating frequency is located in the vicinity of the nonlinear resonant amplitude. Having nonlinear resonant amplitude, instead of a linear resonance, restrains the amplitude of oscillations at a fixed rotating frequency. In the next section, it is shown how the nonlinear behaviour of the structure can be used for RPEB while avoiding the dangerous linear resonant amplitude that may lead to fracture in the blade. On the other hand, it is shown how the stability analysis of the morphing blade helps to better understand the nonlinear dynamics of the structure. The results of stability analysis are then used to determine the safe region of operation. Figure 10 shows the amplitude/phase-frequency diagram of the steady-state pitch response of the blade within the rotating frequency bandwidth Ω 0 = 0 ∼ 6.5 for different values of lag-twist coupling D. In this case, by neglecting the aerodynamic loading, the only excitation on the structure is the actuation force applied to the moving mass. Therefore, the dynamic pitch response depends on the dynamics of the moving mass and the value of the coupling D. The waterfall diagram of the pitch response in Fig. 10a shows that changing the value of D leads to changes in the resonant vibra-tion amplitudes of the pitch angle. For D = 0, as there is no coupling between the pitch angle and the moving mass, the pitch angle shows zero amplitude response. Increasing the magnitude of D leads to increases in the resonant amplitude, as the coupling between the moving mass and the pitch angle becomes stronger. In addition, new resonances appear in the response by increasing the value of D to greater than D = 0.5. The locations of these new resonances also depend on the value of the bend-twist coupling. The static deflection of the pitch angle depends on the sign of D, and the blade will pitch nose up or down, respectively, for negative and positive coupling D, as shown in Fig. 10b. Also, the blade will have greater static pitch deflection for higher magnitudes of D. In contrast to the magnitude of D, Fig. 10c shows that the sign of the bendtwist coupling does not have any effect on the amplitude of the pitch vibration, in the absence of aerodynamic forces. In other words, the amplitude-frequency diagram of the pitch angle is symmetric with respect to the value of D. However, altering the sign of the coupling D results in a change in the phase of the pitch angle by π rad, as shown in Fig. 10d. Therefore, the results of Fig. 10 demonstrate that both the magnitude and sign of Figure 11 shows the amplitude-frequency response of the steady-state pitch dynamics for different levels of actuation force F m . Figure 11a, c illustrates the 3D waterfall diagram and 2D amplitude-frequency diagram of the first harmonic of the pitch oscillation, respectively. Figure 11b gives the static deflection of the pitch response, and the phase of the first harmonic of pitch oscillation is shown in Fig. 11d. α 0 , |α 1 |, and φ α 1 denote the static deflection, and the amplitude and phase of the first harmonic of pitch oscillation, respectively, The results show that increasing the actuation level increases the resonant amplitude of the pitch angle. Furthermore, increasing F m excites the nonlinearity in the structure and multiple solutions appear for higher values of F m . In contrast to the vibration amplitude, the static deflection of the pitch angle is not affected by changes in the actuation force. Thus, the actuation force can be used to change the amplitude of the pitch oscillation without affecting the static pitch deflection. Figure 11d shows that there is a phase difference between the case without actuation force and with actuation force. However, in the presence of actu-ation, the phase of the response is not affected by the actuation level.
Sensitivity analysis
Based on the discussion in the previous sections, a parametric study is performed on the dynamics of the 3DOF model of the blade considering the variation of two important parameters: bend-twist coupling D and the aerodynamic distance d ac . The lower and upper bounds of the variation range of the parameters are determined according to physically meaningful variations of the dimensional parameters of the blade. The selected lower and upper bounds are given in Table 4. First, the effect of the parameters' variability is investigated on the dynamics of the 3DOF model of the blade. Then, the controllability of the pitch response is discussed.
The baseline values of the parameters of Table 2 are used to determine the dynamics of the 3DOF model of the blade using numerical direct integration in MATLAB. The simulation was performed for the frequency range Ω 0 = 0.5 ∼ 6 with frequency step dΩ 0 = 0.025. The simulation was performed for 800 cycles at each frequency and the last 150 cycles are used to ensure the steady-state response is considered. Figure 12 shows the static deflection and the amplitude of the first five harmonics of the pitch angle of the blade. α 0 and |α i | denote, respectively, the static deflection and the amplitude of the ith harmonic of the pitch response. The results show that there are some resonant amplitudes of different harmonics related to the natural frequencies of each degree of freedom. It is observed that by increasing the rotating speed (excitation frequency) Ω 0 , the magnitude of the static deflection of the pitch angle increases as expected. However, it is explained later that the magnitude and sign of the static deflection (pitch nose up or down) depend on the values of the parameters d ac and D and also the rotating frequency. In addition, the amplitudes of the pitch angle oscillations experience several resonances and jumps in the neighbourhood of the natural frequencies.
The jumps in the dynamic response of the pitch angle are due to the nonlinearity of the system and are critical in tuning the parameters of the structure.
To better understand the nonlinear response of the pitch angle, the response obtained from numerical direct integration is compared with the response obtained using CXA. Figure 13 compares the amplitude of the first harmonic of the steady-state dynamic pitch response of the 3DOF model obtained using the CXA method and direct numerical integration in MAT-LAB. This comparison clarifies the exact nonlinear dynamic response of the pitch angle. The stability analysis on the analytical results obtained from the CXA method has been undertaken using Lyapunov's First Theory of Stability. Unless the jump between two different stable branches is targeted for a special purpose, the region of multiple stable solutions is avoided in practical engineering systems. Besides, the existence of unstable branches in addition to various bifurcations generates different types of dynamic responses that is mostly avoided in engineering structures. For example, the results of Fig. 12 in the frequency range Ω 0 = 3.12 to 3.5 shows that the amplitude of vibration changes non-smoothly in this region. This is because the system behaves with a variety of multi-frequency, However, for d ac = 0.25, pitch angle has a periodic response at Ω 0 = 3, while it behaves with a chaotic response at Ω 0 = 3.25. Various dynamic responses including periodic, quasi-periodic, and chaotic responses at different rotating frequencies are shown in Fig. 15. The results of Fig. 13 can also be used to determine the desirable operating range of the structure according to different dynamic responses at various frequencies. Of course, this decision depends on the application and design criteria. For example, the frequency ranges Ω 0 < 2.2, 2.7 < Ω 0 < 3.1, and Ω 0 > 3.8 are safe with respect to undesired behaviours such as multiple stable solutions, jumps, quasi-periodic responses, or chaotic dynamics. However, despite a relatively high amplitude of vibration, an aircraft with variable rotating frequency might avoid the range of 2.7 < Ω 0 < 3.1 which has various undesired dynamic responses. On the other hand, aerospace applications with a constant rotating frequency can benefit from high amplitude vibration for 2.7 < Ω 0 < 3.1.
Controllability of the pitch response
Amplitude and phase of the pitch angle are important features of the dynamics of the blade which are required to be controlled. Sects. 3.1 and 3.2 show that the aerodynamic forcing/moment and the bend-twist coupling are two important parameters in determining the phase of pitch angle. Therefore, this section discusses the effect of aerodynamic forcing and bend-twist coupling on the phase of the pitch angle. The variations of two parameters, d ac and D, which determine, respectively, the signs of aerodynamic force and bend-twist coupling, are considered. For the other parameters, the baseline values of Table 2 are used. The results in this section are obtained using the 3DOF model of the helicopter morphing blade including the aerodynamic loading.
To investigate the effect of these two parameters on the phase of the pitch angle, three different cases are considered: (a) D = 0, (b) d ac = 0, and (c) (a) D = 0. In this case, the bend-twist coupling is neglected and the effect of d ac on the phase of the pitch angle is studied in the absence of bend-twist coupling. The aerodynamic force may have different signs depending on the location of aerodynamic centre AC. Accordingly, the aerodynamic forcing may have beneficial or adverse effects on the pitch angle. Therefore, d ac , which indicates the distance between AC and RC, plays significant role in defining the desired phase. The appropriate d ac (i.e. the location of AC with respect to RC) is selected to obtain a response that is in phase, out of phase, or no oscillating response. The pitch angle of the blade is obtained for the range of d ac = −0.5 ∼ 0.5. Figure 16 shows the static deflection and the amplitude and phase of the first three harmonics of the pitch angle. The results show that without any bend-twist coupling in the blade dynamics, the phase of the pitch angle varies in response to changes in the sign and value of d ac . At d ac = 0, no aerodynamic moment is applied to the blade and therefore no pitching response is observed. For d ac > 0, on the other hand, the pitch angle oscillates with approximately π rad phase difference with respect to the pitch angle for d ac < 0.
(b) d ac = 0. In this case, AC is located at RC and the aerodynamic force will not be able to generate any moment to affect the pitch angle. Hence, the only moment applied to the blade is due to bend-twist coupling. Changing the sign of the coupling will affect the amplitude and phase of the pitching response. For 16 The sensitivity of the dynamics of the system to variation of d ac for D = 0. α 0 , |α i |, and φ α i denote, respectively, the static deflection, and amplitude and phase of the ith harmonic of the pitch response d ac = 0, the effect of variation of bend-twist coupling D on the dynamics of the pitch angle is shown in Fig. 17. In the figure, α 0 , |α i |, and φ α i denote, respectively, the static deflection, and the amplitude and phase of the ith harmonic of the pitch response. The results of the static pitch deflection illustrate that the blade would pitch nose up and down, respectively, for negative and positive values of D. It is also observed that the amplitude of the first three harmonics of the pitch angle is symmetric with respect to the coupling value D = 0. In other words, changing the sign of the bend-twist coupling in this case does not have any effect on the vibration amplitude of the pitch angle. On the other hand, there is almost a difference of π rad between the phase Figure 18 shows that the second harmonic of the pitch angle is excited at rotating frequency Ω 0 = 1.5. Indeed, as Ω 0 = 1.5 is equal to half of the natural fre-quency of the pitch angle, the second harmonic of the pitch angle is excited and for some values of d ac and D its amplitude even exceeds the amplitude of the primary harmonic. Figure 18 also demonstrates that the variation of D for a fixed value of d ac has a small effect on the static deflection and the amplitude of the first harmonic of α. However, this effect is pronounced on the amplitude of the 2nd and the 3rd harmonics of the pitch angle at higher positive values of d ac . The results of the phase of α show that D affects the phase of pitch response for small magnitudes of d ac . This is because the effect of the aerodynamic moments is reduced for low magnitudes of d ac and the effect of D is strengthened. However, the aerodynamic moments are stronger for higher levels of d ac and the effect of D on the phase of the pitch response is weakened. On the other hand, the variation of d ac significantly affects the pitch response. Figure 18a shows that the blade will pitch nose up and down, respectively, for positive and negative values of d ac . The results of vibration amplitude of α in Fig. 18 illustrate that the aerodynamic moment is strengthened by increasing the magnitude of d ac and the amplitude of vibration increases. However, the amplitude of the 2nd harmonic is not significantly changed by the variation of negative values of d ac . That is, d ac can also be used to control the amplitude of the higher harmonics of the pitch angle. It is also observed that the phase of the pitch angle varies by changing the sign of d ac . Figure 19 shows the pitch response of the system for the variation of d ac and D at Ω 0 = 2. Although the significance of D at this frequency is greater than at Ω 0 = 1.5, the variation of D for a fixed value of d ac does not significantly change the static deflection. It is also shown that at this frequency, the variation of D has a stronger effect on the amplitude and phase of the pitch oscillations, particularly for positive values of d ac . Indeed, as the rotating frequency of the blade approaches the natural frequency of the moving mass, the effect of the oscillation of the moving mass on the pitch response becomes stronger. Accordingly, the bend-twist coupling D plays a more significant role at this frequency. In contrast to the response at Ω 0 = 1.5, where the amplitude of the second harmonic is relatively large with respect to the primary harmonic, since Ω 0 = 2 is not in the vicinity of any subor super-harmonic of the natural frequency of the pitch angle, the amplitude of the higher harmonics of the pitch response is significantly smaller than its primary harmonic. On the other hand, Ω 0 = 2 is in the neigh-bourhood of the natural frequency of the moving mass. Therefore, the higher aerodynamic forces at higher values of d ac result in a resonant response of the moving mass. Accordingly, the resonant energy transfer of the moving mass to the pitch angle is increased for higher values of bend-twist coupling D. Hence, the highest vibration amplitudes of the pitch response are observed at the corners of Fig. 19b-d. Similar to the results in Fig. 18, the variation of the vibration amplitude of the pitch angle due to changes in positive values of d ac is more significant than its negative values. The results of the pitch response at Ω 0 = 3 is shown in Fig. 20 for variations in bend-twist coupling D and parameter d ac . The static deflection is function of both the magnitude and sign of D and d ac . The results show that the bendtwist coupling has its greatest effects on the dynamics of the pitch angle at positive values of d ac . The results in Figs. 18,19, and 20 demonstrate that D and d ac are two significant determining factors in the dynamics of the pitch angle. However, the effect of these two parameters on the pitch response may vary at different rotating frequencies. Although most of aerospace applications operate at constant rotating frequencies, there are various applications such as unmanned aircraft that work over a range of rotating frequency. Therefore, the results of the analysis in this study can also be used to find the safe and desirable operating range. Also, Ω 0 denotes the rotating frequency that is nondimensionalized with respect to the lagging natural frequency ω 1 . Hence, Ω 0 considers both the variability of ω 1 and the operating range of rotating frequency.
Conclusions
This study investigates the resonant passive energy balancing of a morphing blade with moving mass at the tip. To this end, the dynamics of the blade was modelled by a 3DOF discrete system in which the pitch angle, the lagwise motion, and the displacement of the moving mass are considered as the three degrees of freedom. A parametric analysis was carried out on the dynamic response of the 3DOF model of a morphing helicopter blade. The dimensions and mechanical properties of the Bo-105 blade with NACA23012 aerofoil section were used to find the baseline for the study. The aerodynamic coefficients are obtained using the experimental results in the literature. The reduced-order model of the rotor blade was used to study the controllability of the dynamic behaviour of the structure. The analyses and the results obtained in this study are given as follows: 1. First, a simplified single-degree-of-freedom model of the 3DOF system is studied to examine the dynamics of the pitch angle in response to changes in important parameters of the structure. The results showed that the two parameters D, the bend-twist coupling, and d ac , the distance of AC to RC, play significant roles in the dynamic response of the pitch angle. 2. Then, neglecting the aerodynamic forces, the dynamic response of the structure of the 3DOF model was studied in response to variations in different structural parameters.
-The aim of this study was to examine the dynamic sensitivity of the structure to different parameters. This can be used to appropriately tune the structure of the rotor blade. For example, the parameters of the structure can be selected so that the natural frequencies of the system are located within the desired rotating speed. -This helps the engineer use the resonant energy of the system to reduce the required actuation power. -The results of this analysis showed that the torsional natural frequency (i.e. the torsional rigidity and the moment of inertia of the blade) can change the location of torsional resonant frequencies. -Also, the natural frequency of the movable mass has a significant effect on the resonances of the pitch angle. -The bend-twist coupling D is the other effective parameter that determines the resonant pitch angle of the blade.
3. Finally, a physically meaningful range of variation was considered for D and d ac and the effects of the variations of each parameter were investigated on the response of the 3DOF system including the aerodynamic forces.
-Various dynamic responses of the structure under study including periodic, multi-frequency, quasi-periodic, and chaotic responses were illustrated. These dynamic responses are important in tuning the parameters of the structure, as quasi-periodic or chaotic responses are avoided in the system. -The controllability of the pitching response was discussed based on the results of the simulation. -The results showed that the bend-twist coupling D and the distance d ac between the aerodynamic centre AC and the rotating centre are the two important parameters in determining the static deflection, vibration amplitude, and phase of the pitch response. However, other structural parameters are used to tune the system desirably.
Although the present study is mainly focused on the dynamic analysis and parametric study of the morphing helicopter blade, the results of this study can be used in practical cases to improve the performance of the aircraft and reduce the required actuation energy. Having a linear resonant amplitude in the structure may be dangerous. However, the nonlinear behaviour of the structure restrains the amplitude of oscillations at the desired fixed rotating frequency. In addition, the stability analysis of the dynamic behaviour helps to better understand the structure and avoid undesired dynamic behaviours such as jumps, quasi-periodic response, or chaotic behaviour. a copy of this licence, visit http://creativecommons.org/licenses/ by/4.0/. | 11,506.6 | 2021-12-04T00:00:00.000 | [
"Engineering",
"Physics"
] |
Recalcitrant Emotions: A Phenomenological View
In this paper, I sketch an account of emotion that is based on a close analogy with a Husserlian account of perception. I also make use of the approach that I have limned, viz., to articulate a view of the kind of “conflict without contradiction” (CWC) which may obtain between a recalcitrant emotion and a judgment. My main contention is that CWC can be accounted for by appeal to the rationality of perception and emotion, conceived as responsiveness to experiential evidence. The conflicts in question can be regarded as obtaining between different strands of evidence, and our perceptual and emotional experiences can be thus conflicted even among themselves, not only in the special case of a conflict with a judgment.
Introduction
According to perceptualist theories, emotions are a kind of perception, or in some important sense analogous to perception. Such views provide an alternative to feeling theories and judgmentalist theories, and can be regarded as occupying a middle ground between the two, insofar as they conceive of emotions as being intentional, i.e., directed to objects or properties, and thus different from mere non-intentional feelings, but not as amounting to judgments. 1 My first concern in this paper is to sketch a perceptualist account of emotion that is based on a close analogy with a Husserlian account of perception, involving the well-known Husserlian ideas of perceptual fulfillment and disappointment, i.e., a kind of experiential confirmation and disconfirmation. 2 The peculiar view that I propose has not, to the best of my knowledge, been rehearsed by other philosophers. I have, however, reason to believe that the view might be of some interest to philosophers of emotion, and would therefore venture to put before the reader a sketch, which may yet be developed in greater detail and nuance, whether by myself or by anyone prepared to take it up. My view amounts to a very straightforward extension of the core Husserlian view of sensuous perception, with the potential to provide a starting point for a discussion which proceeds to suitably qualify the analogy between perception and emotion -a line I have also pursued in Laasik 2018. 3 My second concern will be to make use of the approach that I have limned, viz., to articulate a view of the kind of "conflict without contradiction" (CWC) which may obtain between a recalcitrant emotion and a judgment -thereby making a connection with current debates concerning perceptualism about emotions, and mustering some support for my perceptualist view, insofar as it will be seen to be up to the task of accounting for CWC.
Recalcitrant emotions are such as persist despite our better judgment. E.g., I may judge that I am in no danger of falling, but my fear of falling is not thereby dispelled. 1 The feeling theory originates with William James, who famously argues that emotions amount to non-intentional feelings that are caused by certain bodily changes, "[W]e feel sorry because we cry, angry because we strike, afraid because we tremble, and [it is] not that we cry, strike, or tremble, because we are sorry, angry, or fearful as the case may be" (James 1884: 190). According to the judgment theories, emotions are evaluative judgments. See, e.g., Solomon 1993, Nussbaum 2004 To be clear, when I speak about "a Husserlian account of perception", I mean an account along Husserlian lines, incorporating certain core Husserlian notions and ideas. I do not commit to providing a thoroughgoingly accurate rendition of Edmund Husserl's actual position, supported by textual exegesis.
3 I cannot claim to be the first or sole proponent of a Husserlian perceptualist view of emotions. John Drummond has developed his perceptualist account in a number of papers: e.g., Drummond 1995Drummond , 2004Drummond , 2006Drummond , 2008Drummond , and 2009. I will make further remarks on Drummond's views in another footnote, but here I would note that Drummond has also offered a detailed discussion of recalcitrant emotions, viz., in Drummond 2004.
I would also add that I do not entirely discount the possibility that Husserl may not have held a perceptualist view of emotions at all. E.g., Panos Theodorou (2014: 627) argues that on Husserl's view emotions are a kind of judgment, while pointing out, in a footnote, that several interpreters do not accept this reading of Husserl without qualification.
Last but not least, however, I have recently become aware of Ullrich Melle's discussion of Husserl's unpublished manuscripts, where Melle attributes to Husserl a view which appears very similar, in substance, to what I defend in the present paper, while backing it up with textual evidence. Thus, we learn that Husserl has, indeed, described emotional experiences as achieving gradual fulfillments with regard to aspects of the object, analogous to sensuous perceptual experiences (Melle 2019: 201-202). It may well be that, with an upcoming addition to the Husserliana series, the view that I articulate, defend, and apply in the present paper, will be seen as amounting not to an original view of my own, but to a version of Husserl's actual view.
My basic conception of CWC, and my understanding of its philosophical significance, derive from the views of Sabine Döring, who has covered this ground in several papers. 4 According to her view, the conflict between the emotion and the judgment is rational, not merely psychological, since it obtains between different representations of the world. However, it does not amount to a logical contradiction, since one does not have to give up the conflicting emotion or judgment, on pain of irrationality (Döring 2009: 240-241). 5 Döring claims that the possibility of CWC furnishes an important touchstone for "cognitive" theories of emotion, which hold that the content of emotions is such as to be "made true" by the facts (ibid.: 241). Indeed, if it is agreed that recalcitrance involves CWC, then the phenomenon of recalcitrance would seem to yield a reason to favor perceptual theories of emotion over judgmental theories, insofar as the latter appear difficult to reconcile with the idea that the conflict does not amount to a logical contradiction. Yet, unless we achieve a firm grasp of the idea of CWC, we cannot entirely discount reasons to doubt whether persistent emotions are really involved in this special kind of conflict. Alternatively, it may be that the conflict is not rational but merely psychological, or that, while being rational, it does amount to a logical contradiction after all. The problem, thus, is to give an account of CWC.
While I mainly draw upon Döring's work to set up the present discussion, I will also remark on Döring's solution to the problem of CWC at the end of my sections 2 and 3, and compare it with mine. She has argued that CWC is best explained by appeal to the peculiar attitudes (i.e., intentional modes) and contents of emotional experiences (ibid.: 242). I will give an alternative account of CWC, viz., one that I take to be in some ways clearer and broader than hers. My main contention is that CWC can be accounted for by appeal to the rationality of perception and emotion, conceived as responsiveness to experiential evidence. The conflicts in question can be regarded as obtaining between different strands of evidence, and our perceptual and emotional experiences can be thus conflicted even among themselves, not only with judgments. A conflict that obtains between an emotion and a judgment, and involves emotional recalcitrance, can thus be viewed as a special case that is best understood by recourse to the context that I have just described.
Recalcitrant Perception
I will now present a phenomenological account of perceptual experience, so as to elucidate the phenomenon of recalcitrant perceptual experience. I will begin by articulating certain basics of the view, then focus on aspects of the rationality of perceptual experience. At the end of the section, I will undertake to shore up our rationality in the face of recalcitrant perception, by considering ways in which a subject can manage the recalcitrant experience and CWC. 4 See, especially, Döring 2009Döring , 2015aDöring , and 2015b According to Döring, rational conflicts are "conflicts in content about how the world actually is" (Döring 2009: 240). In her paper, she repeatedly reminds the reader of the rationality, in this sense, of the pertinent conflicts between emotions and judgments. I refer to the conflicts that she regards as a-rational, as being "merely psychological".
My basic Husserlian starting point is the familiar idea that perception necessarily involves perceptual anticipations of possible continuations of the perceptual experience, realizing the conditions of the fulfillment or disappointment of the perceptual experience. E.g., if I turn the object around and the back side appears as anticipated, I attain fulfillments with regard to the back side. If it is not as anticipated, I may experience a disappointment. If the lighting improves or I change my perspective of the object, I may attain other fulfillments or disappointments, e.g., concerning the object's colour or shape. On the Husserlian view, the objects given to us (or "constituted") in perception are conceived just in terms of such possibilities of fulfillment and disappointment, their different aspects providing, as it were, rules for what it would take to fulfill or disappoint a sensuous experience. Once we accept this point, we may say that the contents of perceptual experience can be cashed out in terms of fulfillment conditions, or what it takes to bring aspects of objectivity to degrees of immediate givenness. We may say that the contents of perceptual experience are fulfillment conditions. 6 The basic Husserlian ideas of anticipation, fulfillment, and disappointment, which we have just invoked, form part of a psychological, epistemological, and a constitutive account. We will not be concerned with perceptual psychology here, but will, instead, proceed, to the epistemological significance of the above sketch. The ideas that we have set forth, already enable us to begin to see how perception could be regarded as epistemically rational, in the sense of being responsive to experiential evidence. On our conception, perceptual experience not merely supports beliefs and judgments, but is itself supported by experiential evidence, which accumulates as one explores the object and attains fulfillments. 7 Alternatively, it may be that the perceptual experience is disappointed, e.g., if the color of the object looks green to one, viz., through a series of appearances, under certain lighting conditions, and then, once the lighting conditions are improved, begins to look red instead, yielding another internally harmonious series of colour appearances, which does, however, conflict with the foregoing series. Here we have a kind of CWC, a conflict between strands of experiential evidence, and thus between different perceptual experiences, or phases of perceptual experience, which nevertheless does not amount to a logical contradiction, since we are not dealing with contents of predicative judgments. It seems that, as a matter of perceptual psychology, such conflicts are promptly resolved in disappointments, with one strand of evidence conclusively prevailing over the other. However, it also seems that at least sometimes the conflict could be somewhat drawn-out, and become a focal concern for the subject, before one experience, or one line of evidence, wins out and a resolution is attained.
It is in terms of such anticipations, and fulfillment conditions, that the presence, or constitution, in experience, of objects and their perceptual properties, is conceived. 8 The Husserlian account of constitution is an account of the necessary and, I believe, sufficient conditions, involving various psychological resources, for our having intentional experiences with certain kinds of content. Constitution has also been explicated as the emergence, in experience, of kinds of unity from kinds of multiplicity, e.g., when the experience of a stable, or constant, spatial objectivity arises from an experience of a multitude of sensations. 9 But one should treat this idea with some caution, insofar as constitution can involve the revelation of entirely new realms of sense, giving new meaning to unity and multiplicity in the constituted sphere, and rendering it incommensurable with the realms from which the constituting resources are drawn. 10 In this way, constitution involves what may be referred to as different levels, starting, roughly, from correlations between the most rudimentary forms of subjectivity and objectivity, and evolving towards more complex and realistic forms. One instance of such constitutive stratification is the constitutive dependence of predicative experience on pre-predicative experience. Indeed, the idea of constitutive levels can be best understood if we keep in mind the kind of triangulation of which we have been speaking, viz., involving the present sensuous experience, the circumstances under which one has it, and the experienced aspects of objectivities. E.g., in Husserl's discussion of the visual experience of spatial objectivity, interactions between series of visual sensations and series of kinaesthetic sensations (the kinaesthetic circumstances) lead the subject to anticipate how the visual series will continue, and the visual experience thus comes to present the constant shape of an object. An account of how we experience, e.g., aspects of material thinghood or Lifeworldly thinghood, will involve triangulation on other kinds of items, and it will be possible to regard them in more substantial terms than our example of the spatial objectivity. 11 Thus, when giving an account of the "constitution," in perceptual experience, of aspects of the Lifeworldly thing, we will surely be able to draw upon not just the kinaesthetic sensations, but the experiencing and experienced moving body in a more robust sense, and speak of the subject's bodily movements (as experienced from the subject's point of view). However, despite such variation, the triangulation as such is required at all levels. We cannot do without a third item -while it may, in certain cases, be possible, indeed, necessary, to pack considerable complexity into our idea of the third item, so as to capture, e.g., one's sense that the experience of an object's shape depends not just on how it looks now and the way in which one is moving, but also on the way the object itself is moving, and shifting its shape, as well as how a pathology of one's visual organs may affect the continuation of the experience. 8 I do not propose to equate the meanings of "presence" and "constitution", but I hold that all objectual presence is constituted. 9 For an illustration of this leitmotif, see, e.g., Husserl 1997: 152. 10 Indeed, as is well known, Husserl also refers to the multitudinous sensations by means of the mass term "hyle", regarding them as a sensuous "matter". For a discussion of sensations and their role in perceptual experience, see also Husserl 1997: Sect. II, Ch. 3. 11 For a more detailed account of how different constitutive levels interrelate, with a focus on the levels of the spatial objectivity and material thinghood, see Husserl 1989: Section One.
I have been discussing the Husserlian constitutive approach with a view to making two points. One is that this approach involves the idea of an appropriate direction of clarification, viz., items higher up in the constitutive hierarchy are clarified by recourse to items at the lower levels, in view of the the constitutive dependence of the former on the latter. It will be seen that this is precisely my approach, as I seek to understand Döring's cases of CWC, viz., between a recalcitrant emotion and a judgment, by considering other more basic cases of similar conflicts. My second point will become relevant when, in the next section, we consider emotional experiences and the constitution of emotional properties. It is that when we, as part of our philosophical clarification work, analyze experiences for their constitution, we are by no means limited to considering only realistic scenarios, involving realistic aspects of human psychology. Indeed, the very idea of a constitutive hierarchy already jars with the idea of such a thoroughgoing realism, insofar as our analyses of the lower constitutive levels are barred from drawing upon resources only available at the higher levels, thereby excluding any top-down processes, e.g., accounting for the cognitive penetration of our sensuous or emotional experiences.
The better to prepare us for a discussion of recalcitrant experiences, I will add certain further ideas to the foregoing discussion of the rationality of perception. What we have said thus far may give rise to the concern that the phenomena of fulfillment and disappointment per se do not suffice to establish that perception is rational, insofar as one could perhaps think of them as something that just happens to the perceiver without his active involvement. If it is indeed the case that the perceiver just undergoes fulfillments and disappointments passively, then it would seem that we cannot speak about him as being either rational or irrational, and, so to speak, hold him praiseworthy or blameworthy accordingly. However, on the present view, the subject pursues fulfillments, and opens himself up to disappointments, as part of a pursuit of various epistemic and practical aims. Although we cannot, e.g., choose when to be disappointed, we can nevertheless actively pursue fulfillments and render ourselves open to disappointments, with the idea of "optimality" of givenness as guiding idea. 12 Such a process is responsive to the fullnesses, considered as evidence, that we ongoingly attain. Clearly, there are many ways in which our pursuit of fulfillments could go, when perceptually engaging with an object or a larger scene. E.g., we could be cultivating a focus on certain details in which we are primarily interested, to the exclusion of others, or skipping back and double-checking what we have already covered, so as to deal with possibilities of forgetting and change. We could be primarily seeking to bring into view new aspects of the object, or just keeping an eye on what is already in plain view. Let us call such series and patterns of fulfillment, "coverage" -a term I first introduced in (Laasik 2019b). Let us also say that the pursuit of a certain kind of coverage is due to a perceptual-level "mindset", i.e., perceptual interests and one's ways of going about satisfying them, sensitive to one's perceptual capacities and the changeable perceptual circumstances. 13 For her mindset and the related coverage, the perceiver can be held epistemically and practically praise-or blameworthy. E.g., a failure to open up to possible disappointment, viz., by neglecting to take a closer look at the crucial detail that could reveal the object as other than what one takes it to be, can render one epistemically blameworthy, or irrational.
We are now ready to speak about perceptual illusions, particularly ones that may persist in the face of one's better judgment, as is the case with the Müller-Lyer illusion. Our phenomenological take on illusions (and hallucinations) is rooted in the very idea of perceptual experience that we have hitherto been discussing. I believe that, considered from the phenomenological perspective, illusions are closely connected with disappointments. Indeed, some phenomenologists have argued that an illusion just is what is revealed as such in the further course of one's perceptual experience. 14 One reason to doubt this view is there are illusions like the Müller-Lyer illusion, which seem near-incorrigible in this way: we normally cannot help but see the two lines as being of unequal length. Even so, I believe that disappointment is an important aspect of a first-personal account of illusion. Remember that a constitutive, hierarchical account involves the idea that it is possible to clarify higher-level phenomena by appeal to the more basic, lower-level phenomena. This is the perspective that we ought to cultivate in elucidating persistent illusions. A constitutive account of illusions should take as its starting point the cases where disillusionment takes place by perceptual disappointment, to be suitably complemented, at higher constitutive levels, by references to other, intellectual and intersubjective sources of disillusionment. As for the perceptually near-incorrigible Müller-Lyer illusion, we need to account for it in its specificity, but we should not mistake it for a paradigmatic case of illusion. Rather, it needs to be regarded in the context of the more basic cases, where we may take ourselves to have been subject to an illusion if we have experienced, or expect to experience, a disappointment. In a situation stripped of more complex psychological resources, this is what it takes to grasp the illusoriness of an experience. 13 I borrow this expression ("Einstellung") and perhaps also the rough idea from Herbert Leyendecker, an early phenomenologist who was a member of the Munich and Göttingen Phenomenological Circles. While mindsets are an important concern for Leyendecker, he does not define the term, but merely elucidates it by offering miscellaneous examples and clarifications. E.g., we are told that the mindset of searching "works like a sieve, which lets fall through everything that does not fit, so that only that is spotted wherein I, in my attitude, as I search, "remain hanging" with my glance" (Leyendecker 1913, p. 52). Tracing the notion back to the psychology of Leyendecker's day, Kevin Mulligan elucidates it as "the higher-order unity of modes, tendencies, and dispositions which is often the function of determinate types of interest and attention" (Mulligan 1995, p. 204). Mulligan regards Leyendecker's incorporation of this notion into philosophy as a fruitful, indeed "elegant development of Husserl's account of the connection between optimality and interest" (ibid.). I would translate Leyendecker's "Einstellung" as "attitude", but we have already used this term, viz., in the above introductory remarks on Döring's view, in the sense of an intentional mode (vs. content). Mulligan, on his part, translates "Einstellung" as "set".
14 In a recent debate, Andrea Staiti (2015: 123-141) has argued that this idea captures the very essence of illusion. He presents this view as part of his critique of Claude Romano's "conjunctivist" view of illusion and hallucination. See Romano 2011 and 2012. Staiti's position is, in turn, criticized by Søren Overgaard (2018: 41-42), who espouses a "disjunctivist" view. In Laasik 2019a, I consider this debate in relation to Leyendecker's views. To conclude our discussion of perception, let us briefly compare our ideas with Döring's view, which she brings to bear on emotions. 15 Döring (2009: 243-244) has argued that, in accounting for CWC, we need, on the one hand, to appeal to the non-conceptual content of perceptions (and emotions), which she associates with the idea that perceptions (and emotions) do not enter into inferential relations but have a non-inferential logic of their own. In the paper just cited, the idea of a non-inferential logic of perception (or emotion) is not characterised positively, but is, instead, elucidated and supported by appeal to the failure of the idea of inferential relations involving perceptions (or emotions). For example, we are invited to agree with Tim Crane regarding the impossibility of inferring the perception of an object as being F and G, from the perception of it as F and the perception of it as G. On the basis of this and other examples, we are invited to draw the conclusion that perceptions (and emotions) are unlike beliefs "in that they do not stand in evidential relations, where evidential relations are one kind of inferential relations" (ibid.: 244).
I would draw the reader's attention to the multiple negativity of Döring's discussion, as highlighted by these brief pointers. While Döring effectively argues that there is no inferential perceptual justification, we draw upon Husserl's view that there is noninferential perceptual justification, viz., conceived in terms of fulfillment, as part of a layered constitutive account. This perspective allows us to be open to differences between the various constitutive levels: by contrast with the more basic cases, where it seems, as a matter of psychological fact, that evidential conflicts between phases of sensuous experience tend to be resolved by disappointments fairly straightforwardly, it may well be that the conflicts between the perceptual experience, and the belief or judgment, persist. The subject may fail to revise his beliefs in the face of overwhelming sensuous evidence, or he may be unable to see the object differently, despite harboring a well-supported belief to the effect that he is subject to an illusion.
On the other hand, Döring's explanation of CWC also involves an appeal to what she takes to be a peculiar feature of the perceptual and emotional attitudes (ibid.: 244-246). Specifically, "neither emotion nor perception 'aim at truth' in the sense that the subject must necessarily regard their content as true. … But this need not, and does not, prevent the subject from regarding these contents as true by default" (ibid.: 245). Insofar as "we treat our emotions and perceptions as cognitive mental subsystems whose function is to register stimuli so as to provide us with information about our environment" (ibid.), we regard these systems as reliable but fallible. We do not, Döring avers, regard the content of each particular element of the system as true, as we do in the case of elements of the system of judgment and belief. Even if the perception or the emotion persists in the face of better judgment, there is no contradiction, and the subject is not rendered irrational, and yet this is a "rational conflict" because the perceptions and the emotions are regarded as true by default.
In response to Bennett Helm's view to the effect that the conflict between recalcitrant perception and belief is a-rational, Döring duly notes that in many cases we are able to calibrate our perceptual (as well as emotional) experiences, and, in the recalcitrant cases, are in a position to withdraw our confidence from the illusory experience (ibid: 245-246).
While not objecting to this point, I believe that we can aim for a deeper understanding of the recalcitrant and other cases by invoking the ideas of mindset and coverage. Thus, in all cases of unresolved conflict, we can be regarded as being either rational or irrational, depending on whether we assume the right mindset towards them, and aim for the right kind of coverage. Optimally, in such cases, one needs to render oneself open to disappointment as far as possible, so as to resolve the CWC at the level of perception, viz., by taking a closer look at the crucial details, examining the object from different perspectives, etc. Indeed, even in the Müller-Lyer case, this is the right way to respond to the evidence, except if one is in a position to believe, not just that the two lines are of equal length, but also that the illusion is perceptually incorrigible. In that case, we should, indeed, just quarantine the recalcitrant experience-but it is a case that we are now able to regard in its proper context of other, more basic CWC.
Recalcitrant Emotion
I will now sketch an account of emotions, in particular, recalcitrant ones, based on the example of fear, pursuing a close analogy with the above account of perception. In a nutshell, I propose to consider emotions in terms of the Husserlian ideas of anticipations, fulfillments, and disappointments, and conceive of the presence of value properties in terms of fulfillment conditions; to regard the emotional fulfillments and disappointments (a kind of immediate confirmation and disconfirmation) as possessed of an epistemological and constitutive significance; and to conceive of the constitution of value properties in terms of something like the triangulation among visual sensations, kinaesthetic sensations, and spatial properties. The constitutively basic items will be regarded as suitable for clarifying that which is constitutively non-basic, and we will permit ourselves appeals to certain imaginary, indeed, un-realistic, emotional scenarios as part of our constitutive account.
Take, for example, my episodic fear of my neighbor's Rottweiler. According to our phenomenological account, I experience the dog as having the emotional property of fearsomeness. As I interact with it, I experience fulfillments or disappointments, confirming or disconfirming my emotional experience. Analogous to my sensuous perceptual experience, say, of an object's shape, these fulfillments and disappointments are made possible by my anticipations with regard to how the emotion will modulate as it unfolds, e.g., intensifying as the animal approaches, making shivers run down my spine as it bares its teeth and slobbers, rendering me almost paralyzed with fear as it reaches to sniff at my leg, evoking images of terrific pain and injury as it emits a growl. If the animal then lingers, but without appearing prone to imminent attack, I may expect to feel a cautious, muted relief and a return of composure. When it altogether loses interest in me and trots off, the fear should abate, as I become aware of its psychological and physical toll, leaving me shaken and exhausted. If the episode unfolds in such a predictable manner, I gain fulfillments, evidence of the dog's fearsomeness. If, to my surprise, the approach of the canine just brings a smile to my face, I am disappointed in the sense that the experiential evidence runs counter to anticipation, attesting to the dog's not being fearsome at all. While in the case of the sensuous perceptual experience of shape, the anticipations were due to the interactions of series of visual and kinaesthetic sensations, we are now dealing with the interactions of something like fearful feelings and other first-personal manifestations of fear, and, on the other hand, the relevant perceptually experienced circumstances, e.g., as I hear the dog barking, see it coming, or feel its muzzle move up my leg.
Yet, considering the complexities of real-life fears, there might seem to be aspects and cases of of fearful episodes that do not so clearly fit the proposed approach. A fear may just strike one, without there being any change in one's sensuous perceptual experience of one's circumstances, and then just vanish again-having perhaps to do with one's general mindframe or what thoughts and associations may be running through one's head. Also, different people are likely to experience fear in different circumstances, making it difficult to attribute one specific pattern, or rule, of fulfillments to all cases. Finally, when having a negative emotion like the fear of the Rottweiler, people seem to be primarily pursuing safety and seeking to rid themselves of the emotion, instead of pursuing fulfillments of the various aspects of the fear -as a connoisseur might observantly stroll around a sculpture, taking in the complexities of its shape.
I expect that, being presented with these considerations, the reader is likely to judge that a good deal still needs to be done to duly clarify my view, and may, indeed, harbor objections to it, perhaps along the lines of the above pointers. I will therefore, so to speak, try to put myself into the position of such a reader, casting the following discussion, including various clarifications of my ideas, as replies to three possible objections.
The first objection is that my idea seems an irremediable non-starter, insofar as emotions are not obviously responsive to changes in circumstances in the same way as sensuous perception is, with objects and properties appearing in regular, predictable series of appearances. By contrast, emotions may sometimes seem too mercurial, and at other times too flat, for this idea to work. A person's emotional state may change without any particularly significant changes in his outward circumstances, and sometimes stay the same despite great changes therein. Moreover, different people's emotional lives are obviously rather different, making it difficult to come up with something like a unique rule, or pattern, that captures the fulfillments in terms of which we might be able to conceive of, say, fear.
Yet, I believe that we can defend our account, and the Husserlian analogy between perception and emotion, from this objection. In the context of a Husserlian constitutive account, we can base our view on rule-governed scenarios involving something like proto-emotions, where we abstract away from most of the complexities of actual human emotions. We need a conception on which the rudiments of a certain kind of emotion are still recognizable, and which incorporates the core Husserlian idea of intuitive evidence, integrating fulfillment and disappointment with the changing circumstances. Thus, our conception of fear may be anchored in something like a proto-subject's proto-fear, which displays the simple dynamic of intensifying when the fearsome object looms greater and abating when it looms lesser. Here our conception of fear just barely gains its first foothold, under circumstances suggestive of a less than fully constituted perceptual world. 16 We can think of our realistic emotions as obtaining when sufficient complexity accrues to something like this simple basis. As we pursue the analogy with perception in the more complicated cases, viz., by regarding emotional content in terms of fufillment conditions, we need not identify the emotionally relevant circumstances, and the changes thereof, with the perceptually relevant ones (e.g., the unfolding of series of kinaesthetic sensations, etc.). Indeed, one way of complicating emotional situations is by allowing and providing for circumstances in which the object of the emotion is not (continuously) present in sensuous perception. 17 This constitutive approach offers a kind of grasp as to what the constitutive rules for the various emotional properties might be like, but we cannot expect these rules to be entirely transparent to the subject of the emotion, or even to the phenomenologist. Indeed, if our account pretended to excessive transparency and predictability of emotions, there would be reason to suspect that it has lost touch with the realities of our emotional life. When we normally experience our own and other people's emotions, we can basically make sense of them, but they are not entirely transparent to us: emotions can be confusing and unpredictable. It is not a flaw of our sketch of a constitutive analysis if it reflects this partial opacity. The philosophical yield of the view consists in an analysis of emotional intentionality, viz., in terms of the core elements of the Husserlian account of sensuous perception-which enables us to do better than leave emotional intentionality sui generis and mysterious.
For another objection, it might be suggested that our analogy between perception and emotion fails, because the idea of an emotional disappointment is problematic. In particular, one might question the applicability of the idea of a disappointment as a sudden surprise, explosive, as it were, of the emotional content, revelatory of the object's never having had the pertinent value property.
In reply, I would, on the one hand, point out that even sensuous perceptual disappointments do not need to be of this "explosive" kind. Both in the case of sensuous perception, and emotion, is it, in principle, possible that the evidential conflict is resolved in this abrupt and conclusive manner, or that there is a less abrupt or less definitive resolution. 18 For a closely related point, it seems that there is no necessary connection between a disappointment and the adjunct emotion of a sudden surprise. The more 16 I have conjured up an imaginary scenario that meets our present needs. Somebody else might come up with a different one, and, likewise, hold it before the mind's eye, in seeking to extend to emotions the idea of the kind of constitutive triangulation of which we spoke in the previous section.
17 In this case, there would be no sensuous perceptual fullness. However, if such a scenario is integrated into the fulfillment conditions for an emotion, we could still be achieving emotional fulfillments. Indeed, if there were no emotional fullness involved, we would not be dealing with an emotion at all, but perhaps a mere empty evaluative judgment.
18 Pertinent to this, Husserl discusses a case where perceptual experience vacillates between a man-apprehension and a mannequin-apprehension, remaining doubtful, as it were, even if one of the conflicting apprehensions temporarily gains the upper hand (Husserl 1973: 92). fundamental issue is whether it is possible to tell the difference between cases where an object is revealed as having had and lost a certain value property, and cases where an object is revealed as never having had the value property at all. Here, someone might be inclined to believe that there is no way to tell the difference, or that the latter kind of case is rare, and that emotional disappointment is therefore rare, and somehow insignificant. In my view, the difference between the former and the latter kind of case may often be subtle, and we may not normally give this difference much thought, because many situations do not call for discriminating between them. E.g., whether the object was never really fearsome, or whether it merely ceased to be fearsome, I am not in fear of it now, giving me reason to believe that I am not in any danger and can therefore concern myself with other matters. However, it could be possible to tell the difference by reflection as to whether one has the sense that one's previous episode of fear was appropriate or inappropriate. Its inappropriateness may, for example, be signaled by an oncoming feeling of embarrassment. 19 This would render the embarrassment a mark of emotional disappointment, at least in the case of some emotions.
The more reason to believe that the difference between a disappointment and a mere experience of value change is accessible to us, I believe that a disappointment is never just a rebuttal of one body of evidence by another, but, rather, a kind of undercutting, or undermining. One's sense of appropriateness or inappropriateness is therefore not just associated with one's sense of the weight of two bodies of evidence vis-à-vis each other, but with a sense of whether or not one of the two has been vitiated, corrupted, or enfeebled. E.g., my most recent experiences of the object's color lead me to realize that my previous color experiences must have been due to a trick of the ambient lighting. Or, my initial fears of the fearsome-seeming dog are left discredited by the ensuing experience of how pleasant it feels to interact with the animal. (I may now be embarrassed at these fears.) In sum, I believe that there is a difference between cases where an object is experienced as having lost a value property, and where it is experienced (in a disappointment) as never having had the value property, and I have no reason to believe that the second kind of case is somehow so rare or improbable as to render otious any appeals to emotional disappointments. 19 This idea has been proposed by John Drummond (2004: 122-124). Drummond's view is perceptualist in the sense that he takes emotions to be directed to value properties, and revelatory of them by immediate insight. Importantly, he distinguishes three ways in which an emotion can be revealed as inappropriate. First, the emotion may have a basis in putative facts that fail to obtain. E.g., I may be afraid of what I take to be a wayside snake, but it is, in fact, merely a fallen tree branch. Second, the emotion may be revealed as inappropriate by another emotion. E.g., if I fear dogs to the point that I am even afraid of a cute little puppy, then it may transpire that my fear, at one point, gives way to embarrassment at my fearfulness, and the embarrassment reveals the fear as inappropriate. Third, the emotion may conflict with one's considered value judgment. E.g., one's disgust at seeing a person bearing the marks of terrible injuries, may come up against one's judgment to the effect that this is an inappropriate emotional reaction.. I accept this analysis. As far as I know, Drummond does not expressly discuss whether the conflict between the emotion and the judgment is rightly regarded as a CWC. The crucial difference between my approach and Drummond's is that, unlike Drummond, I regard the emotional experience as presenting value properties through a process of rule-governed variation, thus pursuing the closer analogy between perception and emotion.
Here is a third objection to consider: our account involves the idea of a pursuit of emotional fulfillments, in something like an exploration of an emotional property, with the aim of achieving a fuller revelation of it; yet this idea may not seem to sit well with the way we experience negative emotions. In the case of positive emotions, it does seem plausible that one explores their different aspects, indeed, with relish, to gain a more complete sense of the object's potential for arousing and sustaining positive emotion-in much the same way that one might follow a perceptual interest in examining aspects of an object in sensuous perception. This does not, however, seem like an adequate picture of the way we experience negative emotions like fear, despair, or disgust. To address this worry, we can draw upon the idea of perceptual optimalities. Namely, it seems to me that we often live with negative emotions, and pursue our experience of them, in such a way as to facilitate finding a way out of these emotions: the optimal coverage is such as to render oneself open to an emotional disappointment (or, alternatively, to the waning and disappearance of the emotion), thereby also opening up to other, more positive emotions. One cannot will away negative emotions but one can, as it were, manage them. E.g., confronting one's negative emotions is sometimes a good way to overcome them. Thus, in Werner Herzog's documentary The Great Ecstasy of Woodcarver Steiner, Walter Steiner, a champion ski jumper, suffers a terrible fall. Nevertheless, he is determined to make another jump in the same competition -and he does so -because he knows that if he does not, at once, confront his fear, he may never be able to conquer it and jump again.
Let us take stock of the main aspects of the perception-emotion analogy. We have presented emotions, with a focus on the example of fear, as being responsive to experiential evidence, based on the idea that they are like perceptual experiences in having fulfillmentconditional content. As part of the fulfillment-based idea, we have accepted that emotions can be involved in evidential conflicts, which can be resolved in disappointments, and which involve no logical contradiction. Now we face the task of using these ideas to account for the CWC between recalcitrant emotions and one's better judgment. Our discussion of ski jumper Steiner already implicitly contains the answer to this problem: in response to this kind of CWC, we can and should assume the mindset of managing our emotion by pursuing a certain kind of coverage, which will render us open to a disappointment and show us the way out of the unwarranted (and unwanted) affective mindset. I would emphasize that such management of emotions is not only pragmatically but also epistemically significant: e.g., Steiner, we may suppose, is aiming for an emotional insight into the incorrectness, misguidedness of his fear. This is the way to handle recalcitrant emotions, except perhaps in special cases where one has reason to believe that it would not help. In such exceptional cases, one should, indeed, just "quarantine" the emotion, so that it cannot influence one's beliefs or actions.
This view is similar to Döring's in that we have proposed to account for emotional CWC by offering a view of the contents and attitudes of recalcitrant emotional experiences. We have allied ourselves with Döring in accounting for CWC in quasi-perceptual terms, involving both the contents and attitudes of emotional experiences. Yet, by contrast with Döring, we have given an account of non-inferential justification in positive terms, viz., by invoking fulfillment. The ideas of fulfillment and disappointment also spare us the need to articulate emotional CWC by appeal to the notion of a reliable but fallible emotional cognitive system. Befitting a phenomenological approach, we have tried to be faithful to the subject's perspective of his emotional experiences, and the appeal to a reliable system clearly clashes with this (not particularly parochial, as far as I can tell) commitment. The view that sensuous perceptual experiences are reliable though fallible may not flagrantly clash with first-personal data. However, applied to emotional experiences, the idea clearly amounts to an extrinsic imposition, since subjects are liable to assume all kinds of complex postures with regard to the reliability of emotional experiences.
Conclusion
In this paper, I have rehearsed a kind of Husserlian perceptualist view of emotions. By appealing to the Husserlian ideas of fulfillment and disappointment, and by conceiving of perceptual and emotional contents in terms of fulfillment conditions, I have presented a picture on which both perception and emotion are rational, in the sense of being responsive to experiential evidence. I have also made use of this perceptualist view in accounting for the so-called conflicts without contradiction between a recalcitrant emotion and a judgment. With resolution of evidential conflicts at different constitutive levels being part of the subject's response to evidence, we have elucidated the recalcitrant emotions and the CWC by invoking aspects of the larger context of our emotional lives. In discussing the CWC, I took as my starting point Sabine Döring's setup of the problem of CWC, as well as her instructive reflections on its broader philosophical signficance. I also briefly compared my solution with hers. | 10,431.4 | 2020-04-21T00:00:00.000 | [
"Philosophy"
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Regulation of Epithelial Na+ Transport by Soluble Adenylyl Cyclase in Kidney Collecting Duct Cells*
Alkalosis impairs the natriuretic response to diuretics, but the underlying mechanisms are unclear. The soluble adenylyl cyclase (sAC) is a chemosensor that mediates bicarbonate-dependent elevation of cAMP in intracellular microdomains. We hypothesized that sAC may be an important regulator of Na+ transport in the kidney. Confocal images of rat kidney revealed specific immunolocalization of sAC in collecting duct cells, and immunoblots confirmed sAC expression in mouse cortical collecting duct (mpkCCDc14) cells. These cells exhibit aldosterone-stimulated transepithelial Na+ currents that depend on both the apical epithelial Na+ channel (ENaC) and basolateral Na+,K+-ATPase. RNA interference-mediated 60-70% knockdown of sAC expression comparably inhibited basal transepithelial short circuit currents (Isc) in mpkCCDc14 cells. Moreover, the sAC inhibitors KH7 and 2-hydroxyestradiol reduced Isc in these cells by 50-60% within 30 min. 8-Bromoadenosine-3′,5′-cyclic-monophosphate substantially rescued the KH7 inhibition of transepithelial Na+ current. Aldosterone doubled ENaC-dependent Isc over 4 h, an effect that was abolished in the presence of KH7. The sAC contribution to Isc was unaffected with apical membrane nystatin-mediated permeabilization, whereas the sAC-dependent Na+ current was fully inhibited by basolateral ouabain treatment, suggesting that the Na+,K+-ATPase, rather than ENaC, is the relevant transporter target of sAC. Indeed, neither overexpression of sAC nor treatment with KH7 modulated ENaC currents in Xenopus oocytes. ATPase and biotinylation assays in mpkCCDc14 cells demonstrated that sAC inhibition decreases catalytic activity rather than surface expression of the Na+,K+-ATPase. In summary, these results suggest that sAC regulates both basal and agonist-stimulated Na+ reabsorption in the kidney collecting duct, acting to enhance Na+,K+-ATPase activity.
Alkalosis impairs the natriuretic response to diuretics, but the underlying mechanisms are unclear. The soluble adenylyl cyclase (sAC) is a chemosensor that mediates bicarbonatedependent elevation of cAMP in intracellular microdomains. We hypothesized that sAC may be an important regulator of Na ؉ transport in the kidney. Confocal images of rat kidney revealed specific immunolocalization of sAC in collecting duct cells, and immunoblots confirmed sAC expression in mouse cortical collecting duct (mpkCCD c14 ) cells. These cells exhibit aldosterone-stimulated transepithelial Na ؉ currents that depend on both the apical epithelial Na ؉ channel (ENaC) and basolateral Na ؉ ,K ؉ -ATPase. RNA interference-mediated 60 -70% knockdown of sAC expression comparably inhibited basal transepithelial short circuit currents (I sc ) in mpkCCD c14 cells. Moreover, the sAC inhibitors KH7 and 2-hydroxyestradiol reduced I sc in these cells by 50 -60% within 30 min. 8-Bromoadenosine-3,5-cyclic-monophosphate substantially rescued the KH7 inhibition of transepithelial Na ؉ current. Aldosterone doubled ENaC-dependent I sc over 4 h, an effect that was abolished in the presence of KH7. The sAC contribution to I sc was unaffected with apical membrane nystatin-mediated permeabilization, whereas the sACdependent Na ؉ current was fully inhibited by basolateral ouabain treatment, suggesting that the Na ؉ ,K ؉ -ATPase, rather than ENaC, is the relevant transporter target of sAC. Indeed, neither overexpression of sAC nor treatment with KH7 modulated ENaC currents in Xenopus oocytes. ATPase and biotinylation assays in mpkCCD c14 cells demonstrated that sAC inhibition decreases catalytic activity rather than surface expression of the Na ؉ ,K ؉ -ATPase. In summary, these results suggest that sAC regulates both basal and agonist-stimulated Na ؉ reabsorption in the kidney collecting duct, acting to enhance Na ؉ ,K ؉ -ATPase activity.
Maintenance of intracellular pH depends in part on the extracellular to intracellular Na ؉ gradient, and elevation of intracellular [Na ϩ ] can lead to acidification of the cytoplasm. It has been shown that acidification of the cytoplasm of cells from frog skin and toad bladder by increased partial pressure of CO 2 reduces Na ϩ transport and permeability (1,2). Conversely, the rise in plasma bicarbonate caused by metabolic alkalosis with chronic diuretic use has been shown to increase net renal Na ϩ reabsorption independently of volume status, electrolyte depletion, and/or increased aldosterone secretion (3,4). However, the underlying mechanisms involved in these phenomena remain unclear.
The soluble adenylyl cyclase (sAC) 2 is a chemosensor that mediates the elevation of cAMP in intracellular microdomains (5)(6)(7). Unlike transmembrane adenylyl cyclases (tmACs), sAC is insensitive to regulation by forskolin or heterotrimeric G proteins (8) and is directly activated by elevations of intracellular calcium (9,10) and/or bicarbonate ions (11). Thus, sAC mediates localized intracellular increases in cAMP in response to variations in bicarbonate levels or its closely related parameters, partial pressure of CO 2 and pH. Mammalian sAC is more similar to bicarbonate-regulated cyanobacterial adenylyl cyclases than to other mammalian nucleotidyl cyclases, which may indicate that there is a unifying mechanism for the regulation of cAMP signaling by bicarbonate across biological systems. Although sAC appears to be encoded by a single gene, there is significant isoform diversity for this ubiquitously expressed enzyme (11,12) generated by alternative splicing (reviewed in Ref. 13). sAC has been shown to regulate the subcellular localization and/or activity of membrane transport proteins such as the vacuolar H ϩ -ATPase (V-ATPase) and cystic fibrosis transmembrane conductance regulator in epithelial cells (14,15). Functional activity of sAC has been reported in the kidney (16), and sAC has been localized to epithelial cells in the distal nephron (14,17).
Given that natriuresis is decreased during metabolic alkalosis, when bicarbonate is elevated, and Na ϩ reabsorption is impaired by high partial pressure of CO 2 , we hypothesized that bicarbonate-regulated sAC may play a key role in the regulation of transepithelial Na ϩ transport in the distal nephron. Reabsorption of Na ϩ in the kidney and other epithelial tissues is mediated by the parallel operation of apical ENaC and basolateral Na ϩ ,K ϩ -ATPase, and both transport proteins can be stimulated by cAMP via the cAMP-dependent protein kinase (PKA) (18,53). The aims of this study were to investigate the role of sAC in the regulation of transepithelial Na ϩ transport in the kidney through the use of specific sAC inhibitors and electrophysiological measurements. We found that sAC inhibition blocks transepithelial Na ϩ reabsorption in polarized mpkCCD c14 cells under both basal and hormone-stimulated conditions. Selective membrane permeabilization studies revealed that although ENaC activity appears to be unaffected by sAC inhibition, flux through the Na ϩ ,K ϩ -ATPase is sensitive to sAC modulation. Inhibiting sAC decreases ATPase activity without affecting plasma membrane expression of the pump; thus, tonic sAC activity appears to be required for Na ϩ reabsorption in kidney collecting duct.
EXPERIMENTAL PROCEDURES
Reagents and Chemicals-All of the chemicals were obtained from Sigma-Aldrich unless otherwise stated. The specific sAC inhibitor KH7 was synthesized, purified, and characterized as previously described (20). Estradiol and the catechol estrogen (CE) 2-hydroxyestradiol were obtained from Steraloids, Inc. 8-Bromoadenosine-3Ј,5Ј-cyclic monophosphate (8-Bromo-cAMP) was obtained from Biomol.
Tissue Preparation, Immunofluorescence Labeling, and Confocal Microscopy-All of the animal protocols were approved by the Institutional Animal Care and Use Committee of the University of Pittsburgh. Adult male Sprague-Dawley rats were anesthetized using sodium pentobarbital (65 mg/kg of body weight, intraperitoneally), and their kidneys were perfused via the left ventricle with phosphate-buffered saline (PBS, pH 7.4) followed by a fixative containing 4% paraformaldehyde, 10 mM sodium periodate, 70 mM lysine, and 5% sucrose (PLP fixative), as described previously (21,22). The kidneys were harvested and further fixed by immersion in PLP fixative overnight at 4°C and then cryoprotected in 30% sucrose for 12 h at 4°C. The tissues were embedded in Tissue-TEK OCT Compound (Sakura Finetek), mounted on a cutting block, and then frozen in a Reichert Frigocut microtome. The sections were collected onto Superfrost Plus slides (Fisher).
Immunofluorescence labeling was performed on 4-m cryostat sections. The R21 monoclonal antibody, raised in mouse against amino acids 203-216 of human sAC encompassing the catalytic regions (C1 and C2), was used for sAC immunofluoresence labeling in adult rat kidney (5,14). SDS antigen retrieval was employed as previously described (23). The slides were rehydrated with PBS followed by 1% SDS treatment for 4 min and three washes in PBS of 5 min duration each. The slides were then incubated with blocking solution containing 1% bovine serum albumin in PBS and then incubated with either the anti-sAC R21 antibody (1:300 dilution of 3 mg/ml stock in DAKO background-reducing diluent; DAKO) alone, or in conjunction with chicken polyclonal antibody against the E subunit of the V-ATPase, a marker of intercalated cells (GenWay; 1:4,000), for 75 min at room temperature. For peptide competition controls, the immunizing peptide (EIE-SVPDQRAVKVNA) was preincubated at a concentration of 50 g/ml with the R21 antibody, and this peptide-antibody mixture was then used as the primary antibody. After primary antibody exposure the slides were washed twice for 5 min in PBS with 2.7% NaCl and then once with PBS. The secondary antibodies applied were goat anti-mouse conjugated to fluorescein isothiocyanate (1:100) or donkey anti-chicken conjugated to CY5 (1:100; secondary antibodies from Jackson Immunologicals). After washing off the secondary antibody as above, the slides were mounted in Vectashield (Vector Labs) and coverslipped.
The images were obtained using an ϫ40 plan-apochromat oil objective in a TCS-SL confocal microscope (Leica) equipped with an argon laser, as well as a green and red helium-neon lasers. The images obtained with the CY5 fluorophore were pseudo-colored red. The confocal laser acquisition settings were identical for both the peptide inhibition and the R21 antibody-stained slides, and the contrast levels of the two images were adjusted simultaneously in Photoshop (Adobe).
Transepithelial I sc Measurements-mpkCCD c14 cells were cultured as previously described (24). The cells grown on Transwell filter supports (Costar) were mounted in modified Costar Ussing chambers, and the cultures were continuously short circuited with an automatic voltage clamp (Department of Bioengineering, University of Iowa, Iowa City, IA). Transepithelial resistance was measured by periodically applying a 2.5-mV bipolar pulse and calculated by Ohm's law. The bathing Ringer's solution composition, gassing, and washing techniques have been described previously (25). In some experiments equivalent I sc was measured using a portable epithelial volt ohmmeter (World Precision Instruments), as previously described (26).
To isolate apical membranes electrically, 100 M nystatin was added to the basolateral side to permeabilize the membrane, and an apical (140 mM) to basolateral (25 mM) Na ϩ gradient was established as described previously (25). For apical membrane permeabilization with nystatin, bathing Ringer's solutions were kept identical on both sides of the chamber. In some experiments where the apical membrane was permeabilized, the same modified Ussing chambers were used to record simultaneous I sc and total capacitance (C T ) traces, as described in detail previously (25,27,28).
Oocyte Two-electrode Voltage Clamp Measurements-NH 2terminal glutathione S-transferase-tagged truncated mouse sAC (sACt) was subcloned into the dual mammalian oocyte expression vector pMO (29) using the BamHI and EcoRI restriction sites in pMO and PCR amplification of template sACt (8). An NH 2 -terminal hemagglutinin (HA) tag was also added. The following primers were used for PCR amplification: 5Ј-TCATCAGGATCCACCATGTACCCATACG-ATGTTCCAGATTACGCTTCCCCTATACTAGGTTAT-TGG-3Ј (sense) and 5Ј-TCATCATCGAATTCCTAACAC-GTCACTTTCTCATT-3Ј (antisense). The resulting pMO-HA-sACt plasmid was verified by DNA sequencing. Complementary RNAs (cRNAs) of sACt used for Xenopus oocyte expression were synthesized using the mMessage mMachine kit (Ambion) according to the manufacturer's instructions after linearizing template pMO-HA-sACt plasmid DNA with HpaI. ENaC cRNAs were similarly synthesized, and oocytes were harvested, collagenase-treated, and maintained as described previously (29), and injected with cRNAs as indicated in the Fig. 7 legend. Two-electrode voltage clamp measurements of amiloride-sensitive ENaC currents in oocytes were performed 1-2 days after cRNA injection as described previously (29) after microinjection with KH7 or vehicle (Me 2 SO).
Immunoblotting and Cell Surface Biotinylation Assays-R21 primary antibody against sAC was used at 1:1000 for immunoblotting. For peptide competition controls, immunizing peptide was incubated with R21 antibody diluted in Tris-buffered saline Tween 20 ϩ 5% milk for 30 min prior to blotting. The final concentration of immunizing peptide used was 25 g/ml.
Surface biotinylation studies were performed on mpkCCD c14 cells based on a previously described protocol (30). Cells grown on Transwells (Costar) were washed three times for 5 min with ice-cold PBS containing Mg 2ϩ and Ca 2ϩ with agitation on ice to remove media. The basolateral membrane was biotinylated using 1.6 mg/ml EZ-Link Sulfo-NHS-SS-Biotin (Pierce) in PBS for 20 min. The apical surface was incubated in medium containing 10% fetal bovine serum to prevent biotinylation of apical proteins. The biotinylation reaction was then quenched by adding 10% fetal bovine serum-containing medium to the basolateral surface. The monolayers were washed three times with ice-cold PBS with agitation on ice prior to lysing cells in cell lysis buffer (0.4% deoxycholic acid, 1% Nonidet P-40, 50 mM EGTA, 10 mM Tris-Cl, pH 7.4) plus protease inhibitors at room temperature for 10 min. Protein concentration of the postnuclear supernatant was determined, and 250 g of protein was combined with streptavidin-Sepharose beads (Pierce) and incubated overnight at 4°C. Samples from the streptavidin beads were washed three times in radioimmunoprecipitation assay buffer and collected in 2ϫ sample buffer containing 10% -mercaptoethanol and incubated for 20 min at room temperature. The proteins were heated to 95°C for 3 min, separated by SDS-PAGE, and subjected to Western blot analysis using anti-Na ϩ ,K ϩ -ATPase ␣ subunit antibody (Santa Cruz Biotechnology).
Na ϩ ,K ϩ -ATPase Activity Assays-ATPase assays were performed essentially as described previously (31), based on the method of Forbush (32). mpkCCD c14 cells grown on 6-well Transwells were washed three times for 5 min in ice-cold PBS containing Mg 2ϩ and Ca 2ϩ . The cells were scraped in PBS and pelleted. The cells were then resuspended in lysis buffer (150 mM NaCl, 10 mM Tris-Cl, 2 mM EDTA, pH 7.0) containing protease inhibitors and sonicated for 5 s. The lysate was centrifuged at 13,000 ϫ g for 3 min, and the supernatant was transferred to a high speed microcentrifuge tube. The supernatant was centrifuged at 100,000 ϫ g for 1 h. The pellet containing Na ϩ ,K ϩ -ATPase was resuspended in 50 mM imidazole, 2 mM EDTA, pH 7.0, and protein concentration was determined. To activate latent Na ϩ ,K ϩ -ATPase activity, 50 g of total protein was then added to a final volume of 150 l in buffer containing 0.065% deoxycholic acid in 50 mM imidazole, 2 mM EDTA, pH 7.0, and incubated for 30 min at room temperature. Na ϩ ,K ϩ -ATPase activity was measured by incubating 25 l of the activated sample for 10 min at 37°C with 1 ml of assay buffer (120 mM NaCl, 25 mM KCl, 4 mM ATP, 4 mM MgCl 2 , 60 mM Tris-Cl, 1 mM EDTA, pH 7.5) in the presence or absence of 1 mM ouabain and 100 M strophanthidin. The reactions were stopped with 1 ml of ice-cold 0.5 M HCl containing 30 mg of ascorbic acid, 5 mg of ammonium hetamolybdate, and 10 mg of SDS. The tubes were then transferred to an ice bath for 10 min prior to adding 1.5 ml of color development solution containing 30 mg of sodium meta-arsenite, 30 mg of sodium citrate, and 30 l of acetic acid. The tubes were finally heated for 10 min at 37°C, and absorbance was read at 850 nm. The difference in absorbance between untreated samples and samples treated with Na ϩ ,K ϩ -ATPase inhibitors is reported.
Statistics-Statistical analyses were performed using either StatView (SAS) or SigmaPlot (Jandel Scientific) software. Unpaired Student's t tests were performed to compare relevant data samples from I sc , biotinylation, and ATPase measurements. Analysis of variance was used to compare data obtained from different batches of oocytes for two-electrode voltage clamp experiments. In all cases p values Ͻ 0.05 were considered significant.
RESULTS
sAC Expression in Kidney and mpkCCD c14 Cells-We and others have previously shown sAC expression in rat kidney using immunofluorescence labeling and confocal microscopy in distal tubular epithelial cells (especially thick ascending limb of Henle's loop and collecting duct) (14,17). We confirmed sAC localization in the thick ascending limb of Henle's loop and demonstrated its presence in both collecting duct principal cells, which are the cells that express ENaC, and intercalated cells, which express apical membrane V-ATPase (Fig. 1A, right panel) (33). Immunofluorescence labeling of sAC was fully competed off using the immunizing peptide for this antibody (Fig. 1A, left and middle panels), demonstrating the specificity of this staining for sAC. To confirm that sAC is expressed in immortalized mouse collecting duct cells, we immunoblotted mpkCCD c14 cell lysates using the R21 antibody (Fig. 1B). Several bands are apparent, including major bands at ϳ50 -53 kDa, consistent with the predicted mobility of somatic sAC isoforms previously identified in whole kidney (34). All of the bands were competed off with the immunizing peptide, suggesting that the other bands represent additional, as yet uncharacterized sAC isoforms or degradation bands of the known full-length or sACt splice variants. Thus, sAC is present in kidney epithelial cells, both intercalated cells and principal cells, and in the sodium reabsorbing, principal cell-like mpkCCD c14 cell line.
Knockdown of sAC Inhibits Transepithelial Na ϩ Current in mpkCCD c14 Cells-To test whether sAC plays a role in regulating transepithelial Na ϩ transport under basal conditions, we knocked down sAC protein expression in polarized mpkCCD c14 cells using siRNA oligonucleotides whose sequences are analogous to siRNAs previously shown to be effective in rat cell lines (35,36) and primary cells (37). We then mounted the polarized monolayers in Ussing chambers to measure the effect of sAC knockdown on I sc (Fig. 2). As compared with control (nontargeting) siRNA, transfection of siRNA directed against mouse sAC yielded ϳ60% knockdown of the predominant somatic sAC isoforms of ϳ50 -53 kDa (Fig. 2, A and B). In association with this sAC knockdown, amiloride-sensitive I sc was inhibited to a comparable extent (ϳ70%; Fig. 2C). This finding in kidney-derived collecting duct cells suggests that sAC is required for Na ϩ reabsorption under base-line conditions. However, this experimental approach cannot address the potential role of acute changes in sAC activity on Na ϩ transport.
sAC Inhibitors Block Basal and Stimulated Transepithelial Na ϩ Reabsorption in mpkCCD c14 Cells-To test how quickly and to what extent Na ϩ current responds to sAC modulation, we treated polarized mpkCCD c14 cells mounted in Ussing chambers with the recently characterized sAC-specific inhibitor KH7 (20, 36 -39). Apical KH7 treatment (60 M) caused a rapid reduction of I sc to 40 -50% of control levels by 30 min (Fig. 3A). We observed a similar time-and concentration-dependent inhibition of I sc by an alternative sAC-selective inhibitor (40), the CE compound 2-hydroxyestradiol (20 -120 M; Fig. 3B). The structurally similar compound 17- estradiol (120 M), which does not inhibit sAC, had no effect on I sc (Fig. 3B). Monitoring of transepithelial resistance, as measured by periodic voltage pulses during voltage-clamp recordings of I sc (see "Experimental Procedures"), demonstrated that these sAC inhibitors did not have discernable effects on tight junction Kidney Epithelial Na ؉ Transport Regulation by sAC FEBRUARY 27, 2009 • VOLUME 284 • NUMBER 9 resistance, a marker for epithelial monolayer viability (data not shown).
These results indicate that sAC activity is important in maintaining basal transepithelial Na ϩ transport in mpkCCD c14 cells. We next sought to determine whether sAC activity is necessary for agonist-stimulated transepithelial Na ϩ -dependent I sc . ENaC-dependent Na ϩ transport has been shown to be acutely up-regulated in a wide variety of tissues and cell types following stimulation of tmAC by either vasopressin or forskolin or following addition of cell-permeant analogs of the second messenger cAMP (18,25,41,42). These agonists all lead to a rapid stimulation of ENaC-dependent Na ϩ transport via acute increase in the number (N) of channels at the apical membrane mediated by PKA-dependent exocytosis. To examine the importance of sAC activity on regulated Na ϩ transport, we first explored the effects of KH7 on the I sc response to forskolin, a potent stimulator of cAMP production exclusively by tmACs. We have shown previously that forskolin treatment induces a rapid stimulation of I sc in these cells caused by PKA-dependent insertion of new ENaC channels at the apical membrane (25). Consistent with our earlier results, 10 M forskolin induced a rapid increase in Na ϩ current to ϳ300% of control levels over 60 min following pretreatment with vehicle control (Fig. 4). Interestingly, however, forskolin had no stimulatory effect on the measured I sc following a 30-min pretreatment with KH7. Because forskolin stimulation of tmAC is not directly inhibited by KH7 (20,36,37,39), these results suggest that the cAMP generated by forskolin-stimulated tmACs is not sufficient to overcome sAC inhibition and that sAC activity may be required for the increased transepithelial I sc caused by stimulation of tmACs as well as basal Na ϩ transport.
Because the enzymatic product of sAC is cAMP, we next tested whether treating polarized mpkCCD c14 cells with the cell-permeant cAMP analog 8-Bromo-cAMP could override the inhibition of Na ϩ current by the sAC inhibitor KH7. Treatment for 15 min with 1 mM 8-Bromo-cAMP approximately doubled the amiloride-sensitive equivalent I sc under control conditions (Fig. 5, left bars). KH7 treatment for 30 min inhibited I sc by ϳ50% relative to untreated controls (gray bars). However, the addition of 8-Bromo-cAMP during the last 15 min of KH7 exposure substantially blunted this KH7 inhibition, approximately doubling the current relative to cells treated with KH7 alone (Fig. 5, right bars). These results suggest that treating these cells with membrane-permeable cAMP analogs can at least partially overcome the effects of sAC inhibition.
We next examined the effects of the sAC inhibitor KH7 on stimulation of ENaC-dependent Na ϩ transport by the mineralocorticoid aldosterone, an agonist that acts by fundamentally different mechanisms. Aldosterone stimulates Na ϩ transport primarily through the synthesis of new proteins, although nongenomic pathways have been described in some cell systems and tissues (43). Aldosterone stimulates the synthesis of proteins that enhance ENaC abundance (N) at the apical membrane by inhibiting Nedd4 -2 dependent retrieval of the channel (44) and may also affect open probability (P o ) of the channel by either phosphatidylinositol 1,4,5-trisphosphate or direct methylation of the channel (45,46). In addition, aldosterone induces increased synthesis of both ENaC subunits and the basolateral Na ϩ ,K ϩ -ATPase (47,48). It was thus of interest to determine whether sAC activity is required for the aldosteronedependent stimulation of Na ϩ transport in polarized mpkCCD c14 cells. Cells treated with 1 M aldosterone exhibited a doubling of amiloride-sensitive Na ϩ current over 4 h relative to untreated controls (Fig. 6, closed symbols). However, pretreatment with KH7 for 30 min prior to aldosterone addition caused a substantial reduction in current that was not significantly modulated by subsequent aldosterone treatment (Fig. 6, open symbols). These results suggest that the aldosterone-de-pendent stimulation of transepithelial Na ϩ transport is dependent on sAC activity.
The observations that sAC inhibitors reduce not only basal I sc , but also I sc stimulated by two distinct agonists, forskolin and aldosterone, suggest that sAC activity may be regulating electrogenic Na ϩ transport at a site common to all pathways. The two most obvious sites of action would be either the rate-limiting Na ϩ entry step, ENaC, or the electrogenic exit step, Na ϩ ,K ϩ -ATPase. We therefore sought to determine whether sAC and sAC inhibitors affected the abundance or activity of either of these proteins required for transepithelial Na ϩ transport.
sAC Inhibition Does Not Affect ENaC Currents in Xenopus Oocytes-Because ENaC activity at the apical membrane is typically rate-limiting for total transepithelial Na ϩ transport in mpkCCD c14 cells and in native kidney collecting ducts (24), we initially hypothesized that the target for sAC-dependent regulation of Na ϩ transport was ENaC at the apical membrane. To test whether ENaC is regulated by sAC in an independent system, we expressed ENaC along with or without the highly active, truncated splice variant of sAC in Xenopus oocytes. We then performed two-electrode voltage clamp measurements of amiloride-sensitive currents in the presence or absence of the sAC inhibitor, KH7 (Fig. 7). Of note, neither the expression of sAC nor KH7 treatment (nor the combination of the two) had a significant effect on ENaC currents in oocytes. These results suggest that sAC-generated cAMP does not have a direct effect on ENaC activity in this heterologous expression system. We next explored whether sAC could be involved in ENaC trafficking in native epithelia by examining the specific site of action of sAC on transepithelial Na ϩ transport through selective permeabilization of apical or basolateral membranes of polarized mpkCCD c14 cells.
Selective Membrane Permeabilization with Nystatin Reveals Na ϩ ,K ϩ -ATPase as the Target for sAC Regulation-To determine the likely target of sAC regulation in polarized mpkCCD c14 cells, selective permeabilization of the basolateral or apical membrane was performed using nystatin, which per- Kidney Epithelial Na ؉ Transport Regulation by sAC FEBRUARY 27, 2009 • VOLUME 284 • NUMBER 9 meabilizes the plasma membrane to small univalent ions (49,50). To isolate and examine potential effects on ENaC conductance at the apical membrane, nystatin was added basolaterally, followed by KH7 treatment and then amiloride (Fig. 8A). Under these conditions with basolateral conductance shunted, all current should reflect the activity of the apical Na ϩ channel ENaC. Application of KH7 had no effect on the Na ϩ current under these conditions, whereas subsequent amiloride addition fully inhibited I sc , confirming the presence of a robust apical membrane ENaC conductance (Fig. 8A). Specifically, the treatment-associated change in I sc was not significantly different from 0 in either KH7or vehicle-treated cell monolayers (0.9 Ϯ 2.3 versus 0.4 Ϯ 2.0 A/cm 2 , respectively; p ϭ 0.86), nor was there any difference in amiloride-sensitive current between KH7 or vehicle treatment (17.5 Ϯ 2.9 versus 15.5 Ϯ 1.8 A/cm 2 , respectively; p ϭ 0.57). These data indicate that ENaC inhibition is not responsible for the sAC inhibition of transepithelial Na ϩ current.
To determine whether sAC inhibition affected basolateral membrane conductance, we added KH7 following nystatin permeabilization of the apical membrane. This caused a substantial inhibition of I sc that was further inhibited by subsequent ouabain treatment, thus implicating the basolateral membrane Na ϩ ,K ϩ -ATPase as the target for sAC inhibition (Fig. 8B). The large increase in C T (Fig. 8B, dashed line) within 10 min following nystatin treatment indicates effective apical membrane permeabilization. To test the effects of FIGURE 8. Effects of sAC inhibition on I sc with selective nystatin permeabilization of basolateral and apical membranes. Polarized mpkCCD c14 cells grown on filters were mounted in an Ussing chamber system set up to continuously measure I sc and C T as described under "Experimental Procedures." The data shown are representative of 3-10 experimental runs for each condition. Where indicated schematically by the bars in A-C, 100 M nystatin was added either basolaterally or apically, 60 M KH7 was added apically, 10 M amiloride was added apically, and 0.5 mM ouabain was added basolaterally. A, KH7 fails to inhibit I sc following basolateral nystatin permeabilization, yet amiloride-mediated blockade of apical ENaC inhibits I sc . The mean (ϮS.E.) treatment-associated change in I sc was not significantly different from 0 in either KH7-treated or vehicle (Me 2 SO)-treated cell monolayers (0.9 Ϯ 2.3 versus 0.4 Ϯ 2.0 A/cm 2 , respectively; p ϭ 0.86), nor was there any difference in amiloride-sensitive current between KH7 or vehicle treatment (17.5 Ϯ 2.9 versus 15.5 Ϯ 1.8 A/cm 2 , respectively; p ϭ 0.57; n ϭ 7 filters for both conditions). B, KH7 inhibits I sc (solid line) following apical nystatin permeabilization, and ouabain addition rapidly blocks remaining I sc . The large increase in C T (dashed line) within 10 min of apical nystatin treatment indicates effective apical membrane permeabilization (25). C, acute activation of the Na ϩ ,K ϩ -ATPase through cellular Na ϩ loading triggered by apical nystatin permeabilization was performed to measure pump capacity with prior treatment of vehicle (solid line) or KH7 (dotted line) to inhibit sAC. Ouabain-sensitive I sc was defined as the difference in steady-state I sc following nystatin permeabilization before and after ouabain treatment (indicated for vehicle-treated cells by dashed lines). D, summary of mean (ϮS.E.) ouabain-sensitive currents with or without 60 M KH7 treatment from experiments shown in C (*, p Ͻ 0.001, n ϭ 3-7 filters for each condition).
sAC inhibition on Na ϩ ,K ϩ -ATPase activity, specifically pump capacity in the face of intracellular Na ϩ loading, we compared changes in I sc after initially treating with KH7 or vehicle for 30 min, followed by acute apical membrane permeabilization, and then subsequent ouabain treatment (Fig. 8C). Following a reproducible, transient spike in I sc as nystatin permeabilizes the apical membrane (see also Fig. 8B), the steady-state ouabain-sensitive I sc was significantly reduced in the KH7-treated cells by a mean of ϳ60% (Fig. 8D), indicating that sAC activity is required for Na ϩ pump activity.
sAC Inhibition Blocks ATPase Activity without Affecting Surface Expression of the Na ϩ Pump-Regulation of the Na ϩ ,K ϩ -ATPase by sAC could conceivably occur via effects on basolateral membrane expression of the Na ϩ pump or on its ATPase activity. To test whether decreased membrane expression could account for the inhibition of Na ϩ pump-mediated conductance associated with sAC inhibition, surface biotinylation labeling was performed to measure expression of the Na ϩ ,K ϩ -ATPase catalytic ␣ subunit at the basolateral membrane in polarized mpkCCD c14 cells 0 -30 min after treatment with KH7 ( Fig. 9). Consistent with previous observations in this cell line and in vivo that the Na ϩ pump is localized largely in the basolateral membrane by immunofluorescence staining (51,52), virtually all of the ␣ subunit appeared in the biotinylated fraction (Fig. 9A). Of note, the relative proportion of biotinylated ␣ subunit did not change significantly at 15 or 30 min after the addition of 60 M KH7 (Fig. 9, A and B). Parallel measurements at the 30-min time point demonstrated a reduced equivalent I sc of 5.83 Ϯ 0.24 A/cm 2 in KH7-treated cells (versus 11.43 Ϯ 1.45 A/cm 2 in vehicle-treated cells; p ϭ 0.02, n ϭ 3 filters for each condition). These findings suggest that the KH7-dependent inhibition of current does not result from a reduction in Na ϩ pump expression at the basolateral membrane.
Parallel in vitro Na ϩ pump ATPase activity and equivalent I sc measurements of polarized mpkCCD c14 cells treated for 30 min with 60 M KH7 or vehicle are shown in Fig. 10. In KH7-treated filters ATPase activity was reduced by ϳ60% (Fig. 10A), whereas I sc was reduced by ϳ45% (Fig. 10B) relative to untreated controls. These results suggest that the sAC regulation of the Na ϩ ,K ϩ -ATPase is mediated through effects on its catalytic activity. The greater decrease in measured ATPase activity relative to the decrease in I sc supports the notion that apical ENaC conductance is normally rate-limiting for transepithelial Na ϩ transport and thus that a greater reduction in basolateral pump activity is required to effect a given reduction in I sc .
DISCUSSION
Intracellular coupling between pH changes and transepithelial salt transport has long been recognized, although the mechanisms for such coupling remain unclear. This is the first study to recognize and investigate sAC-dependent regulation of Na ϩ transport across epithelia. Our results confirm that sAC is specifically expressed in distal nephron renal epithelial cells (Fig. 1) and demonstrate that its activity is required for Na ϩ transport under basal conditions both acutely and chronically (Figs. 2 and 3) and after cAMP or aldosterone stimulation (Figs. 4 -6). The addition of the cell-permeant cAMP analog 8-Bromo-cAMP partially restored the KH7-inhibited Na ϩ current, demonstrating that the cells exposed to KH7 retained their ability to respond to cAMP (Fig. 5). The finding that 8-Bromo-cAMP was not able to activate I sc fully in the presence of KH7 to a level FIGURE 9. Na ؉ ,K ؉ -ATPase ␣ subunit expression at the basolateral membrane is unaffected by sAC inhibition. Surface biotinylation assays to measure Na ϩ ,K ϩ -ATPase ␣ subunit expression at the basolateral membrane of polarized mpkCCD c14 cells were performed at 0, 15, and 30 min after treatment with 60 M KH7, as described under "Experimental Procedures". A representative blot comparing the surface-biotinylated fraction with one-sixth of total cell lysate is shown (panel A), along with summary relative surface biotinylation (normalized to the value at time 0; panel B). There were no significant differences in relative surface biotinylation at any of the time points (p Ͼ 0.20; n ϭ 3 replicate experiments).
FIGURE 10. sAC inhibition inhibits ouabain-sensitive ATPase activity in parallel with transpithelial I sc . Equivalent transepithelial I sc was measured by epithelial volt ohmmeter in 12 replicate filters treated for 30 min with either 60 M KH7 or vehicle control prior to cellular lysis and subsequent ATPase measurements on six replicate filters, as described under "Experimental Procedures." A, ATPase activity of KH7-treated filters was reduced by 60% relative to untreated controls (p ϭ 0.004). B, current was reduced by ϳ45% in KH7-treated filters relative to untreated controls (p Ͻ 0.001).
Kidney Epithelial Na ؉ Transport Regulation by sAC FEBRUARY 27, 2009 • VOLUME 284 • NUMBER 9 similar to that achieved in the absence of KH7 raises the possibility that sAC effects on the Na ϩ pump in these cells may be compartmentalized or sequestered in microdomains not readily accessible to 8-Bromo-cAMP. Alternatively or additionally, the Na ϩ transport inhibition caused by the sAC inhibition may not be rapidly reversible. Because ENaC-dependent Na ϩ transport at the apical membrane is rate-limiting in mpkCCD c14 cells under normal conditions (24), we initially suspected that ENaC was the relevant target for sAC regulation. However, direct co-expression of ENaC and sAC in oocytes (Fig. 7) and selective permeabilization of the basolateral membrane in CCD cells to isolate ENaC conductance (Fig. 8) did not support the hypothesis that ENaC is modulated by sAC or by sAC inhibition. On the other hand, selective apical permeabilization studies to isolate pump current strongly suggest that the basolateral pump is the target of sAC inhibition (Fig. 8). Direct measures of ATPase activity confirmed this hypothesis and demonstrated that sAC-dependent regulation of the Na ϩ pump occurs via effects on ATPase activity (Fig. 10) rather than basolateral membrane expression (Fig. 9). This result is not unexpected given the rapidity of the current modulation in the face of sAC inhibitors (i.e. within minutes). Moreover, it has been widely recognized that, unlike in the case of ENaC, a very high proportion of total cellular Na ϩ pump expression exists at the basolateral membrane rather than in intracellular or cytoplasmic compartments in epithelial cells. (cf. Fig. 9 and Refs. 51 and 52). The mechanism of sAC-dependent regulation of the Na ϩ ,K ϩ -ATPase is currently unclear. Because sAC activity generates cAMP, PKA is an attractive candidate mediator. Indeed, PKA-dependent phosphorylation of ␣ and ␥ (FXYD) subunits has been reported to regulate Na ϩ pump catalytic activity (53)(54)(55). In addition, PKA phosphorylation may regulate association of the ␣ and ␥ subunits, which may also be an important mechanism of pump activity regulation (56). Although cAMP and PKA have been implicated in the regulation of trafficking of membrane transport proteins (e.g. V-ATPase, aquaporin 2, and cystic fibrosis transmembrane conductance regulator) (14,19,57,58), our results demonstrate that surface expression of the ␣ subunit of the pump was not affected by the sAC inhibitor KH7 (Fig. 9). However, we cannot exclude the possibility that translocation of either the  or ␥ subunits may be affected. Nevertheless, the reduction in ATPase activity with sAC inhibition appears to be sufficient to account for the current inhibition given the reductions in both current and ATPase activity observed following KH7 treatment (Fig. 10). Thus, a direct effect on catalytic activity appears to be the simplest explanation to account for our results. Other candidate mediators of the sAC effect are Epacs, which are small guanine nucleotide exchange factors that are activated by cAMP and function independently of PKA (59). These unresolved mechanistic issues are questions for future investigation.
Potential future approaches to confirm our in vitro data could involve knock-out or tissue-specific and temporal knockdown approaches in vivo. Importantly, however, there is specificity to our data because both RNA silencing and treatment with two different classes of sAC inhibitors (KH7 and CEs) yielded similar dramatic effects on Na ϩ transport. Transepithe-lial resistance was also well preserved following these treatments, confirming the integrity and viability of the cell monolayers. Moreover, ENaC activity was not affected in any detectable manner, arguing against a generalized effect of sAC on ion transport proteins or cellular processes.
In summary, our results demonstrate that sAC activity is an important regulator of Na ϩ transport in collecting duct epithelial cells via regulation of the Na ϩ ,K ϩ -ATPase at the basolateral membrane. Further characterization of the sAC-dependent regulation of transepithelial Na ϩ transport is warranted and could identify novel targets for the treatment of hypertension and diuretic resistance. Moreover, because the Na ϩ pump is expressed ubiquitously in cells of all organs, its potential regulation by sAC could be important in other tissues such as cardiac muscle and neurons. Indeed, it would be of interest to determine whether sAC-dependent regulation of the Na ϩ pump plays a role in the pathogenesis of certain cardiac and nervous system disorders, such as heart failure, arrhythmias, and seizures. | 8,687 | 2009-02-27T00:00:00.000 | [
"Biology"
] |
Thyroid volume’s influence on energy deposition from 131I calculated by Monte Carlo (MC) simulation
Background It is well known that the success of the radiomethabolic 131I treatment of hyperthyroidism could depend on the absorbed dose to the thyroid. It is, thus, very important to calculate the individual radiation dose as accurately as possible for different masses of thyroid lobes. The aim of this work is to evaluate the influence of thyroid volume on the energy deposition from beta and gamma rays of 131I by Monte Carlo (MC) simulation. Materials and methods. We have considered thyroid lobes having an ellipsoidal shape, with a density of 1.05 g/ cm3 and the material composition suggested by International Commission on Radiological Protection (ICRP). We have calculated the energy deposition of 131I rays for different volumes of thyroid lobes by using the MCNPX code, with a full transport of beta and gamma rays. Results and conclusions. The results show that the total energy deposition has a significant difference, till 11%, when the lobe’s volume varies from 1 ml to 25 ml, respect to the value presented in MIRDOSE for a 10 g sphere. The absorbed energy fraction increases by volume, because the increasing volume to surface ratio of ellipsoidal lobe causes the decrease of beta ray fraction escaping from the lobe.
Introduction
Thyroid gland consists of two linked lobes and is located in the middle of the low neck, overlying the trachea. Radioactive iodine 131 I has become the most widely used therapy for patients with hyperthyroidism due to Graves' disease. 1 This kind of therapy has largely replaced surgery as the definitive treatment for such benign disease in contrast with malignant ones 2-4 , because it is easier than surgery to perform and has proved to be more effective. A number of dosing regimens have been proposed, ranging from those based on thyroid volume evaluation and Iodine test-activity uptake determination for high precision dosimetry , to large, fixed activities of 131 I administration, intended to cause hypothyroidism soon after treatment. [1][2][3] Physicians generally determine the 131 I activity on an empirical basis: the decision is based on the volume of the thyroid evaluated by scintigraphy, SPECT, MRI or ultrasonic methods and, sometimes, on the basis of 131 I/ 123 I test-activity uptake at 24 hours post-administration. 5 It is well known that the success of this therapy could depend on the absorbed dose to the thyroid: it is thus very important to calculate the individual radiation dose as accurately as possible for different mass of thyroid lobe. Many authors have developed algorithms for the calculation of the radiation absorbed dose to a target organ, starting from a basic absorbed dose rate equation represented by the Medical Internal Radiation Dose (MIRD) models. 6 Traino et al. evaluated the influence of the volume reduction on the calculation of the absorbed dose to the thyroid by presenting a mathematical model. 1 The aim of this work is to evaluate the influence of thyroid volume on the energy deposition from 131 I by Monte Carlo (MC) simulation.
Materials and methods
MCNPX is a general purpose, continuous and discrete energy, generalized-geometry, time-dependent code to simulate particles transport, based on Monte Carlo method. It is an extremely useful tool for radiations transport simulation and tracks about 40 particles including some light ions. 7 The code is written in Fortran 90 and contains flexible source and tally options; it utilizes the latest nuclear cross section libraries with a data library of photons cross-section ranging from 1 keV to 100 GeV.
This code has been used to calculate the energy deposition from beta and gamma rays of 131 I for a thyroid lobe of ellipsoidal shape, with the major axis two times of the minor axis, 1.05 g/cm 3 density and with a mass varying from 1 g to 25 g.
In running MCNPX code, we have considered the "full transport" for both gamma and beta rays; that is, we have considered that beta rays do not deposit their energy in a starting point, but they undergo many Coulomb interactions, so that a significant portion of their energy, near the surface of lobes, escapes and is stored out of the thyroid lobes. Figure 1A shows the real beta spectrum of 131 I that we have used for our simulation, and the average beta spectrum used in MIRD, according to the Evaluated Nuclear Structure Data File (ENSDF) decay data. In the MIRD format, the beta spectrum includes 5 discrete lines, each representing the average beta energy and the yield for 131 I beta radiations. 8 As well as, the gamma spectrum is presented in Figure 1B.
The adult 70 kg human MIRD5 phantom has been used: the source organ was the thyroid gland with a uniform 131 I distribution; the neck has been simulated with more detailed organs including skin, adipose layer under the skin, bone, spinal cord, thyroid lobes, and the remaining part as soft tissue. We have considered for soft tissue 1.05 g/ cm 3 density and the ICRP composition.
As it is well known, the basic formula for absorbed dose rate used in MIRD formulation is: [1] where w is a proportional constant, A is the radionuclide activity within the source organ, n i is the number of radiations with energy E i emitted per one decay, Φ i is the fraction of energy emitted in the source that is absorbed in the target organ, and m is the mass of the target. When the thyroid is considered both as source and target organ, the beta and gamma rays absorption fraction (Φ i ) depends on thyroid volume.
We have selected σ as proper parameter to evaluate, by rewriting of Equation [1]: [2] The activity administrated for hyperthyroidism and thyroid cancer therapy is varying inversely with σ. In many literatures, such as MIRDOSE code, σ is taken as a constant value 0.0313 (mGy g MBq -1 s -1 ), calculated by MC method for gamma rays and considering all beta energy deposited in a thyroid lobe of spherical shape, with fixed mass of 10 g. We have calculated the total (beta and gamma) energy deposition and σ for different volumes of thyroid lobes. Figure 2 shows the variation of the total energy deposition per decay of 131 I for both beta and gamma rays against the volume of thyroid.
Results and discussion
The total energy deposition per decay is the term in brackets and it increases by volume, because the increasing volume to surface ratio of ellipsoidal lobe causes the decrease of radiations fraction escaping from the lobe (Figure 2).
The calculated value of σ against the thyroid volume lobe has been presented in Figure 3. It can be seen that σ has a significant difference with the previous constant value, ranging from 10% to -1% when the lobe's volume varies from 1 ml to 25 ml. For a 10 g lobe, our calculation shows about 2.2% difference with MIRDOSE3 σ value. This difference comes from two main sources: the first is the beta spectrum, as we have used the spectrum of 131 I taken from a reference published by Eckerman et al. in 1994 in Health Physics 9,10 , with a mean beta energy of 0.1822 MeV per disintegration; the second is due to considering in our calculation the full beta and gamma transport in an ellipsoidal thyroid lobe (Figure 3).
We have used the photon energy deposition tally, called F6:p in MCNPX code, to calculate the photon energy deposition per unit of mass, in the other organs of the body, due to a decay in the source organ. It is clear that the result is proportional to the dose organ per one decay in the source.
The energy deposition in other organs of neck as a function of the thyroid lobe volume per decay of 131 I has been shown in Figure 4. As it is predictable, by increasing the lobe volume the dose in the bone and spinal cord increases but for other organs it decreases. The energy depositions per decay to organs far from the thyroid, including head, body and legs have been presented in Figure 5.
Conclusions
The result shows that considering the lobe volume or mass has a significant effect over the absorbed dose calculation in thyroid gland. So, an accurate determination of the active volume of thyroid is very important in activity evaluation for radiomethabolic therapy by Iodine-131. As well as, according to our calculation, we suggest re-evaluating the Φ i value for gamma and beta sources when the source organ is the same as target and its volume or mass variation among different patients is considerable. | 2,023 | 2011-03-29T00:00:00.000 | [
"Medicine",
"Physics"
] |
Fate of Bioactive Compounds during Lactic Acid Fermentation of Fruits and Vegetables
Consumption of lactic acid fermented fruits and vegetables has been correlated with a series of health benefits. Some of them have been attributed to the probiotic potential of lactic acid microbiota, while others to its metabolic potential and the production of bioactive compounds. The factors that affect the latter have been in the epicenter of intensive research over the last decade. The production of bioactive peptides, vitamins (especially of the B-complex), gamma-aminobutyric acid, as well as phenolic and organosulfur compounds during lactic acid fermentation of fruits and vegetables has attracted specific attention. On the other hand, the production of biogenic amines has also been intensively studied due to the adverse health effects caused by their consumption. The data that are currently available indicate that the production of these compounds is a strain-dependent characteristic that may also be affected by the raw materials used as well as the fermentation conditions. The aim of the present review paper is to collect all data referring to the production of the aforementioned compounds and to present and discuss them in a concise and comprehensive way.
Introduction
Lactic acid fermentation has been applied for centuries on substrates of plant and animal origin. The seasonal and geographical diversity of the raw materials results in a great variability of products. The qualitative and quantitative composition of the micro ecosystem that is developed during fermentation; the biotic and abiotic factors that direct it, along with the physicochemical changes of the substrate itself, have been in the epicenter of intensive research for many decades. Nowadays, the interest in lactic acid fermentation has been re-fueled, and its value has again been praised due to the health benefits that their consumption may confer. Indeed, a series of health benefits, including anti-allergic, antihypertensive, anti-inflammatory, anti-diarrheal, anti-infection, and anti-aging, as well as prevention and control of chronic diseases such as cardiovascular diseases, type 2 diabetes, obesity, and cancer, has been associated with the consumption of lactic acid fermented commodities. These health benefits have been attributed to the lactic acid bacteria that drive the fermentation as well as to the bioactive compounds that are present in the final product [1][2][3][4][5][6][7][8]. Their presence depends upon the occurrence of the necessary precursor molecules in the raw materials and the capacity of the lactic acid bacteria strains to carry out the required biotransformations.
In addition, specific health benefits have been associated with the consumption of specific products, such as the antioxidant, anti-obesity, anti-cancer, anti-hypertensive, and immunomodulatory potential of kimchi [14].
The biotic and abiotic factors that affect the production of vitamins (especially of the B-complex), gamma-aminobutyric acid, bioactive peptides, as well as phenolic and organosulfur compounds during lactic acid fermentation of fruits and vegetables have attracted specific attention over the last decade. In addition, the production of biogenic amines has also been intensively studied due to the adverse health effects that are caused by their consumption. The aim of the present review paper is to collect all relevant information and to present and discuss them in a concise and comprehensive way.
Vitamins
The role of vitamins in human life and well-being is very important; they facilitate metabolic reactions, including energy-yielding ones, as well as many physiological processes. Depending on their chemical nature, they may be distinguished into water-soluble (B-complex, C) and fat-soluble (A, D, E, K) vitamins. They are considered essential micronutrients since the human body is not able to synthesize the majority of them. Thus, adequate dietary supply is necessary to prevent deficiency. Biofortification, i.e., the utilization of microorganisms capable of producing them, has been proposed as a strategy to improve the vitamin content of certain commodities. This approach is particularly valuable in the case of fermented fruits and vegetables.
The vitamin content of fruits and vegetables has been extensively studied. Fruits are recommended as sources of vitamin C; they also contain vitamin K and carotenoids, and leafy vegetables contain vitamin C, folate, and carotenoids [15]. More specifically, cucumbers and Chinese cabbage contain vitamins C, B1, B2, B11, B3, B6, A, E, and K, with Chinese cabbage appearing to contain more per 100 g. Olives contain vitamins B1, B3, B6, A, E, and K; black olives also contain vitamin C, while green olives also contain vitamin B11. Green olives appear to contain quantitatively more vitamins than black olives, with the exception of vitamin K, where they both contain 1.4 mg/100 g. Vitamins B12 and D seem to be absent from cucumbers, Chinese cabbage, and olives (data from fdc.nal.usda.gov, accessed on 29 July 2021).
Although fruits and vegetables and, especially, green vegetables have been recognized as the main sources of folates for humans [39] and certain fruits and vegetables and, especially, dark green vegetables are very good sources of riboflavin [40], the fate of vitamins during lactic acid fermentation has only been marginally studied. Jagerstad et al. [41] reported that folate production takes place during lactic acid fermentation, depending on the starter culture. More accurately, the starter culture, consisting of a mixture of Lp. plantarum, Lc. lactis/cremoris and Leuconostoc sp. strains, was able to produce up to 125 µg/kg 5-CH3-H4 folate during fermentation of a mixture of beetroots, turnips, and onions and 110 µg/kg during fermentation of a mixture of roots consisting of carrots, turnips, parsnips, celeriacs, and onions. Thompson et al. [42] used four Lp. plantarum strains and 110 μg/kg during fermentation of a mixture of roots consisting of carrots, turnips, parsnips, celeriacs, and onions. Thompson et al. [42] used four Lp. plantarum strains to ferment cauliflower, white beans, and their 50:50 mixture and reported a statistically significant increase in riboflavin and folate content. More accurately, after fermentation of the latter at 30 °C for 44 h, riboflavin increased to 75.64-91.60 μg/100 g fresh weight from the 42.83 μg/100 g fresh weight of the unfermented control; folate increased to 48.74-58.82 μg/100 g fresh weight from the 36.84 μg/100 g fresh weight of the unfermented control. In addition, Lp. plantarum strain 299 was able to produce vitamin B12, increasing its concentration to 0.048 μg/100 g fresh weight from the 0.029 μg/100 g fresh weight of the unfermented control.
Gamma-Aminobutyric Acid
The occurrence of gamma-aminobutyric acid (GABA) in plants, microorganisms, and vertebrates has been adequately exhibited. In plants and humans, GABA is mostly associated with signaling functions. Indeed, its role in plant growth and stress response has been established [43][44][45]. In humans, it acts as the major inhibitory neurotransmitter in the central nervous system. The latter has played a decisive role in the ongoing trend of enriching food with this molecule; however, Hepsomali et al. [46] mentioned that although GABA oral intake resulted in various responses [47][48][49], it is still unknown whether brain GABA concentration is increased. On the other hand, it seems to have a different role in microorganisms; it has been associated with resistance to acidic conditions [50] as well as spore germination, at least in Neurospora crassa [51] and Bacillus megaterium [52]. In lactic acid bacteria, GABA production has been reported as a strain-dependent characteristic. It takes place mostly through L-glutamate decarboxylation since it also contributes to acid resistance through proton consumption [53]. L-glutamate supply may be exogenous through the glutamate/GABA antiporter or endogenous through the activity of glutamate synthase on α-ketoglutaric acid. Then, GABA may be transported extracellularly through the aforementioned antiporter or degraded to succinic acid through GABA aminotransferase and succinate semialdehyde dehydrogenase ( Figure 1) The amount of GABA synthesized by a plant depends upon several factors, such as variety, type, and severity of biotic and abiotic stresses; however, its occurrence has been characterized as ubiquitous [57]. Indeed, GABA amount may range from the 0.007 mg/g dry weight in an epicarp/mesocarp mixture of apples and the 0.019 mg/g dry weight of chestnuts to the 1.86 mg/g dry weight of mulberries and the 174.30 mg/g fresh weight of Vitis vinifera L. cultivar Pinot Noir [58][59][60][61]. Regarding the raw materials mostly used as substrates for lactic acid fermentation, the occurrence of GABA has also been reported. In olives and in extra virgin olive oil, the amount of GABA was cultivar-dependent [62,63]. In the latter case, its amount was less than 0.00014 mg/g. Leaves and roots of Chinese cabbage were reported to contain 4.69 and 7.02 µmol/g dry weight, respectively, accounting for the 8% and 26.86% of total free amino acids, respectively [64]. Finally, fresh cucumbers were reported to contain 105 mg/kg GABA [65]. Current evidence shows that lactic acid fermentation may increase GABA content. Indeed, spontaneously fermented cucumbers were reported to contain 150 mg/kg GABA, with the majority of it being formed during the first day of fermentation [65]. Notably, GABA concentration remained stable throughout the 6-month storage period at 28 • C. In the case of spontaneously fermented olives, GABA was formed only upon monosodium glutamate addition [66]. The amount of GABA formed was proportional to the amount of monosodium glutamate added and irrespective of the osmotic dehydration of olives, which was applied as a pre-fermentation treatment. GABA production was also reported during spontaneous kimchi fermentation [67]. In that study, GABA production took place within the first 25 days of storage at 4 • C, reaching approximately 4 mM; this amount of GABA remained stable until the end of storage (120 days). Analysis of the microecosystem identified strains of Leuconostoc spp. and Lt. sakei as the GABA producers. Seok et al. [68], Cho et al. [69], and Lee et al. [70] studied GABA production during kimchi fermentation inoculated with GABA producing strains. Seok et al. [68] used Lactobacillus sp. strain OPK 2-59 and 5 g monosodium glutamate and managed to produce 18 mg/100 g GABA, a notable increase from the initial amount of 2.84-4.06 mg/100 g. Interestingly, rapid GABA production was observed after the 9th day of storage. In the kimchi produced by the addition of either the GABA-producing strain or monosodium glutamate, the GABA amount at the end of storage (21 d) was less than 6 mg/100 g. Cho et al. [69] analyzed commercially available kimchi and Mukeunjee kimchi products and reported that the GABA content ranged from 1.9 to 12.9 mg/100 g and from 18.2 to 99.0 mg/100 g, respectively. Then, a GABA-producing Le. buchneri strain was employed as a starter culture, resulting in kimchi with 61.7 mg/100 g GABA, which was significantly higher than the 8.1 mg/100 g of the spontaneously fermented one. Notably, the sensory scores of the products were comparable. Lee et al. [70] prepared kimchi with the addition of Lv. zymae strain GU240 as a starter culture and evaluated the effect of L-glutamic acid, monosodium glutamate, and kelp extract as GABA precursors. Storage took place at −1 • C for 20 weeks. Monosodium glutamate was the most effective GABA precursor. The most rapid increase was observed between weeks 2 and 4, and the maximum GABA concentration reached 120.3 mg/100 g in week 8. Then, it was reduced to the final amount of 95.6 mg/100 g. The GABA content of the kimchi that was prepared without the addition of starter or precursor, as well as the kimchi prepared with only the addition of a starter, was 47 mg/100 g. The addition of kelp extract resulted in the accumulation of 55 mg/100 g GABA, and the addition of L-glutamate resulted in 62.5 mg/100 g. In all cases, maximum GABA concentration was observed in weeks 8 and 10, which was then reduced until the end of storage (week 20).
Bioactive Peptides
Bioactive peptides are short peptides that, upon release from the parent protein molecule, exert a biological function. Decryption from the parent protein molecule may take place during gastrointestinal digestion or due to the proteolytic activity of microorganisms, such as the LAB that direct a fermentation process. Their occurrence depends on the activity of extracellular and cell envelope proteinases, as well as the peptide transportation capacity into the cell, towards their complete hydrolysis to amino acids [71] (Figure 1). A wide range of biological activities has been described for such peptides, including anti-diabetic, antioxidant, anti-microbial, anti-thrombotic, hypocholesteromic, hypotensive, mineral-binding, opioid, and anti-opioid.
In general, fruits and vegetables are not rich in protein; however, the occurrence of bioactive peptides in some of them has been reported (recently reviewed by Sosalagere et al. [91]). Cucumbers, Chinese cabbage, and green and black olives contain 0.65%, 1.5%, 1.03%, and 0.84% protein, respectively (https://fdc.nal.usda.gov/, accessed on 21 August 2021). In olive seeds, the occurrence of the peptide LLPSY exhibited significant anti-proliferative capacity on prostate cancer cells (PC-3) and breast cancer cells (MDA-MB-468) [92]. Occurrence of bioactive peptides in cucumbers that were raw, acidified, spontaneously fermented, or fermented with the addition of Lp. pentosus strain LA0445 was assessed by Fideler et al. [93]. Five peptides with potential anti-hypertensive activity were detected, namely, IPP, LPP, VPP, KP, and RY. KP was present in all cases; the amount in the fermented ones was significantly higher than the rest. Acidified cucumbers also contained KY, a peptide that was not detected in spontaneously fermented ones. The cucumbers that were fermented with the addition of the starter culture contained all five peptides [93].
Phenolic Compounds
The occurrence of phenolic compounds in plants has been extensively assessed. They are the third-largest group of secondary metabolites, after terpenes and alkaloids; they hold a very important physiological role as they participate in processes such as photosynthesis, respiration, and cell development. Regarding the total phenolic content (TPC) of the fruits and vegetables mostly used as a substrate of lactic acid fermentation, it seems to be rather low; it has been reported to vary between 0.58-1.42 mg GAE/g fresh weight for Chinese cabbage, 0.17 mg GAE/g fresh weight for cucumbers, and 82.29-287.29 mg GAE/100 g for olives [94,95]. Their amount depends upon factors associated with the plant type and variety, cultivation conditions, processing, and storage [96,97]. The interest in phenolic compounds is fueled by the correlation that has been achieved between them and antioxidant capacity as well as the prevention of chronic diseases and inflammation [98].
Based on the fact that lactic-acid-fermented fruits and vegetables consist of two phases, namely, a solid and a liquid one, Ciniviz and Yildiz [99] studied the TPC of both juice and pulp portions of 30 kinds of lactic acid fermented fruits and vegetables. In all cases but two, namely, wild pears pickle and sour grapes pickle, the amount of TPC in juice was higher than the respective in the pulp portion. In the latter, TPC ranged from below detection limit in carrots pickle and white cabbage pickle to 135.39 µg GAE/mg in pinecone pickle, while in the juice portion, it ranged from 16.94 µg GAE/mg in tomatoes pickle to 235.19 µg GAE/mg in pinecone pickle. The most common phenolic acid seemed to be sinapic acid, which was detected in all juice and pulp samples at concentrations ranging from 135.91 mg/L in sour grapes pickle to 236.32 mg/L in sweet long green pepper pickle and from 104.25 mg/kg in white cucumber pickle to 107.43 mg/kg in unripe melon pickle, respectively. Vanillic acid, caffeic acid, and chlorogenic acid were present in all juice samples, ranging from 0.08 mg/L in white cabbage pickle to 31.81 mg/L in carrot pickle, from 30.06 mg/L in unripe melon pickle and chard pickle to 74.61 mg/L in hot pepper pickle, and from 62.21 mg/L in cauliflower pickle to 200.30 mg/L in rock samphire pickle, respectively. 4-hydroxybenzoic acid and p-coumaric acid were not detected in any sample.
The fate of phenolic compounds during lactic acid fermentation has only been marginally studied. The mode by which lactic acid fermentation may increase the TPC of the raw materials is either through the lysis of the cell wall of the plant cells with concomi-tant facilitation of their release from the vacuole, in which they are mainly localized, or by enzymatic conversion of their glycosides into their aglycone form [100]. The latter may take place through β-glycosidase activity, which several lactic acid bacteria strains have exhibited [101,102]. Indeed, several Lp. plantarum strains have been reported to hydrolyze oleuropein, which is the main phenolic glucoside of olives [103]. More accurately, an initial action of β-glycosidase, followed by an esterolytic activity on the aglycone moiety, has been reported to produce olenoic acid and hydroxytyrosol [100]. Moreover, through the production of phenolic acid decarboxylases, some Lp. plantarum strains may decarboxylate phenolic acids [104,105].
In the case of kimchi, Park et al. [111] reported that over-ripened kimchi contained more TPC than short-term fermented ones. Park et al. [112] reported that the TPC of mustard kimchi increased during the first two months to 482.4 mg GAE/g extract powder but then decreased during the third month to 475.3 mg GAE/g extract powder, which had no statistically significant difference from the control. Regarding the specific phenolic compounds assessed, the amount of caffeic acid increased throughout the three months of fermentation; the amount of naringin, catechin gallate, and epigallocatechin gallate initially increased, but after three months of fermentation, their amount was less than that of the control. The amount of chlorogenic acid and epicatechin gallate decreased throughout the three-month fermentation compared to the control; p-coumaric acid and gallocatechin gallate were only detected after one month of fermentation, and catechin was only detected after one and two months of fermentation. Epicatechin and rutin were present in the control, and their amount increased after two months of fermentation. However, they were not detected after three months of fermentation. Finally, gallic acid and epigallocatechin were not detected to the control and throughout fermentation. Oh et al. [113] studied the TPC of Dolsan leaf mustard kimchi and reported that the TPC of leaves decreased during the first 21 days of fermentation but then increased to the initial amount of ca. 100 mg GAE/100 g. On the contrary, the TPC of stems gradually increased from the initial ca. 40 mg GAE/100 g to a final of ca. 110 mg GAE/100 g. A novel insight was provided by Jung et al. [114]. In that study, the increase of TPC over the 24-day fermentation of kimchi made of young Chinese cabbage was reported. However, the initial TPC and the TPC at the end of fermentation were determined at 83.2 and 102.5 mg GAE/100 g, respectively, when the young Chinese cabbage was cultivated using nature-friendly composts. These amounts of TPC were higher than 63.2 and 98.2 mg GAE/100 g, respectively, when the young Chinese cabbage was cultivated using general composts and higher than 57.9 and 81.0 mg GAE/100 g, respectively, when the young Chinese cabbage was cultivated using chemical fertilizers.
Ciska et al. [115] and Kapusta-Duch et al. [116] studied the TPC of sauerkraut. The first study reported that sauerkraut extract contained 8.25 mg/g TPC while white cabbage contained 5.72 mg/g. In white cabbage, only esterified phenolic acids were detected, with sinapic acid being the most prevalent (278 µg/g). On the contrary, apart from esterified phenolic acids, their glycosides were also detected in the sauerkraut extract. As in the previous case, sinapic acid was the prevalent one, with 20 µg/g being quantified as esterified acid and 84 µg/g as its glycoside. Kapusta-Duch et al. [116] assessed the effect of package type, namely, low-density polyethylene and metalized polyethylene terephthalate with polyethylene bags, on the TPC content during four months of chilled storage of white sauerkraut. It was revealed that package type had no effect on the TPC levels as in both cases, the reduction was at ca. 12% and 20% after three and four months of storage, respectively.
The fate of phenolic compounds has also been assessed in less known regional lactic acid fermented fruit and vegetable products, such as African nightshade leaves and kiwi fruit. In the first case, the effect of fermentation that was carried out at 37 • C for 3 days on the phenolic profile of the product was strain-dependent [117]. For example, fermentation with Lp. plantarum strain 75 resulted in an increase of the amount of gallic acid, vanillic acid, 2,5 dihydroxybenzoic acid, p-coumaric acid, and ellagic acid, as well as the flavonoids assessed, namely, catechin, quercetin, and luteolin. On the contrary, fermentation with Leu. pseudomesenteroides strain 56 resulted in an increase of the amount of ellagic acid and quercetin and a decrease in gallic acid, caffeic acid, vanillic acid, 2,5 dihydroxybenzoic acid, p-coumaric acid, ferulic acid, and catechin. The effect of fermentation at 37 • C for 28 h by Lp. plantarum on the phenolic profile of kiwifruit pulp was studied by Zhou et al. [118]. The TPC increased after the 21st hour of fermentation. The amount of protocatechuic acid, esculetin, and p-coumaric acid was increased due to the fermentation, while the amount of gallic acid, chlorogenic acid, catechin, and epicatechin was decreased.
Organosulfur Compounds
Vegetables of the family Brassicaceae are very rich in organosulfur compounds in general and glucosinolates in particular. Among others, this family includes all types of cabbage and mustard greens, which are very important raw materials for lactic acid fermentation.
Glucosinolates are secondary metabolites, the stability of which depend upon their contact with myrosinase, a β-thioglucosidase that catalyzes its decomposition. In intact plant cells, they are spatially separated; however, upon conditions that compromise plant tissue integrity, such as infection by herbivores and phytopathogenic microorganisms, the substrate and the enzyme are mixed, leading initially to the formation of the unstable thiohydroximate-O-sulfonate and β-D-glucose. The fate of the former depends on the nature of the side chain present in the glucosinolates molecule as well as the environmental conditions. Especially regarding the latter, neutral pH favors the formation of isothiocyanates while acidic pH in the presence of ferrous ions and epithiospecifier protein favors the formation of nitriles [119][120][121]. The physiological role of glucosinolates and their breakdown products, especially isothiocyanates, against biotic stresses has been verified [122]. Their concentration depends upon plant species, variety, and tissue, as well as environmental conditions and agricultural practices [123]. Although this response may indicate a possible role in abiotic stresses as well, this has not been yet clarified [122].
The interest on glucosinolates and their breakdown products results from their biological activity; many of them have exhibited anti-bacterial, anti-fungal, and anti-proliferative activity against human cancer cells [124]. The biotransformations of glucosinolates during lactic acid fermentation of Brassica vegetables have been studied to some extent. In general, fermentation seems to facilitate glucosinolates decomposition and an increase of the concentration of the breakdown products, the type and concentration of which are related to the glucosinolate type and concentration in the raw material as well as the capacity of the microbial strains that drive the fermentation.
Glucosinolate decomposition during fermentation has been exhibited in the case of sauerkraut [125][126][127][128] and has been primarily attributed to the shredding of the cabbage that precedes fermentation and secondarily to hydrolysis by lactic acid bacteria [129,130]. Interestingly, the capacity of LAB to produce nitriles instead of reduced glucosinolates, which were produced by Enterobacteriaceae, was highlighted by Mullaney et al. [129].
Ciska and Pathak [131] reported that glucobrassicin and sinigrin were the most abundant glucosinolates in the shredded cabbage used for fermentation. Ascorbigen, indole-3-carbinol, and indole-3-acetonitrile were identified as degradation products of the former, while allyl isothiocyanate, allyl cyanide, and 1-cyano-2,3-epithiopropane were identified as degradation products of the latter.
Penas et al. [132] highlighted the importance of the starter culture, cabbage cultivar, and fermentation conditions on the volatile glucosinolate breakdown products. Iberin, iberin nitrile, allyl isothiocyanate, sulforaphane, and allyl cyanide were detected, with the latter being the most abundant, ranging from 65 to 75 µmol/100 g DM. Ascorbigen has been reported as the most abundant glucosinolate degradation product in sauerkraut [126,128,131,133]. Ciska and Pathak [131] reported that ascorbigen concentration could be as high as 14 µmol/100 g. Palani et al. [126] quantified ascorbigen at the end of fermentation at 13 µmol/100 g FW. Indole-3-acetonitrile was also present at the end of fermentation at 4.52 µmol/100 g FW. The concentration of both compounds decreased during storage at 4 • C. These results concur with the ones presented by Penas et al. [133] but only as far as the decrease of ascorbigen concentration is concerned; the concentration of indole-3-carbinol and indole-3-acetonitrile was stable throughout three-month storage at 4 • C. Ascorbigen was also reported by Ciska et al. [128] as the main glucobrassicin breakdown product in sauerkraut, which, at the end of fermentation, reached 9.59 µmol/100 g. The concentration of indole-3-acetonitrile and 3,3 -diindolylmethane also increased during fermentation to 0.036 and 0.0099 µmol/100 g, respectively. After 17 weeks of storage at 5 • C, the concentration of ascorbigen decreased to 8.59 µmol/100 g, but the respective of indole-3-acetonitrile and 3,3 -diindolylmethane increased to 0.057 and 0.0187 µmol/100 g, respectively. Regarding the decomposition products of aliphatic and aryl glucosinolates, an increase in the concentrations of allyl isothiocyanate, but-3enyl isothiocyanate, 3-(methylthio) propyl isothiocyanate, 1-cyano-3-(methylthio) propane, 4-(methylthio) butyl isothiocyanate, 3-(methylsulfinyl) propyl isothiocyanate, 1-cyano-3-(methylsulfinyl) propane, 4-(methylsulfinyl) butyl isothiocyanate, and 2-phenethyl isothiocyanate was reported at the end of fermentation. Isothiocyanates increased during the first days of fermentation, reaching their peak on the 4th day and then decreasing. Allyl isothiocyanate was the most abundant breakdown product, with 2.848 µmol/100 g, followed by 3-(methylsulfinyl) propyl isothiocyanate, with 2.453 µmol/100 g. The concentration of all compounds decreased after 17 weeks of storage at 5 • C, with the exception of 1-cyano-3-(methylthio) propane, which increased [128].
The significance of starter cultures in the fate of glucosinolates during the fermentation of broccoli puree and juice was highlighted by Cai et al. [134], Ye et al. [135], and Xu et al. [136]. Ye et al. [135] studied the effect of lactic acid fermentation of autoclaved broccoli puree using five Lp. plantarum and 2 Leu. mesenteroides strains on the glucosinolate content. In general, a total of 10 glucosinolates have been detected in broccoli florets, namely, glucoalyssin, glucobrassicanapin, glucobrassicin, 4-hydroxy glucobrassicin, 4-methoxy glucobrassicin, glucoerucin, glucoiberin, glucoraphanin, neoglucobrassicin, and progoitrin [137][138][139]. A strain-dependent increase in the concentration of glucoraphanin, glucoiberin, and progoitrin to 29.0-236.5, 16.1-56.2, and 24.5-65.9 µg/g, respectively, from the initial trace levels, was reported. Notably, the maximum amounts were achieved by Lp. plantarum strain F1. Xu et al. [136] reported an increase of glucoraphanin, a decrease of gluconapin, glucoerucin, 4-hydroxy-glucobrassicin, and neoglucobrassicin, and no statistically significant change in glucobrassicin and 4-methoxy-glucobrassicin when juice made of broccoli florets was fermented with two P. pentosaceus strains at 37 • C for 36 h, in a strain-dependent manner. Finally, Cai et al. [134] reported that the preheating of broccoli florets at 65 • C for 3 min increased the concentration of sulforaphane, a glucoraphanin decomposition product, from the initial 806 to 3536 µmol/kg DW. Fermentation by a mixture of Lp. plantarum and Leu. mesenteroides strains at 30 • C for 15 h further enhanced sulforaphane concentration to 13,121.3 µmol/kg DW, most likely by facilitating the release and accessibility of glucoraphanin for decomposition.
Endogenous myrosinase inactivation and concomitant sinigrin retention after lactic acid fermentation of Indian mustard leaves at 22 • C for 7 d were assessed by Nugrahedi et al. [140].
Although oven heat treatment at 35 • C for 2.5 h and microwave treatment at 180 W for 4.5 min effectively reduced myrosinase activity, complete inactivation was achieved by microwave treatment at 900 W for 2 min, leading to the production of sayur asin with the sinigrin concentration of 11.4 µmol/10 g d.m. Mustard leaves are also the basic ingredient for the production of mustard leaf kimchi. Oh et al. [113] studied the fate of glucosinolates during the fermentation of mustard leaf kimchi at 0 • C for 35 d. Sinigrin, gluconapin, glucobrassicin, and glucoraphanin were detected at day 0 in both mustard leaves and stems; gluconasturtiin was only detected in leaves, while glucoiberin was only detected in stems. Reduction of the total amount of glucosinolates was evident throughout fermentation in both leaves and stems, which is mainly assigned to the reduction of sinigrin concentration, which was the most abundant glucosinolate; it was quantified at 21.43 and 22.47 mg/100 g at day 0 and 12.5 and 10.4 mg/100 g at day 35 in leaves and stems, respectively.
Regarding microbial physiology, the role of biogenic amines in gene expression [174,175], protection against oxidative stress [176][177][178][179], biofilm formation [180,181], signaling [182,183], and virulence [184,185] has been indicated. From a fermentation perspective, the most important role seems to be the response mechanism against acid stress. This mechanism involves a membrane antiport, which couples amino acid uptake with biogenic amine excretion, and intracellular amino acid decarboxylases, which decarboxylate the inserted amino acid with simultaneous proton consumption ( Figure 1). Then, the amine is excreted, and ATP synthesis through proton motive force is directed [186,187]. Such mechanisms have been reported for histidine/histamine, lysine/cadaverine, ornithine/putrescine, and tyrosine/tyramine [186,188,189].
Based on the above, the occurrence of biogenic amines in plant tissues seems justified even without microbial infection and proliferation. Indeed, several studies have reported their presence in nonfermented fruits, vegetables, nuts, legumes, and cereals (reviewed by Sanchez-Perez et al. [190]). Putrescine seems to be commonly occurring and may be accompanied by tyramine, cadaverine, spermine, spermidine, and even histamine [190,191]. This is also the case for white cabbage, Chinese cabbage, and cucumbers, which are commonly used as raw materials for lactic acid fermentation [192][193][194][195][196][197][198]. On the other hand, the occurrence of biogenic amines has not been reported in the flesh of fresh olives at any ripeness stage [199].
The level of biogenic amines in sauerkraut was lower than that of kimchi, with the exception of tyramine (Table 1). In the latter case, Kalac et al. [209] analyzed 53 samples of Czech sauerkraut and reported the mean amount at 235 mg/kg and the highest amount at 951 mg/kg. Reports on the biogenic amine content of fermented cucumbers and olives are generally lacking in the literature. Based on the available data (Table 1), fermented cucumbers seem to contain more biogenic amines than fermented olives but less than kimchi and sauerkraut. Regarding fermented olives, they seem to contain less biogenic amines than kimchi, sauerkraut, and fermented cucumbers. Regarding the rest of the fermented fruits and vegetables, the high amounts of agmatine (6.73 mg/kg) and spermidine (74.58 mg/kg) detected in champignon, of histamine (55.60 mg/kg) in white cabbage, of phenylethylamine (9.41 mg/kg), putrescine (252.58 mg/kg), and tyramine (166.58 mg/kg) in Brussels sprouts, of cadaverine (119.42 mg/kg) in broccoli, of spermine (49.63 mg/kg) in pumpkin, and of tryptamine (21.58 mg/kg) in cauliflower should be noticed ( Table 1).
The increase in the amount of biogenic amines in fermented foods compared to that of raw materials has been correlated with the microbiota that drive the fermentation. Indeed, the capacity of lactic acid bacteria to decarboxylate amino acids has been adequately exhibited [211]. However, it should be noted that this is a strain-dependent property. Thus, the haphazard nature of the biogenic amine content of spontaneously fermented fruits and vegetables is indicated. On the other hand, qualitative and quantitative control of biogenic amine production is an option that is offered when lactic acid fermentation is performed with the addition of starter cultures.
In the case of sauerkraut, the effect of raw materials on the production of biogenic amines has been highlighted by Majcherczyk et al. [212] and by Satora et al. [213]. In the latter study, eight cabbage varieties were employed to make sauerkraut through spontaneous fermentation; statistically significant differences in tyramine, histamine, cadaverine, putrescine, and tryptamine content were reported. Interestingly, a positive correlation between biogenic amine production and yeast presence was reported. The contribution of yeasts in the accumulation of biogenic amines is already known in products of alcoholic fermentation, such as wine [214]. The addition of ingredients that have an organoleptic impact, such as onion and caraway, affected the accumulation of some biogenic amines; the most pronounced effect was the reduced amounts of cadaverine and tyramine at the end of the 14-day fermentation period [212]. On the other hand, at the end of the 12-month storage at 4 • C, the sauerkraut made at 18 • C, with the addition of onion, accumulated significantly less cadaverine and phenethylamine compared to the control [212]. During spontaneous sauerkraut fermentation, the accumulation of biogenic amines seems to be affected by the aforementioned parameters, along with fermentation temperature and time. Indeed, Rabie et al. [215] reported an accumulation of histamine, tyramine, putrescine, and cadaverine after 10 days of fermentation at 15 • C, while Majcherczyk and Surowka [212] reported accumulation of cadaverine, tryptamine, and tyramine during fermentation at 18 • C for 14 d and of putrescine and tryptamine during fermentation at 31 • C for 14 d. Similarly, accumulation during sauerkraut storage seems to be affected by the same parameters as above. Regarding the effect of cultivar, the accumulation pattern seems to be affected by the cabbage cultivar [216][217][218]; however, no details were provided on the capacity of the members of the microecosystem to perform amino acid decarboxylation. The addition of onion seemed to prohibit the accumulation of cadaverine and phenethylamine but only in sauerkraut fermented at 18 • C and not 31 • C [212]. The paramount effect of a lactic acid bacteria strain's decarboxylating capacity in the accumulation of biogenic amines has also been adequately exhibited. Indeed, statistically significant differences in the accumulation during storage were observed and assigned to the Lp. plantarum and Leu. mesenteroides strains that were used as inocula [219]. In addition, suppression of biogenic amine accumulation during fermentation and storage through inoculation with Lp. plantarum, Lt. curvatus, and La. casei was reported by Rabie et al. [215]. Interestingly, the importance of the interaction between the selected starter culture and the cabbage cultivar was highlighted by Kalac et al. [216] and Spicka et al. [220].
In the case of kimchi, the accumulation of biogenic amines during fermentation of four kimchi types, namely, Pa, Gat, Kkakdugi, and Chonggak, has been assessed. Lee et al. [204] prepared Pa and Gat kimchi and studied the effect of myeolchi-aekjeot, a fermented anchovy sauce, the addition of which has been correlated with increased biogenic amine content [202,221,222]; tyramine-producing Lv. brevis strains and Lp. plantarum strains were unable to produce biogenic amines. During fermentation of Pa and Gat kimchi, the amount of tryptamine and histamine was reduced. During Pa fermentation, accumulation of tyramine, putrescine, and cadaverine in all experimental cases was noted. Spermine was accumulated only in some cases, while β-phenylethylamine and spermidine amounts were stable throughout fermentation. During Gat fermentation, only the cadaverine amount remained unchanged throughout the fermentation, and the accumulation of tyramine, β-phenylethylamine, putrescine, and spermidine was recorded. Spermine was also accumulated but only in some cases. In general, the addition of myeolchi-aekjeot and the tyramine-producing Lv. brevis strain enhanced biogenic amine accumulation, with the exception of spermine. Jin et al. [203] prepared Kkakdugi and Chonggak kimchi and studied the effect of myeolchi-aekjeot and saeu-jeotgal, a fermented shrimp product, the utilization of which has also been correlated with increased biogenic amine levels [221] in tyramine-producing Lv. brevis strains and Lp. plantarum strains. During fermentation of both products, the histamine amount decreased and the spermidine amount increased. In the case of Kkakdugi, tyramine was accumulated only in the samples inoculated with Lv. brevis, the putrescine amount slightly increased only in the uninoculated sample and the one inoculated with Lv. brevis JCM 1170, and cadaverine accumulated in all samples with the exception of the one that did not contain myeolchi-aekjeot, saeu-jeotgal, and inoculum. The latter sample was the only one in which spermine content increased, while in the rest, it was decreased. In the case of Chonggak, cadaverine remained stable in all samples but seemed to increase in the sample that did not contain the fermented fish condiments and inoculum; the tyramine amount increased in all samples with the exception of the one inoculated with Lp. plantarum, and cadaverine was accumulated only in the sample prepared with the addition of the fish condiments but without inoculum. In the same sample, along with the samples inoculated with Lv. brevis, the amount of spermine decreased. Combining the studies of Lee et al. [204] and Jin et al. [203], it can be concluded that the accumulation of biogenic amines could not always be predicted through the addition of ingredients that have been correlated with increased biogenic amine content (fish condiments) of starter cultures with known capacities. This indicates the existence of additional parameters that, at least in some cases, may affect biogenic amine accumulation. Since biogenic amine accumulation and decomposition are strain-dependent properties, it can be hypothesized that the native microbiota, and especially the proportion of which that manages to participate in the developing microecosystem, may be this additional parameter.
In the case of fermented cucumbers, biogenic amine accumulation during fermentation was assessed by Alan [223]. In the latter study, gherkin fermentation was performed spontaneously or with the addition of Lp. plantarum, Lp. pentosus, or Lp. paraplantarum strains as starter cultures. Spermidine was not detected in any experimental case. On the contrary, putrescine, cadaverine, histamine, and tyramine were detected, and their amount was strain-dependent. More accurately, spontaneously fermented gherkins contained an equal amount of putrescine with the one started with Lp. plantarum strain 49, less than the one started with Lp. plantarum strain 51, and more than the ones started with Lp. plantarum strain 13, Lp. pentosus strain 2, and Lp. paraplantarum strain 16. Cadaverine and histamine were not accumulated in the gherkins started with all three Lp. plantarum strains, but larger amounts were detected in the gherkins started with Lp. pentosus strain 2 and Lp. paraplantarum strain 16 compared to the spontaneously fermented ones. Finally, an equal amount of tyramine was accumulated in the gherkins started with Lp. plantarum strain 13 comapred with spontaneously fermented ones and larger amounts in the ones started with Lp. plantarum strains 49 and 51, Lp. pentosus strain 2, and Lp. paraplantarum strain 16.
The fate of biogenic amines during the fermentation of olives of the Manzanilla cultivar was assessed by Garcia-Garcia et al. [224]. Putrescine, tryptamine, β-phenylethylamine, spermidine, spermine, histamine, and agmatine were not detected during storage at 15, 20, and 28 • C for 12 months. Only cadaverine and tyramine were accumulated. The former was produced only at 20 and 28 • C, and the production rate increased after 7 and 5 months, respectively. Washing was correlated with increased production. Tyramine production followed a similar trend, with the exception that accumulation also occurred during storage at 15 • C.
Conclusions
The functional potential of lactic acid fermented fruits and vegetables relies on the interplay between the quality of the raw materials and the capacity of the microbial consortium to carry out certain biotransformations. The former depends on the type and variety of the raw materials, climatic conditions, and agricultural practices, as well as the occurrence and conditions of processing and storage. On the other hand, the production of bioactive compounds by microorganisms is a strain-dependent characteristic that also depends on the fermentation temperature and time. Thus, optimization of the functional potential requires a thorough study of all the aforementioned parameters. Although a lot of information is available in some cases, e.g., the production of biogenic amines, the trophic relationships within the microecosystem are very complex, and, thus, further study is still necessary to enable practical recommendations. | 9,093 | 2022-03-01T00:00:00.000 | [
"Environmental Science",
"Biology",
"Chemistry",
"Agricultural and Food Sciences"
] |
Valuation Fuzzy Soft Sets: A Flexible Fuzzy Soft Set Based Decision Making Procedure for the Valuation of Assets
: Zadeh’s fuzzy set theory for imprecise or vague data has been followed by other successful models, inclusive of Molodtsov’s soft set theory and hybrid models like fuzzy soft sets. Their success has been backed up by applications to many branches like engineering, medicine, or finance. In continuation of this effort, the purpose of this paper is to put forward a versatile methodology for the valuation of goods, particularly the assessment of real state properties. In order to reach this target, we develop the concept of (partial) valuation fuzzy soft set and introduce the novel problem of data filling in partial valuation fuzzy soft sets. The use of fuzzy soft sets allows us to quantify the qualitative attributes involved in an assessment context. As a result, we illustrate the effectiveness and validity of our valuation methodology with a real case study that uses data from the Spanish real estate market. The main contribution of this paper is the implementation of a novel methodology, which allows us to assess a large variety of assets where data are heterogeneous. Our technique permits to avoid the appraiser’s subjectivity (exhibited by practitioners in housing valuation) and the well-known disadvantages of some alternative methods (such as linear multiple regression).
Introduction
Zadeh's [1] fuzzy set theory deals with impreciseness or vagueness of evaluations by associating degrees to which objects belong to a set.Its appearance boosted the rise of many related theories that attempt to model specific decision problems.In particular, the hybridization of fuzzy sets with soft sets as proposed by Molodtsov [2] (see also Maji et al. [3,4]) yields the notion of fuzzy soft set (Alcantud [5], Ali [6], Ali and Shabir [7], Maji et al. [8]).Decision-making methodologies and applications have proliferated and are the subject of relevant analyses on a regular basis.Among the most recent papers that exemplify noteworthy fuzzy decision-making trends, we can cite Alcantud et al. [9,10], Faizi et al. [11,12] and Zhang and Xu [13] in hesitant fuzzy sets, Zhan and Zhu [14] in (fuzzy) soft sets and rough soft sets, Alcantud [15] in fuzzy soft sets, Ma et al. [16] in hybrid soft set models, Chen and Ye [17] and Ye [18] in neutrosophic sets, Peng et al. [19] and Peng and Yang [20] in interval-valued fuzzy soft sets, and Fatimah et al. [21] in (dual) probabilistic soft sets.With respect to applications, in a clinical environment, Chang [22] uses the fuzzy sets theory and the so-called VIKOR (VIsekriterijumska optimizacija i KOmpromisno Resenje) method to evaluate the service quality of two public and three private medical centres in Taiwan, in the same context of uncertainty, subjectivity and linguistic variables as our study; Espinilla et al. [23] apply a decision analysis tool for the early detection of preeclampsia in women at risk by using the data of a sample of pregnant women with high risk of this disease; and Alcantud et al. [24] give a methodology for glaucoma diagnosis.On the other hand, in the field of management, Zhang and Xu [13] deal with the problem of choosing material suppliers by a manufacturer to purchase key components in order to reach a competitive advantage in the market of watches; Xu and Xia [25] provide a management case study by using the hesitant fuzzy elements to estimate the degree to which an alternative satisfies a criterion in a decision-making process; Taş et al. [26] present new applications of a soft set theory and a fuzzy soft set theory to the effective management of stock-out situations.In the field of finance, Xu and Xiao [27] apply the soft set theory to select financial ratios for business failure prediction by using real data sets from Chinese listed firms; Kalaichelvi [28] and Özgür and Taş [29] apply fuzzy soft sets to solve the investment decision making problem.
In this work, we introduce the notion of partial valuation fuzzy soft set as a tool to perform valuations of assets.Then, we apply a suitable valuation methodology, based on fuzzy soft sets, to a real case study.Fuzzy soft sets, with their ability to codify partial membership with respect to a predefined list of attributes, seem to be a useful tool to make decisions in this context.Unlike the standard approach, which selects one from a set of possible alternatives, our decision is the valuation that should be rightfully attached with some of the assets.In passing, we introduce rating procedures as well as the problem of data filling in partial valuation fuzzy soft sets.
Our application concerns the real estate market.
There is ample variety of real estate valuation methods.Following [30], we classify them into traditional and advanced.Traditional methods are: comparison method, investment/income capitalization method, profits method, development/residual method, contractors/cost method, multiple regression method, and stepwise regression method.As advanced valuation methods, we can cite: artificial neural networks (ANNs), hedonic pricing method, spatial analysis methods, fuzzy logic, and autoregressive integrated moving average (ARIMA).
In Spain, real estate valuation is regulated by Orden ECO/805/2003 (Ministerio de Economía, 2003) [31], which recommends the use of four of the previously mentioned methods: comparison, investment/income capitalization, residual, and cost methods.There are some interesting works that compare certain methods used in real estate appraisal, e.g., [32] compare fuzzy logic to multiple regression analysis, or [33] compare artificial-intelligence methods with non-traditional regression methods.We also find new hybrid methodologies, e.g., [34], which relies on the introduction of fuzzy mathematics in a spatial error model.
We contribute to this growing literature by proposing a flexible mechanism that can be specialized in several ways.The input data is a partial valuation fuzzy soft set that characterizes the problem.The practitioner can select one from a sample of rating procedures in order to start the algorithm.Then, a suitable regression analysis permits filling the missing data in the original partial valuation fuzzy soft set.The structure of the available data often allows the researcher to perform sophisticated regression analysis beyond the standard, linear case.
This paper is organized as follows.Section 2 recalls some notation and definitions related to soft sets and fuzzy soft sets.Section 3 presents the main new notions in this paper, namely, valuation and partial valuation fuzzy soft sets.We also define rating procedures for fuzzy soft sets and prove some useful fundamental properties of these concepts.Section 4 briefly introduces data filling for partial valuation fuzzy soft sets, and a flexible methodology is proposed in order to implement that concept.Then, in Section 5, we take advantage of such design in order to valuate goods through a fictitious streamlined example.In Section 6, we present an application to a real case study on the Spanish real estate market.We also examine its traits in comparison with other standard methodologies.We conclude in Section 7.
Notation and Definitions
Let X denote a set.Then, P (X) is the set of all subsets of X.A fuzzy subset (also, FS) is the degree of membership of x in that subset.The set of all fuzzy subsets on X will be denoted by FS(X).Now, we are going to recall some basic concepts such as soft sets and fuzzy soft sets.
Soft Sets and Fuzzy Soft Sets
In soft set theory, we refer to a universe of objects U, and to a universal set of parameters E.
Definition 1 ([2]
).Let A be a subset of E. The pair (F, A) is a soft set over U if F : A −→ P (U).
The pair (F, A) in Definition 1 is a parameterized family of subsets of U, and A represents the parameters.Then, for every parameter e ∈ A, we interpret that F(e) is the subset of U approximated by e, also called the set of e-approximate elements of the soft set.
Other interesting investigations expanded the knowledge about soft sets.The notions of soft equalities, intersections and unions of soft sets and soft subsets and supersets are defined in [4].Various types of soft subsets and soft equal relations are studied in [35].Soft set based decision-making was initiated by [3].Further applications of soft sets in decision-making contexts were given, for example, in [24,36,37].
The concept of soft set can be expanded so as to include fuzzy subsets approximated by parameters: Definition 2 ([8]).Let A be a subset of E. The pair (F, A) is a fuzzy soft set over U if F : A −→ FS(U), where FS(U) denotes the set of all fuzzy sets on U.
The set of all fuzzy soft sets over U will be denoted as F S(U). Due to the natural identification of subsets of U with FSs of U, any soft set can be considered a fuzzy soft set (cf., [5]).If, for example, our universe of options are films that are parameterized by attributes, then fuzzy soft sets permit to deal with properties like "funny" or "scary" for which partial memberships are almost compulsory.However, soft sets are suitable only when properties are categorical, e.g., "Oscar awarded", "3D version available", or "silent movie".
In real practice, both U and A use to be finite.Then, k and n will denote the respective number of elements of U = {o 1 , . . ., o k } and A = {e 1 , . . ., e n }.In such case, soft sets can be represented either by k × n matrices or in their tabular form (cf., [38]).The k rows are associated with the objects, and the n columns are associated with the parameters.Both practical representations are binary, that is to say, all cells are either 0 or 1.One can proceed in a similar way in fuzzy soft sets, but now the possible values in the cells lie in the interval [0, 1].
A matrix representation of a soft set is shown in the following Example 1: Example 1.Let U = {h 1 , h 2 , h 3 } be a universe of houses.Let A = {e 1 , e 2 , e 3 , e 4 } be the set of parameters, attributes or house characteristics (e.g., "centrally located" or "includes a garage").Define a soft set (F, A) as follows: 1. h 1 ∈ F(e 1 ) ∩ F(e 4 ), h 3 ∈ F(e 2 ) ∪ F(e 3 ).Suppose that a soft set (F, A) can be expressed by the k × n matrix (t ij ) i,j .Then, the choice value of object o i ∈ U is defined as c i = ∑ n j=1 t ij .According to Maji, Biswas and Roy [3], an optimal choice can be made by selecting any object o i such that c i = max j=1,...,k c j .Put differently, any choice-value maximizer is an acceptable solution to the problem.
However, fuzzy soft set decision making is far more complex thus controversial.Approaches to that problem are included in [15,[39][40][41]].
Anyhow, the example above shows that fuzzy soft sets are a suitable tool to capture the characteristics of complex representations of assets.Section 6 below clarifies this argument with a real example.
Basic Operations
Basic operations among soft sets were established in Ali et al. [42]: Definition 3 ([42]).Let (F, A) and (G, B) be soft sets over U, such that A ∩ B = ∅.The restricted intersection of (F, A) and (G, B) is denoted by (F, A) ∩ R (G, B) and it is defined as where H(e) = F(e) ∩ G(e) for all e ∈ A ∩ B.
Definition 4 ([42]
).The extended intersection of the soft sets (F, A) and (G, B) over U is the soft set (H, C), where C = A ∪ B, and ∀e ∈ C, Definition 5 ([42]).Let (F, A) and (G, B) be soft sets over U, such that A ∩ B = ∅.The restricted union of (F, A) and (G, B) is denoted by (F, A) ∪ R (G, B) and it is defined as (F, A) ∪ R (G, B) = (H, C), where C = A ∩ B and for all e ∈ C, H(e) = F(e) ∪ G(e).
Definition 6 ([42]
).The extended union of two soft sets (F, A) and (G, B) over U is the soft set (H, C), where C = A ∪ B, and ∀e ∈ C, Maji et al. [8] defined some relations and similar operations for fuzzy soft sets as follows.
Definition 7 ([8]
).Let (F, A) and (G, B) be fuzzy soft sets over U. We say that (F, A) is a fuzzy soft subset of (G, B) if A ⊂ B and F(e) is a fuzzy subset of G(e) for all e ∈ A.
When (F, A) is a fuzzy soft subset of (G, B) and (G, B) is a fuzzy soft subset of (F, A) we say that (F, A) and (G, B) are fuzzy soft equal.
Their intersection is (H, C) where C = A ∩ B and H(e) = F(e) ∩ G(e) for all e ∈ C = A ∩ B. Their union is (H , C ), where C = A ∪ B, and ∀e ∈ C ,
Some Novel Concepts Related to Valuation Fuzzy Soft Sets
In this section, we are going to introduce the main new notions in this paper, namely, valuation and partial valuation fuzzy soft sets.We also prove some fundamental properties of them.
Valuation and Partial Valuation Fuzzy Soft Sets
In order to define our novel notions, we refer to a universe U of k objects, and to a universal set of parameters E.
Definition 9.
Let A be a subset of E. The triple (F, A, V) is a valuation fuzzy soft set over U when (F, A) is a fuzzy soft set over U and V = (V 1 , . . ., V k ) ∈ R k .Henceforth, we abbreviate a valuation fuzzy soft set by VFSS.We denote by V(U) the set of all valuation fuzzy soft sets over U.
If we restrict Definition 9 to soft sets over U, a particular concept of valuation soft set is naturally produced.
The motivation for valuation (fuzzy) soft sets is that, in many natural situations, option o i from U is associated with a valuation, appraisal or assessment V i , in addition to the standard parameterization of U as a function of the attributes in A. For example, in the usual example where the options are houses, this valuation may be the market price.
Such valuation can also be defined through elements from fuzzy soft set theory, or otherwise.We proceed to formalize these ideas.Definition 10.A rating procedure for fuzzy soft sets with attributes A on a universe U is a mapping Every rating procedure associates each FSS over U with a VFSS over U.For example, one can use scores associated with decision making mechanisms from the literature (e.g., fuzzy choice values, the scores computed in [39], or the refined scores computed in [15]), in order to produce particularly noteworthy rating procedures.We formalize them in the following definitions: Definition 11.The fuzzy choice value rating procedure is defined by the expression Recall that c i is the fuzzy choice value of option i.
Definition 12. Roy and Maji's rating procedure is defined by the expression
, where Π i r is the score S i associated with option i in the Algorithm in Section 3.1 of [39] (or alternatively, s i in Algorithm 1 in [15]).Definition 13.Alcantud's rating procedure is defined by the expression Π a (F, , where Π i a = S i is the score associated with option i in Algorithm 2 of [15].
In this paper, we are especially concerned with Definition 13.In order to make this paper self-contained, we proceed to recall its construction.
We describe our fuzzy soft set (F, A) on k alternatives o 1 , . . ., o k in tabular form.Let t ij denote its cell (i, j) for each possible i, j.Now, for each parameter j = 1, ..., q, let M j be the maximum membership value of any object (M j = max i=1,...,k t ij ).Then, we construct a k × k comparison matrix A = (a ij ) k×k , where for each i, j, a ij is the sum of the non-negative values in the finite sequence Of course, such matrix can also be expressed as a comparison table.
For each i = 1, . . ., k, let R i be the sum of the elements in row i of A, and T i be the sum of the elements in column i of A. Finally, for each i = 1, . . ., k, the score of object i is S i = R i − T i .
The following toy example illustrates the notions above.
Example 2. Consider the fuzzy soft set (G, B) in Section 3.3 of [40].Its tabular form is in Table 2.The application of Definitions 11, 12 and 13 to (G, B) produces three respective VFSSs, namely, In order to obtain these results, we note that the fuzzy choice values c i in Definition 11, and the scores s i in Definition 12, are calculated in Table 6 of [40].In addition, the scores S i associated with the options by Definition 13 are computed in Figure 2 of [15].These c i , s i and S i scores produce the respective VFSSs above.Such VFSSs are summarized in Table 3.In order to select a suitable rating procedure, Definition 13 is the natural choice that we recommend for the valuation of fuzzy soft sets.Our advice is based on the following arguments.Firstly, most authors agree that it seems untenable to use Definition 11, which is a simple adapted version of choice values.Although choice values are widely acceptable in soft set theory, they cannot capture the subtleties of the more general model by FSSs.Therefore, we discard Definition 11.Secondly, Definition 12 does not capture whether an alternative beats another one by a narrow or a large margin, while Definition 13 explicitly rewards more ample differences in the degree of satisfaction of the characteristics.In applications like real estate valuation, the wide range of the feasible assessments demands a method that incorporates these differences.Otherwise, the results will be affected by the odd fact that alternatives with striking differences in their characteristics should be equally valuated, which is clearly a blunt mistake.For these reasons, we must discard Definition 12 and recommend Definition 13.
For practical purposes, the following definition will be very useful.It concerns the cases where some of the valuations are unknown.Definition 14.Let A be a subset of E. The triple (F, A, V * ) is a partial valuation fuzzy soft set over U when (F, A) is a fuzzy soft set over U and V * ∈ (R ∪ { * }) k .We abbreviate partial valuation fuzzy soft set by PVFSS.
The set of all partial valuation fuzzy soft sets over U will be denoted as V * (U).If we restrict Definition 14 to soft sets over U, then we define the particular concept of partial valuation soft set.As in the case of VFSSs, each option from U is associated with a valuation in addition to the standard parameterization of U as a function of the attributes in A. However, in PVFSSs, it may happen that some of the valuations is unknown or missing.In such case we represent the unknown information or missing valuation data by the * symbol.Now the motivation for PVFSSs goes as follows.Quite often some options o i from U have an intrinsic valuation V i ∈ R (for example, market price), whereas the valuation of other options o j are unknown (for example, because it is our own house that we want to put up for sale).The model by PVFSSs permits collecting all that information in a concise format.
Data Filling in Partial Valuation Fuzzy Soft Sets
Valuation is an abstract concept that can be specialized in many ways.We can take advantage of this issue in order to fill missing data in PVFSSs through an adjustable approach.The motivation for this novel problem is the following.If there are missing valuation data in a PVFSS, then the assessments of the corresponding alternatives are unknown.Should we need them (for example, because the valuation of our house means the market price that we might expect when we put it up for sale), then we must fill the missing data.
Therefore the problem of data filling in PVFSSs is associated with solving an original decision making problem for alternatives that are characterized by FSSs.
Remark 1.The idea of partial valuations should not be mistaken with the well-known notion of incomplete (fuzzy) soft sets [36,[43][44][45][46].In the latter case, the parameterization has missing values.In our model, the parameterization of the universe is complete, whereas the valuation is not necessarily complete.Thus, the statement of our data filling problem is original with this paper.
We proceed to define our class of procedures for the valuation of goods when (a) these goods are characterized by parameters, and (b) there are comparable goods that are characterized by the same parameters.In other words, we have information about the goods in the form of PVFSSs.
Our methodology is very direct.It works as follows.Let us select a rating procedure (cf., Definition 10).
2.
We use the rating procedure in order to associate a unique number with each alternative.In this way, we obtain a VFSS (F, A, W) associated with the same FSS (F, A) as the original PVFSS.
3.
Now, as long as there are two values in V * that belong to R (i.e., two valuations that are not missing in the input data), we calculate a regression equation to fill the missing valuation data.
In order to run the regression, the independent variables (or abscissas) are the values W i given by the rating procedure that has been singled out, and the dependent variables (their respective ordinates) are the corresponding V i ∈ R valuations.
4.
Once the regression function has been calculated, we can estimate the real values of the missing valuations V i = * by its evaluations in the corresponding W i values.
This procedure solves our original data filling problem.
This methodology is flexible because we can use any rating procedure to produce the abscissas of the data plots and also because we can use regression models other than linear regression in order to fill the missing data (step 3).Observe that in such cases we need a larger set of non-missing data.
The flowchart in Figure 1 summarizes the steps in our solution to the problem of data filling for PVFSSs.Section 5 below presents an illustrative example in the context of valuation of goods.Later on, in Section 6, we apply the current proposal to a real case study on the Spanish real estate market.
Valuation of Goods: An Example
For a given a list of options characterized by a PVFSS, the information on the known values can be used to fill the missing data.Observe that at the end of the process we are valuating the assets with missing values.Therefore, we can use the data filling procedures described in Section 4 in order to make decisions e.g., as to which prizes should be attached to properties that are put into the market.
In this section, we explain this possibility with the following fully developed example.Table 4 represents a PVFSS denoted (F, A, V * ).It uses the input data of Table 6 of [15], which we complement with valuations of some of the six alternatives.We can interpret Table 4 as follows.We are interested in selling property o 4 , whose market value we want to assess ourselves.The options o i include our property and other real state properties for sale, and they are all characterized by the p j attributes.An inspection of the market shows that recent purchases in the same area or street amounted to the respective V i 's.With this practical information, we are ready to valuate our property.
Let us select the rating procedure Π a .We are ready to apply the remaining steps in Section 4. As explained above, Π a valuates the options by using Alcantud's scores.Therefore, W = V Π a = (−1.3,−3.2, −3.78, −2.24, 5.24, 5.26) because these figures are computed in Table 8 of [15].Hence, the VFSS that we obtain at step 2 of our data filling solution in Section 4 is (F, A, W).
Observe that the 4th values have been discarded because the valuation of the 4th alternative is missing.Some easy computations (see for example [47]) show that the regression line equation in step 3 is y = 142.02204039129+ 10.310719839438x, with a coefficient of determination R 2 = 0.9854.Figure 2 displays these computations.Finally, in step 4, we evaluate such function at the score value x = −2.24associated with o 4 , which produces the evaluation value 118.92602795094888.
In conclusion, option o 4 should be valuated by 118, 926.03 euros.
A Real Case Study
In this section, we propose a method to appraise real estate based on fuzzy logic as we concur with [48] on "the applicability of fuzzy logic for expressing the inherent imprecision in the way that people think and make decisions about the pricing of real state".As far as we know, no methodology based on fuzzy soft sets has ever been applied to real estate valuation using real data from the market.We here use the novel procedure that relies on the new notion of data filling in PVFSSs (as applied in Section 5) in order to provide an assessment of a property based on real data from Almería, in Southeast Spain.The data were obtained by one of the coauthors who acted as appraiser in 2016.Lastly, we compare our existing methodologies.
To be precise, for such real application, we intend to assess an apartment (the subject property) using the data of six apartments (the comparable properties), with known sale prices.We also know the values of four selected attributes (cf., Table 5): surface, number of bathrooms, quality, and number of bedrooms.The values for the attribute "surface" are expressed in square meters.Apartment 6 has 1.5 bathrooms, which means that it has a complete bathroom with a bathtub and another bathroom without a bathtub.There are other attributes, like location and age that we did not include in the table because the six comparable properties and the subject property had similar values (they were located in the same area and were built approximately in the same year).
The property we have to assess has a surface of 114.44 square meters, one bathroom, two bedrooms and a "good" quality.
To apply the method explained in Sections 4 and 5, we first adapt the data to fuzzy soft set format, and, for this purpose, we perform the following adjustments: 1.The maximum surface in our sample of seven apartments is 114.44 square meters.We have divided the surface of each apartment by this maximum figure.2. We have divided the number of bathrooms of each apartment by two, the maximum number of bathrooms per apartment in our sample.3.In order to rank the attribute "quality", we have considered four levels of quality: bad, normal, good, and luxury.We assign the values 0, 1/3, 2/3 and 1 to each level, respectively.4. For the attribute "number of bedrooms", we have divided the actual number of bedrooms by the maximum number of bedrooms, which, in our sample, is four.
Table 6 shows the PVFSS that captures the statement of our real valuation problem.If we select the rating procedure Π a , then we first compute the comparison table associated with Table 6.Such item is given in Table 7 (the values have been rounded off for the purpose of presentation).These values are given by Alcantud's scores S i in Table 7.
We now need to calculate the linear regression equation from the bivariate data that combine the known valuations with the corresponding components of our rating procedure, which are ((−3.1038,95), (3.6, 157), (−4.8538, 115), (1.1231, 132), (−0.6269, 132), (1.85, 157)).Some easy computations show that the regression line equation is y = 133.54+ 6.5722x, where y are prices, x represent the scores, and the coefficient of determination takes an acceptable value (R 2 = 0.7516).Hence, for x = 2.0114, the value of the y variable is 146.75948, and we conclude that the property should be priced at 146, 759.48 euros because prices were given in thousands of euros.Figure 3 displays these computations.
Sensitivity Analysis
Prices in the real estate market are subject to volatility.In addition, the appraiser can select the small sample in accordance to the existing regulations.Therefore, we have to account for some degree of uncertainty in the valuation of the subject property.
Sensitivity analysis studies how the uncertainty in the output of a mathematical model can be associated with different sources of uncertainty in its inputs [49].The techniques of sensitivity analysis are sundry and the choice of a suitable methodology is often dictated by the structure of the model.Since we work with given data, we can screen for submodels and check how much the selection of a subsample affects the output.We proceed to check that under such variations the differences in the outputs are small, which allows us to conclude that our valuation model is fairly robust.If p i , i = 1, 2, . . ., n denotes the price of the i-th apartment, S i its surface, and ω ik * , k = 1, 2, . . ., m, represents the weight assigned to the k-th attribute of the i-th element in the sample, the normalized average price of a square meter is: . Therefore, where the subscript 0 corresponds to the house to be assessed.The multiple linear regression method consists of regressing the variable P (price of the house) on the rest of variables involved in the valuation process, e.g.: • X 1 : "Surface".• X 2 : "Number of bathrooms".• X 3 : "Quality".• X 4 : "Number of bedrooms".
Thus, we are able to obtain a regression hyperplane in the following form: The concrete values of variables X 1 , X 2 , . . ., X n corresponding to the house to be appraised will allow us to estimate P. Indeed, the main advantage of this method is the objectivity of the result.Unfortunately, this procedure may present two noteworthy drawbacks.First, the goodness of fit in the regression analysis can be very low, which means that the result that produces is not significant at a certain level.Second, a concrete coefficient β k may exhibit a "wrong" sign in the way that the estimated sign on a variable is the opposite of what we anticipated it should be.For example, it is expected that the price of a house is ceteris paribus inversely related to its age, but the practical implementation of this technique can lead to a positive coefficient for this variable.A possible solution could be to restrict the coefficients to the set of positive or negative real numbers, but, unfortunately, the coefficient of determination does not measure, in this case, the goodness of the fit.
When the linear relationship between the dependent variable (the price) and the regressors (the rest of variables involved in the analysis) has been computed, the values of the attributes of the house to be assessed are included in the equation, which produces an estimated market price.Indeed, a drawback of this method is that the goodness of fit (given by the coefficient of determination) may be very low.This is the reason why it seems convenient to find an appropriate sample (composed by, at least, six houses) for which the fitting should be acceptable.
We return to these issues in the next section.
Evaluation with Alternative Procedures and Discussion
The routine application of the multiple regression technique to the data included in Table 5 leads to the following three-dimensional hyperplane: which leads to a price p = 189, 605.86 euros.Although the coefficient of determination is very high (R 2 = 0.9656), this outcome is rather disappointing for two main reasons.The coefficient of x 4 has the wrong sign because ceteris paribus the price of an apartment should increase both with the number of bedrooms.Moreover, observe that the coefficient of x 3 vanishes.The reason is that all the apartments with a valuation in the sample have a "normal" quality, even though there are other values for this attribute in the sample.This is another important drawback of this method since, in our real case study, such zero value implies the fact that the apartment being assessed has a "good" quality cannot be used to increase its valuation.
Let us now approximate the price of the apartment according to the weights shown in Table 9.According to the Orden ECO/805/2003 (Ministerio de Economía, 2003) [31], the coefficients to standardize the value of the square meter of each element in the sample will be chosen by applying the criteria suitable for the house to be assessed.Nevertheless, this procedure, called the homogenization method, "has got some problems which should be solved and that are related, for example, with valuer's subjectivity" [50].Therefore, in this paper, we have implemented the standard weights used by practitioners, which are based on a proposal by González-Nebreda et al. [51].The application of this information to the characteristics of the apartments in the sample and the apartment to be assessed produces Table 10, where, for completeness, the price of each apartment is shown too.By applying Formula (1), we obtain a price of 171,747.78euros.All in all, along this paper, we have compared three methodologies to approximate the value of an apartment from the information supplied by the housing market about the characteristics (price, surface, number of bathrooms, number of bedrooms and quality) of a sample composed by six other apartments.
The first method uses the linear multiple regression where the dependent variable is the price and the independent variables are the rest of the characteristics of the apartments.This technique is subject to at least three noteworthy inconveniences, which dramatically reduce the validity of its results: 1.The possible existence of coefficients with the wrong sign (in our case, the coefficient of variable x 4 ).2. The possibility that a coefficient vanishes (in this section, the coefficient of variable x 3 is zero).
In such case, the characteristic associated with the corresponding variable is of no use for evaluation purposes.3. The coefficient of determination may be small (although, in the example in this section, R 2 is pretty high).
The second procedure uses the weights assigned by practitioners to highlight the "good" characteristics of all apartments and to penalize their "bad" figures.This methodology presents an important disadvantage, viz. the enormous subjectivity in choosing these weights.
The third technique is new with this paper.It produces a much more reasonable result, which is partially due to the reduction of subjectivity in the weights.
Despite the disparities between prices, let us stress that the price finally agreed in the transaction of this apartment was much closer to the value given by the proposed methodology.
Conclusions
In this work, we propose the new notion of partial valuation fuzzy soft sets and we briefly introduce the problem of data filling in that setting (cf., Sections 3 and 4).The use of fuzzy soft sets permits quantifying qualitative attributes, such as the finish of housing construction or the quality of materials used in the construction of a house.Therefore, we can apply these ideas in real estate valuations.By doing so, we depart from fuzzy soft sets and extend their scope with the target of real applications.In our approach, we first use a rating procedure in order to associate a unique number (score) with each alternative and then we apply regression for the purpose of data filling in partial valuation fuzzy soft sets (cf., Section 4).We have explained our model both algorithmically and with a flow diagram.
Then, we have shown how this new methodology works in a fictitious (cf., Section 5) and a real case study (cf., Section 6).With these examples, we have proved the implementability and feasibility of our methodology.We have also performed a sensitivity analysis in order to avail its robustness.The real case study concerns apartments.Obviously, it can be also applied in the valuation of other kind of assets, such as rural properties, cars, etc.We have obtained a very reasonable price for the house under valuation, which proves the feasibility and implementability of our suggestion.On the other hand, the two alternative methods (that were based on the linear multiple regression and used by practitioners) exhibit serious troubles that restrict their ability to fit real situations.
To conclude, let us point out that our technique can be useful for practitioners using other models of uncertain behavior.For example, the idea that scores can be used to perform a regression can easily be exported to models based on hesitant fuzzy sets [11,12,[52][53][54][55] for which scores are already available [56][57][58].It seems also feasible to export it to other hybrid soft set models (cf., Ali et al. [59], Fatimah et al. [60], Ma et al. [16], Zhan and Zhu [14], and Zhan et al. [61]).
Figure 1 .
Figure 1.Flow diagram with the solution to the data filling problem in Section 4.
Figure 2 .
Figure 2. The regression line in Section 5.The black square shows the valuation of the missing option o 4 , with score −2.24 at the horizontal axis.
Figure 3 .
Figure 3.The regression line in the case study.The black square shows the valuation of the missing option h 7 , with score 2.0114 at the horizontal axis.
Table 1 .
Tabular representation of the soft set (F, A) in Example 1.
Table 2 .
Tabular representation of the fuzzy soft set (G, B) in Example 2.
Table 3 .
Summary of the tabular representations of the three VFSS in Example 2.
Table 4 .
Tabular representation of the partial valuation fuzzy soft set (F, A, V * ) in Section 5.All V i s are expressed in thousands of euros.
Table 5 .
Attributes of the comparable six apartments.Source: Real data from the Spanish real estate market (Almería, Spain, 2016).
Table 6 .
The PVFSS in the real case study in Section 6. Sale prices are given in thousands of euros.
Table 7 .
Comparison table and scores associated with Table6.The values have been rounded off.
Table 10 .
Weights assigned to all apartments. | 8,915.2 | 2017-10-27T00:00:00.000 | [
"Business",
"Engineering",
"Mathematics"
] |
Performance Evaluation of Carbon-Based Printed Perovskite Solar Cells under Low-Light Intensity Conditions
, and a systematic comparison of their PV performance under commonly available fl uorescent (FL) and light-emitting diode (LED)-based lamps at various low lux light intensities that replicate standard indoor environmental conditions. To consolidate the proven stability of these CPSCs, the results of one stability test standardized as ISOS-D-1, which supports the motivation of their possible deployment under mild indoor lighting conditions are presented. The effective functioning of these CPSCs is also demonstrated for energizing an electrical node as evidence of their potential to be used as an alternative light-harvesting solution for the targeted futuristic IoT-based ecosystem. These results greatly support the goal of developing all printed and sustainable IoT devices with robust performance stability
Introduction
Energy harvesting technologies collect various forms of ambient energies such as heat, light, or vibrations to generate electricity at micro scales. [1,2]Provided that the wasted energy dissipated in the environment is ubiquitous, energy harvesters present the potential to be self-sustaining with an ideal infinite functioning lifetime.Therefore, they have been considered a potential alternative to the traditional battery-based energy solutions presently enforced to energize electronic consumer goods, the Internet of Things (IoT), or other distributed electronic-based ecosystems. [3,4]ince many of these electronic devices are typically located inside buildings, there is great potential for energizing them via integrating photovoltaics (PVs) that can harvest abundantly available ambient indoor light energy from LED, halogen, and FL lamps or other types of light sources.[7][8][9] Keeping this motivation in mind, established silicon (Si) solar cell-based PV technologies have initially been deployed to harvest ambient light energy for energizing various low-powered electronic appliances such as calculators, digital thermometers, and electronic clocks. [10]However, the low power conversion efficiency under lowlight conditions, combined with high production costs have limited their widespread use in indoor applications. [7,8,11]][24][25][26] As expected, the striking conversion efficiencies of PSCs achieved in recent years (Table 1) under these ambient light intensity conditions provide preliminary evidence for considering them as another potential light-harvesting solution for energizing DOI: 10.1002/adem.202200747 The use of photovoltaics (PVs) to harvest energy inside modern building environments has great potential for energizing a wide range of futuristic selfpowered electronic devices, Internet of Things (IoT), and sensors using available ambient light.Among the various PV technologies, hole-conductor-free carbonbased printable perovskite solar cells (CPSCs) have attracted significant interest, owing to their impressive PV performance under standard full sunlight conditions, robust stability, and printable fabrication methods.Nevertheless, their ability to harvest indoor light has been rarely explored.Here we report PV performance characterization of these printable CPSCs, and a systematic comparison of their PV performance under commonly available fluorescent (FL) and light-emitting diode (LED)-based lamps at various low lux light intensities that replicate standard indoor environmental conditions.To consolidate the proven stability of these CPSCs, the results of one stability test standardized as ISOS-D-1, which supports the motivation of their possible deployment under mild indoor lighting conditions are presented.The effective functioning of these CPSCs is also demonstrated for energizing an electrical node as evidence of their potential to be used as an alternative light-harvesting solution for the targeted futuristic IoTbased ecosystem.These results greatly support the goal of developing all printed and sustainable IoT devices with robust performance stability.advanced self-powered electronic devices, IoT, electrical nodes and sensor-based applications. [22,27,28][55] Contrary to these traditional configurations of PSC technology, hole-conductor-free carbon-based triple mesoscopic printable perovskite solar cells (CPSCs) [56,57] offer unique opportunities including low cost of fabrication with established scalable methods such as screen-or inkjet-based printing techniques. [58,59]oreover, their robust and long-term PV operational stability outperforms other reported traditional device configurations of PSC technology, as frequently proven under various simulated and natural environmental conditions since they were first reported. [56,60,61]These characteristics make CPSCs an ideal candidate to be used as potential energy harvesters for the aforementioned robust and self-sustaining targeted applications.
Interestingly, despite their robust stability and frequently proven high performance under standard illumination conditions, only a few reports mention their brief PV performance analysis under low light intensity conditions. [62,63]This calls for more independent experimental evidence to reach a systematic and consistent consensus for projecting this promising device configuration of PSC technology as a reliable and alternative energy harvesting solution, and how it compares to other emerging PV technologies or unstable PSC device configurations reported in the past decade.
To this end, we characterize the fundamental PV performance of these printable CPSCs under various light intensity conditions.To consolidate the proven stability of these CPSCs, we also present the results of one stability test standardized as ISOS-D-1, [64] which supports the potential for their deployment under mild indoor conditions.Moreover, we demonstrate a systematic comparison of the PV performance of these CPSCs under commonly available FL and LED-based lamps at various light intensities that replicate standard indoor environmental conditions.As a further advance, we also present the integration of these CPSCs for energizing an electrical node as evidence of their potential to be used as an alternative light-harvesting solution for the targeted futuristic IoT-based ecosystem.Our results not only consolidate and contribute to the limited studies on this promising configuration of PSCs, but also support the goal of achieving all printed and sustainable IoT devices with robust performance stability.
Results and Discussion
To begin our analysis, we first characterized the lab-sized (1.5 cm 2 ) CPSCs to demonstrate their initial PV performance Solar modules were also produced and reported under low-intensity light conditions in these reports.
][67] For the standard full sunlight condition, the fabricated batch of CPSCs in this work exhibited impressive (10.1 AE 1.5%) solar-to-electrical conversion efficiency over a small area (0.14 cm 2 ), with the champion device reaching as high as %12% conversion efficiency (Table 2, Figure 1a).This closely aligns with the PV performance for this device configuration indicated in various reports with similarly small aperture areas under standard full sunlight illumination conditions. [56,68]nterestingly, the same batch of fabricated CPSCs revealed striking (11.1 AE 1.6% and 12.6 AE 1.8%) conversion efficiencies when measured under half and 0.1 sunlight illumination conditions, with the champion devices attaining an impressive %13% and >14% conversion efficiencies, respectively (Table 2, Figure 1a).As a more realistic approach, we also measured the PV performance of the same batch of CPSC devices with a greater (0.64 cm 2 ) active area, which is rarely reported for similar lab-sized devices of this configuration. [69]As expected, the fabricated CPSCs once again Table 2. Average PV parameters (4 CPSCs) achieved at 1 Sun, 0.5 Sun, and 0.1 Sun light intensity conditions.The active area for small area measurements was 0.14 cm 2 and was 0.64 cm 2 for large area measurements.The values in brackets are of the champion device.revealed comparable PV performance, i.e., without compromising the conversion efficiencies (average batch: 9.3 AE 1.6%; highest 11.4%) on a relatively larger active area under full sunlight illumination conditions (Table 2, Figure 1b).Systematically, we further extended our characterization with this larger active area to determine the PV performance of these CPSCs under half and 0.1 sunlight intensities, which again indicated higher conversion efficiencies (10.9 AE 1.8% and 13.2 AE 2.2%, respectively, Table 2).Motivated by these initial characterizations, we further investigated the preliminary operational PV performance stability with a simulated maximum power point tracking test (MPPT) that was conducted under full sunlight illumination for more than two hours (as shown in Figure 1d).Contrary to traditional device structures, which often degrade rapidly under such stressful conditions, the fabricated CPCSs exhibited robust operational stability without showing any performance degradation for up to 150 min (i.e., >2 h, Figure 1d).These simulated conditions seem far more stressful with higher temperatures (38.5 AE 2.1 °C) combined with strong illumination compared to standard indoor conditions and provide a fair indication of reliable deployment of this printable device configuration of PSCs under more relaxed indoor building environmental-based ecological conditions.
To further support our perspective, we also simulated one of the standardized tests (ISOS-D-1) suggested for the indoor deployment of next-generation-based PV devices. [64]In this regard, another batch of CPSCs was stored in dark conditions (see Supplementary Information) for a period of 1065 h after characterizing their initial PV performance.They were then re-measured to determine the long-term stability at room-temperature (RT)based indoor ecological conditions.Table 3 summarizes the details of the dark storage test, while Figure 2 depicts the initial and final J-V curves of the champion CPSC that was measured under standard full sunlight intensity conditions.
As expected, reproducible and robust PV performance was achieved, where the fabricated devices of this batch showed >19% and %17% PV performance enhancements upon re-measuring with both the small (0.14 cm 2 ) and large (0.64 cm 2 ) active area after 1065 h.This is mainly attributed to the gradual improvements within the device structure interface, fabricated contacts over the nonactive area of the cells, along with the sealing materials (i.e., slow drying epoxy), as frequently discussed in numerous other studies upon storing them in versatile environments. [68,70,71]Moreover, these preliminary results also endorse those from previous studies that have shown stable PV performance for this device design of PSCs when investigated under similar storage conditions. [56,60,72,73]he striking PV performance combined with robust operational stability of CPSCs consequently stimulate further tests of their performance under versatile low light intensities, which remain available as a free energy source under various building environments.
Hence, we extended our characterizations and further investigated their PV performance under versatile low light intensity conditions by selecting two types of commonly available light sources (FL and LED lamps) through their measured spectra as shown in Figure 3.78] Moreover, to contribute to the traditional rationale regarding the PV performances for numerous architectures of PSC technology with small active areas, it is equally valuable to initially compare the performance of CPSCs with similarly small active areas as reported with traditional device configurations of PSCs (Table 1).Hence, the small active area (0.14 cm 2 ) based PV performance of the fabricated CPSCs was initially investigated under both the LED and FL light sources with the selective low light intensity conditions and is summarized in Table 5.
Output power as high as >72 μW cm À2 under 1000 lux light intensity of a LED light source was achieved, corresponding to an impressive (%21%) conversion efficiency observed for the best CPSC (Table 5 and Figure S3a, Supporting Information).The same CPSC exhibited >19% and >17% conversion efficiencies with corresponding %33 and >12 μW cm À2 P MAX values when measured under 500 and 200 lux light intensities, respectively (Table 5 and Figure S3a, Supporting Information).For the FL light source, the trends of PV performance also remained quite similar, where the same champion CPSC revealed comparable power output (Table 5 and Figure S3b, Supporting Information) with a range of >73, 34 and 13 μW cm À2 when tested under similar light intensity values, respectively.Followed by these initial investigations, measuring the power output of CPSCs with a far larger active area provides the opportunity to more reliably assess their targeted integration into a variety of sustainable energy harvesting solutions. [3,79,80]able 6 summarizes the average PV performance of the same batch of CPSCs measured with a larger (0.64 cm 2 ) active area, which revealed an impressive >80 μW cm À2 power output (with striking conversion efficiencies, i.e., >20-23% utilizing both the light sources) for the champion CPSC when measured under 1000 lux (Figure 5a,b).Similarly, >38 and >14 μW cm À2 values were achieved under 500 and 200 lux light intensities, respectively.These results not only confirm that there are no performance compromises despite the significant increase (>350%) in active area, but also establish better standards for comparing the performance of various traditional configurations of lab-sized PSCs often reported with marginal active areas, as listed in Table 1.
In addition, the dependence of the PV performance of CPSCs on light intensities (I) was further investigated, where V OC and J SC were obtained in response to varying light intensities used in this study (Figure 6).
3] V By using Equation ( 1), several recombination mechanisms can be predicted by calculating the ideality factor values, such as the bimolecular recombination process if it remains close to 1, whereas the monomolecular recombination mechanism dominates when it approaches 2. [67,81,82,84,85] Based on the results of the measurements performed under the solar simulator (Figure 6a) and under indoor light sources (Figure 6b), we deduce the ideality factor values of the fabricated CPSCs as %0.9 and %1.8, respectively.This reveals the domination of the bimolecular recombination process under strong light intensity conditions, whereas the monomolecular recombination (i.e., trap-assisted recombination) process persisted under low lux light intensities, in agreement with previous reports. [67,86,87]90][91] J SC ∝ I α Equation ( 2) similarly predicts recombination processes according to values achieved for α.The second-order bimolecular recombination dominates if α approaches 0.5, whereas the first-order monomolecular recombination processes have been reported when the values remained close to 1. [82,[92][93][94][95][96] With linear dependence of J SC over varying light intensities, the α values in our results remained %1 under low-intensity lights (Figure 6d), indicating the dominance of the monomolecular (i.e., trap-assisted) recombination process.In contrast, the slope of J SC reduces to 0.87 (Figure 6c), indicating the evolution of bimolecular recombination as the light intensities increase.102][103][104] Furthermore, to reconsolidate the operational performance stability, we conducted another MPPT test for the fabricated CPSCs under these ambient ecological conditions for >10 h while using 1000 lux of one of the light sources (i.e., FL lamp).As expected, no sign of degradation was observed among any individual PV parameter, thus confirming the performance durability as also previously presented in a MPPT test under full sunlight illumination conditions (Figure 2d).Such ranges of output power combined with robust operational performance potentially validate the vast opportunities for this unique device design of PSC technology to realize its application in achieving novel, self-sustaining and advanced electronic ecosystems Figure 7. [3,6,80] Table 6.Average PV parameters (4 CPSCs) and PV parameters of the best CPSC (in brackets) achieved under LED and FL lamps at 1000, 500 and 200 lux light intensity conditions.The active area was 0.64 cm 2 (large area).Finally, the capability of CPSCs is demonstrated by energizing a Light-based Internet of Things (LIoT) concept-based temperature sensing node (TSN) [105] by harvesting ambient light (1000 lux) energy through them from the FL light source.The setup was made by constructing three individual units, which can be categorized as: 1) Energy Harvesting Unit, 2) TSN Electronics Control Unit (TSN -ECU), and 3) Data Control Unit (DCU), as shown in Figure 8.
In brief, the harvested energy from an array of CPSCs (in the energy harvesting unit) was first supplied to charge a prismatic supercapacitor (Capxx 0.4F 4.5 V). [106] An Atmega 328p microcontroller [107,108] (in the TSN-ECU) was selected as the TSN's controller component, which was programmed to function at a frequency of 8 MHz and voltage of 3.3 V to perform the operations between the TSN and optical wireless transceiver (OWT) [105] with minimum power consumption.In addition, an ultra-low-power step-down DC-DC voltage converter [109] was used to provide steady voltage (3.3 V) to the TSN-ECU (Figure 8).Moreover, the bidirectional optical communication links were established between the TSN-ECU and the DCU, which could be categorized as: a visible light communication link as a "downlink" (from DCU to TSN-ECU) and an infrared communication link as an "uplink" (from TSN-ECU to DCU). [105]igure 9a represents the generated temperature data profile in response to the above-described experimental setup.The supercapacitor (Figure 9b) gets fully charged through CPSCs and maintained its operating voltage of %4.5 V during light harvesting intervals (i.e., illumination mode).It was supplied with a step-down voltage (3.3 V) to the TSN-ECU to enable the steady communication link between the TSN-ECU and the DCU.
The stored energy of the charged super capacitor was utilized (resulting in a voltage decay) to confront the uninterrupted operation of the TSN during the dark mode.The trends (Figure 9b) were progressively repeated during the testing period (6 days), thus confirming the stable and sufficient energy harvesting and delivering capability of the exposed CPSCs with the selected light intensity (i.e., 1000 lux) conditions.
With such proof of concept, novel and exciting user experiences, as well as applications, can be forecasted, where IoT-based solutions could provide sustainable and wirelessly connected sensor networks to promote among others, smart working environments and safer livings in homes and buildings.In this regard, ambient indoor light harvesting has been envisioned to play a key role in achieving low cost, fully printed, and energy-efficient solutions for massive data exchange and communication inside modern-built environments.112] Interestingly, the lifetime of supercapacitors at RT-based operating conditions, in general, remains far higher than traditional rechargeable batteries [113][114][115][116] and offers opportunities for realizing infinite functioning lifetime-based maintenance-free IoT solutions as demonstrated in this work.From such key viewpoints, the printable CPSC devices fabricated in this work hold immense potential for meeting numerous above-mentioned characteristics and developing self-power-based autonomous solutions for indoor applications.With an extended FTO-glass substrate, advanced intelligent electronic circuits to perform versatile operations could be designed and printed adjacent to the CPSC stack, as illustrated in Figure 10.This could allow wireless connectivity between the CPSCs and the intelligent printed circuits through depositing high-performance printable conductors such as copper ink-based innovative strategies offered to facilitate printed electronic-based solutions in recent years. [117,118]As a result, low cost, fully printed, and durable light-harvesting solutions could be envisioned to meet the rapidly increasing demands of IoT-based solutions.
Conclusions
To conclude, we successfully demonstrated various capabilities of a low-cost and printable configuration of PSC technology through fundamental PV performance characterizations to consolidate their possible deployment in indoor environments.The fabricated lab-sized CPSCs revealed high performance with impressive conversion efficiencies, which reached between 11% and 15% when tested under standardized conditions with various light intensities and the significantly larger active area selected for this study.Moreover, the devices exhibited robust stability when exposed to one of the tests (ISOS-D-1) recommended for next-generation-based PV technologies and did not show any performance deviation for a period of 1065 h.Followed by these findings, we also investigated their PV performance under various low light intensity conditions with FL and LED light sources.Output powers as high as 81.5, 38.4, and 14.5 μW cm À2 with impressive conversion efficiencies were achieved over significantly larger (0.64 cm 2 ) active areas under 1000, 500, and 200 lux light intensities, respectively.These output powers are likely sufficient to energize a wide range of low-powered electronic devices located inside buildings, [3,79] and provide a far more reliable state-of-the-art compared to the PV performance of other configurations of PSC technology, often reported with very small active areas for lab-sized devices under similar low-intensity light conditions.
As a further advance, we also demonstrated the successful functioning of an IoT-based TSN via harvesting ambient light energy through these CPSCs to record the continuous temperature data of selected indoor ecological conditions.The results presented in this work provide opportunities to further develop fully printed and maintenance-free energy harvesting-based solutions to meet the growing demand for self-powered IoT-based electronic ecosystems presently needed for various applications inside modern building environments.
Figure 1 .
Figure 1.Characterization results of the champion device a,b) J-V curves achieved at 1 Sun, 0.5 Sun, and 0.1 Sun light intensity conditions.a) The active area for small area measurements was 0.14 cm 2 (b) The active area for large area measurements was 0.64 cm 2 (c) Incident photon to collected electron efficiency (IPCE) response of the best CPSC.d) Results of maximum power point tracking test (MPPT) of the best CPSC under 1 Sun light intensity condition.
Figure 2 .
Figure 2. a,b) J-V curves and PV parameters of the best CPSC achieved at 1 sun light condition during the initial measurements (blue) and after 1065 hours (red) of the RT aging test.a) The active area for small area measurements was 0.14 cm 2 .b) The active area for large area measurements was 0.64 cm 2 .
Figure 3 .
Figure 3.Typical light intensities that remain available at common indoor spaces.
Figure 4 .
Figure 4. Irradiance spectra of LED and FL lamps at 1000 lux.
Figure 5 .
Figure 5. J-V curves of the best CPSC under: a) LED lamp and b) FL lamp at various light intensity conditions.The active area was 0.64 cm 2 for large area measurements.
Figure 7 .
Figure 7. Results of maximum power point tracking test (MPPT) of a CPSC under FL lamp at 1000 lux.
Figure 6 .
Figure 6.Light intensity (I) dependent (a,b) V OC and (c,d) J SC characteristics of the CPSCs.The experimental data (symbols) for (a,b) and (c,d) was fitted (dashed-dotted lines) using equations V OC ¼ lnðIÞ þ C and J SC ∝ I α respectively.
Figure 8 .
Figure 8. Schematic diagram of light-based Internet of Things (LIoT) concept-based bi-directional communication capable temperature sensing node that was operated by harvesting ambient light (1000 lux) energy with a fluorescent (FL) light source.
Figure 9 .
Figure 9. a) Generated temperature data profile from the temperature sensing node (TSN) used in this work b) Charging-discharging profile of the supercapacitor used to energize the TSN and electronics control unit (ECU).
Table 1 .
PV performance of traditional perovskite solar cell configurations reported under various low-light-intensity conditions.
Table 3 .
Average PV parameters (3 CPSCs) achieved at 1 sun light intensity condition during the initial measurements and after 1065 h of the room temperature (RT) aging test.The active area for small area measurements was 0.14 cm 2 and was 0.64 cm 2 for large area measurements.
Table 4 .
Incident power of LED and FL light sources at 1000 lux, 500 lux and 200 lux.
Table 5 .
Average PV parameters (4 CPSCs) and PV parameters of the best CPSC (in brackets) achieved under LED and FL lamps at 1000, 500 and 200 lux light intensity conditions.The active area was 0.14 cm 2 (small area). | 5,061 | 2022-10-01T00:00:00.000 | [
"Materials Science",
"Engineering",
"Environmental Science",
"Physics"
] |
A pH‐Switchable Triple Hydrogen‐Bonding Motif
Abstract A stimuli responsive linear hydrogen bonding motif, capable of in situ protonation and deprotonation, has been investigated. The interactions of the responsive hydrogen bonding motif with complementary partners were examined through a series of 1H NMR experiments, revealing that the recognition preference of the responsive hydrogen bonding motif in a mixture can be switched between two states.
Data for Condition B
The use of condition B: trifluoroacetic acid (TFA) and 1,4-diazabicyclo [2.2.2]octane (DABCO), to protonate 1 and deprotonate 1-H + HBM was studied. 1 H NMR analysis revealed a downfield shift of diagnostic resonances, Ha, Hb, Hc and Hg. on the addition of 1 equivalent of TFA to UIM 1 (5 mM in CDCl3) as observed for condition A ( Figure ESI 3 (d)-(c)). This suggests TFA is also able to protonate UIM 1 to form UIM-TFA 1-H + . To reverse the protonation, one equivalent of DABCO was added to the 5 mM solution of UIM-TFA 1-H + ( Figure ESI 3 (c)-(b)). This resulted in small changes in the chemical shifts of the diagnostic proton resonances Ha, Hb, Hc and Hg but the resonances did not fully align with those observed for neutral UIM 1 (or a 1:1 UIM:DABCO mixture) suggesting a mixture of neutral and protonated UIM. However, with addition of excess DABCO (3 eq.) the diagnostic protons shifted further upfield consistent with formation of UIM 1 as the dominant species ( Figure ESI 3 (a)). The lower pKa of DABCO in comparison to sodium hydrogen carbonate dictate that a greater concentration of DABCO for full deprotonation is to be expected. Similarly the pKa of DABCO is close to imidazolium (which forms the core of UIM). The switching 'off' behaviour of the 1·2 dimer interaction was tested using condition B. On the addition of 1 equivalent of TFA to the 1·2 dimer the diagnostic Hg resonance moved significantly downfield and became well resolved, unlike in the 1·2 dimer (Figure ESI 4 (c)-(b)). Additionally the presence of NH resonance (Hd) of UIM, not seen in neutral UIM 1 or UIM·AIC 1·2 dimer, indicated protonation of UIM 1 to give UIM-TFA 1-H + . The addition of DABCO to this mixture indicated that the ADD-DAA dimer was reformed by the upfield shift and broadening of the Hg resonance ( Figure ESI 4 (a). However, some of the resonances associated with 1 (Ha and Hc) did not fully match in the 1·2 dimer as anticipated. This could be a result of partial deprotonation using DABCO, compared to sodium hydrogen carbonate (used in condition A), leading to a mixture of species as well as TFA and DABCO salts. The recognition preferences of complementary and competing HBMs, 2 and 3, with protonated and neutral HBM 1 formed using condition B were studied. Addition of TFA to a mixture of the UIM·AIC 1·2 dimer and HBM BB1 3 disrupted the UIM·AIC 1·2 dimer generating a mixture of UIM-TFA·BB1 1-H + ·3 dimer in presence of AIC 2 ( Figure ESI 5 (b)). This switch is highlighted by a change in UIM resonances; the sharpening and downfield shift of diagnostic Hg resonance and the presence of NH resonance Hd. As well as more subtle chemical shifts in the resonances of AIC 2 and BB1 3. The addition of 3 equivalents of DABCO to this mixture did not fully switch back 'on' UIM·AIC 1·2 dimerization (Figure ESI 5 (a)); although some shifts in the spectra are observed these do not return to those observed for the spectrum of UIM·AIC 1·2 dimer and HBM BB1 3 (Figure ESI 5 (c)) before the protonation/deprotonation cycle. This likely results from greater competition between DABCO and the 1·3 complex for the proton i.e. a reduced difference in pKa between the two. Aside from the diminished reversibility, the interactional preferences for conditions B are in line with the observations for conditions A.
NMR Titration Experiments
For 1 H NMR titrations anhydrous CDCl3 was purchased from Aldrich and stored over molecular sieves (type 4A, 1 to 2mm beads). For the qualitative titration study of hydrochloric acid into UIM 1 the 1 H NMR spectrum was recorded for a solution of host (5 mM) in CDCl3 and the change in chemical shift of key proton resonances was recorded upon sequential additions of a solution of guest (0.25-3 equivalents) in CDCl3. For the quantitative titration study of UIM 1 and UIM-HCl 1-H + into BB1 3, the 1 H NMR spectrum was recorded for a solution of host (0.5 mM) in CDCl3 and the change in chemical shift of key proton resonances was recorded upon sequential additions of a solution of guest (0.2-12.3 equivalents) in CDCl3. The solutions of guests (UIM 1 and UIM-HCl 1-H + ) were made through a half dilution series and added to a solution of host (BB1 3). The equivalents were calculated by the ratio of integration of individual resonances. The data was subsequently analysed using the Supramolecular.org online bindfit program using the appropriate model to give an association constant. [1,2] Supramolecular.org uses data from multiple resonances for curve fitting. Representative 1 H NMR spectra and exported binding curves can be seen below.
Studies with Hexafluorophosphate Anion
Reflecting on the crystal structure of the intermediate I (Figure 1(a)) where the chloride ion bridges two NH groups, the chloride ion may influence the equilibria (Scheme ESI 1); although the time averaged nature of the 1 H NMR analysis reports provides information that can be related to the interactions of the HBMs, the coordination of chloride ion could alter the desired hydrogen bonding interactions between the HBMs. To assess this, the chloride ion was exchanged for a non-interacting anion, hexafluorophosphate (PF6) using silver hexafluorophosphate to create UIM-HPF6 1-H + PF6 (Figure ESI 10). 1 H NMR suggested that after the addition of silver hexafluorophosphate the species was still protonated; as the chemical shift of the imidazole CH resonance (Hg) was similar to that observed for UIM-HCl 1-H + and the NH resonances (Hd, He, Hf and Hh) were well-resolved ( Figure ESI 10 (b)). However, the NH resonances (Hd, He, Hf and Hh) shifted significantly for UIM-HPF6 1-H + PF6 compared to the resonances observed for UIM-HCl 1-H + . Next, proton dependent switching of UIM-HPF6 1-H + PF6 was explored, revealing it was possible to deprotonate motif UIM-HPF6 1-H + PF6 by washing with NaHCO3 in the same way that UIM-HCl 1-H + was deprotonated using condition A ( Figure ESI 10 (a)). ). Efforts were made to switch this self-sorting behaviour 'off' by the addition of base to reform the UIM·AIC 1·2 dimer in the presence of BB1 3. However due to the lower solubility of BB1 3 and the process of washing with NaHCO3, sample was lost, thus it was not possible to obtain a well resolved 1 H NMR spectra with equal ratios of hydrogen bonding motifs. The limited solubility of BB1 3 in CDCl3 was more profound in the system using PF6 salts than the hydrochloric acid containing systems. Overall the recognition behaviour exhibited by UIM-HPF6 1-H + PF6 closely resembled the preferences exhibited by HBM UIM-HCl 1-H + indicating that whilst the counter anion may influence the equilibria under analysis, the 1 H NMR data reflect accurately on the recognition preference of the HBMs in these mixtures. Figure 1 for the resonance assignment and chemical structure.
General materials and methods for synthesis
Solvents and reagents were purchased from Sigma Aldrich or Fisher Scientific and used without further purification unless otherwise stated. Where anhydrous solvents were required, dichloromethane, chloroform, tetrahydrofuran and acetonitrile were obtained from the in-house solvent purification system Innovative Inc. PureSolv®. Anhydrous dimethyl formamide and N,N-diisopropylethylamine were obtained from Sigma Aldrich equipped with Sure/Seal™. All non-aqueous reactions were carried out under a nitrogen atmosphere. Chloroform-d was dried over Linde 5Å molecular sieves or placed on CaCl2 before being distilled and stored on KOH prior to use in 1 H NMR experiments. For reactions under non-anhydrous conditions, the solvents used were HPLC quality and provided by Sigma Aldrich or Fisher. Water in aqueous solutions and used for quenching was deionised. Mixtures of solvents are quoted as ratios and correspond to a volume: volume ratio. Analytical thin layer chromatography was performed on Merck Kieselgel 60 F254 0.25 mm pre-coated aluminium plates. Product spots were visualised under UV light (λmax = 254 nm) or using a suitable stain. Flash chromatography was carried out using Merck Kieselgel 60 silica gel using pressure by means of head bellows or using disposable RediSepRf silica flash columns on an automated Biotage Isolera One system. Nuclear magnetic resonance spectra were obtained at 298 K (unless stated) using a Bruker AV500 spectrometer operating at 11.4 T (500 MHz for 1 H and 125 MHz 13 C) and JEOL ECA600ii operating at 14.1 T (150 MHz for 13 C) and NOESY spectra as stated. Infra-red spectra were obtained using a Bruker Alpha Platinum ATR where absorption maxima (νmax) are quoted in wavenumbers (cm -1 ) and only structurally relevant absorptions have been included. High Resolution Mass Spectra (HRMS) were recorded on a Bruker Daltonics Micro TOF using electrospray ionisation (ESI). Liquid Chromatography and Mass Spectrometry (LC-MS) was performed using an Agilent Technologies 1200 series LC and a Bruker HCT ultra ion-trap MS.
3, 5-diiodo-2,6-diaminopyridineamine
Compound prepared using minor adaptations to a previously described procedure. [4] To a solution of 2,6-diaminopyridine (0.99 g, 9.09 mmol) in dry DMF (28 mL) N-iodosuccineimide ( 4.50 g, 19.9 mmol) in DMF (20 mL) was added dropwise at -30 o C (cooled with dry ice) over 1 hr. After the addition was completed, the cooling bath was removed and the reaction mixture was stirred for 1 hr and then poured into ice-cold water and stirred for 30 min. Resulting precipitate was filtered and washed with water (2 x 20 mL) and pentane (2 x 15 mL) and dried in vacuum oven at 40 o C for 24 hrs. Product was obtained as grey solid with 94 % yield. 1
4-tert-Butyl-1H-imidazole-2-amine hydrochloride (I)
Tert-butyl 5-tert-1H-imidazol-2-yl-carbamate (750 mg, 3.10 mmol) was dissolved in 1M HCl in ethanol (30 mL) and refluxed for 16 hrs. The reaction was allowed to cool, concentrated and dried under pressure to give a colourless solid (400 mg, 2.28 mmol, 74%) 1 Measurements were carried out at 120K on an Agilent SuperNova diffractometer equipped with an Atlas CCD detector and connected to an Oxford Cryostream low temperature device using mirror monochromated Cu K radiation ( = 1.54184 Å) from a Microfocus X-ray source. The structure was solved by intrinsic phasing using SHELXT [6] and refined by a full matrix least squares technique based on F 2 using SHELXL2014. [7] The compound crystallised as colourless prisms from acetonitrile. The compound crystallised in a triclinic cell and was solved in the P1 space group, with two imidazolium cations and two chloride anions in the asymmetric unit. All non-hydrogen atoms were located in the Fourier Map and refined anisotropically. All carbon bound hydrogen atoms were placed in calculated positions and refined isotropically using a "riding model". All nitrogen bound hydrogen atoms were located in the Fourier Map and refined isotropically. Data and structure refinement given in Table 1 and was deposited via the joint CCDC/FIZ Karlsruhe deposition service, deposition number CCDC 1916237.
General procedure for sample preparation for NMR switching experiments Condition A
The mass of each component was calculated to make a final concentration of 5 mM in 0.6 mL of CDCl3. The required mass of the starting component(s) was dissolved in 0.6 mL of CDCl3. The sample was allowed to equilibrate for a minimum of ten minutes before acquisition. After acquisition the sample was protonated by the addition of 1 equivalent of 4M HCl in 1,4-dioxane solution directly to the sample tube. The sample was allowed to equilibrate for a minimum of ten minutes before acquisition. After acquisition the sample was transferred to a vial and deprotonated by the addition of excess basic NaHCO3 solution. The aqueous layer was separated, and the organic layer was dried and added to an NMR sample tube. The sample was allowed to equilibrate for a minimum of ten minutes before acquisition. Any additional components were added to the same sample when required and the protonation and deprotonation method was repeated as required.
Condition B
The mass of each component was calculated to make a final concentration of 5 mM in 0.6 mL of CDCl3. The required mass of the starting component(s) was dissolved in 0.6 mL of CDCl3. The sample was allowed to equilibrate for a minimum of ten minutes before acquisition. After acquisition the sample was protonated by the addition of 1 equivalent of TFA directly to the sample tube. The sample was allowed to equilibrate for a minimum of ten minutes before acquisition. After acquisition the sample was deprotonated by the addition of 1 or 3 equivalents of DABCO directly to the sample tube. The sample was allowed to equilibrate for a minimum of ten minutes before acquisition. Any additional | 3,033.8 | 2020-01-01T00:00:00.000 | [
"Chemistry",
"Materials Science",
"Physics"
] |
Structural properties of epitaxial α -U thin films on Ti, Zr, W and Nb
,
I. INTRODUCTION
Many of the actinides and their compounds exhibit fascinating condensed matter physics, including a plethora of unusual structural and electronic ground states (e.g.complex polymorphism, unconventional magnetic ordering and heavy fermion superconductivity).These properties often arise as a result of the outer-shell 5f electrons being situated on the boundary between itinerancy and localisation [1][2][3][4][5].The mid-series actinide metals (U, Np, Pu) exemplify these characteristics, with each of the three distinct crystallographic structures adopted by bulk U exhibiting notable collective electronic phenomena at low temperatures [6,7].
The thermodynamically stable phase of uranium under ambient conditions is orthorhombic α-U (Cmcm).This phase is unique amongst the elements, both for its low symmetry crystal structure and for its unusual electronic properties, with bulk α-U crystals undergoing a series of three charge density wave (CDW) transitions before entering a superconducting (SC) state.Although the superconducting transition temperature (T c ) appears to vary unpredictably with sample crystallinity and purity (T c = 0.02 − 0.78 K), it is generally accepted that isotropic compressive pressure can be used to suppress the CDW transitions and enhance T c to a maximum of 2 K near 1.5 GPa [8][9][10].The exact nature of the interaction between the SC and CDW states in α-U is yet to be understood, but a combination of bulk and thin film studies have since confirmed that pressure-induced changes to the low temperature states are related primarily to the length of the a-axis [11,12].
Epitaxial strain engineering can often be used to explore regions of phase space that are inaccessible in bulk experiments involving uranium.For example, epitaxial layers of α-U with a film ≈ a bulk host an incommensurate 'bulk-like' CDW below 43 K, while U layers with a film > a bulk (i.e. a strain that would be difficult to at-tain in bulk crystals) host a near-commensurate CDW with an increased onset temperature of 120 K [12,13].Compression of the c-axis and expansion of the b-axis are both predicted to stabilise the CDW state in α-U [14], but the influence of uniaxial strain along these axes has not yet been explored.
It is also known that deposition onto other crystallographic templates can produce well-ordered overlayers that are difficult to stabilise in the bulk.Recently, crystalline layers of the tetragonal β-U phase have been stabilised at room temperature via deposition onto Si(111) [15] and single crystal layers of a pseudo body-centred cubic γ-U structure have been realised by the co-deposition of U and Mo onto Nb(110) [16].Uranium may also form a 'hexagonal close-packed' (hcp) structure that is not found in the bulk when deposited on W(110) [17][18][19], Gd(00.1)[13,20] and Cu(111) or Ir(111) buffer layers, although the U layers in the final two systems gradually transition back into α-U [21].
Given the rich array of nearly degenerate structural ground states, it is often difficult to predict the phase and orientation that a uranium layer will form under specific growth conditions.A key task in this area is, therefore, to examine a range of metallic buffer layers that can be used to stabilise high quality epitaxial layers of each U allotrope.The range of strains, structures and orientations will allow further exploration of their intriguing electronic properties, provided the complex crystallographic domain structures are also fully characterised.In this work we investigate the epitaxy of α-U onto two new buffer layers (Ti, Zr) and revisit the Nb and W systems from Ref. [22] to add new information to the previously reported domain structures.
Section II of this paper describes the growth and characterisation procedures for each thin film system.Section III explores the structure and orientation of crystalline α-U grown onto Ti, Zr and W buffers as discerned from laboratory-based X-ray diffraction (XRD) and X-ray reflectivity (XRR).The epitaxy and interface quality in the Ti/U and Zr/U systems are explored as a function of temperature using these techniques.Also included in Section III are synchrotron X-ray diffraction measure- ments of epitaxial Nb/α-U(110) systems which reveal a which reveal a previous unreported domain.The physical origin of the domain is discussed.
A. Growth of epitaxial α-U films
All samples in this study were grown using the actinide d.c.magnetron sputtering system at the University of Bristol, UK.This ultra-high vacuum system operates at base pressures of the order 10 −10 mbar and contains four sputtering guns inside a load-locked chamber [23].Substrates are loaded onto an adjustable height stage adjacent to a resistive heater capable of achieving temperatures of up to 850 • C. The substrates for epitaxial Ti(00.1) and Zr(00.1)growth were c-plane Al 2 O 3 (00.1)and the substrates for Nb(110) and W(110) growth were a-plane Al 2 O 3 (11.0).All substrates (sourced from MTI Corp) were polished to optical grade.
The nominal layer thicknesses and growth temperatures are given in Table I.The buffer growth temperature is denoted as T B and the uranium growth temperature as T U with respective film thicknesses, t B and t U .Each sample was capped with a layer of a corrosion resistant metal deposited at room temperature in order to protect the U from ex-situ oxidation.All layers were deposited using approximately 7.5×10 −3 mbar high purity argon gas as the sputtering medium.
B. Structural characterisation
Structural characterisation of the Ti/U, Zr/U and W/U systems was performed using a Philips X'Pert diffractometer with a Cu-K α source.XRR profiles were modelled using the GenX package, where the error bars on each fitting parameter are calculated from a 5% change in the optimal figure of merit [24].Characterisation of the Nb/U system was performed using the diffuse scattering diffractometer at the ID28 beamline (ESRF, France) [25].Synchrotron data were treated using the CrysAlis Pro software package [26], high resolution reciprocal space maps were produced using in-house programs and visualised in the DECTRIS Albula package [27].All X-ray measurements were conducted at room temperature.
III. RESULTS AND DISCUSSION
A. Titanium buffered system Titanium was sputtered onto Al 2 O 3 (00.1)substrates at 600 • C to produce epitaxial hexagonal close-packed Ti(00.1)layers with the in-plane relationship [10.0]Ti ∥ [1 1.0] Al2O3 and thickness 180 Å.Uranium layers with a nominal thickness of 520 Å were subsequently deposited at various temperatures.Fig. 1 shows the coupled 2θω scans and rocking curves from the temperature series.XRR profiles with discernible Kiessig fringes are included as Supplemental Information [28].Table II summarises the d 110 spacings, widths of each rocking curve (∆ω) and the XRR-derived root-mean-square roughnesses (σ) across the series.
At T U = 200 • C, the specular α-U(110) peak is instead symmetric and close to the bulk value, with lattice parameters of a = 2.858 Å (+0.14%), b = 5.854 Å (-0.25%), c = 4.993 Å (+0.76%) and an atomic volume of V = 20.885Å3 (+0.65%) indicating that the b-axis strain has changed from tensile to compressive while the c-axis expansion persists.The Laue fringes are suggestive of high crystallinity and a sharp U-Ti interface.The periodicity of the oscillations can be used to extract the crystalline ordered volume, with the agreement between t Laue = 500 ± 10 Å and the XRR derived thickness of t U = 514±6 Å suggesting that crystalline order is maintained throughout the full thickness of the U layer.The rocking curve also adopts the distinctive two-component lineshape common to many high quality thin films [30,31].
The in-plane epitaxial relationships in these two wellordered systems were determined from the in-plane (ϕ) dependence of the Ti(10.
B. Zirconium buffered system
A similar series was grown using zirconium buffer layers deposited onto c-plane sapphire at 700 • C.These single crystal Zr(00.1)layers adopt an in-plane epitaxial relationship of Al 2 O 3 [10.0]∥Zr[10.0]and exhibit rocking curves with widths of 1-2 • .This limits the mosaic spread and grain size of subsequent U layers, but the epitaxial relationships are still of interest.Fig. 3 shows the coupled 2θ-ω scans for the series.
As the deposition temperature is increased toward 400 • C, the sample gradually becomes pure α-U(001), with the (002) U reflection gaining relatively weak Laue fringes.The orientation relationship between the layers determined from the Zr(10.5)and α-U(023) reflections (Fig. S3 in Supplemental Information is bulk-like at V = 20.67Å3 .Again, six-fold symmetry is seen in the α-U(023) ϕ-scan due to the six equivalent matches with the hexagonal Zr(00.1)surface.
The transition from an α-U(110) layer with a low strain epitaxial match and a large atomic volume, to an α-U(001) layer with a large misfit strain and a bulk-like atomic volume suggests it is energetically favourable for the α-U structure to revert to a bulk-like atomic volume at the expense of the epitaxial match and quality of the interface.The formation of a interfacial U-Zr layer that may influence the epitaxy is also suggested by the data.
A 1-2 nm reduction in t U with increasing T U is seen via the XRR-derived U layer thicknesses and, at 500 • C, the reflectivity profile no longer shows Kiessig fringes.A gradual reduction in the intensity of the (00.2) Zr reflection with increasing T U also suggests the formation of a interfacial U-Zr layer that increases in thickness with T U .The strains generated by the unusually large mismatch between the Zr(00.1)and α-U(001) layer (+4.6 %) may be relieved by such a transition region, facilitating the observed change in orientation and reduction in atomic volume.
C. Tungsten buffered systems
The growth of complex, multi-domain α-U(001) was first reported in 2008 [22].Ward in the top panel of Fig. 4. In this idealised system, certain U domains (shown here in light blue and purple) are 'degenerate' with respect to the buffer and so a total of six peaks should be resolvable using a point detector and in-plane ϕ-scans.However, only four domains were seen in the original study [22].
The bottom panel of Fig. 4 shows a ϕ-scan of the α-U(023) reflections in a new, high quality W/U sample.This scan maps the relative orientations of any (010) planes (i.e. the b-axes) in the α-U(001) layer.The scan shows six well-resolved peaks at angular separations that correlate well with the matches predicted by Ward et al..A total of eight peaks are required for an accurate fit as there is a slight misorientation between the reflections from the two 'degenerate' (light blue and purple) pairs of domains, presumably due to strains in the buffer.These strains are also likely to be the cause of the unequal peak intensities, which imply there are strong preferences for certain U orientations.The crystalline quality of the U layer is significantly improved by reducing the deposition temperature to 450 • C used in Ref. [12] as opposed to 600 • C used in Ref. [22].
D. Niobium buffered systems
To date, all epitaxial films of α-U(110) on Nb(110) have been reported as single domain systems where the epitaxy is governed by a uni-directional in-plane match between 264 Å and a Nb = 3.311 Å [13,22].New reciprocal space maps (RSMs) taken at the ID28 beamline (ESRF) reveal a second domain consistently missed by point-detector measurements.These domains are referred to as primary 'red' and secondary 'blue' in the following discussions.
This unusual situation has arisen as the (hhl) reflections -i.e.those commonly used to check the symmetry of the U layer in laboratory ϕ-scans -are coincident, but the degeneracy is clearly lifted outside of this plane.The (h,h+2,l) RSM in Fig. 5(a) shows an example of a fully non-degenerate plane of reflections in a Nb(110)/U system, while the (h,k,2) type RSM in Fig. 5(b) demonstrates both the coincidence of reflections in the (hhl) plane and splitting away from this plane.Fig. 5(c transforms from primary to secondary Miller indices.The reverse operation is found by taking the inverse of the 3 × 3 matrix in Eq. 1. The origin of this 'hidden' domain can be understood as follows.As U atoms are deposited onto the Nb(110) surface, each nucleation event initiates the growth of a proto-domain of α-U with a ⟨110⟩ U growth axis.In each of these newly forming proto-domains, the atomic arrangements in the growth plane (i.e. the lowest layer in Fig. 6) can be considered identical.However, atoms in the subsequent monolayer have an energetically degenerate choice of bonding with the long bond on the left (and short bond on the right) or the reverse, creating either a left-skewed (B) or right-skewed (B') layer.This choice fully constrains the growth axis and defines the domain.It is important to note that a 180 • in-plane rotation fails to map one domain onto the other, instead stacking A/A' directly above B/B'.The secondary domain origin must be shifted in-plane to ensure that the atomic sites are coincident in layer A.
If the growth mode is purely island-like, the presence of these left-and right-skewed domains is likely to result in a columnar domain structure with in-plane anti-phase domain boundaries.Pure layer-by-layer growth would preferentially create a layer with either left or rightskewedness, as vertical switching of the 'skewedness' would require the energetically unfavourable stacking of atoms almost directly above each other as shown in Fig. 6.The equal intensities of the two sets of reflections indicates equal domain occupations and the unlikelihood of direct atomic stacking suggests an island-like or mixed-type growth mode, but a fully conclusive determination of the atomic stacking pattern across the domain boundaries requires the application of a non-averaged technique, e.g.atomic resolution transmission electron microscopy.
It is important to acknowledge that this 'hidden' do- main should also be present in the Ti(00.1)/α-U(110)and Zr(00.1)/α-U(110)systems from previous sections.Indeed, these twin domains have been observed in (241) ϕ-scans for both systems, but the scans have been omitted from this report due to their complexity.The true number of domains is then double the value suggested by the symmetry of the (221) ϕ-scans.
IV. CONCLUSIONS
Several epitaxial α-U systems have been stabilised using both new (Ti, Zr) and known (Nb, W) elemental metallic buffer layers, with some U layers forming wellordered systems without the need for substrate heating.The range of epitaxial strains and atomic volumes observed are expected to produce significant variations in the low temperature electronic properties.A combination of magnetotransport (e.g.Hall coefficient, resistivity and magnetoresistance) and synchrotron diffraction measurements can now be used to probe the interplay between the CDW and SC ground states in these α-U thin films.Specifically, studies of the superconducting transitions in Ti, Zr and W buffered samples (where T c < 1 K in the buffer) should be used to probe the longstanding issue of unpredictable superconductivity in bulk α-U crystals.Measurements of superconductivity in the Nb buffered systems will be more challenging (T c ≈ 9.2 K in bulk Nb), but T c in the buffer could be suppressed by reducing its thickness or adding magnetic impurities.The complex structural information determined here will be essential for the accurate analysis and understanding of future electronic transport measurements conducted using α-U thin films.
FIG. 1. Left: Specular XRD (2θ-ω) scans of layers of U deposited onto Ti(00.1)buffers at various temperatures shown on a logarithmic scale to highlight the Laue fringes.The system transitions from pure, strained α-U(110) into a mixture of elemental metals and intermetallic compounds as TU increases.Center: Detail around 2θ = 35 • showing a systematic shift of the U(110) peak position with TU.Vertical dashed line shows the bulk 2θ position.Right: Evolution of the α-U(110) rocking curve.In all cases, datasets are offset vertically for clarity and solid lines are fits to the data.
3) and U(221) off-specular reflections.The example dataset shown in the top panel of Fig. 2 indicates an approximate alignment of (00.1)Ti ∥ (110) U and [01.0]Ti ∥ [1 10] U .The epitaxy is likely to be governed by the match shown in the bottom panel of Fig.2where the misfit strain, (d U − d Ti )/d Ti at room temperature is −3.2 %.As hcp-Ti is six-fold symmetric in the (00.1) plane, any 60n • (n ∈ Z) in-plane rotation of the U layer brings the relevant planes into alignment.This should result in six energetically equivalent ways for the first monolayer of uranium to nucleate on the Ti(00.1)surface, as confirmed by the 60 • separation of the (114) U peaks in the ϕ-scan.The stability of epitaxial α-U at these relatively low deposition temperatures was unexpected, as epitaxial Nb(110)/α-U(110) and W(110)/α-U(001) systems are typically grown at 450-600 • C[12,13,22].In the case of Ti/U, temperatures above 200 • C are clearly detrimental to the quality of the interface.The degradation of the XRR signal, rocking curve profile and U/Ti Laue fringes all suggest that the sharp U-Ti interface, and hence the coherent epitaxial match, has been partially lost at T U = 400 • C and fully lost at T U = 600 • C. The additional, non-elemental diffraction peaks seen in the 2θ-ω scans are likely to originate from Ti-rich alloys (2θ = 36 − 38 • ) and U 2 Ti (2θ 110 = 37.2 • )[32].
1 )FIG. 2 .
FIG. 2. Top: Angular dependence of the off-specular reflections in an epitaxial Ti(00.1)/α-U(110)sample deposited at 200 • C. Bottom: Two-dimensional illustration of the expected epitaxial match for a single U domain, showing the alignment of dU = cU = 4.955 Å and dTi = 2d100 = 5.12 Å.All quoted lattice parameters are bulk experimental values at room temperature from literature.
et al. proposed a model wherein eight domains of α-U nucleate on a twinned W(110) buffer as a result of a close match between the distances d U = 2.556 Å (d 110 ) and d W = 2.584 Å (2d 112 ).The two W domains and eight U domains are illustrated
2 FIG. 4 .
FIG. 4. Top: Expected epitaxial matches for α-U(001) deposited onto a twinned W(110) buffer layer, adapted from [22].Tungsten domains 1 and 2 represented by filled and open circles.Colors used to represent 'unique' uranium domains.Each vertical tungsten axis is aligned with Al2O3[00.1].Bottom: New ϕ-scan of the off-specular U(023) reflection in a new α-U(001) system.Each peak has been matched to the relevant colored domains, (colored images below) and individual fitted peak components (black dotted lines) are ascribed to the relevant W domain, with labels 1 and 2, respectively.
) shows the location in reciprocal space for a selection of the observed reflections, where the overlapping reflections from the two distinct domains (red and blue) are represented by purple spheres.The two α-U domains are related by an approximately 52 • clockwise rotation about a shared c * axis set into the page, where the experimentally determined reciprocal space transformation
FIG. 5 .
FIG. 5. RSMs for a) the (h, h+2, l) and b) the (h, k, 2) type planes reconstructed and denoted within he primary domain setting.Scale is linear white-black and log 10 black-red-white.Single reciprocal space net units for the primary (red) and secondary (blue) domains are shown by dashed lines with select reflections indexed.Examples of sharp sapphire reflections and weak, broad Nb buffer reflections are highlighted within black dashed circles.c) 3D reciprocal space schematic showing a selection of indexed reflections.Sphere colour corresponds to domain origin consistent with left-hand panels.Degenerate reflections in the "specular plane" indicated by purple spheres.Reciprocal unit cells are shown as dashed cuboids with reciprocal lattice vectors marked.A section of the (h, h + 2, l) type plane shown in panel (a) is highlighted by a dashed black box and asterisk.
FIG. 6 .
FIG. 6.Schematic representation of the crystallographic relationship between the two domains.Atoms are shown as coloured spheres, unit cells by dashed cuboids and axes by compass (bottom left).Colours are consistent with Fig. 5.The growth plane (translucent grey) corresponds to the (110) (primary) and (1 10) (secondary) planes.The first, degenerate, monolayer is marked with a purple label.The choice of atomic positions for the second monolayer are indicated by B/B', with example bonds shown by dashed lines, and the resulting third monolayer positions by A/A'.The hypothetical atomic positions corresponding to non-rotational domain switch are shown as dashed black circles and labelled A". | 4,594.8 | 2023-08-07T00:00:00.000 | [
"Materials Science",
"Physics"
] |
Chromatic Dispersion Compensation in Phase-Stabilized Dissemination System of Broadband Signals Based on Phase Conjugation
We present a dispersion-independent phase stabilized distribution architecture for broadband signal based on photonic microwave phase conjugation. RoF signals are distributed from the central station to each base station via a fiber ring network. The elimination of dispersion-induced optical phase decorrelation is achieved because the backward transmission of the phase-conjugated signal, thus the EVM of the RoF signal is optimized. A proof-of-concept experiment is demonstrated. A distribution of QPSK modulated 23-GHz, 400M Baud RoF signals from the central station to a remote base station is obtained via a fiber optic loop. The demodulated constellation and error vector magnitude with and without dispersion compensation are measured at the remote base station. When we set the length of the fiber loop to 58 km, the EVM is reduced by 8% after dispersion compensation, and the compensated EVM can reach the threshold value of 17.5% specified by 3 GPP for 5G when the received optical power of PD is 4 dBm.
I. INTRODUCTION
P HASE-STABILIZED transmission of radio frequency (RF) signals in distributed antenna system has received a lot of attention due to its important applications in many fields, such as distributed synthetic aperture radar, deep space network detection, navigation and positioning, and precision measurements [1], [2], [3], [4]. Considering weight and cost, remote distribution of stable radio frequency (RF) signal along optical Manuscript fibers is advantageous [5]. Fiber-based frequency synchronization has been under extensive research, and it achieves high precision frequency synchronization by compensating phase fluctuation in real time. However, most studies have focused on phase fluctuation caused by temperature drift and mechanical vibration in the environment where the fiber is located [6], [7]. In addition, phase decorrelation due to fiber dispersion will become important after long-distance transmission, especially when using lasers with wide linewidths, because dispersion introduces different delays in different optical tones [8]. In the last few years, several studies on compensating chromatic dispersion to improve the signal quality have been reported and can be divided into two categories. One is hardware-based techniques, such as spectral processing-based phase adjustment techniques, which can effectively eliminate the delay difference due to dispersion, but are limited by the response speed of the spectral processor [9]. Another approach is algorithm-based, using stochastic theory to calculate and compensate the deterioration caused by the de-correlated phase jitter term [10], [11]. However, with further deterioration in noise level, the huge computational effort makes it impossible to guarantee the feasibility of applying real-time demodulating. Moreover, previous methods are usually designed for the propagation of monophonic signals, and a new stable phase transmission scheme for broadband signals is proposed in [12], however, the bandwidth is limited because it does not involve microwave photonic frequency multiplication techniques. The generation of photonic vector RF signal based on frequency multiplication has been extensively studied, not only because of its huge bandwidth, but also because it is effectively compatible with radio-over-fiber systems [13]. There are two main methods of photonic vector RF signal generation. One is the use of precoding-assisted techniques at the transmitter [14], [15]. However, for higher order modulation formats, the system performance will deteriorate. The other is based on single sideband (SSB) modulation to generate millimeter waves, which avoids precoding and thus improves spectral efficiency [16], [17]. In addition, single sideband avoids the periodic fading of power introduced by dispersion.
We propose a dispersion-independent distributed antenna system for stable distribution of the broadband signals based on phase conjugation, in which different delays in optical tones due to dispersion is automatically eliminated. This structure has better adaptability compared to active dispersion compensation devices and receiver-side algorithms for dispersion compensation, which are not limited by response speed or computational effort. The phase conjugator at the central station also helps to generate SSB vector signals, simplifying the architecture of remote base stations. An automatic cancellation of the time delay difference is deployed to compensate the dispersion and improve the signal quality. This process is implemented because the phase-conjugated signal undergoes reverse transmission and photonic microwave mixing operations at each remote station. We perform a proof-of-concept experiment to implement the distribution of a vector signal with modulation format QPSK, code rate 400M, and frequency 23 GHz in a fiber optic loop system consisting of SMF1 and SMF2. We adjust the loop length to explore the compensation performance. When we fix the length of SMF2 to 8 km and adjust SMF1 to 50 km, the EVM of the compensated signal still meets the threshold of 17.5% specified by 3GPP for 5G. And in this case, the EVM can be reduced by 8% after compensation.
II. SYSTEM ARCHITECTURE AND OPERATION PRINCIPLE
The schematic diagram of the dispersion-independent distributed antenna system based on the photonic microwave phase conjugation is shown in Fig. 1(a). The central station is connected to each remote base station with a fiber optic loop. Broadband RF signals are generated remotely in each base station unit. If there are N remote base stations, the fiber loop will consist of N+1 single-mode fibers (SMF). For simplicity, we will analyze the case of only one remote antenna unit, however, the corresponding principles apply to any remote base station with the same configuration. In our previous studies, it has been shown that a similar structure can suppress phase fluctuation caused by fiber temperature drift and achieve stable transmission of a single frequency [18], [19]. In this paper, we derive in detail the process of automatic elimination of dispersion and explain the structural principles of vector signal generation without precoding modulation verification.
It is assumed that both the optical carrier wave from the laser diode (LD) and the electrical drive signal from the microwave source (MS) are essentially continuous waves (CW). Therefore, they can be expressed as and where ω o and ω e are the angular frequencies of the optical carrier and electrical drive signal, respectively, ϕ o (t) and ϕ e (t) are two independent random processes that introduce phase fluctuations into the optical and electrical signals, respectively. Because phase noise dominates our research, the amplitude and intensity noise can be ignored. The Mach Zehnder modulator (MZM1) is biased at its null point to get the carrier suppression double sideband (CS-DSB) signal. Then the output of the modulator is approximately an optical dual tone signal, E 1 , which can be expressed as It is worth noting that the phase noise of the dual tone signal is completely correlated. However, when transmitting through SMF1, different time delays will be introduced to both sidebands due to dispersion. The delay difference between the first order sideband and the optical carrier is given by the following equation [20] where D is the dispersion parameter of the optical fiber, L 1 is the length of the SMF1, λ o is the central wavelength of the optical carrier, f e is the frequency of the electrical drive signal, and c is the speed of light in free space. Therefore, at the end of SMF1, the expression of the optical signal is Similarly, when transmitted back to the central station through SMF2, the optical signal expression is where, τ d is the total loop delay difference, τ d = τ d1 + τ d2 . Similar to (4), τ d2 is the time delay difference caused by dispersion when passing through SMF2. The arbitrary wave generator (AWG) is used to generate the RF SSB signal. The generation principle is shown in Fig. 1(b). A pseudo-random binary sequence (PRBS) with a certain length is fed to the constellation mapping module. The constellation mapping module is responsible for generating the SSB baseband signal. Subsequently, the SSB baseband signal is upconverted to a RF SSB signal by mixing with a complex sinusoidal source with an angular frequency of −2ω e from the MS1. The real and imaginary parts of the RF SSB signal are then summed with the real and imaginary parts of another complex sinusoidal RF source with a frequency of 2ω e from the MS2 as the in-phase and quadrature components of the signal, respectively. The IQ data is then uploaded to a digital-to-analog converter (DAC). Then, the I and Q signals output from the DAC are used to drive the I and Q ports of the dual parallel modulator (DPMZM), respectively. The I/Q modulator is operated at the quadrature point and both MZMs in the embedded modulator are operated at the null point [21]. Next, the spectrum evolution of the modulation process is shown in Fig. 2. The I and Q signals generated by the AWG modulate the optical signals E 3 at frequencies of ω o − ω e (red) and ω o + ω e (blue), and then generate their own CS-SSB RoF signals (with the same color as them in Fig. 2). Since the frequency interval between the two optical carriers is 2ω e , which is equal to the frequency of the IQ signal, the two intermediate first-order optical sidebands achieve phase switching, and then the other two first-order OSBs are filtered out by an optical bandpass filter (OBPF). The output optical signal is expressed as: The phase conjugation signal E 4 propagates backward along SMF2 to the base station. Due to the same fiber length (including length fluctuations due to environmental changes), forward and backward signals transmitted through SMF2 will experience the same dispersion delay difference loss τ d2 . Therefore, E 5 extracted from the reverse signal through OC can be written as Due to τ d = τ d1 + τ d2 , (8) can be simplified as The optical coupler (OC) extracts E 2 from the forward signal, and then passes through a photodetector (PD1) to obtain the RF signal carrying the dispersion in SMF1, which is represented as ) In MZM2, V 2 modulates the phase conjugated signal E 5 . After the optical mixing at PD2, the phase of V 2 is canceled out by the reverse phase term of the electrical signal in E 5 . Therefore, the fourth harmonic term in the mixed product is filtered out by an electrically bandpass filter (EBPF), denoted as There is no item like ϕ o (t) in V 3 which is related to the phase noise of the LD, so the decorrelation caused by the chromatic dispersion have been automatically removed. Note that in PD1 and PD2, the phases of the vector signals are not doubled when beating to generate the RF signals, which means that precoding operation is not required.
III. EXPERIMENT AND RESULTS
The experimental setup is based on the configuration in Fig. 3. RoF signals are transmitted in a ring network through non-dispersion shifted fibers (G652D), which is suitable for metropolitan area networks. An isolator (ISO) is connected after SMF1 to avoid backward light return to the central station. At the central station, a distributed feedback laser (DFB) with a linewidth of 10 MHz is used and its wavelength is set to 1550.0 nm to ensure minimal attenuation in the fiber loop. The wide linewidth of the laser makes the de-correlation introduced by dispersion obvious. The MZM1 (Fujitsu FTM7920) is used to modulate a 5.75-GHz LO reference, and DPMZM (Fujitsu FTM7961EX) is used as a tool for phase conjugation and single-sideband modulation. To reduce the interference from the backward optical signal, a circulator with the isolation of 60 dB is used. A PRBS with the length of (2 14 ) is mapped to QPSK and then converted to an 11.5 GHz SSB signal with a bandwidth of 400 MHz in the AWG (Tektronix AWG70002A), which uses the same clock reference as the LO. The IQ outputs of the AWG are then amplified equally by two identical electronic amplifiers (SHWLNA-0618-29P7S) to drive the DPMZM. The remote station consists of PD, BPF, EDFA, MZM and EA. The MZM2(Fujitsu FTM7920) is used for photonic microwave mixing. Two 43 Gb/s photodetectors (Finisar MPRV1331A) have consistent detection characteristics. Two electrical bandpass filters (BPF) with the same bandwidth of 600 MHz are focused at 11.5 GHz and 23 GHz, respectively. They are used to filter out the required signals. In addition, polarization controllers PC1, PC2, and PC3 are added in front of all modulators in the system in order to reduce polarization losses.
To demodulate and recover the original data, we use a digital oscilloscope (OSC, Keysight UXR0134A) with the sampling rate of 40G to sample the data for offline DSP processing. The sampled data then are upload to the computer for demodulation processing which includes down conversion, constant modulus algorithm (CMA), frequency offset estimation (FOE), carrier phase recovery (CPR). constellation plotting and error vector magnitude (EVM) calculating. In order to evaluate the compensation performance of the system at different fiber dispersion levels, the length of SMF1 is set to 25 km, 50 km and 80 km, and the length of SMF2 is kept at 8 km. Fig. 4 shows the constellation of compensated and uncompensated QPSK signals with different lengths of SMF1. Observing Fig. 4(a), (c) and (e), the effect of the de-correlation caused by dispersion becomes obvious as the transmission length increases. By comparing Fig. 4(a) with (b), (c) with (d) and (e) with (f), it shows that the dispersion compensation makes the points in the constellation more concentrated. Fig. 5 records the correlation between the EVM of the signal and the SMF1 whose distance is swept by 2 km per step. For G652D fiber, the corresponding dispersion is 34ps/nm. The results show that the compensation performance of the system becomes more effective as the dispersion increases. It is worth noting that the EVM of the compensated signal (the green line in Fig. 5) still deteriorates as the transmission distance increases. This is due to the degradation of signal-to-noise ratio (SNR) caused by signal attenuation and ASE of the EDFAs. The EVM of remote transmission can be optimized by adding optical filters after EDFAs to improve the SNR. Fig. 6 shows the EVM versus received optical power for the transmission of a QPSK signal at 400M Baud under different scenarios. Due to the limitations of the PD device used in the experiment, the maximum received optical power we measured is 4 dBm.When the SMF1 length is set to 10 km, the curves with and without compensation approximately overlap, as shown in Fig. 6(a), with a 1 dB power penalty compared to the BTB transmission. The power penalty of the signal with compensation in Fig. 6(b), (c), (d) and (e) are 1.3 dB, 5 dB, 10 dB and 12 dB at 17.5% EVM compared to BTB. As shown in Fig. 6(b), when set to 20 km, the EVM with compensation can be kept within the range of 17.5% specified by 3GPP at a received optical power of −9.7 dBm, while the EVM value without compensation can be kept within 17.5% at the received optical power of −7 dBm. Therefore, the dispersion compensation increases the receiver sensitivity by 2.7 dB. As shown in Fig. 6(c)-(e), the receiver sensitivity of the compensation signal is −6 dBm, −2 dBm and 1 dBm when the SMF1 is 30 km, 40 km and 50 km. However, in all three cases, the EVM of the uncompensated signal cannot reach the threshold of 17.5%, which reflects the necessity of the dispersion compensation. Furthermore, in Fig. 6(a)-(e), the average EVM of the compensated signals can be stabilized at 14.11%, 14.36%, 15.71%, 16.65% and 17.48% within the threshold specified by 3GPP for 5G, respectively.
IV. CONCLUSION
In summary, we propose an automatic compensation system for decorrelation induced by dispersion. This structure is applicable to the distribution system for phase-stabilized distribution of broadband signals. We successfully demonstrate the distribution of 23 GHz vector RoF signal with a bandwidth of 400 MHz from the central station to the remote base station in this structure. And the compensation performance of the structure for the RoF vector signal was compared under different fiber lengths and received optical powers. The results show that the suppression of dispersion becomes obvious with the increase of length of fiber. After 58 km transmission, the EVM decreases by 8%. The signal after compensation can reach the EVM standard of 17.5% specified by 3GPP at a received optical power of 4 dBm. | 3,782.8 | 2023-10-01T00:00:00.000 | [
"Physics"
] |
Meta-Atoms with Toroidal Topology for Strongly Resonant Responses
A conductive meta-atom of toroidal topology is studied both theoretically and experimentally, demonstrating a sharp and highly controllable resonant response. Simulations are performed both for a free-space periodic metasurface and a pair of meta-atoms inserted within a rectangular metallic waveguide. A quasi-dark state with controllable radiative coupling is supported, allowing to tune the linewidth (quality factor) and lineshape of the supported resonance via the appropriate geometric parameters. By conducting a rigorous multipole analysis, we find that despite the strong toroidal dipole moment, it is the residual electric dipole moment that dictates the electromagnetic response. Subsequently, the structure is fabricated with 3D printing and coated with silver paste. Importantly, the structure is planar, consists of a single metallization layer and does not require a substrate when neighboring meta-atoms are touching, resulting in a practical, thin and potentially low-loss system. Measurements are performed in the 5 GHz regime with a vector network analyzer and a good agreement with simulations is demonstrated.
Introduction
Toroidal multipoles are a class of fundamental electromagnetic excitations that complement the more familiar electric and magnetic multipole families [1][2][3][4][5]. The toroidal dipole, the lowest order member of the toroidal family, first considered by Zel'dovich [6], originates from conduction or displacement currents circulating on a torus along the meridians, producing a closed loop of magnetic field circulation. Although it is distinctly different in its construction from the electric dipole (p, a simple separation of electric charges), it emits radiation with the same angular momentum and parity properties as the electric dipole. As a result, the two cannot be easily discerned by observing the far field radiation.
Recently, metamaterials have provided fertile ground for the observation of the toroidal dipole and higher order multipoles through the ability to judiciously shape the meta-atom/meta-molecule geometry in the unit cell. The first demonstration was published in 2010 by Kaelberer et al. [7]. Since then, a broad range of structures have been studied, based on both dielectric materials (displacement currents) [8][9][10][11][12] and metals (conduction currents) [13][14][15]. In particular, planar and, ideally, single-metallization-layer structures are favorable for easier fabrication [16][17][18][19][20]. An important point of attention is the possibility to attain a quasi-dark (almost non-radiating) state, which is termed a "dynamic anapole", and results from the near-destructive interference of the toroidal dipole, T, with the electric dipole, p [21]. As perfect destructive interference is approached through p + ikT→0, one can obtain arbitrarily high radiation quality factors, Q rad (provided that contribution from other multipoles is suppressed). The total quality factor, Q tot , can be very high as well, provided that a material system with low absorption is used [22]. This concept is related to the topics of trapped [23], broken-symmetry [24,25] and BIC (bound states in the continuum) [26] resonances. In such cases, sharply resonant responses and narrow spectral linewidths can be achieved, which are particularly useful for functionalities requiring enhanced local fields. Examples of such applications with metasurfaces supporting anapole states are, for instance, nonlinear effects [27][28][29], lasers [30] and (bio)sensing [31,32].
In recent years, a broad range of metasurfaces (single-layer metamaterial structures) have been proposed for demonstrating toroidal dipole-and anapole-based phenomena [33]. In most cases, the designs are based on a toroidal topology. Here, we adopt such a design aimed at supporting an anapole state [13]; it consists of a unit cell geometry meant to enhance the toroidal character, it is planar and it requires a single metallization layer that can be free-standing (without a substrate), which are important advantageous traits regarding fabrication and practical applications. We show that, indeed, a quasi-dark resonant state can be supported, which leads to an arbitrarily narrow linewidth, limited only by the resistive quality factor. Varying the appropriate geometric parameters, both the linewidth and lineshape of the resonance can be controlled, offering valuable degrees of freedom in shaping the spectral response. By performing a rigorous multipole expansion, we find that the toroidal dipole moment in the structure is strong. However, the corresponding far-field scattering is cancelled exactly by the magnetic quadrupole, Q m . Thus, a quasi-dark resonance is achieved by controlling the residual electric dipole moment through asymmetry in the unit cell geometry (central vs. outer gaps) and not by satisfying the anapole condition. Subsequently, we experimentally verify our calculations through measurements within a rectangular metallic waveguide setup. More specifically, toroidal meta-atom samples, fabricated by a very low-cost technique based on 3D printing and subsequent metallization with a conductive paste, are loaded in the waveguide cross-section, and the S parameters (reflection and transmission coefficients) are measured with a vector network analyzer.
One goal of our work is to demonstrate a practical, easily realizable meta-atom geometry that provides freedom in shaping the electromagnetic response in terms of both linewidth and lineshape. Importantly, this study also clearly demonstrates that an interpretation suggested by the unit cell geometry (its topology) does not necessarily lead directly to the physical interpretation of the phenomenon taking place. Instead, in order to reveal the actual physical behavior, a careful analysis should be performed in all cases. Thus, our work can act as a reference for the mindful discussion of the physical mechanisms behind the resonant response of toroidal metamaterials (but not limited exclusively to this special class of structures). In this paper, the physical evidence is provided by the rigorous multipole expansion and is supported by the experimental verification of the spectral response.
Metasurface Full-Wave Simulations and Multipole Expansion
The metasurfaces studied in this work are composed of a unit cell made of conductive material. In order to study the effect of finite conductivity and increasing resistive loss, conductivities in the range of 10 3 -10 7 S/m have been assumed. Full-wave simulations are conducted with the finite element method (FEM) using the commercial software COMSOL Multiphysics. They concern scattering and guided-wave simulations with a CW excitation and eigenvalue simulations without excitation.
Two types of metasurfaces are considered. The first is a free-space metasurface, where the excitation is a normally incident plane wave with E y polarization ( Figure 1a). In this case, a single unit cell is simulated with periodic boundary conditions in the xand y-axes.
In the second case, two periods of the metasurface along the x-axis are inserted within a rectangular metallic waveguide (Figure 1b), since the aspect ratio of the waveguide cross-section (a × b) is approximately 2:1. The structure is excited with the TE 10 mode of the waveguide, exhibiting the characteristic field distribution E y (x) ∼ sin(πx/a). The waveguide walls are modeled as perfect electric conducting (PEC) walls.
The multipole expansion is performed for the free-space geometry by using the expressions found in ref. [3]. The field scattered by the terms of the multipole expansion can be used for reconstructing the reflected and transmitted field [3,34,35]. The correctness of the calculated multipole moments is checked through the agreement between the direct and reconstructed reflection/transmission. This way, we can also specify where to truncate the multipole expansion without sacrificing reconstruction accuracy.
Meta-Atom Fabrication with 3D Printing
For a fast and cost-effective fabrication of the metasurface under study, 3D printing technology was employed. A commercial fused filament fabrication (FFF) 3D printer was utilized (MakerBot Replicator 2x, New York, NY, USA). A common polylactic acid (PLA) filament was used as a spool material for building the unit cell geometry (Figure 1c). Details regarding the printing process and conditions can be found in refs. [36,37]. Freestanding meta-atoms, such as those depicted in Figure 1c, were successfully fabricated. The fabricated metasurfaces exhibit negligible electrical conductivity, since PLA is an insulator. Therefore, the meta-atoms were subsequently coated with a thin (∼100 µm) layer of conductive silver paste, as shown in Figure 1d. The silver epoxy exhibits electrical conductivity as high as 10 4 -10 5 S/m. We have deduced these values in earlier works [36,37] by comparing experimental results with simulations. Such a meta-atom configuration, in which an insulating core is coated with an adequately thick metallic paint, has been successfully employed at microwave frequencies [36,38].
Electromagnetic Characterization with Rectangular Waveguide Setup
The electromagnetic response of the investigated structure was experimentally confirmed through microwave measurements. To obtain a well-defined and highly reproducible measurement environment, which is not susceptible to external perturbations, we employed a rectangular metallic waveguide setup. More specifically, we fitted 2 × 1 unit cells inside the waveguide to fill the cross-section (aspect ratio 2:1). A test fitting of the two-unit-cell structure within the cross-section of a waveguide-to-coax adapter is shown in Figure 1e.
Measurements were conducted in the vicinity of 5 GHz by using an HP 8722ES vector network analyzer (Agilent Technologies Inc., Santa Clara, CA, USA). WR-187 rectangular waveguides (cross-section: 47.55 mm × 22.2 mm) were used, able to cover the frequency range of 3.95-5.85 GHz. The measurement setup is depicted in Figure 1f and allows for measuring both the reflection (S 11 ) and transmission (S 21 ) coefficients.
Free-Space Metasurface with Controllable Strongly Resonant Response
The meta-atom considered in this work is depicted in Figure 2a. Its geometry is selected in such a way so as to lead to a circulation of induced magnetization giving rise to a toroidal dipole moment [13]; we will come back to this while discussing Figure 2c. The gap in the inner branch is denoted by g 1 and the gaps in the outer branches are denoted by g 2 . For the inner and outer radii, R inn and R out , it holds R inn = R out − w, where w is the width of the central and outer branches. The lattice constant (pitch) is denoted by a for both x and y axes (square periodicity). When R out > a/2, the neighboring meta-atoms are touching; in this case, the conductive meta-atoms can form an interconnected metasurface and no substrate is strictly required. This can be important for avoiding additional resistive loss from the substrate and avoiding excess thickness. Preserving the vertical symmetry of the structure has been also shown to lead to higher modulation depth in transmission [39].
First, we examined a periodic metasurface. The reflection/transmission/absorption power coefficients (R/T/A) for plane wave scattering under normal incidence (E y polarization) are depicted in Figure 2b. The dimensions of the specific example are a = 15 mm, R out = 7 mm, R inn = 5 mm (w = 2 mm), g 1 = 0.5 mm and g 2 = 0.5 mm. The height of the conductive meta-atom is h = 1 mm. In this case, the meta-atoms are not touching. We observed a Fano lineshape associated with the excitation of a resonance at ∼8.71 GHz and its interference with a non-resonant electric polarizability background. Even if the gaps are closed and the meta-atom is non-resonant, the conductive unit cell would still produce significant reflection. The conductivity adopted in these simulations is high (σ = 10 7 S/m), leading to low absorption.
We subsequently performed an eigenvalue analysis to identify the nature of the supported resonance. The mode profile is depicted in Figure 2c; the color corresponds to the E y component (real part) and the arrows to the magnetic field. The magnetic field circles around the central branch and this should produce a toroidal dipole moment along the y axis (T y ). Looking at the fields in the gaps, one realizes that the central electric dipole moment is opposed by the two contributions of the outer gaps; when the opposing p y contributions compensate each other exactly, no coupling via the electric dipole moment is possible. This balance can be used to tune the radiative strength of an electrically coupled meta-atom [40].
To further study the physics of the scattering process, we performed a multipole expansion based on the induced conduction currents on the meta-atom using the expressions found in ref. [3], and we focused on the multipole moments that produce scattered fields toward the z-axis with E y (H x ) polarization. The eight leading terms of the expansion that satisfy the above criterion are p y , m x , T y , Q m xz , Q e yz , Q T yz , O m xzz and O e yzz . The results are depicted in Figure 2d. It can be seen that the rationale behind the meta-atom geometry has indeed resulted in a strong toroidal dipole moment contribution in the spectral neighborhood of the resonance frequency. However, the magnetic quadrupole moment is equally dominant. In fact, their scattered fields cancel out, since on resonance it holds exactly E T y sca = −E Q m xz sca . As a result, the response is dictated by the residual electric dipole moment, p y , which is the third most dominant contribution. This can be further verified in Figure 2e. We first confirm the validity of the multipole expansion by reconstructing the reflection coefficient. The agreement is excellent and shows that using the eight leading terms up to the electric octupole is more than adequate in this case. Importantly, if we use only the field scattered by the electric dipole moment, we obtain a fairly accurate description of the scattering process, especially near the resonance, where there is mutual cancellation of the dominant T y and Q m xz terms. Next, we investigated different geometric degrees of freedom for tuning the resonance linewidth and lineshape. In Figure 3a, we varied the central gap (g 1 ) while keeping the outer gaps (g 2 ) constant at 0.5 mm. This controls the residual electric dipole moment and consequently the radiative strength of the resonance. For g 1 = 0.4 mm, the two opposing contributions (see Figure 2c) cancel each other out almost perfectly. In this case, very little coupling via the electric dipole moment is possible and the resonance becomes quasi-dark, resulting in a very narrow linewidth (high quality factor). The non-negligible reflection that remains is due to the non-resonant electric polarizability background. For g 1 > 0.4 mm, the central p y contribution dominates over those originating from the outer gaps, while the opposite occurs for g 1 < 0.4 mm. In both cases, the linewidth (and radiative strength) increases. The corresponding total quality factors are compiled in Table 1. They have been obtained from the solution of an eigenvalue problem using the complex eigenfrequencỹ ω = ω + iω (the eigenvalue) through the expression Q = ω /(2ω ). For additional details regarding approaches to calculating the quality factor we refer the interested reader to ref. [22]. We document the total quality factor, Q tot , which is directly associated with the linewidth of the spectral feature, along with the corresponding resonant frequency. Note that Q rad ≈ Q tot holds, since Q res → ∞ ("res" stands for resistive) for such a high value of the conductivity (σ = 10 7 S/m). Figure 3a. g 2 is held constant at 0.5 mm. They have been calculated using the complex eigenfrequency through Q = ω /(2ω ). A different option is explored in Figure 3b, where we tune the outer radius. In all cases, the inner radius is also appropriately modified, so that the branch width is kept constant, i.e., R inn = R out − w, with w = 2 mm. This primarily modifies the non-resonant (background) electric dipole moment, leading to changes in the Fano lineshape from highly asymmetric to quasi-Lorentzian. For R out values of 7.6, 7.7, and 7.8 mm, the meta-atoms are touching, this additionally modifies the residual electric dipole moment, as the outer gaps of each meta-atom begin to merge with those of the neighboring atom, producing high values of background reflectance. Importantly, by tuning R out we are able to achieve very narrow linewidths and, at the same time, a large resonance depth (compare Figure 3b with Figure 3a). The total quality factors for R out = 7.7 and 7.8 mm are ∼5000 and ∼30,000, respectively. Note that this quality factor corresponds to radiation losses and will drop if resistive losses increase.
Meta-Atoms in a Rectangular Waveguide Setup-Experimental Verification
In this Section, the unit cells under study are inserted inside a rectangular waveguide environment (see Figure 1). This is exercised in order to end up with a well-defined and highly reproducible measurement environment, which is not susceptible to external perturbations. Furthermore, the electromagnetic response is anticipated to be similar to the free-space periodic structure, since the top/bottom PEC walls emulate a periodic repetition along the y axis and the main difference is the sin(πx/a) profile of the incident guided wave along the x axis [35,37,41].
We first performed simulations. We tuned the dimensions in order to bring the resonant frequency near to the center of the band of the WR-187 rectangular waveguide (3.95-5.85 GHz) and fit 2 × 1 meta-atoms in the cross-section (a × b = 47.55 mm × 22.2 mm). The dimensions are R out = 12 mm, R inn = 8.6 mm, w = 3.4 mm, g 1 = 0.7 mm and g 2 = 1 mm. The thickness of the conductive meta-atom is h = 3.4 mm. The response is depicted in Figure 4, where the reflection, R = |S 11 | 2 , transmission, T = |S 21 | 2 , and absorption, A = 1 − |S 11 | 2 − |S 21 | 2 , are plotted. The meta-atoms are touching and the resonance lineshape resembles the respective cases in Figure 3b. The meta-atoms will be fabricated via first 3D printing a dielectric (PLA) scaffold and then by coating with a silver paste, which is characterized by a limited conductivity of approximately σ = 10 4 -10 5 S/m. Thus, in Figure 4 we examine the conductivities σ = 10 5 S/m, σ = 5 × 10 4 S/m, σ = 10 4 S/m and σ = 5 × 10 3 S/m. As the conductivity decreases, the spectral features become broader and the absorption increases up to a maximum of 0.5 (for an electrically polarizable structure) before starting to decrease again (under-coupling regime). The mode profile is depicted in the inset of Figure 4d. Notice that the gaps near the edges of the waveguide do not accommodate strong fields, since the incident TE 01 waveguide mode is zeroed out at the side walls (cf. Figure 2). In Figure 5, we depict the measurements of the 3D-printed conductive unit cells within the WR-187 rectangular waveguide. The reflection (R = |S 11 | 2 ) and transmission (T = |S 21 | 2 ) power coefficients are plotted in the frequency range of 4.5-5.5 GHz. The lineshape of the spectral feature and the linewidth (full-width half maximum of approximately 100 MHz, as extracted from the spectral feature in reflection) are in good qualitative agreement with those predicted by the simulations and specifically Figure 4c, which corresponds to a conductivity value we anticipate for the silver epoxy. The resonant frequency is slightly different; we attribute this discrepancy to the limited accuracy of the geometric dimensions achieved in the actual fabricated sample.
Discussion and Conclusions
We have studied a conductive meta-atom of toroidal topology, meant to enhance the toroidal dipole moment. We have performed simulations of both a periodic freespace metasurface comprised of this meta-atom and, subsequently, we have inserted two such meta-atoms into a metallic, rectangular waveguide setup. The latter configuration has allowed for experimentally verifying the resonance characteristics (lineshape and linewidth) and thus supports the physical claims arising from the theoretical analysis and multipole expansion.
One goal of our work was to demonstrate a practical, easily realizable meta-atom geometry that provides freedom in shaping the electromagnetic response in terms of both linewidth and lineshape. Another important goal was to reveal and highlight the physical mechanisms dictating the resonant response. Importantly, despite the physical interpretation suggested by the unit cell geometry (its toroidal topology), a rigorous multipole expansion has revealed that, although the toroidal dipole moment is indeed strong, the corresponding scattered field is cancelled out exactly by that of the magnetic quadrupole. As a result, the scattering response can be described accurately by simply considering the electric dipole moment alone. Thus, we conclude that a multipole expansion must be performed in all cases, in order to reach safe conclusions regarding the multipole components that mediate the scattering process.
The studied meta-atom allows to control the residual electric dipole moment through the geometric asymmetry between the central and outer gaps. This is a very similar concept to "accidental BIC" or "trapped/broken-symmetry" resonances. It becomes possible to achieve a controllably sharp resonant response, reaching very high radiation quality factors (Q rad ). This is also possible in finite meta-atom arrays through spatially extended dark (sub-radiant) eigenmodes, as has been discussed in ref. [24]. Note, however, that ultimately the spectral linewidth is dictated by the total quality factor (Q tot ), which will be limited by resistive losses as well. As a result, pushing for very high Q rad values which require slight asymmetry and precise fabrication is not necessary when it cannot be supported by low material losses. Interconnected meta-atoms that do not require a substrate can help to avoid excess losses stemming from the substrate material and excess radiation losses stemming from the breaking of the vertical symmetry.
Data Availability Statement:
The data presented in this study are available on request from the corresponding author. | 4,971.4 | 2023-02-01T00:00:00.000 | [
"Physics"
] |
Why are IPTp coverage targets so elusive in sub-Saharan Africa? A systematic review of health system barriers.
BACKGROUND
Use of intermittent preventive treatment (IPTp) is a proven cost-effective intervention for preventing malaria in pregnancy. However, despite the roll-out of IPTp policies across Africa more than ten years ago, utilization levels remain low. This review sought to consolidate scattered evidence as to the health system barriers for IPTp coverage in the continent.
METHODS AND FINDINGS
Relevant literature from Africa was systematically searched, reviewed and synthesized. Only studies containing primary data were considered. Studies reveal that: (i) poor leadership and governance contribute to slow decentralization of programme management, lack of harmonized guidelines, poor accountability mechanisms, such as robust monitoring and evaluation systems; (ii) low budgetary allocation towards policy implementation slows scale-up, while out-of-pocket expenditure deters women from seeking antenatal services that include IPTp; (iii) there are rampant human resource challenges including low staff motivation levels attributed to such factors as incorrect knowledge of IPTp recommendations and inadequate staffing; (iv) implementation of IPTp policies is hampered by prevailing service delivery barriers, such as long waiting time, long distances to health facilities and poor service provider/client relations; and (v) drug stock-outs and poor management of information and supply chains impair sustained availability of drugs for IPTp.
CONCLUSIONS
For successful IPTp policy implementation, it is imperative that malaria control programmes target health system barriers that result in low coverage and hence programme ineffectiveness.
Background
Each year, about 50 million women living in malariaendemic countries throughout the world become pregnant, of whom over 50% live in high-transmission areas in Africa [1]. The disease poses serious risks to the mother, her foetus and the neonate [2]. Malaria in pregnancy is a major public health concern for which the WHO recommends a package of interventions for pregnant mothers. In areas of stable malaria transmission, recommended control measures include effective case management of malaria and anaemia, use of insecticide-treated nets and intermittent preventive treatment (IPTp).
Intermittent preventive treatment is highly cost-effective in reduction of malaria in pregnancy and consequently in reduction of neonatal mortality [3]. Reductions in neonatal mortality by up to 61.3% have been reported following IPTp administration [4]. Current IPTp guidelines stipulate that all pregnant women in areas of stable malaria transmission should receive at least two doses of intermittent preventive treatment after quickening. As the current practice of focused antenatal care recommends at least four antenatal visits, it is envisaged that a high proportion of women can receive at least two doses of IPTp. In fact, the Roll Back Malaria's Global Action Plan target was to ensure that 80% of pregnant women received intermittent preventive therapy by 2010 [5].
However, evidence suggests elusive utilization of IPTp in Africa [6]. A recent publication in the Lancet reported that 83% of the 47 countries studied had a malaria IPT policy. In these countries, only 25% of pregnant women received at least one dose of treatment. Coverage of IPT was lowest in areas of high-intensity transmission of malaria. This phenomenon was widespread. In Malawi and Kenya, among the earliest countries to implement IPTp policy, coverage is estimated at 80.7% and 35.5% respectively. Many countries such as Somalia, Benin, Burkina Faso and Congo have coverage rates of below 10%. Madagascar and the Central Africa Republic have coverage rates of 12% and 11.8% respectively. These low coverage rates are in spite of high antenatal care attendance [7].
Why is IPTp coverage so low in Africa? Studies have shown that performance of global and national health interventions, such as IPTp, is linked to performance of health systems within which the interventions are delivered [8]. Therefore, in order to comprehensively respond to this question, it is important to consider components of the health system in order to identify IPTp scale-up barriers. Various studies have attempted to identify individual elements of the health system and the barriers related to these elements with regard to IPTp scale-up. However, a comprehensive review of these barriers is critical in order to provide consolidated evidence. By examining health system building blocks, this paper reviews existing evidence in an attempt to elucidate why achievement of optimal IPTp coverage remains elusive.
From an initial pool of 19 papers, 12 relevant original research publications were selected by two independent reviewers based on the following criteria: original research study (containing primary data) addressing barriers to IPTp in Africa; and published between 2005 and 2012. References cited in these selected papers were also reviewed for additional evidence. Six papers were rejected because they were based on secondary data.
The WHO framework for health systems strengthening was used to analyze the main barriers related to health systems (Table 1). This analysis was conducted in the context of IPTp policy implementation.
Results
Findings of reviewed studies presented in this section are summarized in Table 2.
Poor leadership and governance
Leadership is a central pillar that binds other health system components [9]. With respect to malaria control programmes, multilateral and bilateral organizations have provided global leadership, planning and organization support for African governments [10]. Numerous networks of alliances and programmes are in operation. What lacks in some countries is proper coordination and facilitation of regional networks to ensure harmonized approaches to IPTp policy implementation. Multiple IPTp guidelines are a challenge in some countries while in other areas multiple partners are involved in implementation of IPTp components of malaria programmes, and there have been reports of duplication of activities and running of parallel programmes [11]. It has been reported that low IPTp coverage levels could be attributed to unclear IPTp guidelines that lead to lost effectiveness of the IPTp strategy [12]. Evaluation of an IPTp roll-out programme in an African country revealed existence of conflicting health care worker guidelines for IPTp [13]. The national agency recommended two doses while sub-national agencies recommended other dosages. This conflict was cited as a source of confusion to frontline workers thereby hampering coverage of IPTp through a harmonized approach. Other supply side barriers that could be mitigated through effective leadership include limited dissemination of guideline booklets to health workers. Inadequate integration of IPTp into reproductive health programmes causes failure of health workers to consider IPTp as part of the antenatal care service package [13,14]. Centralized malaria control programmes are common in some parts of Africa [10]. In the Fifteenth Ordinary Session of the Assembly of the African Union, African leaders recognized the need for decentralization of malaria programmes, with IPTp components as a critical prerequisite to increased coverage and sustained programme effectiveness [15]. They reiterated the importance of effective leadership and governance in guiding utilization of resources, such as finances for malaria programming including IPTp. In Tanzania, in-depth interviews among national level malaria control officers revealed a need to address leadership constraints to IPTp policy implementation through decentralization [14].
Inadequate and unsustainable financing
Many sub-Saharan countries rely on donor funding for IPTp supply and distribution. Countries with greater domestic budgetary allocations for IPTp and other malaria interventions have better performing IPTp programmes. Examples of these are Malawi, Senegal and Zambia [16]. The governments of these countries provide all of the funding for IPTp drugs, with central-level shortages reportedly due more to poor quantification than funding inadequacy. In fact, Zambia achieved a coverage of 62% of women receiving at least two doses of IPTp [17]. IPTp coverage for Malawi and Senegal are at 80.7% and 78.1% respectively, reflecting better performance than their sub-Saharan counterparts [7]. This was significantly attributed to increased domestic financing [16].
Patterns of inequity in access to IPTp are visible in Africa. These inequities can be linked to patterns of donor funding. Whilst the Global Fund against HIV, TB and malaria is geographically comprehensive in its Tanzania Conflicting guidelines [11][12][13] Tanzania Policy factors and slow decentralization processes for programme management [12,14,15] Health financing Zambia, Senegal, Malawi Budgetary allocation [16] Tanzania Out-of-pocket expenditure [13] Human resources Nigeria Lack of health worker training on existing recommendations Incorrect knowledge [20] Tanzania Under-staffing,
Inadequate skills
Poor motivation [13] Tanzania Unfriendly supervision Limited training opportunities [14] Products, infrastructure and logistics Tanzania, Zambia Drugs shortages, Water shortages [11,13,17] Service delivery Tanzania, Zambia Long distance, long waiting time, ineffective Poor organization of educational services and lack of explanation to patients
Failure to link intervention with benefits
Lack of respect to clients [13,17] Nigeria Poor quality of services [20,21] Tanzania¸Uganda Inadequate time for service delivery [22,23] Zambia, Malawi, Senegal Inadequate supervision of service delivery [16] Tanzania Low rate of administration of IPTp by health workers at ANC [12] Information systems Tanzania Weak monitoring and evaluation systems [13,14,16] funding strategy, providing funding largely in proportion to populations at risk, the disbursement patterns of other donors are more targeted and thus introduce inequity in the continent-wide pattern of funding. For example, of the 17 countries that received the US President's Malaria Initiative (PMI) support by 2010, 14 had higher than equitable funding on malaria when compared to their neighbours [18]. Attendance of ANC clinics and IPTp access in countries is limited by lack of health insurance systems that would otherwise alleviate the problem of cash availability. Out-of-pocket payments for services are prohibitive to mothers in malaria-endemic areas. In a continent where women are burdened with domestic chores that require cash-at-hand financing, the women are faced with numerous priorities. Out-of-pocket health expenditure rates in 15 countries in East, South, West and Central Africa varied between 6% and 62.2% [19].
Further, indirect costs such as lost time and opportunity costs for acquiring IPTp also limit access of this intervention to mothers [13].
Human resource challenges
Human resource inadequacy compounds challenges of leadership, governance and financing. Not only does the continent grapple with inadequate staffing to support IPTp, but the inequity in distribution of the available workforce continues to impact on IPTp delivery. Well qualified staff are often concentrated in urban areas leaving rural areas inadequately staffed [20]. Yet, it is in the rural areas where majority of pregnant mothers at risk of malaria in pregnancy live. Even where health workers are relatively more available, a multiplicity of pressing needs such as high HIV/AIDS prevalence render malaria prevention through IPTp administration a lesser priority.
Knowledge of recommended IPTp practices is also a challenge among health care workers. In a study on supply factors influencing IPTp coverage, it was revealed that only 14.7% of health providers had correct knowledge of all four recommendations for provision of IPTp [20]. Directly Observed Therapy (DOT) strategy was only practised by twenty two out of the 34 providers studied. The assumption that mothers would adhere to treatment instructions if left on their own was predominantly reported among health workers [20]. Other reported human resource challenges are lack of motivation, poor health care quality and client-provider relations. Supervision of peripheral health facilities is inadequate. Unfriendly supervision by facility health management teams has also been reported as a challenge among health facility staff. Further, limited opportunities for training and career development among staff dampens motivation, a factor that indirectly influences coverage of administration and coverage of IPTp. Moreover, indirect motivating factors for the health workforce have been cited as a challenge. These factors include adequate staff housing, reasonable quality of health facility infrastructure and essential material conditions such as adequate lighting in consultation rooms, functional and adequate equipment in laboratories and availability of furniture [14].
Challenges with medical products, technology, infrastructure and logistics
Even when staff wish to deliver IPTp services free-ofcharge as most policies stipulate, it is not always practical due to drug shortages that result from weak procurement systems. It is reported that up to 9% of clients miss IPTp due to drug shortages in some parts of Africa [14]. A case in point is a study in Tanzania where inadequate stocks of SP were reported to be a common problem [13]. This occurrence results from an interplay of several factors. Poor leadership and governance promotes lack of accountability and planning. This causes haphazard procurement procedures that fail to recognize systematic monitoring and evaluation of product flows and availability, causing delays in delivery and disbursement. Another factor contributing to these shortages is misuse of drugs such as sulphadoxine-pyrimethamine for clinical cases and RDT-negative malaria cases, not only in pregnant women but also in the general population [11].
Implementation of directly observed treatment strategies for IPTp is hindered by frequent water shortages at health facilities; attributing to the reported 7% and 2% coverage of DOTs at rural and urban health facilities respectively in Tanzania [14].
Quantification of required amounts of IPTp drugs is a challenge [11]. Lack of accurate consumption data, particularly at district levels adds to the challenge of quantification. Health facility catchment population estimates are often flawed due to under-reported census figures and failure to account for clients coming from other catchment areas. In fact for countries such as Zambia, areas near national borders experience inflow of clients from countries such as Mozambique and the Democratic Republic of Congo. Even when commodities are available, limited storage facilities limit the amount of stock available at any given time. Transportation of these commodities is not only expensive but also lacking in remote parts of Africa. Fuel, an indirect commodity requirement has progressively experienced a soaring cost trend [17]. Shortages of procurement and logistics staff also causes overburdening of available staff. The effect of this is slow procurement and delivery processes that compromise quality service delivery.
Barriers to service delivery
Service delivery barriers are a critical impediment to IPTp scale-up. Long distances from health facilities limit access to health services particularly among women in far-to-reach communities [13]. This either totally hinders ANC attendance or prevents mothers from returning to health facilities for follow-up clinics. Even though reviewed studies report over 70% ANC attendance in most countries [21], poor quality of service delivery is evident. Reported bottlenecks in health service delivery are long waiting time [13], ineffective organization of educational sessions, lack of explanation to patients, failure to link the intervention with benefits and occasional lack of respect to clients [22]. Inadequate time for service delivery also hampers administration and follow up for IPTp [23]. An assessment in three countries -Zambia, Malawi and Senegal -that are regarded to have successful IPTp programmes revealed that quality assurance in health facilities through regular supervision is among attributed success factors [16].
Weak information systems
Countries that perform relatively well in terms of effective IPTp coverage generally have better accountability systems [16]. This is ensured by regular tracking and feedback through monitoring and evaluation systems. In the continent, these systems are not always robust.
Programmes and staff at the local level require monitoring and evaluation indicators that are simple and easy to collect, yet in many countries information on IPTp is not collected as part of routine health management information systems. Instead, reported coverage figures have until now been based on Demographic Health Surveys (DHS), Multiple Cluster Indicator Surveys (MCIS), and national surveys. DHS and MCIS occur at intervals of approximately five years. Sub-Saharan Africa countries lack routine systems for data collection that are linked to regular supervision and feedback at health facility. Such feedback would have the dual benefits of informing on progress as well as incentivizing health workers to improve performance.
Core coverage and effect indicators for monitoring and evaluation of IPTp have been piloted in Nigeria, Kenya and Uganda [11]. The challenge is ensuring that these indicators are collected in a rigorous and systematic manner through routine data monitoring systems. The potential of technology is yet to be fully optimized in setting up monitoring and evaluation systems. Many countries rely on hand-written registers, the completion of which is not only time-consuming for health workers but may also be erroneous.
Discussion
This review underscores the need to consider a health systems approach towards resolving programmatic bottlenecks and gaps for IPTp. It highlights fundamental barriers whose resolutions are likely to see improved outcomes and eventual impact of IPTp policies.
Successful IPTp scale-up will require effective leadership and governance to ensure that first, resources are allocated for IPTp and secondly, that these resources are effectively and efficiently utilized for the benefit of pregnant mothers in need of IPTp. It is this leadership that will ensure effective utilization of financial resources, human resources, commodity availability and quality service delivery. Through robust health information systems, this leadership will also ensure that systems are in place for accurate and timely monitoring and evaluation of relevant IPTp data. The exemplary performance of Zambia, Malawi and Senegal is partly attributed to effective leadership [16].
Without financial resources, implementing IPTp policies is nearly impossible. Sub-Saharan countries grapple with over-reliance on donor funds. Out-of-pocket expenditure for health deters positive health-seeking behaviour, thereby contributing to low demand for ANC services including IPTp [24]. Again, successes attained in some countries with regard to IPTp coverage are partly attributed to increased government commitment towards funding provision of IPTp drugs [16]. Sustainable financing mechanisms complement adequate human capital.
In many health facilities within sub-Saharan Africa, staff are often overworked, poorly remunerated, and thus not adequately motivated. For instance, studies examining nurses wellbeing in a sub-Saharan setting show high burnout and low job satisfaction [25]. Overworked and underpaid workers manifest burnout through depersonalization leading to a negative attitude towards their clients [26]. Hostile treatment by health workers strongly influences health services-seeking behaviour of clients. Perceptions on quality of services received at the health facility may influence IPTp utilization. Therefore, health workers need to be encouraged through supportive supervision to employ DOT strategy in order to boost adherence. Even though missed opportunities for delivery of IPTp are prevalent in Africa, perhaps one of the most overlooked determinant factors for IPTp utilization is health worker awareness. Development of simplified guidelines for health workers may resolve the problem of inconsistent messaging and poor adherence to policy guidelines experienced in some countries [13]. Guidelines for administration of IPTp stipulate the use of Directly Observed Therapy (DOT), yet in Nigeria, over three quarters of those that took SP reported that they were allowed to take the drug home [21]. This problem further compounds poor access to services and coverage. Treatment and preventive guidelines for malaria are dynamic, and continuous professional development is imperative. However it is noted that this alone cannot translate awareness to practice and, therefore, supportive supervision from credible peers, linked to feedback on performance and benchmarking with other facilities will be game changing [27]. Such an approach is likely to enforce the practice of administration of IPTp among health workers.
While service delivery provides the frontline interface between the health system and its beneficiaries, reviewed evidence reveals that this interface is fraught with challenges of inaccessibility and poor quality. Experience from successful countries demonstrates that interventions, such as community mobilization through involvement of community health workers, plays a role in promoting ANC attendance and educating on the need to prevent malaria in pregnancy [16]. Once demand for ANC services is enhanced, efficiency in service delivery may be improved through such approaches like service and programme integration and improved clientprovider relations. Training on customer service and IPTp policy recommendations is necessary for health workers. Concurrently, health systems must ensure that the supply chain is effective to deliver essential commodities such as IPTp and related anti-malarial drugs. Lack of supplies at health facilities due to chronic stock outs reduces the motivation of frontline health workers to effectively deliver high impact interventions such as IPTp. Also it may reduce the use of health services by clients. These could be overcome through improved management of supply chain systems that are responsive to the demand at health facilities. Robust information management systems not only contribute to better accountability but also to responsive rather than reactive systems. They provide real-time data on demands, shortages and stocks. Staff training on the need for and set-up of functional monitoring and evaluation systems is imperative. Some countries such as Senegal have taken significant steps to improve their information systems. The country has hired new staff and established a webbased management system [16].
While this review consolidates existing evidence on health system barriers, it is recognized that health systems research specific to identifying programmatic gaps for IPTp scale-up is scanty. More studies should be undertaken in order to inform country specific programmes. In particular, it is important to explore determinants of supply side practices that limit coverage of IPTp. In fact, missed opportunities for IPT administration could be an important indicator in monitoring and evaluation systems for malaria programmes at sub-national, national and regional levels. Lastly in consideration of the evidence provided, it is noted that the scope of reviewed literature is limited by scarcity of data from across all regions of Africa. Though the cited barriers are likely to be widespread, one cannot decisively conclude so. Again, most reviewed studies are limited in the degree to which they holistically explored barriers relating to the supply and demand side of IPTp policy implementation, both quantitatively and qualitatively. Such limitations may have trickled down to this review.
Conclusion and recommendations
Though IPTp remains an important strategy in the prevention of malaria in pregnancy, health system hurdles need to be overcome. To sustain the gains attained in IPTp implementation, and to improve coverage, intervention programmes must adopt a health system approach towards resolving barriers that hamper optimal coverage of IPTp. Furthermore, these challenges are common to most public health programmes in Africa and, therefore, health systems strengthening should be a component of all public interventions. Research and regular assessments must accompany programme implementation to gather more evidence and provide adequate guidance. Innovative approaches such as combination of interventions and enhanced integration are needed to better prevent malaria among pregnant women.
Limited individual level factors strongly associated with the use of IPTp in literature combined with some findings that adherence levels are high among women offered IPTp suggest that factors related to health-care provider behaviour are more influential in the coverage of IPTp than most measurable individual level factors. Evaluations of both health care provider practices and community perceptions and demand regarding IPTp uptake are needed to measure the extent of the problem and develop targeted interventions at improving access to IPTp. | 5,139.4 | 2013-10-03T00:00:00.000 | [
"Economics",
"Medicine"
] |
Identifying longevity associated genes by integrating gene expression and curated annotations
Aging is a complex process with poorly understood genetic mechanisms. Recent studies have sought to classify genes as pro-longevity or anti-longevity using a variety of machine learning algorithms. However, it is not clear which types of features are best for optimizing classification performance and which algorithms are best suited to this task. Further, performance assessments based on held-out test data are lacking. We systematically compare five popular classification algorithms using gene ontology and gene expression datasets as features to predict the pro-longevity versus anti-longevity status of genes for two model organisms (C. elegans and S. cerevisiae) using the GenAge database as ground truth. We find that elastic net penalized logistic regression performs particularly well at this task. Using elastic net, we make novel predictions of pro- and anti-longevity genes that are not currently in the GenAge database.
Introduction
Identifying the genetic and molecular basis of aging is a longstanding goal in medical science [1,2]. Advances in aging research have uncovered several common denominators of aging that are conserved across a wide range of organisms [3], and several drugs have been identified that have remarkable pro-longevity effects in model organisms [4]. However, much remains unknown about the biology of aging. Many studies have investigated whether individual genes are pro-longevity or anti-longevity on a case-by-case basis [5]. Typically, an intervention such as a knockout/knockdown or overexpression is applied to a small number of genes in a model organism such as nematode worm (Caenorhabditis elegans) or yeast (Saccharomyces cerevisiae) followed by quantification of lifespan. A gene is considered pro-longevity if its expression is directly related to lifespanfor instance, if overexpression increases lifespan or underexpression decreases lifespan [6]. Conversely, a gene is considered anti-longevity if its expression is inversely related to lifespan. Meanwhile, many genes do not fall clearly into either category, for instance, a gene might have no discernable effect on lifespan. The GenAge database [6] contains a catalogue of putative pro-and anti-longevity genes based on current evidence. Pro/anti-longevity genes can be identified by intervening on individual genes, but this is slow and expensive. Alternatively, a common technique is to randomly knock out or disrupt many genes in a population of organisms, screen for the longest living individuals, and then determine which genes were disrupted in these individuals. This screening technique can rapidly identify anti-longevity genes, but systematically identifying pro-longevity genes is less straightforward. Indeed, among the small number of genes annotated as having some impact on longevity in worms and yeast, there are considerably more anti-longevity genes than prolongevity genes.
To prioritize which genes to investigate and speed up the discovery process, recent studies have sought to computationally predict the effect of gene interventions on aging, using annotations like Gene Ontology (GO) terms [7] as predictors. A survey of such efforts is provided by Fabris et al [8]. However, these recent studies suffer from several limitations. First, annotations like GO may be biased by the scope of the existing literature [9]. Second, it is difficult to compare results across studies since there is a lack of consistency in the choice of algorithms, feature sets, and predictive target/outcome. Finally, most recent studies do not report predictive performance on a held-out test dataset, leading to possible overestimation of performance.
We address these gaps by systematically assessing the performance of five popular machine learning algorithms on the task of predicting the pro-versus anti-longevity status of genes in S. cerevisiae and C. elegans. We use a consistent outcome in all comparisons based on GenAge annotations [6]. We compare the efficacy of GO terms versus gene expression profiles as feature sets for prediction. Further, we predict possible pro/anti-longevity genes that are not currently annotated in GenAge to suggest directions for future experimental studies.
We define the outcome (that is, the target of prediction) to be the pro-versus anti-longevity annotation of individual genes from GenAge. After data cleaning, we identified 398 yeast genes and 848 worm genes with unambiguous annotations. Of these, the majority were labeled as anti-longevity (347 for yeast and 565 for worm). For validation and comparison, in yeast, we also consider replicative lifespan (RLS) outcome data for a comprehensive set of 4,698 single-gene deletions [15]; we refer to this as the McCormick dataset. In yeast, it is more common to use replicative lifespan rather than chronological lifespan to study aging.
As features for prediction, we consider using GO terms [7] and ARCHS4 gene expression profiles [16] for both yeast and worm. For yeast only, we also consider using the Deleteome dataset [17], which contains gene expression profiles for nearly 1500 single-gene deletions. For worm only, we also consider using the Worm Cell Atlas dataset [18], which contains gene expression profiles for around 50,000 cells. We write GXP to signify Deleteome and Worm Cell Atlas for yeast and worm, respectively. Altogether, we compare the performance of five feature sets for each species: (1) ARCHS4 alone, (2) GO alone, (3) GXP alone (Deleteome for yeast, Worm Cell Atlas for worm), (4) GO combined with ARCHS4, and (5) GO combined with GXP. Normalization, filtering, and other preprocessing steps are described in the Methods section.
To predict whether a particular gene g is pro-or anti-longevity, we construct features in the following manner. Each GO term is considered a separate binary feature taking a value of one if gene g is annotated to the term and zero otherwise. For the ARCHS4, Deleteome, and Worm Cell Atlas data each experimental condition (e.g., a perturbation or tissue sample) is considered a feature and its value is given by the expression of gene g under that condition. Note that this is the transpose of how gene expression data are usually investigated. However, by treating experimental conditions as features and genes as observations, this allows us to exploit arbitrary gene expression data for gene g, not just data from when g is perturbed.
Comparative performance of algorithms and feature sets
To assess predictive performance, we use the following cross-validation scheme. For each of the two species, we split the GenAge-annotated genes into five cross-validation folds, and then for each combination of fold, algorithm, and feature set, we compute the area under the receiver-operator curve (AUC). Thus, in total, we compute 2 × 5 × 5 × 5 = 250 AUC values, 50 for each algorithm (S1 and S2 Figs).
To summarize the relative performance of the five algorithms, Fig 1 shows how frequently algorithm a has higher AUC than algorithm b for each pair a, b. More precisely, for each pair of algorithms, Fig 1 shows the fraction of times algorithm a has higher AUC than algorithm b across the 50 combinations of species, fold, and feature set. The pglm and svm algorithms consistently outperform the others in terms of AUC. The ranking of algorithms is unchanged when compared using only yeast data. Using only worm data, svm slightly outperforms pglm (0.52 instead of 0.46 in Fig 1), and knn slightly outperforms nb (0.56 instead of 0.34 in Fig 1).
To compare the relative performance of the five different feature sets, Fig 2 shows boxplots of the AUC values over the five cross-validation folds, stratified by species, algorithm, and feature set. For visual clarity, here we only show the results for pglm and svm (the two best algorithms); see S2 Fig for the other algorithms. Generally speaking, using GO terms yields better predictions than gene expression features alone (ARCHS4 or GXP). However, combining GO with gene expression (GO+ARCHS4 or GO+GXP) tends to increase AUC performance compared to GO alone.
Comparing gene expression feature sets, the ARCHS4 features give better performance than GXP (Worm Cell Atlas) for worms, but for yeast, GXP (Deleteome) is superior to ARCHS4. This could be simply due to the fact that the number of features in the worm ARCHS4 data is much larger than in the Worm Cell Atlas data. Alternatively, it could be due to the greater variation in experimental conditions across Deleteome features (which covers a comprehensive set of gene knockouts) compared to Worm Cell Atlas features (which consists of expression profiles of different cell types in normal worms). Overall, for worms, pglm with GO+ARCHS4 features yields the best performance, whereas for yeast, pglm with GO+GXP is best (Fig 3).
Novel predictions of pro/anti-longevity genes
Given the encouraging performance of pglm for predicting pro/anti-longevity genes in Gen-Age, we applied the algorithm to make novel predictions of pro/anti-longevity genes in C. elegans (worm) and S. cerevisiae (yeast). To do this, for each species separately, we retrained a pglm model on the full GenAge database, using the combined GO terms plus ARCHS4 gene expression as features (see the Methods section for details on hyperparameter selection). Although for yeast the GO+GXP (Deleteome) features had slightly higher median predictive performance than GO+ARCHS4, we used the latter instead to maintain consistency across the two species. We then used the trained model to generate a predictive score for the pro/antilongevity effect of each gene not in the GenAge database. Specifically, the predictive score is defined to be the probability that the gene is pro-longevity under the trained model. A score close to 1 indicates that the gene is predicted to be pro-longevity, whereas a score close to 0 indicates that the gene is predicted to be anti-longevity. An intermediate score indicates a gene with unclear pro-or anti-longevity status. Table 1 shows the unannotated genes with the highest confidence levels of being pro-and anti-longevity for worm and yeast, respectively. These genes do not significantly overlap with predictions from the pglm model trained using only GO terms as features (S2-S5 Tables, S3 Fig), suggesting that these predictions are not simply recapitulating the known biology represented in the GO terms. Complete lists of predictions for all genes are provided in S1 and S2 Data.
To assess the accuracy of the predictions, we looked at the literature to see if there is experimental evidence of pro/anti-longevity effects for these genes. Based on the existing experimental evidence, we find that the model predictions are remarkably good. It turns out that-even though they are not in GenAge yet-there is experimental evidence for the pro/ anti-longevity status of most of the predicted genes.
Predicted pro-longevity worm genes. For many of the predicted pro-longevity genes in Table 1, there already exists direct experimental evidence of pro-longevity status. Note that this evidence was not used in making the predictions, implying that the model is producing reliable out-of-sample predictions. We discuss what is known about the top 10 predicted prolongevity genes: CLEC-196, F44E5.4, CEH-13, LPR-3, HIL-7, W04A8.4, TTH-1, GST-1, F44E5.5, and F20C5.6. F44E5.4 and F44E5.5 encode members of the hsp70 family of heat shock proteins. The heat shock response is well-known to have strong pro-longevity effects in C. elegans. Indeed, knocking in extra copies of hsp70 extends lifespan [19] and knocking down hsp70 via RNAi decreases lifespan and leads to rapid aging phenotypes [20]. GST-1 (Glutathione S-transferase P) is also involved in stress response-particularly, immune response-and GSTs are well-known to be pro-longevity. Overexpression (underexpression) of GSTs has been found to increase (decrease, respectively) lifespan and stress resistance [21,22]. W04A8.4 is an uncharacterized protein that is involved in the pro-longevity effect of metformin on C. elegans [23]; specifically, knockdown of W04A8.4 leads to metformin resistance. This is intriguing, since metformin treatment has been shown to promote health and extend lifespan in many organisms. Homeobox protein CEH-13 exhibits pro-longevity characteristics based on experimental evidence-specifically, a ceh-13 mutant strain has decreased lifespan compared to wildtype controls [24]. LPR-3 (LiPocalin-Related protein) is known to be involved in nematode worm locomotion, and appears to mediate the longevity-inducing effect of daf-7 mutation [25]; additionally, expression of lpr-3 is increased in worms fed with rBm αTX14, an α-neurotoxin that increases worm lifespan [26].
For the remainder of the genes in Table 1, there is suggestive experimental evidence of prolongevity status based on associations. C-type Lectin clec-196 expression increases and lifespan increases when hsb-1 is knocked out [27]. Also, clec-196 is directly adjacent to hsp-1 on chromosome IV, suggesting possible co-involvement, and hsp-1 (heat shock protein) is wellknown to be pro-longevity. HIL-7 (Histone H1 Like) gene expression may be associated with Ethosuximide treatment, a drug that increases worm lifespan and affects DAF-16/FOXO target gene expression [28]. TTH-1 (Thymosin beta) is significantly increased in daf-2 mutants, which are very long-lived, suggesting possible pro-longevity status by association [29]. F20C5.6 is affected by the well-known longevity genes clk-1 and sir-2.1, as well as by treatment with 1-methylnicotinamide and rotenone, which are well-known for increasing worm lifespan.
This validating evidence from the literature indicates that the model predictions are surprisingly accurate. The predicted pro-longevity genes CLEC-196, HIL-7, TTH-1, and F20C5.6 are candidates for further experimental exploration.
Major sperm proteins appear to be anti-longevity based on the experimental evidence. A mutation reducing sperm production leads to significantly increased lifespan [30]. Additionally, the expression of sperm-related genes-especially major sperm protein (MSP) genes-is decreased in adult daf-2 mutants, providing further support for an anti-longevity role of MSP genes [31].
RSP-39 and RPL-11.1 are 60S ribosomal proteins. RNAi knockdown of genes encoding ribosomal proteins consistently increases lifespan in C. elegans, both in the case of 40S and 60S ribosomal proteins [32]. This supports the predicted anti-longevity status.
NLP-27 (Neuropeptide-Like Protein) is the only other predicted anti-longevity gene in the top 10 list. Expression of nlp-27, along with other nlp genes, is increased in long-lived daf-2 mutants. Further, nlp-27 expression is reduced in a short-lived mir-71 deletion strain. This indirect evidence by association suggests a possible pro-longevity role of NLP-27-which would contradict the predicted anti-longevity-but direct over/under-expression of nlp-27 would be needed to establish its pro/anti-longevity status.
Predicted pro-longevity yeast genes. Table 1 lists the top 10 predicted pro-longevity yeast genes. Several of these predictions are borne out by direct experimental evidence via single-gene deletions-specifically, Marek & Korona [33] found that deletion of ACS1, ETR1, UBI4, and POR1 leads to decreased lifespan.
Marek & Korona did not find a significant proor anti-longevity effect for UBC5, HSP12, or SBA1, and they do not report results for the remainder of the top 10 genes. However, UBC5 is a strong pro-longevity candidate, since it is involved in cellular stress response and mediates selective degradation of short-lived and abnormal proteins [34]. HSP12 (heat shock protein) is required for the lifespan-extending effect of dietary restriction in yeast [35], validating the pro-longevity prediction. SBA1 is also a strong pro-longevity candidate, as a chaperone-binding protein that is involved in heat shock response and is required for telomere length maintenance [36,37]. PRE3 and PRE7 are part of the proteasome, and it is known that increased proteasome capacity extends lifespan [38], providing indirect validation of their predicted pro-longevity status. PDI1 is a downstream target of the unfolded protein response (UPR), which is well-known to be pro-longevity [39].
Predicted anti-longevity yeast genes. Table 1 lists the top 10 predicted anti-longevity yeast genes. As in worms, depletion of ribosomes increases lifespan [40], validating the predictions of the ribosome-biogenesis proteins RPS30B, TMA23, RPS29B, and RLP24 as anti-longevity. HOR7 is reported to influence lifespan, but the direction of the effect may be contextdependent: HOR7 deletion increases lifespan [15], whereas Schleit et al [41] find that HOR7 deletion decreases lifespan under dietary restricted conditions. For URA3, COX9, TOM7, MFA1, and TAR1, we do not find pre-existing corroboration of the predicted anti-longevity status in the literature. TOM7 deletion has been reported to decrease chronological lifespan [42], and it does not appear to have a strong effect on replicative lifespan [33]. TOM7 is part of the translocase of the outer mitochondrial membrane (TOM) complex, and the mitochondrial membrane is well-known to be important in yeast longevity [43]. Marek
Validation on a secondary dataset
To further evaluate the predictive accuracy of the trained pglm model, we compare the model predictions to actual lifespan measurements from a non-GenAge validation dataset. For this purpose, we use the McCormick et al [15] dataset of replicative lifespan for a comprehensive set of 4,698 single-gene deletions in yeast. Since the McCormick dataset contains lifespan measurements for deletions of many genes that do not appear in GenAge, in principle it should be well-suited as a secondary validation dataset. Using the pglm model trained on the full GenAge database for yeast with the GO+ARCHS4 feature set as predictors, we made predictions of the longevity effect of all 4,698 genes in the McCormick dataset.
First, as a sanity check, we observe that among genes in GenAge, the predicted probability of a gene being pro-longevity is clearly inversely related to the change in lifespan after deletion (Fig 4, left panel). This is not surprising since it simply means that the GenAge annotations are roughly consistent with the McCormick data, and the model was able to fit the GenAge-based training data. More interestingly, we see that the model is able to predict which genes have a larger or a smaller effect on lifespan (Fig 4, left panel). For instance, among pro-longevity genes, the genes with predicted probability near 1 do indeed tend to lead to a larger decrease in lifespan. Meanwhile, among anti-longevity genes, the genes with predicted probability near 0 do indeed tend to lead to a larger increase in lifespan. Since the training data contain no information about the magnitude of the effect on lifespan, this indicates that the model is not simply recapitulating the training data, but is indeed making generalizable predictions.
Next, we compare the model predictions to the lifespan data for genes outside the GenAge database. Fig 4 (right panel) shows the change in lifespan versus the predicted probability of a gene being pro-longevity, for genes in the McCormick dataset that are not in GenAge. A downward trend in this plot would indicate concordance between model predictions and the validation data. There is an extremely slight but not convincing downward trend; thus, while suggestive, this does not provide a compelling out-of-sample validation of the model predictions. Note that the pglm classifier trained on GenAge has a strong bias toward predicting genes to be anti-longevity; see Fig 4 (right panel) and S4 Fig. This bias is due to class imbalance in the training data, since the majority of genes annotated in GenAge are anti-longevity. This is common when the training data are imbalanced, and can easily be addressed by selecting the classification threshold to yield appropriately balanced predictions.
The lack of concordance between the out-of-sample model predictions and the McCormick lifespan data may be attributable to the fact that for many genes, the McCormick data are not in agreement with the GenAge annotations of pro/anti-longevity. Specifically, many putatively pro-longevity genes led to large increases in lifespan when deleted, and many putatively antilongevity genes led to large decreases in lifespan when deleted (Fig 4, left panel). It is not clear whether this discrepancy is primarily due to limitations of the GenAge database (e.g., bias and relatively small sample size) or limitations of the McCormick assay. Focusing on the latter possibility, recent studies have identified mechanisms by which disruption of a gene through knockout can activate compensatory mechanisms leading to a dramatically different phenotype than disruption of the same gene through knockdown, which reduces but does not eliminate expression [44]. If deletion of a single gene activates similar compensatory mechanisms in yeast, then this could explain the lack of concordance, since it would imply that the change in lifespan under a single-gene deletion is not necessarily related to that gene's pro/ anti-longevity status. A comprehensive assay of knockdowns (rather than deletions or knockouts) would shed light on this intriguing question. The discrepancy between GenAge and McCormick could also partially be due to the fact that GenAge includes results for both replicative and chronological lifespan. However, this does not fully explain the discrepancy since many of the most discordant genes were annotated as affecting replicative lifespan in GenAge.
Functional interpretation of model predictions
To interpret the biological basis for the model predictions in terms of functional categories, for each species we retrained the pglm model on the full GenAge dataset using only GO terms as features. We extracted the 20 most influential GO terms from the trained model by ranking the regression coefficients from largest to smallest in absolute value ( Table 2). Note that in this model, the coefficient is equal to the log-odds ratio (logOR) of a gene being pro-longevity when it is annotated to a GO term versus when it is not annotated to that GO term. If a GO term has a positive logOR value, then genes annotated with that GO term are more likely to be pro-longevity under the model. Conversely, a negative logOR indicates that genes annotated with that GO term are more likely to be anti-longevity.
Top GO terms for worm. The current literature supports a strong longevity effect for many of the top categories in Table 2. Translation inhibition is known to increase lifespan [32], so a large negative coefficient for the translation and ribosome GO terms makes sense. Protein homeostasis is known to be key to longevity [45], so it makes sense that the model has positive coefficients for protein transport, endoplasmic reticulum membrane, and endoplasmic reticulum. Ubiquitin-mediated proteolysis is known to be important for promoting longevity, implying that a positive coefficient for ubiquitin-dependent protein catabolic process makes sense. Heat shock response is known to extend lifespan, and indeed, the model has a positive coefficient for response to heat. Activation of the mitochondrial unfolded protein response is known to promote longevity [46], so a positive coefficient for protein import into mitochondrial matrix makes sense. Mitochondria are known to be important for longevity [47], so a large coefficient for mitochondria makes sense; further, inhibition of mitochondrial respiration is known to extend lifespan [48], so a negative sign for the coefficient could make sense. Similarly, the importance of DNA repair makes sense, and surprisingly, in some cases, DNA repair gene knockdown increases lifespan, possibly due to compensatory biological mechanisms [49]; thus, a negative coefficient is, in fact, consistent with the literature.
Top GO terms for yeast. For yeast, Table 2 shows the top longevity-related GO terms in the model. The importance of these terms is consistent with the current literature, but the appropriate sign of the coefficient is not always clear, since the genes annotated to each GO term may have contradictory pro/anti-longevity effects and further, there may be compensatory relationships between terms due to correlated predictors.
Replicative cell aging, apoptotic process, and cell cycle obviously make sense as related to yeast aging and longevity. Mitochondrial membrane maintenance is known to be important in yeast longevity [43], and other membranes (e.g., the vacuole membrane) may also be important [50]; thus, large coefficients for mitochondrion, integral component of mitochondrial outer membrane, mitochondrial intermembrane space, membrane, membrane fraction, and transmembrane transport are consistent with the literature. Depletion of ribosomes is known to increase lifespan [40], so a negative coefficient for chromatin silencing at rDNA is appropriate.
Telomeres are known to be important in yeast longevity [51,52], so a large coefficient for telomere maintenance makes sense. Longevity effects of cellular response to oxidative stress are corroborated in the literature [53]. Finally, a negative coefficient for zinc ion binding is consistent with experimental evidence that zinc limitation extends chronological lifespan [54].
Pathway enrichment analysis of model predictions
To further interpret the model predictions in terms of known biology, we performed pathway enrichment analysis. First, we took the list of non-GenAge genes that were predicted to be prolongevity and tested for enrichment of KEGG pathways using the Database for Annotation, Visualization and Integrated Discovery (DAVID) v6.8 [55,56]. Adjusting for multiple testing using the Benjamini-Hochberg correction, we found that the "Proteasome" pathway was significantly enriched (corrected p-value 0.0031). The KEGG pathway diagram in S5 Fig (used with permission from Kanehisa Laboratories [57]) indicates that several of the predicted pro-longevity genes are in the 20S proteasome core particle, particularly in β subunits. This is intriguing, since the proteasome is a protein complex that breaks down unneeded or damaged proteins by proteolysis, and the β subunits play a central role in this process [58]. Sustained proteasome activity appears to be associated with longevity based on studies of long-lived humans and rodents, and directly elevating proteasome activity increases longevity in yeast [38]. We performed the same enrichment analysis using the top predicted anti-longevity genes for yeast, and separately, the pro-and anti-longevity genes for worm. In each case, we capped the number of genes at 100. S6 Table shows the top KEGG pathway hit in each case. Notably, in both yeast and worm, the "Ribosome" pathway was highly significantly enriched with predicted anti-longevity genes (corrected p-values 7.1 × 10 −15 and 8.1 × 10 −27 , respectively). These results are consistent with known aging biology, and since these genes are not currently in GenAge, the model predictions may offer new avenues of research.
Limitations
A limitation of our models is that the pro/anti-longevity status of a gene is predicted based on how similar its GO terms and/or gene expression pattern are to genes with known pro-or anti-longevity status. This similarity does not necessarily imply that manipulation of these genes will have the predicted effect on lifespan, and further, the predictions are limited by the accuracy of the input data. This is illustrated by SIR2 and DNL4, the top two hits in S4 Table for yeast when using the GO-only model. Both SIR2 and DNL4 are annotated with the "replicative cell aging" GO term, which is strongly indicative of pro-longevity status in this model, as indicated by the odds ratio of 5.8 in Table 2. Experimental evidence is consistent with the SIR2 prediction, but not the DNL4 prediction [59]. This appears to be due to the interesting fact that although DNL4 is required for DNA repair by nonhomologous end joining (NHEJ), apparently NHEJ does not affect replicative aging in yeast [59]. Thus, in the case of DNL4, the discrepancy between prediction and experiment may be viewed as an inadequacy of this particular GO term annotation.
Another limitation is that although S. cerevisiae (yeast) can be haploid or diploid, our models are not ploidy-specific since much of the data we use (GenAge, GO terms, and gene expression) are not annotated in a way that indicates whether they pertain to haploid or diploid. Significant differences have been observed between haploid and diploid yeast aging [59,60], making it difficult to know whether results for one would extend to the other. That said, overall we would expect the set of genes that are strongly involved in longevity to be similar for haploid and diploid, although the magnitude (and possibly the direction) of the pro/anti-longevity effect may vary.
Similarly, our models do not distinguish between chronological lifespan and replicative lifespan in yeast. In future work, it would be interesting to analyze chronological lifespan separately from replicative lifespan since there may be major differences.
By a fortunate coincidence, the best performing algorithm, pglm (GLM-Net), enabled us to perform functional interpretation of the results by simply considering the largest regression coefficients. In future studies on alternative datasets, higher predictive performance might be obtained with other algorithms lacking easily understandable coefficients. Under that scenario, we would recommend researchers consider alternative feature importance metrics such as those provided by the caret R package [61].
Conclusions and future directions
We systematically compared the performance of popular machine learning algorithms in classifying genes as pro-or anti-longevity using the GenAge database and combinations of gene expression and gene ontology (GO) feature sets. We identified elastic net penalized logistic regression (pglm) as the most effective classifier and made predictions for unannotated genes. We offer our predictive probability scores as one possible tool to prioritize future experimental studies which can validate individual genes as pro-longevity mechanistically. Our approach of combining feature sets to improve predictive performance is generalizable in principle to a wider variety of model organisms as more annotations and datasets become available over time.
We encourage other computational researchers to use metrics such as area under receiveroperator curve (AUC) on held-out data from standard databases such as GenAge to assess classification performance and facilitate comparisons across studies. We suggest that future comprehensive longevity assays consider using knockdowns instead of deletions and knockouts, due to the existence of compensatory mechanisms that are known to mitigate the effects of knockouts [44]; this may improve the concordance between predictions and experimental evidence. Additionally, there appears to be a need for increased focus on pro-longevity genes as opposed to anti-longevity genes, since pro-longevity genes are much less common in the Gen-Age database.
In addition to genetic variation, environmental factors such as exposure to drugs or other chemical compounds are known to influence longevity [4,62,63]. Future studies may benefit from our computational framework in this context, for example, by using outcome variables from the DrugAge database [64] to train classifiers or regression models. However, a key challenge will be to identify suitable covariates analogous to gene expression or GO terms. One intriguing possibility would be to convert the molecular structure of each drug into a vector of continuous features [65].
Finally, it is clear that genes act in networks rather than individually-for instance, topdown analysis has identified the nutrient sensing pathway, the mitochondrial effector pathway, and the proteostasis pathway as collectively regulating single-cell longevity [66]. Thus, network-based approaches are likely to yield further insights into the molecular mechanisms of aging. In particular, while we have considered only single-gene manipulations, it would be valuable to be able to predict the effect of multiple simultaneous interventions. This is very challenging in general, but it might be possible to exploit special structure in the mechanisms of aging-for instance, recent papers have argued that aging may be governed by a single global state variable, based on the finding that many diverse interventions lead to a temporal scaling of survival curves in C. elegans and S. cerevisiae [67,68].
Acquisition and preprocessing of datasets
Binary pro/anti-longevity annotations were accessed from the GenAge model organisms database build 19 [6], available at http://genomics.senescence.info/genes. We used the subset of genes for yeast and worm, and we excluded ambiguous annotations (e.g., if GenAge lists two studies for a gene, one finding it to be pro-longevity and the other finding it to be anti-longevity). GO annotations for all genes were downloaded from the BioMart ENSEMBL database (release 93, July 2018) using the biomaRt package in Bioconductor (version 3.7). For both species, gene expression data in the form of RNA-Seq read counts were obtained from the ARCHS4 database version 1 [16], currently available at https://amp.pharm.mssm.edu/archs4/ archs4zoo.html. For yeast only, we acquired the Deleteome gene expression microarray dataset [17], currently available at http://deleteome.holstegelab.nl (no version available but last updated May 2014). For worm only, we obtained gene expression data from the single-cell RNA-Seq Worm Cell Atlas [18], currently available at http://atlas.gs.washington.edu/wormrna (no version available but last updated August 2017). We reduced the dimensionality of the Worm Cell Atlas data by summing the unique molecular identifier (UMI) counts across all cells within the same tissue, so that each feature is a "pseudobulk" tissue rather than a single cell.
Replicative lifespans (RLS) for 4,698 single-gene deletion yeast strains were obtained from McCormick et al [15] in June 2017. Perturbation genotypes with percent_change greater than 30 and set_lifespan_count less than or equal to 5 were excluded based on the authors' recommendations. We merged results for the same genotype across replicate experiments in the following way. The outcome for each genotype in a single replicate was quantified as the mean of RLS in the perturbation group minus the mean of RLS in the control group. To obtain a single value for the genotype across all replicates, we then computed a weighted average of the outcome values from each replicate, where the weights corresponded to the sample sizes in each group. This ensured that replicates with more observations contributed more to the final value. We refer to this as the McCormick dataset.
Data normalization and quality control
All gene expression measurements were normalized to account for sample-specific biases. Specifically, the Deleteome data were already normalized, the ARCHS4 read counts were converted to transcripts-per-million (TPM), and the Worm Cell Atlas UMIs were converted to counts-per-million (CPM). The normalized counts were then log transformed with a pseudocount of one. For Deleteome, genes that were variable in controls and non-responsive mutants were excluded, since these data were likely to contain mostly noise. For each species, we used the subset of genes with no missing values across all feature types (GO features and the two sources of gene expression features), resulting in 703 worm genes (246 pro-longevity, 457 antilongevity) and 368 yeast genes (46 pro-longevity, 322 anti-longevity). Features with no variation across the included genes were discarded. For yeast, the number of retained features was 3268, 700, and 1390 for ARCHS4, Deleteome, and GO terms, respectively. For worms, the number of features was 2935, 270, and 2051 for ARCHS4, Worm Cell Atlas, and GO terms, respectively. All gene expression features were centered and scaled to have mean zero and standard deviation 0.5 as suggested by [69], while binary features (GO) were not centered and scaled. The five sets of features considered for each species were (1) ARCHS4 alone, (2) GO alone, (3) GXP alone (Deleteome for yeast, Worm Cell Atlas for worm), (4) GO combined with ARCHS4, and (5) GO combined with GXP.
Comparison of predictive performance by algorithm and feature set
To assess predictive performance of different combinations of feature sets, each dataset (consisting of the binary GenAge outcome for a single species matched with one of the five feature sets) was split into 5 external cross-validation (CV) folds. Within each fold, machine learning classifiers were fit to the training data using the caret package version 6.0 [61] in the R programming environment (version 3.5). The same partitioning of the data was preserved across algorithm runs to ensure identical training and test conditions. The algorithms used were knearest neighbors (knn, R package kknn version 1.3.1), naive Bayes (nb, R package naivebayes forked at version 0.9.2 and modified for numerical stability, https://github.com/willtownes/ naivebayes), gradient boosted trees (xgb, R package xgboost version 0.8.0), support vector machine with radial basis function (svm, R package kernlab version 0.9), and logistic regression with elastic net penalty (pglm, R package glmnet version 2.0). Hyperparameters (S1 Table) were selected by grid search using repeated 10-fold internal CV with two repeats within each training fold using the Kappa criterion. Note that this means each algorithm could potentially use different hyperparameter values across the five external CV folds. For all algorithms except naive Bayes, the grid consisted of default caret values. For naive Bayes, the Laplace correction was set to zero, kernel smoothing was always used, and the adjustment to the probabilities was chosen between 0.5 and 1.0. Additionally, for naive Bayes only, many features with near-zero variance caused numerical instabilities and were excluded. Having chosen a final set of hyperparameters for each training fold, the predicted probabilities were computed for the held-out test data and the area under the receiver-operator curve (AUC) was computed to quantify prediction performance (discrimination). An AUC value of 1 indicates perfect classification performance, whereas an AUC of 0.5 signifies performance no better than random, or simply always predicting the majority class.
Model fitting for novel predictions and validation
For the results in sections 'Novel predictions of pro/anti-longevity genes' and 'Validation on a secondary dataset', the best-performing algorithm (pglm) was retrained on all of the GenAge data for each species with the combined GO plus ARCHS4 feature set. The hyperparameter grid was expanded to 21 alpha values (evenly spaced between zero and one, inclusive), and 97 automatically selected lambda values using five-fold CV. For worm, the optimal alpha was 0.05 (close to an L2 ridge penalty). For yeast, the optimal alpha was 0.5 (an even mix between ridge and the L1 lasso penalty). Using the optimal hyperparameters, predictive probabilities were computed for all genes.
Model fitting for functional interpretations
For the results in section 'Functional interpretation of model predictions', for each species the pglm algorithm was retrained on the full GenAge dataset using GO features only. This choice of feature set was used to enable interpretation of regression coefficients. Here, the hyperparameter grid was the same 21 alpha values and 97 automatically selected lambda values with fivefold CV. The optimal alpha values were 0.15 for worm and 0.10 for yeast (both closer to ridge than lasso). | 8,461.6 | 2020-02-02T00:00:00.000 | [
"Biology"
] |
Economic growth and the arts: A macroeconomic study
Abstract Arts proponents frequently argue that the arts have a positive impact on the economy, yet this assertion is not supported by satisfactory statistical testing. Using the U.S. Gross Domestic Product (GDP) and National Arts Index (NAI), this study seeks to verify the contention that arts activities enhance economic growth. The test results signify, at the national level, a positive correlation between arts activities and economic growth in the U.S. between 2002 and 2013. However, the results do not yield strong statistical evidence for a causal relationship between GDP and NAI during the same time period. These findings do not necessarily invalidate the economic impact argument, but they do align with a call for further inquiry into the economic impact of the arts as expressed by other scholars. This study includes an overview of the development of the arts’ economic impact argument as well as a discussion of ancillary research implications in the concluding section.
Introduction
Many believe that arts activities are directly influenced by the economy. Intuitively, many expect economic growth to boost an increase in the arts activities. For instance, the rapid increase in the Chinese GDP and the concurrent and unprecedented degree of growth in the Chinese arts market may be interpreted as signifying a positive causal link between GDP and arts activities. In many cases, it seems logical that the arts activities would benefit from high economic growth, just as other industries do.
ABOUT THE AUTHORS Rawon Lee, Ph.D. is a researcher in arts management and cultural policy. Recent works discuss management strategies for arts organizations.
KiHoon Hong, Ph.D. is an assistant professor of finance at Hongik University. Research areas include asset pricing, quantitative finance, risk management and blockchain technology.
WoongJo Chang, Ph.D. is an assistant professor in arts and cultural management at Hongik University. Recent works have examined entrepreneurship and sustainability in the arts.
PUBLIC INTEREST STATEMENT
Arts activities, such as going to symphony concerts and visiting arts museums, often entail economic activities such as paying for transportation and eating out. Supporters of the arts often persuade policymakers and businessmen to support the arts sector by arguing that subsidies granted to arts institutions contribute to boosting the economy at large. This study seeks to test the ground by examining the economic impact of arts activities at the macroeconomic level. The results are somewhat surprising yet inconclusive on the strength and accuracy of the economic impact argument for arts activities.
Meanwhile, there is an intriguing competing interpretation. A few studies (Myerscough, 1988;Whitt, 1987), which have articulated a positive causal link between arts activities and economic growth, have proposed that the economic growth can be attributed to the arts' ability to increase labor productivity by increasing the level of life satisfaction for arts participants.
Both perspectives have garnered scholarly support. Yet a review of the literature reveals no empirical study that has provided macroeconomic evidence to support either of the arguments. Surprisingly, current assumptions about the relationship between the arts and the economy await thorough empirical research and fair testing. Left unstudied, doubts about the economic impact of the arts (see Carstensen et al., 2000;Cohen, 2004;Sterngold, 2004a) may continue to prevail.
Given this background, this study tests the research hypothesis: "arts activities enhance economic growth." As far as is known, this is one of very few studies to investigate this proposition using macroeconomic data. It was only in 2013 that the U.S. Bureau of Economic Analysis (BEA) and the National Endowment for the Arts together developed The U.S. Arts andCultural Production Satellite Account: 1998-2013, a dataset-first of its kind in the United States-intended to track the U.S. creative sector's contribution to the U.S. GDP. In 2018, BEA announced that 'arts and cultural economic activity accounted for 4.2 percent of gross domestic product (GDP), or 763.6 USD billion, in 2015ʹ (Bureau of Economic Analysis, 2018, p. 1). Due to a lack of a properly specified econometric model of arts activities, this research does not test the hypothesis: 'economic growth enhances arts activities." It should be noted in advance that these test results are not a decisive measurement for the value of the arts in society; the value of the arts in its aggregate extends beyond its economic traits. Instead, this research provides an additional anchor to the study of the arts and the economy and how they impact one another.
The remainder of this paper is organized as follows: Section 2 presents the literature review; Section 3 presents the data and the proposed macroeconomic model; Section 4 provides the empirical results; and Section 5 concludes the paper.
The development of economic impact studies in the arts
Traditionally, researchers have seldom doubted or tested the validity of the assumption that economic growth leads to greater artistic and cultural proliferation. Instead, researchers have tended to measure the impact of economic crises or recessions on the arts. In the analyses of the 2008 economic crisis, for example, many studies have reported the adverse effects of the crisis on the arts, including an increased unemployment rate for artists (Marlowe, 2010), a decline in arts participation (Miringoff & Opdycke, 2010), reduced private giving for the arts (Courchesne et al., 2014;Helicon Collaborative, 2009), a decrease in cultural organizations' endowment assets (Courchesne et al., 2014), and measurable harm to the quality of cultural activities (Moldoveanu & Ioan-Franc, 2011). At the same time, some other studies have found mixed results concerning the impact of the crisis, while still concluding that the crisis debilitated more than strengthened the arts sector (Madden, 2009;Nicholls, 2011).
A significant impetus for the study of the relationship between the arts and the economy comes from arts stakeholders who advocate for continued financial support for the arts. As famously stated by Baumol and Bowen (1966), the arts-especially the performing arts-are believed to suffer an inevitable "cost disease" in the market economy. The arts and cultural sector rely heavily on public and philanthropic giving in order to sustain its operations.
In defense of public and private giving for the arts, arts advocates articulate a mix of justifications. For instance, McCarthy et al. (2004) have described the arts as delivering a set of "intrinsic" benefits (such as aesthetic values and positive feelings) and a set of "instrumental" benefits (namely cognitive, attitudinal and behavioral, health, social, and economic benefits) to both arts participants and the society at large. Additionally, scholars frequently strive to substantiate various benefits of the arts. In doing so, studies that are aimed at quantifying the impact of the arts on the economy-often referred to as economic impact studies-have risen as one of the most effective tools in constructing a compelling argument for arts giving over the years.
The first economic impact studies in the arts date back to the 1970s when the National Endowment for the Arts (NEA) and other arts-supporting organizations started conducting studies that highlight the arts' contribution to the economy. Since then, the economic impact studies have newly characterized the arts sector and arts organizations as an economy-generating industry as opposed to a burdensome luxury to the local economy. In the following decades, economic impact studies have been extended to study the arts' utility in urban development (Bianchini, 1993;Brooks & Kushner, 2001;Whitt, 1987) as well as in cultural tourism and the creative economy.
One of the most significant economic impact studies for the arts is the Arts and Economic Prosperity (AEP) study conducted by Americans for the Arts (AFTA) in 1994, 2002, 2007, 2012, and 2017. The AEP has been characterized as "the most comprehensive study of its kind" (Americans for the Arts, 2017, p. 1). The most recent AEP (Americans for the Arts, 2017) reported an array of tangible evidence for the economic value of the arts industry. For instance, according to the study, "the nonprofit arts industry generated 166.3 USD billion of economic activity in 2015-$63.8 billion in spending by arts and cultural organizations and an additional 102.5 USD billion in event-related expenditures by their audiences. This activity supported 4.5 million jobs and generated 27.5 USD billion in revenue to local, state, and federal governments" (Americans for the Arts, 2017, p. 1). The AEP's findings are actively utilized in the AFTA's advocacy endeavors, especially in its lobbying efforts.
Criticisms for the economic impact studies in the arts
Beginning in the 1980s, however, some researchers (Hunter, 1989;Krikelas, 1992;Mills, 1993;Toepler, 2001) have raised questions regarding the validity of the claims made by some of the economic impact studies. Issues have been raised regarding the adequacy of research methodology and, subsequently, these studies have been criticized as inadequate grounds for policymaking decisions. For instance, based on the study findings published in 2002, AEP stated that financial support for the arts sector is "a financially wise investment in state and local economies throughout the nation" (Americans for the Arts, 2002, p. 168). However, the AEP's claim was soon critiqued by Sterngold who has problematized the validity of AEP (Americans for the Arts, 2002), pointing out that "economic impact analyses that use only gross measures of impact, such as the AEP study, fail to provide any evidence to support their claims because the studies overlook the substitution effects of (nonprofit arts and cultural organizations)-related spending" (Sterngold, 2004b, p. 169). In support of his argument, Sterngold quoted other studies (Crompton et al., 2001;Tyrrell & Johnston, 2001) that have also raised issues with the way some of the economic impact studies quantify the economic impact of the arts. Although AEP author R. Cohen responded to Sterngold's argument (Cohen, 2004) and Sterngold responded in turn (Sterngold, 2004a), Cohen has not fully answered to the criticism nor has the criticism invalidated the significance of AEP and its findings. This study, in effect, responds to the need to further investigate the validity of the economic impact case for subsidizing the arts from the perspective of economic growth promotion as presented by the arts advocates.
Data
Data on population, real GDP per capita and investment spending as a fraction of GDP are from the Penn World Table, World Bank. All estimates reported below are based on GDP per capita. For consistency with most previous studies, analysis here is based on the Laspeyres index, base year international prices series on GDP per capita. This makes sure that the results are comparable to the existing line of literature. As discussed inconclusions are generally insensitive to the use of the chain index of income available in the Penn World Table and to the use of GDP per worker. In any regression starting and ending years t and T, the steady-state physical capital accumulation rate s is measured by the year t to year T average ratio of investment to GDP. The steady-state population growth rate n is taken to be the average rate of population growth between years t + 1 and T.
Following the notation of Clark (1997), the variable y denotes income (real GDP) per capita, n denotes exogenous population growth, g represents the exogenous rate of growth of laboraugmented technology, δ is the common rate of depreciation of physical and human capital, and s and h denote the rates of physical and human capital accumulation, respectively. Following Clark (1993), the sum of capital depreciation and technology growth δ +g is assumed to be constant at 0.05. This indicates that the technological progress is proportionate to the rate of capital depreciation. Steady-state human capital accumulation h is measured by the primary and secondary school enrollment rates at the start of the period (year t).
The National Arts Index (NAI) provides a measure for the arts activities in the United States. NAI is an annual report on the U.S. arts and cultural sector creative vitality and economic health. The 2016 NAI, which offers a 12-year span (2002-2013) Table 1 presents the descriptive statistics of Arts Index growth rate and real GDP growth rate.
Preliminary analysis
The Arts Index is designed to be mean reverting; therefore, it is not surprising to have zero expected growth rate. Thus, the volatility of the Arts Index growth rate is lower than that of real GDP growth rate. The Arts Index growth rate is less negatively skewed with lower kurtosis relative to real GDP growth rate. Table 2 presents the correlation between real GDP growth rate and Arts Index growth rate.
In Table 2, the statistical significance of the correlation estimate is computed in a standard way as t ¼ r ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi n À 2 1 À r 2 r where t is the t-statistic, r is the correlation estimate, and n is the number of observations. The result shown in Table 2 indicates there is no apparent statistically significant lead and lag relationship between GDP growth rate and art activity growth rate. However, the correlation indicates that there is a potential concurrent relationship. Investigation of the correlation between art activity growth rate and GDP growth rate implies that the two are related. However, the fact that there is no clear lead-lag relationship does not resolve the question of whether art activities cause economic growth or are only influenced by economic growth.
Macroeconomic model of GDP
In order to empirically investigate whether art activities can enhance economic growth, the model of Mankiw et al. (1992) is employed; it is one of the most straightforward macroeconomic models for investigating GDP growth. Although it is one of the oldest models of GDP growth, it is still one of the most popular models in macroeconomics (see Cuaresma et al., 2019;Hanuschek & Woessmann, 2020). As many subsequent researches emphasize, this simplicity is powerful. The implications from one of the most straightforward, but still very popular model could deliver powerful insights.
As presented in Mankiw et al. (1992), the Solow Growth Model expands the existing models to incorporate human capital in order to derive a very simple relationship between economic growth and initial income, population growth and the rates of physical and human capital investment. More specifically, the Solow model takes the rates of savings, population growth, and technological progress as exogenous. There are two inputs, capital and labor, and a Cobb-Douglas production function is assumed. As a result, they derive the following equation: The variable y denotes income (real GDP) per capita, n denotes exogenous population growth, g represents the exogenous rate of growth of labor-augmented technology, δ is the common rate of depreciation of physical and human capital, and s and h denote the rates of physical and human capital accumulation, respectively. As previously stated, g t þ δ t is assumed to be constant at 0.05. The model of Equation (1) is shown by Clark (1997) to be effective in explaining real GDP growth rate with the introduction of inflation's effects. Clark (1997) shows that estimates the relationship suffer two robustness problems which plague a variety of model specifications. This paper closely follows the model of Clark (1997) but incorporates a time series aspect, and hence expands the existing analysis. Incorporating time series component could allow us to understand whether the explanatory relationship persists over certain period of time.
Introducing the arts
Now the Arts Index growth rate is incorporated as an explanatory factor to the above model described in Equation (1) and converts the model to time series. The following is derived: This table reports correlation and its statistical significance between real GDP growth rate and the Arts Index growth rate. Arts Lead correlation is estimated as the correlation between Arts Index growth at time t-1 and the real GDP growth rate at time t and GDP Lead correlation is estimated as the correlation between Arts Index growth at time t and the real GDP growth rate at time t-1. The sample data ranges from 2001 to 2013.
Estimated result
With the data from 2001 to 2013, the model in Equation (2) is estimated. The result is presented in Table 3.
The data reveals that the Arts Index growth rate does not provide a statistically significant explanation for the GDP growth rate. As expected, all other macroeconomic variables have statistically significant explanatory power over GDP growth rate.
The empirical results stand in agreement with the concern that overemphasizing or exaggerating the arts' economic impact could potentially backfire on arts advocacy endeavors if not supported with thorough research and sound evidence. Arts advocacy endeavors may not be able to withstand inquisitions into the legitimacy of public subsidy for the arts without continued substantiation of the noneconomic (or extraeconomic) value of the arts.
Robustness test: Leading relationship
Thus, there is not enough empirical evidence to conclude that the concurrent Arts Index growth rate can explain the GDP growth rate. However, investigation into whether the previous period arts activities can explain the current period GDP growth rate is needed. If this is the case, it can be argued that art activities enhance economic growth. Therefore the following model is estimated: The estimated result is presented in Table 4. Thus, the lagged Arts Index growth rate does not have statistically significant explanatory power over the GDP growth rate. This assures that the change in arts activities does not have statistically significant explanatory power over GDP growth rate.
Conclusion
Using the U.S. GDP and NAI, this study tested the proposition that arts activities enhance economic growth. First, a positive correlation was found between GDP and NAI between 2002 and 2013 leading to the conclusion that arts activities and economic growth appear to be positively related at the national level. Test result interpretations indicate that the arts grow with the economy in the United States, suggesting that the arts are an integral part of U.S. society in which economic growth does not constrain artistic activities, nor do artistic activities hamper economic growth. Rather, the vitality of the arts sector seems to reflect the strength of the national economy and vice versa.
At the same time, the test results do not provide statistically significant support for the view that an increase in arts activities spurs economic growth. No lead-lag relationship between U.S. GDP and NAI between 2002 and 2013 has been confirmed by the test results either. Rather, they suggest that a causal relationship between arts activities and economic growth may not be as evident or present as believed, at least at the national level.
In light of the mixed study conclusions on the arts' impact on the economy as previously described in this research, several interpretations and implications may be proposed for the test results. Foremost, the test results prolong an unsettlement in the evaluation of the impact of the arts on the national economy. Hence, the test results support Sterngold's concern that overemphasizing or exaggerating the arts' economic impact could potentially backfire on arts advocacy endeavors if not supported with sound evidence (Sterngold, 2004b). At this time, given the sparse macroeconomic evidence available, it is suspected that arts advocates may not be able to effectively counter challenges to the legitimacy of public subsidy for the arts if the noneconomic benefits of the arts are underestimated and undervalued by arts administrators, legislators, and the public.
In the meantime, interpreting the test results as invalidating the arts' economic impact argument may prove to be a mistake for at least two reasons. First, given the confirmed positive correlation between GDP and NAI in this research, one or more intervening variables may further clarify or confirm a causal impact of arts activities on economic growth. Second, although the NAI has well served the purpose of testing the research hypothesis at the macroeconomic level, the fact that the NAI encompasses a wide array of arts activities in its formulation-including some fading industries-should be noted in the evaluation of the test results' generalizability. Different types of arts activities may have different sets of impact on the economy. Hence, it is proposed to use a test that utilizes subsets of the 81 NAI indicators. Such an approach would expose multiple layers of specificity that this macrolevel study has not revealed, showing different clusters of arts activities or arts industries as having varying impacts on economic growth.
As previously mentioned, the results of this research do not constitute a conclusive measurement for the value of the arts. From an economic standpoint, nevertheless, these findings call for a more critical approach to evaluating the ramifications of economic impact studies. The relationship between the arts and the economy has been dynamic and continues to evolve. Continued scholarly investigation is required for extending the current debate on the impact of the arts on the economy in a way that better assists effective and legitimate policymaking.
Funding
For KiHoon Hong, this research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education [NRF-2016R1D1A1B03930195]. | 4,831.4 | 2020-01-01T00:00:00.000 | [
"Economics"
] |
Porous hypercrosslinked polymer-TiO2-graphene composite photocatalysts for visible-light-driven CO2 conversion
Significant efforts have been devoted to develop efficient visible-light-driven photocatalysts for the conversion of CO2 to chemical fuels. The photocatalytic efficiency for this transformation largely depends on CO2 adsorption and diffusion. However, the CO2 adsorption on the surface of photocatalysts is generally low due to their low specific surface area and the lack of matched pores. Here we report a well-defined porous hypercrosslinked polymer-TiO2-graphene composite structure with relatively high surface area i.e., 988 m2 g−1 and CO2 uptake capacity i.e., 12.87 wt%. This composite shows high photocatalytic performance especially for CH4 production, i.e., 27.62 μmol g−1 h−1, under mild reaction conditions without the use of sacrificial reagents or precious metal co-catalysts. The enhanced CO2 reactivity can be ascribed to their improved CO2 adsorption and diffusion, visible-light absorption, and photo-generated charge separation efficiency. This strategy provides new insights into the combination of microporous organic polymers with photocatalysts for solar-to-fuel conversion.
titania as well as further references such as the composite without titania, titania supported on graphene oxide-HCP composite etc. The results are presented in a systematic and sound manner.
Concerning the impact, the contribution is clearly important but justification for a publication in Nature Communications is not sufficiently provided. In addition, the hypothesis of the contribution is based on CO2 adsorption and diffusion length as crucial parameters to enhance catalytic activity. Following this line of argument, the major aspects to critically consider are: -CO2 adsorption on or close to the active site is important, as surface coverage presents the concentration subsequently determining the reaction rate to be achieved (r=k*surface coverage of reagents, considering a Langmuir Hinshelwood type of activation). In line, a higher surface coverage of the substrates enables reaching a higher reaction rate, while the intrinsic catalytic activity of the active site remains unaltered. Following this argument, the authors have to carefully proof their hypothesis that CO2 adsorption within the material indeed causes enhanced coverage on or close to the active sites, increasing reaction rate. Kinetic experiments varying partial pressure, temperature etc. and providing assessment of the influence on the reaction rate are indispensable to justify the hypothesis. In addition, a careful representation of the literature state of the art including rates achieve in previous contributions normalized to the active sites content of the different catalysts are essential.
-The second argument relates to diffusion length as important element of catalyst design. The provided data do not allow any conclusion of the role of surface diffusion within the overall system. Following the argument of a diffusion governed process, the rate of surface diffusion should be somewhat rate determining. Consequently, kinetic analysis following e.g. the temperature dependence are needed to support such a hypothesis. Diffusion limitation should cause a limited apparent activation energy according to the reduced temperature dependence of various types of diffusion compared to chemical reactions.
-As a minor point, the experimental data are not provided with sufficient information to understand the used experimental setup, e.g. in the related figure captions. Where the reactions carried out in a flow reactor or a batch system? What was the temperature? Partial pressure of CO2 and H2O were constant (was there water in the system)?
-Concerning CO2 adsorption experiments, data in presence of water appear important and water vapor sorption experiments would be complementary.
HOMO level is found to be enough for water oxidation.
The quantitative measurement of O2 evolution was conducted using an optical fiber oxygen sensor. The O2 evolution rate over HCP-TiO2-FG under visible-light irradiation was determined to be 1.6 μmol h -1 , while the O2 evolution over other photocatalysts was too low to be detectable (Supplementary Fig. S13). The electrons from the water oxidation are slightly higher than the total consumed electrons for the reduced products including CH4 and CO. To the best of our knowledge, this is the first example achieving the quantitative detection of the oxygen production during photocatalytic CO2 conversion in such a gas-solid reaction system. Moreover, the isotopic labeled H2 18 O vapors was used to verify the origin of the detected O2. The formation of 18 O2 suggests that the evolved O2 gas is derived from the photocatalytic water oxidation (Supplementary Fig. S16). Finally, we corrected the energy levels and proposed a mechanism for the overall CO2 conversion process over the HCP-TiO2-FG photocatalyst as shown in Fig. 4f.
In the revised manuscript, we have added the following text on page 9 and 11: "As a result of the relatively high photocatalytic performance of porous HCP-TiO2-FG, the O2 evolution can be measured to provide the evidence of the oxidation cycle offering a better insight of the mechanism that is seldom discussed in the literature 43 .The O2 evolution rate over HCP-TiO2-FG under visible-light irradiation was determined to be 1.6 μmol h -1 , while the O2 evolution over other photocatalysts was too low to be detectable (Supplementary Fig. S13). The electrons from the water oxidation are slightly higher than the total consumed electrons for the reduced products including CH4 and CO." "In an isotopically labeled experiment, the 13 CH4 and 13 CO signals at m/z = 17 and m/z = 29 appeared after the photocatalytic reaction. The results confirmed that the CO and CH4 products are indeed originating from the photocatalytic reduction of CO2 gas ( Supplementary Fig. S15). The isotopic labeled H2 18 O vapors led to the formation of 18 O2 (Supplementary Fig. S16), suggesting that the evolved O2 gas was derived from the photocatalytic water oxidation." "The HCP-FG showed that its highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy levels were located at −5.34 eV and −3.00 eV (vs. vacuum level) as calculated by optical absorption (Fig. 4d) and cyclic voltammetry (CV) measurement (Supplementary Fig. S25), which are more negative than the valence band (VB) and conduction band (CB) levels of TiO2 respectively. To further confirm, ultraviolet photoelectron spectroscopy (UPS) technique was employed to measure the HOMO location, (Supplementary Fig. S26), which was found to be very close to that of CV measurement. Based on the position of HOMO and LUMO energy levels, a tentative mechanism for the overall CO2 conversion process over the HCP-TiO2-FG photocatalyst is proposed and is shown in Fig. 4f." "The excited HCP-FG was recovered to its neutral state by oxidizing the absorbed water molecules to produce oxygen gas." The work function (Φ) can be determined by the difference between the photon energy (21.2 eV) and the binding energy of the secondary cutoff edge. Φ = 21.20-16.86 = 4.34 eV The HOMO location is measured to be 1.10 eV below the Fermi level (E F ), corresponding to -5.44 eV vs vacuum level.
2. The reviewer wonders if the origin of CO production might be polymer degradation even though they showed good repeated property. The authors described that CO evolution increased in the absence of water, which implies that CO generation would be induced by partial oxidation of polymer or graphene. The reviewer recommends the authors to conduct isotope labeling experiment using carbon thirteen CO2 to show that the origin of their product would be CO2.
Response: This is a good suggestion. As suggested, we have conducted the isotope labeling experiment by using 13 CO2 as the substrate to detect the origin of the products.
The results indicate that the origin of CO and CH4 production is CO2 instead of polymer degradation (Supplementary Fig. S15).
We have now also included the corresponding description on page 9 in the manuscript.
"To verify the evolution of CO Fig. S15)." Figure S15. GC-MS spectra of 13 CH 4 (m/z=17) and 13 CO (m/z=29) after the photocatalytic reaction over . The isotopic labeled 13 CO 2 was used as the substrate in normal experiment condition.
3. The authors emphasized that their originality is the efficient adsorption of CO2, thus, they should show the reasonable experimental evidence like FT-IR to claim their efficient CO2 adsorption.
Response:
In most of the cases, FT-IR analysis was done to study the chemisorption of CO2 molecules on the catalysts. It is well established that the physical adsorption property of porous polymer materials can be evaluated by CO2 adsorption/desorption isotherms. The CO2 adsorption/desorption isotherms in Fig. 3e-f indicate the efficient adsorption of CO2 on HCP-TiO2-FG as 12.87 wt% at 1.00 bar and 273.15 K, which is more than 4-fold higher than that of TiO2 and TiO2-G.
Moreover, we have also conducted TGA-DSC analysis under CO2 atmosphere to get further evidence for CO2 adsorption. The results are shown in Supplementary Fig. S11.
The adsorption mode displays the pressure and temperature-dependent features with excellent recyclability for the repeated CO2 adsorption and desorption. Based on the literature reports (Energy Environ. Sci. 2014, 7, 3478;Chem. Soc. Rev. 2017, 46, 3322), the CO2 adsorption by such porous polymer materials is in consistent with the characteristics of physical adsorption, which cannot affect the signals in FT-IR spectra.
We have now also included corresponding description on page 6 in the manuscript: "It is well established that the CO2 uptake by porous polymer materials mainly results from its physical adsorption 34,35 . Such adsorption mode displays the pressure and temperature-dependent features with excellent recyclability for the repeated CO2 adsorption and desorption (Supplementary Fig. S11)." Figure S11. The temperature-dependent adsorption ability of porous HCP-TiO 2 -FG checked by TGA-DSC at CO 2 atmosphere.
Reviewer 2
This work by Wang et al. presents the fabrication of a porous hypercrosslinked polymer-TiO2-graphene (HCP-TiO2-FG) sandwiched structure for visible-light-driven CO2 conversion. The structure possesses relatively high surface area and CO2 uptake capacity, and shows relatively high photocatalytic performance for CO and CH4 production without the use of sacrificial reagents or precious metal co-catalysts. The authors argue that the superb catalytic activity is attributed to the improved CO2 adsorption and diffusion, visible-light absorption and photo-generated charge separation. Indeed, it is a topic of interest to the researchers in the related areas; however, the manuscript still cannot meet the level of Nature Communications. No deep understanding and important scientific issues have been given in this manuscript.
Several issues need to be clarified, and part of the conclusions cannot be supported by the current data.
Response: Thanks much for appreciating the quality of work presented in this manuscript. We believe that this work is novel and would have great impact in the field.
To date, there is no report on the combination of microporous organic polymers with photocatalytic materials for CO2 uptake and conversion. The photocatalytic performance is dramatically enhanced by the design and synthesis of porous HCP-TiO2-FG sandwiched photocatalysts. Based on the results obtained, we have presented the understanding of such superior structure from the aspects of improving CO2 adsorption and diffusion, visible-light absorption, and photogenerated charge separation efficiency. These factors are widely studied scientific issues in the related areas. In the revised version, we have conducted the kinetic experiments to provide further understanding. We also thank the reviewer's kind suggestions. We have addressed all the issues point-by-point in our response below.
Specific comments are listed below: 1. The authors have stated that this is the first example involving microporous organic polymers for CO2 conversion among numerous photocatalysts. This may overstate the significance of this work. As far as I know, conjugated microporous polymers have been used as materials for the capture and conversion of CO2 (Nature Communications, DOI: 10.1038/ncomms2960) and visible-light-driven conversion of CO2 (Green Chem., 2017, 19, 5777).
Response: While we appreciate the reviewer's comments, we want to emphasize that the present work is fundamentally different from those reports i.e., Nature Commun., 2013, DOI: 10.1038/ncomms2960 and Green Chem., 2017 The microporous polymers in the above-mentioned Nature Commun are developed as heterogeneous catalysts for the reaction of CO2 and propylene oxide for the formation of propylene carbonate. Indeed, there are many such reports on the use of microporous polymeric catalysts for chemical conversion of CO2 (Chem. Commun. 2015, 51, 11576;Adv. Mater. 2017, 29, 1700445;J. Mater. Chem. A 2018, 6, 374;et al). We also reported a metalporphyrin-based microporous polymer for catalyzing the reaction of CO2 with propylene oxide (J. Mater. Chem. A 2017, 5, 1509. Compared to the chemical conversion, the photocatalytic CO2 reduction is of great significance because it utilizes the abundant and sustainable solar energy to produce carbonaceous fuels.
Another report in the above-mentioned "Green Chem" journal is related to the photocatalytic conversion of CO2. However, the optimized pyrene-based polymer catalyst do not display porosity because it has extremely low surface area i.e., 23.9 m 2 g -1 . The photoreduction of CO2 depends on the chemical capture of CO2 molecules by a task-specific ionic liquid i.e., [P4444][p-2-O]. In addition, CO and H2 are detected as the main products from the photocatalytic system, whereas the desired CH4 production is absent. Thus the idea of using microporous organic polymers for CO2 uptake and photocatalytic conversion is missing in this work.
The previous studies were indeed focusing more on developing polymer materials for catalyzing CO2 conversion. These findings inspired us to incorporate the microporous organic polymers as CO2 capture materials into the photocatalytic system. As a result, we achieved high CO2 conversion efficiency with a rate of total consumed electron number (Re) as 264 μmol g -1 h -1 , including 83.7% selectivity for CH4 production and negligible side reaction of H2 production under visible-light irradiation.
To date, there is no report on the combination of microporous organic polymers with photocatalytic materials for CO2 uptake and conversion. We believe this strategy will be very helpful to overcome the constraint of deficient pore structure for semiconductor-based composites and to open a new pathway for the design and synthesis of well-defined porous materials with high CO2 uptake and photocatalytic conversion efficiency.
2. The authors have demonstrated that TiO2 crystals are supported on graphene sheets and encapsulated by ultrathin HCPs layer. As such, the TiO2 should be in the middle of the sandwiched structure. As stated in the manuscript, the photogenerated electrons migrate from HCP to TiO2 via their interfacial interaction. In this case, what is the role of the graphene? How can graphene improve the charge separation efficiency? The authors should clarify these issues in the manuscript.
Response:
The TiO2 crystals are located in the middle of the sandwiched structure because they are supported on graphene nanosheets and encapsulated by ultrathin HCPs layer ( Fig. 2 and Supplementary Fig. S1-4). It should be pointed out that the HCPs and graphene are not freestanding in the composite. Benefiting from the in-situ knitting strategy, ultrathin HCPs layers were integrated with the functionalized graphene nanosheets through the methylene linkers. The structures have been verified by XPS, FT-IR, and CP/MAS NMR characterizations (Fig. 3b-c and Supplementary Fig. S6-
S8).
As far as the role of the graphene is concerned, we have now added the EIS analysis of HCPs and HCPs-TiO2, which are compared with HCPs-FG and HCPs-TiO2-FG ( Supplementary Fig. S23). The covalent linking with graphene effectively improves the electronic conductivity of the HCPs and thus facilitates the electron transfer in the composite. The comparison of photocatalytic performance between HCP-TiO2 and HCP-TiO2-FG photocatalysts is also shown in Supplementary Fig. S24. The less efficient CH4 production over HCP-TiO2 photocatalyst can also reflect the influence of graphene on improving the charge separation efficiency.
The corresponding description has been revised on page 10 and 11 in the manuscript as: "The lower Ret of TiO2-FG than that of TiO2 indicates that FG modification favors the electronic conductivity due to its high electron mobility. Moreover, the covalent linking with graphene effectively improves the electronic conductivity of the HCPs and thus facilitates the electron transfer in the composite. The less efficient CH4 production over HCP-TiO2 photocatalyst can also reflect the influence of graphene on improving the charge separation efficiency (Supplementary Fig. S24). As a result, the porous sandwich structure possesses the improved efficiency in separating the photogenerated charge carriers." 3. In "Characterization of the resulting materials" part, the authors have stated that the percentage of the exposed {001} facets in the TiO2 crystal is calculated to be approximately 30%. What is the relationship between the {001} facets and the photocatalytic performance for CO2 conversion? If the {001} facets are more reactive, would it be better to use TiO2 nanosheets with dominant (001) facets?
Response: The exposed crystal facets have great impact on the photocatalytic performance of TiO2 crystals. In the studies of crystal facet engineering of anatase TiO2, both theoretical and experimental evidence demonstrates that the {001} facets are much more reactive but less thermodynamically stable than {101} facets due to higher average surface energy of the {001} facets than that of the {101} facets. As reported, the products with large percentage of {001} facets usually have a large size of micrometers or hundreds of nanometers and low surface area (Nature 2008, 453, 638;J. Am. Chem. Soc. 2009, 131, 4078;J. Am. Chem. Soc. 2009, 131, 3152;Chem. Commun. 2009, 29, 4381). When decreasing the particle size, the specific surface area increased, whereas the high-energy {001} facets tend to transform to the more thermodynamically stable {101} facets to reduce the high surface energy. For example, the TiO2 crystals with size of ~20 nm only exposed 9.6% {001} facets, but the photoactivity could be comparable to that of micro-sized TiO2 with dominant {001} facets (Nano Lett. 2009, 9, 2455. The TiO2 crystals with size of 30-85 nm only exposed 18% {001} facets, but they showed an increase in the specific surface area as 21 m 2 g -1 , and exhibited 5.6 times stronger photoactivity than microcrystals with 72% {001} facets (Chem. Commun. 2010, 46, 755).
Thus there should be a balance between the particle size and percentage of exposed {001} facets. The study on photocatalytic CO2 conversion indicated that the TiO2 crystal with 60% {001} facets (60 nm) showed 15% and 90% higher CO production than that with 92% {001} facets (150 nm) and 95% {101} facets (20 nm), respectively (ACS Catal. 2016, 6, 1097. Yu et al. systematically studied the influence of factors on the photocatalytic CO2 conversion including percentage of {001} facets, size, and surface area (J. Am. Chem. Soc. 2014, 136, 8839). The table below shows that the highest CH4 production was achieved by the TiO2 crystals with 58% {001} facets, size of 60 nm, and surface area of 45 m 2 g -1 (Table R1). 4. In thermogravimetric analysis (TGA, Figure S9), the authors have stated that the HCP-TiO2-FG composite structure exhibits excellent thermal stability compared to TiO2-G with resistance of degradation up to 400 °C. However, according to Figure S9, the thermal stability of TiO2-G is even better than HCP-TiO2-FG with resistance of degradation up to 400 °C.
Response: Sorry for this mistake. We have revised the sentence on page 6 as follows, "the HCP-TiO2-FG composite structure exhibited the excellent thermal stability comparable to TiO2-G with resistance to degradation up to 400 °C".
5.
For the photocatalytic test, the authors should provide the details for the optical density of light source and the illuminated area.
Response:
The details for the photocatalytic test are as follows: Under visible-light (λ≥420 nm) irradiation, the optical density of 300 W Xe lamp was measured to be 433 mW cm -2 and the illuminated area of photocatalyst is about 3.14 cm 2 .
In the revised manuscript, the following information is added, The optical density was measured to be 433 mW cm -2 and the illuminated area of photocatalyst was about 3.14 cm 2 ." In addition, to verify the origins of produced CO and CH4, the isotopic 13 CO2 must be used as a reactant to trace the carbon sources in the photocatalytic reaction.
Response: As suggested, to verify the origin of the products, we have conducted the isotopic labeling experiment using 13 CO2 as a reactant to trace the carbon sources in the photocatalytic reaction. The results are shown in Supplementary Fig. S15.
We have also included corresponding description on page 9 in the manuscript as follows: Fig. S15)." Figure S15. GC-MS spectra of 13 CH 4 (m/z=17) and 13 CO (m/z=29) after the photocatalytic reaction over HCP-TiO 2 -FG under visible-light irradiation (λ≥420 nm). The isotopic labeled 13 CO 2 was used as the substrate in normal experiment condition.
6. According to Figure 4a and b, the HCP-FG material also exhibits a photocatalytic activity for CO and CH4 production. The authors have stated that the catalytic sites are located on TiO2. In this case, it remains elusive whether the catalytic sites are located on TiO2 or HCP-FG. The authors should clarify this point.
Response:
Yes, the HCP-FG material also exhibits a photocatalytic activity for CO and CH4 production. The porous property and photocatalytic performance of samples are shown in Fig. 3d-f, Fig. 4a-c, Fig. S10, Fig. S12 size distribution that calculated using DFT methods (slit pore models, differential pore volumes).
Time-dependent production of CH 4 (d) and CO (e) in photocatalytic CO 2 reduction with different catalysts under visible-light (λ≥420 nm). (f) Average efficiency of photocatalytic CO 2 conversion with different catalysts during 5 h of visible-light (λ≥420 nm) irradiation. 7. In Figure 8. According to the time-dependent production of CH4 and CO as shown in Figure S13, it remains unclear why the production of CH4 increases linearly while the production of CO has a stagnation effect.
Response: Yes, the CH4 production increased linearly with irradiation time, whereas the CO production was fast at initial irradiation time and then showed a sluggish increase during the photocatalytic reaction ( Fig. 4a-b and Fig. S19). In fact, the stagnation effect in CO production has also observed in photocatalytic CO2 reduction by many researchers (J. Am. Chem. Soc. 2018, 140, 38;J. Am. Chem. Soc. 2017, 139, 7217;J. Am. Chem. Soc. 2017, 139, 6538;Adv. Mater. 2016, 28, 6485;ACS Nano, 2015, 9, 2111. For example, Luo's group studied the mechanism of photoreduction of CO2 to CH4 on TiO2 surface by theoretical calculations. They proposed that CO was the initial product of CO2 photoreduction that could be further photo-reduced to CH3OH or CH4 (ACS Catal. 2016, 6, 2018. That is possibly why the CO production rate is fast at initial irradiation time and then shows a sluggish increase during the photocatalytic reaction. In contrast, the CH4 as the final product showed a steady increase. 9. In the electrochemical impedance spectra (EIS, Figure S15), HCP-FG has a much larger semi-circle diameter than HCP-TiO2-FG. Why the addition of TiO2 can dramatically reduce the electron-transfer resistance?
Response: In the EIS analysis ( Supplementary Fig. S23), the smaller arc in HCP-TiO2-FG sandwich structure than HCP-FG suggests that the formation of sandwich structure improves the electronic conductivity. According to the gas adsorptiondesorption analysis, it was found that the surface area and CO2 uptake of HCP-TiO2-FG were higher than those of HCP-FG (Supplementary Tab. S2). Thus we can infer that the TiO2 intercalation somewhat restricted the aggregation of HCPs layers on graphene nanosheets resulting in the reduced electron-transfer resistance.
In abstract, "…and highlights the importance of MOPs in combination with
photocatalysts for solar energy conversion.", there is no definition for the "MOPs" in the manuscript.
Response:
We are sorry for missing the definition of the "MOPs". In the revised manuscript, we have replaced it by "microporous organic polymers".
Reviewer 3:
The authors report on a novel catalyst for photocatalytic CO2 activation using visible light enabling unprecedented activity and CH4 selectivity. This high performance is achieved by tailoring the CO2 adsorption of the material together with short diffusion length to the active sites.
To achieve these features, the authors prepare a composite material composed of TiO2 anatase crystals with exposed {001} facets as active sites grown on graphene oxide.
The latter was functionalized by PhPh3 serving as anchoring groups enabling coating of a thin layer of hypercrosslinked polymer (HCP).
The material is comprehensively characterized. Its catalytic activity is reported compared to pure titania as well as further references such as the composite without titania, titania supported on graphene oxide-HCP composite etc. The results are presented in a systematic and sound manner.
Concerning the impact, the contribution is clearly important but justification for a publication in Nature Communications is not sufficiently provided. In addition, the hypothesis of the contribution is based on CO2 adsorption and diffusion length as crucial parameters to enhance catalytic activity.
Response: First, we would like to thank the reviewer to realize and appreciate the importance of work reported in this manuscript. We also thank the reviewer's overall comments and kind suggestions that helped us to improve the manuscript significantly.
We have now addressed all the reviewer's query point-wise in our response below.
Following this line of argument, the major aspects to critically consider are: -CO2 adsorption on or close to the active site is important, as surface coverage presents the concentration subsequently determining the reaction rate to be achieved (r=k*surface coverage of reagents, considering a Langmuir Hinshelwood type of activation). In line, a higher surface coverage of the substrates enables reaching a higher reaction rate, while the intrinsic catalytic activity of the active site remains unaltered.
Following this argument, the authors have to carefully proof their hypothesis that CO2 adsorption within the material indeed causes enhanced coverage on or close to the active sites, increasing reaction rate. Kinetic experiments varying partial pressure, temperature etc. and providing assessment of the influence on the reaction rate are indispensable to justify the hypothesis. In addition, a careful representation of the literature state of the art including rates achieve in previous contributions normalized to the active sites content of the different catalysts are essential.
Response: This suggestion inspired us to investigate the kinetic characteristics of the photocatalytic CO2 conversion which has never been discussed in the related literatures to the best of our knowledge. Generally, the reaction kinetics in a gas-solid system is studied by varying the partial pressure and temperature.
The photocatalytic reactions were carried out in a batch system under standard atmospheric pressure. Since the pressure in the photocatalytic reactor was settled as standard atmospheric pressure, we conducted the kinetic experiments by varying the partial pressure of CO2. The HCP-TiO2-FG photocatalyst exhibits a high CO2/N2 selectivity ratio of 25.8 calculated by the initial slopes of adsorption isotherms shown in Supplementary Fig. S20 (Adv. Mater. 2012, 24, 5703). The partial pressure of CO2 can be adjusted from 2.5% to 100% by varying the volume ratio of CO2 to N2. Since the kinetic model and reaction mechanism of photocatalytic CO2 conversion are ambiguous so far, the quantitative relationship between CO2 coverage and CH4 evolution rate is still unclear. Interestingly, it is observed that they show a similar trend of increase with CO2 proportion, e.g. both showed a dramatic increase at lower partial pressure and then displayed a sluggish increase at higher CO2 concentration ( Supplementary Fig. S21).
As far as temperature-dependent kinetics is concerned, the results and related discussion given below in our reponse would be helpful to address this comment.
In addition, the literature state of the art including rates normalized to the active sites content of the different catalysts are reviewed in the revised manuscript. Based on the discussions, we can deduce that the more efficient CH4 production over HCP-TiO2-FG should not result from the difference in the number of catalytic sites but mostly come from the higher surface coverage of CO2 on the active sites. Thus we can furthermore demonstrate the superiority of such porous sandwich structure towards the visible-lightdriven photocatalytic CO2 conversion.
On page 10, we have added the following content: The second argument relates to diffusion length as important element of catalyst design.
The provided data do not allow any conclusion of the role of surface diffusion within the overall system. Following the argument of a diffusion governed process, the rate of surface diffusion should be somewhat rate determining. Consequently, kinetic analysis following e.g. the temperature dependence are needed to support such a hypothesis.
Diffusion limitation should cause a limited apparent activation energy according to the reduced temperature dependence of various types of diffusion compared to chemical reactions.
Response: As suggested, we have conducted the kinetic experiments by varying the temperature on the photocatalyst surface. The temperature has a complicated influence on the rate of photocatalytic conversion from the aspects of adsorption, diffusion and photocatalytic processes.
The results are shown in Fig. 3e-f and Fig. R2-3. By elevating the temperature, the surface coverage of CO2 molecule on the catalyst surface was decreased due to the exothermic effect of adsorption process ( Fig. 3e-f), while the diffusion rate was increased as a result of the increased thermal motion of CO2 molecules (Fig. R2). For the photocatalytic process, it is well-known that the Gibbs free energy increases in the photocatalytic conversion of CO2 to CO and CH4. The increase of chemical potential originates from the energy of photons rather than heat, so the change in temperature by dozens of degrees would not cause a measurable difference in the photocatalytic reaction. That is why the activation energy is seldom discussed in the photocatalytic reaction in literatures. From our experience, the photocatalytic CO2 conversion efficiency over pure TiO2 photocatalyst under UV-light is indeed independent of temperature from 291 K to 353 K. Interestingly, we observed an obvious increase in CH4 evolution rate over porous HCP-TiO2-FG photocatalyst with temperature ( Fig. R3).
Now we can conclude as follows: by increasing the temperature, the surface coverage of CO2 molecule declined, the diffusion rate speeded up, the photocatalytic reaction rate kept constant, and the overall reaction rate for CO2 conversion was increased.
Based on Arrhenius plot, the adsorption activation energy for CO2 adsorption is calculated to be 5.20 kJ mol -1 (Fig. R3a) using a microporous diffusion model (Ind.
Since the CH4 production increases linearly and possesses dominant electron consumption selectivity as 83.7%, we can adopt the pseudo-zero order model to estimate the rate constant for the overall reaction, obtaining apparent activation energy as 9.34 kJ mol -1 (Fig. R3b). By noting the temperature-dependent characteristics with activation energy values, we can conclude that the rate of surface diffusion is somewhat rate determining to the photocatalytic CO2 conversion.
In the present study, we aim to provide new insights into the design and synthesis of well-defined porous photocatalysts for CO2 uptake and conversion, and present an important first example towards solar-to-carbonaceous fuels conversion employing microporous organic polymers in combination with photocatalytic materials. The kinetic analysis is indeed very important to the study and applications of photocatalytic CO2 conversion but still there are many challenges that need to be addressed to unveiling the fundamental understanding of each reaction step. Therefore, we now intend to adopt the simple photocatalytic system such as pure TiO2 photocatalyst to probe the kinetics model and reaction mechanism of CO2 conversion, and then extend to complicated models involving adsorption, diffusion and photocatalytic processes. On page 9, we have added the following content: "Although the porous HCP-TiO2-FG also exhibits a high adsorption capacity towards water vapors, about 30 wt% at 90% humidity (Supplementary Fig. S17), the existence of water vapors brings a slight increase in CO2 uptake (Supplementary Fig. S18), presumably due to their affinity with the water molecules." Figure S17. The water adsorption of HCP-TiO 2 -FG at different humidity. Figure S18. CO 2 adsorption experiments, data in presence of water. q e is the equilibrium adsorption capacity at pure CO 2 atmosphere with 1 bar. q/q e represents fractional uptake at pure CO 2 atmosphere and mix atmosphere of 99% CO 2 +1% water vapors with 1 bar.
Reviewers' comments:
Reviewer #1 (Remarks to the Author): The authors reasonably answered to my comments and properly revised the paper. If the other reviewers also agree to accept, the revised version is publishable in Nature Communications.
Reviewer #2 (Remarks to the Author): Comments: I am pleased to see that the authors have made a big effort to improve the quality of this manuscript by performing new experiments, adding new discussion and completing a number of changes. Indeed, some comments have been partially addressed. However, the evidences are still insufficient to support their key conclusions. Although it is a topic of general interest, the current revised manuscript still cannot meet the level for publication in Nature Commun.
Specific comments are listed below: 1. In the isotopically labeled experiment, why the 13CH4 and 13CO signals are only at m/z = 17 and m/z = 29, respectively? Why there are no fragment signals at m/z = 13 and m/z = 16 for 13CH4 and 13CO?
2. As the authors stated that the catalytic sites are located on TiO2, the functions of the formed HCP-TiO2-FG sandwich structure remain not clear. In the sandwich structure, what are the TiO2 crystals directly contacting with (the porous hypercrosslinked polymer (HCP) or graphene)? If the TiO2 crystals are directly contacting with the HCP, the photogenerated electrons will migrate from HCP to TiO2 via their interfacial interaction. In this case, how can graphene improve the charge separation efficiency? If the TiO2 crystals are directly contacting with the graphene, the function of porous HCPs layers in enriching the adsorptive sites to achieve the high CO2 uptake may not work.
3. In the CV measurement for calculating the HOMO and LUMO energy levels of HCP-TiO2-FG catalyst in CH2Cl2, the reference electrode Ag/AgCl is not correct. The reference electrode Ag/AgCl is commonly suitable in aqueous solution. In organic solvent, the reference electrode should be Ag/Ag+ using the Fc/Fc+ couple as an internal standard.
4. The authors demonstrated that ultrathin HCPs layers were integrated with the functionalized graphene nanosheets through the methylene linkers. However, there is no direct evidence to conclude that HCPs layers were integrated with the graphene nanosheets through the methylene linkers. The current data can only support that there exists the methylene.
Reviewer #3 (Remarks to the Author): The authors were asked to provide further evidence for the governing nature of their two main Arguments, namely the superior CO2 adsorption as pre-requisite of high substrate concentration close to or on the active site and their hypothesis on the shortend diffusion lengths.
Indeed, a suitable kinetic analysis has been carried out illustrating that the investigated photocatalytic CO2 reduction is not under intrinsic kinetic control of the catalyst but the observed rates of CO and CH4 formation are rather determined by some transport effects.
The observed limited dependence of rate on temperature may hind towards diffusion control. I fully agree that kinetic analyses is a yet under-represented aspect in photo-catalysis. Though, the little rate dependence on temperature appears to point towards film diffusion effects. Hast the stirring speed or the main particle size been varied?
It remains unclear for me why the authors conclude on a reduced Diffusion length for the Optimum System, although they do not know which Diffusion is rate limiting: CO2 from bulk to the film, through the fild, in/on the porous material or Charge charrier diffusion?
The authors made an effort to identify the corresponding oxidation Reaction which has to balance the observed reduction reactions. Oxygen has been proven but quantitative Analysis is not yet available.
What about oxidation of the formed products, e.g. CO and CH4 to CO2 as reverse reactions of the attempted CO2 reduction. I suggest reference Experiments with these Substrates.
Overall, the contribution may become suitable for Nature Communications after providing further evidence and comments to the points made before.
Response to Reviewers' Comments
Many thanks for forwarding us the reviewers' comments that have helped us a lot to significantly improve the manuscript. Below are our responses (in BLUE colour) to the editor's queries. In the revised manuscript, more explanations on the HCP-TiO 2 -FG structure are presented in the response to Comment 4#. The diagram in Figure 1 has been updated to show the connections between HCPs and functionalized graphene. We are hoping that the structure is now much clear and clearly understandable. According to the suggestion, the CV measurement using Ag/Ag + as reference electrode was also performed to ensure the identical electrolyte in the system. The CV curves were updated in Figure the peak of C at 137 ppm is obviously enhanced, which indicates that the benzene ring in TiO 2 -FG has electrophilic substitution reaction with dichloromethane (DCM). It is noteworthy that the peaks belong to methylene at 37-39 ppm, which were commonly seen in HCPs materials and disappeared in Fig. R1a (Macromolecules 2011, 44, 2410; Sci. Adv. 2017, 3, e1602610). Instead, a new peak at 62.5 ppm was shown in Fig. R1b, which was corresponding to the methylene C peak of benzyl alcohol group (-CH 2 -OH). This indicates that the phenyl groups of TiO 2 -FG change into benzyl chloride group (-C 6 H 4 -CH 2 -Cl) in the reaction process firstly (Fig. R2a). However, due to the barrier effect of TiO 2 nanoparticles on graphene sheets, benzyl chloride groups can only exist in the form of original states instead of crosslinking with other benzene rings. With the quenching of dilute hydrochloric acid, the active benzyl chloride groups react with water and formed the benzyl alcohol groups (-C 6 H 4 -CH 2 -OH) (Fig. R2b). The model experiment indicates that the phenyl groups on TiO 2 -FG can react electrophilically with DCM to form benzyl chloride groups (-C 6 H 4 -CH 2 -Cl), which cannot undergo the further crosslinking reaction due to the blocking effect of TiO 2 nanoparticles. Meanwhile, the specific surface area of HO-CH 2 -TiO 2 -FG (128 m 2 g -1 ) obtained from the model experiment did not change compared with TiO 2 -FG, which also prove the above-mentioned conclusion.
Figure R2
Schematic diagram of reaction process in model experiment.
As co-monomer of synthesis for HCP-TiO 2 -FG, syn-PhPh 3 can be self-crosslinked to obtain SHCP-3a with a high specific surface area of 2525 m 2 g -1 by solvent knitting method (Sci. Adv. 2017, 3, e1602610). If TiO 2 -FG and SCHP-3a were mixed simply according to same mass ratio of co-monomers, the specific surface area and CO 2 uptake amount of the mixtures were lower than these of HCP-TiO 2 -FG, which suggest two monomers form a homogenous "sandwich" structure (Tab. R1).
Meanwhile, no freestanding SHCP-3a blocks were observed in SEM, TEM and scanning transmission electron microscopy (STEM) images (Fig. 2c-f and Supplementary Fig. S1d). This is because benzyl chloride group (-C 6 H 4 -CH 2 -Cl) formed has high reactivity for TiO 2 -FG and was linked to co-monomer syn-PhPh 3 , and the "sandwich" structure was formed in which the HCPs porous organic layers and TiO 2 -FG were linked by methylene. a Mass ratio of co-monomers for syn-PhPh 3 and TiO 2 -FG. b the sum of surface area for SHCP-3a and HCPs-TiO 2 -FG-X with mass ratio of co-monomers. c Surface area calculated from nitrogen adsorption at 77.3 K using Langmuir equation. d the sum of CO 2 uptake for SHCP-3a and HCPs-TiO 2 -FG-X with mass ratio of monomers at 1.00 bar and 273.15 K. e CO 2 uptake determined volumetrically using a Micromeritics ASAP 2020 M analyzer at 1.00 bar and 273.15 K.
Reviewer 3:
The authors were asked to provide further evidence for the governing nature of their two main Arguments, namely the superior CO 2 adsorption as pre-requisite of high substrate concentration close to or on the active site and their hypothesis on the shortend diffusion lengths. Indeed, a suitable kinetic analysis has been carried out illustrating that the investigated photocatalytic CO 2 reduction is not under intrinsic kinetic control of the catalyst but the observed rates of CO and CH 4 formation are rather determined by some transport effects. The observed limited dependence of rate on temperature may hind towards diffusion control. I fully agree that kinetic analyses is a yet under-represented aspect in photo-catalysis. Though, the little rate dependence on temperature appears to point towards film diffusion effects. Hast the stirring speed or the main particle size been varied? It remains unclear for me why the authors conclude on a reduced Diffusion length for the Optimum System, although they do not know which Diffusion is rate limiting: CO 2 from bulk to the film, through the fild, in/on the porous material or Charge charrier diffusion?
Response: Many thanks for appreciating our efforts on the kinetic analysis presented in the previous revision. The photocatalytic reactions were carried out in a gas-solid batch system without stirring the gas mixture. According to the suggestion, we studied the diffusion process by varying the stirring speed from zero to maximum. As shown in Supplementary Fig. S33, the increase in stirring speed greatly facilitates the photocatalytic conversion of CO 2 to CH 4 product, indicating that the diffusion plays a significant role in such a gas-solid reaction system. The related results and discussions have been added as a separate section "kinetic analysis" in the revised manuscript.
The particle size is another factor affecting the diffusion process, especially for internal diffusion. We would like to mention that the HCP-TiO 2 -FG composite produced through this strategy possesses the specific particle size. In the experience of optimizing synthesis conditions, TiO 2 crystals with larger or smaller size are inclined to form agglomerates, which cannot uniformly decorate on graphene or be fully wrapped by ultrathin HCPs layers. In the current system, we cannot achieve the varied particle size while keeping the designed structure with similar surface area, CO 2 uptake capacity and the number of active sites.
In order to reduce the diffusion length, we tried to construct the HCP-TiO 2 -FG sandwich structure with ultrathin HCP layers. The reduced diffusion length should be beneficial for the diffusion of CO 2 and photo-generated charges to the catalytically active sites, both of which may contribute to the improved CO 2 conversion efficiency.
Based on the gas diffusivity measurement, the diffusion coefficient of CO 2 in the HCP-TiO 2 -FG sandwich structure is calculated to be 1.8×10 -11 cm 2 s -1 at room temperature (Supplementary Fig. S32). Typical polymers for photoconversion application, the exciton diffusion and charge transfer dynamics of poly(3-hexyl thiophene) (P3HT) and phenyl-C61-buryric acid methyl ester (PCBM) have been studied, giving the diffusion coefficient of 1.8×10 -3 and 2.7×10 -4 cm 2 s -1 , respectively (Adv. Mater. 2008, 20, 3516; Nanoscale 2011, 3, 2280). The diffusion of charge carrier is much faster than that of the adsorbed gas by several orders of magnitude, implying that the gas diffusion should have more crucial influence at the rate limiting rather than the charge carriers.
In the present study, we aim to provide new insights into the design and synthesis of well-defined porous photocatalysts for CO 2 uptake and conversion. The designed sandwiched structure is somewhat complicated and makes it impossible to establish individual kinetic models. Although the kinetic mechanism cannot be clearly clarified in the current study, we indeed have made much progress on the kinetic analysis of photocatalytic CO 2 conversion that is seldom discussed in the literature. Inspired by the reviewers' suggestions, we have realized that the kinetic analysis is indeed very important for photocatalytic CO 2 conversion and there are yet many challenges that need to be addressed. In future study, we will use the simple photocatalytic system such as pure TiO 2 photocatalyst to probe the kinetics model and reaction mechanism of CO 2 conversion, and then extend to the complicated models involving adsorption, diffusion and photocatalytic processes.
On pages 12-13, all results and discussions on kinetic analysis are included and displayed as a separate section "kinetic analysis" in the revised manuscript.
"Kinetic analysis. The kinetics experiments were carried out to understand the contribution of CO 2 adsorption and diffusion to the enhancement of photocatalytic efficiency. The relationship between the CO 2 adsorption and CH 4 production can be explored by varying the surface coverage of CO 2 on the active sites. The partial pressure of CO 2 is adjusted in CO 2 /N 2 mixture because of a high CO 2 /N 2 selectivity ratio of 25.8 over the HCP-TiO 2 -FG photocatalyst (Supplementary Fig. S29). Since the kinetic model and reaction mechanism of photocatalytic CO 2 conversion are ambiguous so far, the quantitative relationship between CO 2 coverage and CH 4 evolution rate is still unclear. Interestingly, it is observed that they show a similar trend of increase with CO 2 proportion, e.g. both of them dramatically increased at lower partial pressure and then displayed a slow increase at higher CO 2 concentration (Supplementary Fig. S30). Generally, the reaction rates that are normalized to the active sites allow the direct comparison of intrinsic reactivity on different catalysts [47][48][49] . For the catalytic system employing same catalyst, the reaction rate appears to be independent of the loading amount of catalyst after normalization to the same amount 50, 51 . In this regard, the porous HCP-TiO 2 -FG photocatalyst possesses equivalent catalytic active sites to TiO 2 /HCP-FG hybrid due to the same content of TiO 2 photocatalyst. That is, the more efficient CH 4 production over HCP-TiO 2 -FG should not result from the difference in the number of catalytic sites but mostly come from the higher surface coverage of CO 2 on the active sites.
The temperature has a complicated influence on the rate of photocatalytic conversion from the aspects of adsorption and diffusion. By increasing the temperature, the surface coverage of CO 2 molecules on the catalyst surface was decreased due to the exothermic effect of adsorption process ( Fig. 3e-f), while the diffusion rate was increased as a result of the increased thermal motion of CO 2 molecules (Supplementary Fig. S31). Based on Arrhenius plot, the adsorption activation energy for CO 2 adsorption is calculated to be 5.20 kJ mol -1 (Supplementary Fig. S32a) using a microporous diffusion model 52,53 . Since the CH 4 production increases linearly and possesses dominant electron consumption selectivity as 83.7%, we can use the pseudo-zero order model to estimate the rate constant for the overall reaction, obtaining apparent activation energy of 9.34 kJ mol -1 (Supplementary Fig. S32b). The diffusion process was further studied by varying the stirring speed. As shown in Supplementary Fig. S33, the increase of stirring speed greatly facilitates the photocatalytic conversion of CO 2 to CH 4 product. Combining the diffusion effect with pressure-/temperature-dependent characteristics, we can conclude that the photocatalytic CO 2 reduction over HCP-TiO 2 -FG is not under intrinsic kinetic control of the catalyst but the efficiency is rather determined by gas adsorption and diffusion. The elucidation of adsorption and diffusion that contributed to the photocatalytic reaction, and is seldom discussed in the literature, provides valuable information for understanding the relationship between the catalytic performance and structure properties. As a result, it clearly demonstrates the superiority of such porous sandwich structure towards the visible-light-driven photocatalytic CO 2 conversion. Further kinetic study is required to probe the kinetics model and reaction mechanism of photocatalytic CO 2 conversion." Figure S30. Influence of the partial pressure of CO 2 on the CO 2 uptake (a) and CH 4 production rate (b). The photocatalytic reactions were carried out in a batch system under standard atmospheric pressure. The partial pressure of CO 2 can be adjusted from 2.5% to 100% by varying the volume ratio of CO 2 to N 2 . q e is the equilibrium adsorption capacity at pure CO 2 atmosphere with 1 bar. q/q e represents fractional uptake at different partial pressure of CO 2 . Figure S31. (a, b, c, d) (Supplementary Fig. S25), the amount of CO and CH 4 remained almost constant when the light was turned off. The extremely slow rate of reverse reaction indicates that the oxidation of CO and CH 4 to CO 2 is efficiently controlled over the HCP-TiO 2 -FG photocatalyst under such mild reaction conditions.
In the revised manuscript, we have added the following text on page 11: Fig. S25)."
Figure S25. Changes in CH 4 and CO production over the HCP-TiO 2 -FG photocatalyst under dark conditions and visible-light (λ≥420 nm) irradiation and dark conditions.
Reviewers' comments: Reviewer #2 (Remarks to the Author): Comments: I am pleased again to see that the authors have made some efforts to improve the quality of this manuscript by performing new experiments, adding new discussion and completing a number of changes. Indeed, some comments have been partially addressed. However, the key issue in terms of structure-performance relationship is still ambiguous, which makes it insufficient to meet the level for publication in Nature Commun. For this reason, I have to recommend the rejection toward the publication in Nature Commun.
Specific comments are listed below: 1. By TEM images and EDX mapping, the authors demonstrated in the current revised manuscript that a distinct sandwich structure of HCP-TiO2-FG, in which the graphene surface and TiO2 crystals were covered by the HCPs layers and the TiO2 crystals were supported on the graphene sheets and encapsulated by the ultrathin HCPs layer, was formed. However, in the Response Letter, the authors pointed out that the HCPs and graphene existed as an integrated structure instead of freestanding parts in the composite. This seems to be very ambiguous.
2. According to Fig. 3d, the TiO2 intercalation somewhat restricted the aggregation of HCPs layers on graphene nanosheets and thus dramatically enlarged the specific surface area. As a result, the enhanced performance of HCP-TiO2-FG cannot support the argument that the catalytic sites are located on TiO2. As the HCP-FG material also exhibits a photocatalytic activity for CO and CH4 production, it remains elusive whether the catalytic sites are located on TiO2 or HCP-FG.
Reviewer #3 (Remarks to the Author): The careful revision of the authors is acknowledged. With regard to kinetic analysis and mass Transfer, all parameters reasonable well accessible by experiments were investigated and a careful discussion was added. The presented additional data appear comprehensive. I support acceptance.
Therefore we believe that the description of "sandwich structure" and "integrated structure" are not much contradictory. While responding to the comment 2# of Reviewer 2#, we used "integrated structure" in the response letter only to emphasize that the charge carriers can be moved throughout the whole HCP-FG structure.
Here we would like to explain the relationship between HCPs and graphene as HCPs being covalently linked on graphene through the methylene linkers. The TiO 2 crystals were intercalated into the HCPs layers and graphene sheets at discrete sites, as shown in Fig. 1. Therefore, the "HCP-TiO 2 -FG sandwich structure" is used to describe these sites with TiO 2 crystals loading. At the other sites without TiO 2 crystals, the HCPs are covalently linked on graphene that seems to be a "HCP-FG integrated structure". The model of covalent linking is now also presented in Fig. 1 according to the structural characterizations.
2. According to Fig. 3d, the TiO 2 intercalation somewhat restricted the aggregation of HCPs layers on graphene nanosheets and thus dramatically enlarged the specific surface area. As a result, the enhanced performance of HCP-TiO 2 -FG cannot support the argument that the catalytic sites are located on TiO 2 . As the HCP-FG material also exhibits a photocatalytic activity for CO and CH 4 production, it remains elusive whether the catalytic sites are located on TiO 2 or HCP-FG.
Response:
We have also explained the identification of catalytic sites in our previous response to R1 (response to the Comment 6# of Reviewer 2#). Given below is further explanation to clarify it.
Let's first compare the porous property and photocatalytic performance to clarify the location of catalytic sites. The results of HCP-FG, HCP-TiO 2 -FG, and TiO 2 /HCP-FG samples are taken from the manuscript and supplementary information, as shown in the Fig. R1 and Table R1 below. Obviously, the introduction of porous HCPs layers enriched the adsorptive sites to achieve the high CO 2 uptake and improved the visible light absorption. Thus the formation of well-defined HCP-TiO 2 -FG sandwich structure resulted in much higher photocatalytic CO 2 reduction rate. The HCP-FG material also exhibited broad visible-light absorption, high surface area and notable CO 2 uptake. However, its photocatalytic performance was far less than that of HCP-TiO 2 -FG, especially in the eight-electron reduction to CH 4 . These results show that the catalytic sites on TiO 2 are much more active for CO 2 reduction than those on HCP-FG. Besides, the catalytic sites can be further clarified by the comparison between HCP-FG and TiO 2 /HCP-FG hybrid. When TiO 2 crystals were supported on HCP-FG to form TiO 2 /HCP-FG hybrid, it is found that TiO 2 deposition blocked most of the adsorptive sites of HCP-FG and resulted in a dramatic decrease to less than one-third of CO 2 uptake. However, the CH 4 production over TiO 2 /HCP-FG was 7.4 times more than that over pristine HCP-FG. These results confirm that the TiO 2 crystals are introduced as catalytically active sites to facilitate the photocatalytic CO 2 conversion.
Second, the pathway of charge carriers transfer and separation was studied to clarify the location of catalytic sites. As shown in Fig. 4f, the lowest unoccupied molecular orbital (LUMO) level of HCP-FG is more negative than the conduction band (CB) level of TiO 2 . It is well-known that the polymer materials usually possess the excitons with high binding energy, which usually recombine at the excited states.
The photogenerated electrons of the excited HCP-FG can migrate to the CB of TiO 2 due to their matched energy levels (Type II heterojunction model: Semiconductors 1998, 32, 1; Angew. Chem., Int. Ed. 2012, 51, 10145;ACS Catal. 2014, 4, 3637;Energy Environ. Sci. 2015, 8, 731;Adv. Mater. 2017, 29, 1606198). Thus the photogenerated carriers of HCP-FG can be separated at the interface with TiO 2 , which largely reduced the recombination loss. Since the electrons are located on TiO 2 crystals, the adsorbed CO 2 molecules are more readily converted to CO than CH 4 at the catalytic sites of TiO 2 .
Based on the discussion above, it can be inferred that the CO 2 reduction better achieved at the catalytic sites on TiO 2 rather than those on HCP-FG. The identification of catalytic sites could better explain the difference in photocatalytic performance among HCP-FG, HCP-TiO 2 -FG and TiO 2 /HCP-FG.
We have also mentioned the above discussion at page 9 and 11 of the manuscript. Pore size distribution that calculated using DFT methods (slit pore models, differential pore volumes). Time-dependent production of CH 4 (d) and CO (e) in photocatalytic CO 2 reduction with different catalysts under visible-light (λ≥420 nm). (f) Average efficiency of photocatalytic CO 2 conversion with different catalysts during 5 h of visible-light (λ≥420 nm) irradiation. uptake determined volumetrically using a Micromeritics ASAP 2020 M analyzer at 1.00 bar and 273.15 K. c Pore volume calculated from nitrogen isotherm at P/P 0 =0.995, 77.3 K. d,e average of gas evolution rate (r) during 5 h of photocatalytic CO 2 reduction. f R e is the rate of total consumed electron number for the reduced product; R e = 8r(CH 4 )+2r(CO).
Reviewers' comments:
Reviewer #2 (Remarks to the Author): I still think that the key issue of structure-performance relationship remains ambiguous, which makes the manuscript insufficient to meet the level for publication in Nature Commun. If the authors could address the comments, I would recommend it for publication.
Specific comments are listed below: 1. The advantage of the "sandwich structure" is still not clear. As described by the authors, the catalytic sites are located on TiO2 while the adsorptive sites are on HCP, and the graphene improve the photogenerated electrons transfer from HCP to TiO2. In this case, the best structure may be TiO2-FG-HCP rather than HCP-TiO2-FG.
2. The authors demonstrated that the photogenerated carriers of HCP-FG can be separated at the interface with TiO2. However, according to the "sandwich structure", there is no interface between HCP-FG and TiO2. Instead, the interface should be formed between FG and TiO2 or HCP and TiO2. In addition, according to the "HCP-TiO2-FG sandwich structure", the TiO2 intercalation somewhat restricted the aggregation of HCPs layers on graphene nanosheets, but also blocked the charge transfer from HCP to TiO2 through graphene.
3. In the "sandwich structure", the catalytic sites are located on TiO2 while the adsorptive sites are on HCP, as stated by the authors. This requires a short diffusion length for the transfer of CO2 molecules from adsorptive sites to catalytic sites. However, there is no direct evidence to support this argument.
sites with TiO 2 crystals loading. Considering that this name caused confusion to the reviewer, we have replaced it by the "porous HCP-TiO 2 -FG composite". For better understanding, we have now revised the models in the diagram to show the interface between TiO 2 and HCP-FG (Fig. 1). As you will see, the photogenerated electron-hole pairs of the excited HCP-FG can move throughout the HCP-FG structure and then be separated at the interface with TiO 2 via their interfacial interaction, as depicted in Supplementary Fig. S31. The proposed structure was previously demonstrated by TEM, STEM, HRTEM, SEM and AFM observations. In order to display the spatial distribution of HCP layers, we conducted further characterization by high-angle annular dark field (HAADF) mapping and three-dimensional rotating techniques. The results are now presented in Fig. 2f-i, Supplementary Fig. S6 and Supplementary Video, which could verify the above porous HCP-TiO 2 -FG composite structure. The detailed descriptions of the structure have been added in the morphology characterization section. We are hoping that the structure is now much clear and clearly understandable.
As suggested, another type of composite, HCP-FG supported TiO 2 (TiO 2 /HCP-FG), has already been prepared for comparison in this work. The HCP layers were hypercrosslinked on the functionalized graphene to form the HCP-FG structure with graphene surface rarely exposed, and then the HCP-FG was used as a supporting material for TiO 2 crystals growth during the solvothermal process. For better understanding of structure, we present the models in the diagram below (Fig. R1).
Model ( Table R1 below. Based on the above discussions, when TiO 2 was supported on HCP-FG instead of graphene, the TiO 2 deposition blocked most of the adsorptive sites of HCP-FG and resulted in a dramatic decrease in surface area, CO 2 uptake and photocatalytic efficiency. As a result, the designed HCP-TiO 2 -FG composite structure appears to be much superior to the TiO 2 /HCP-FG composite in our system. Of course, we expect that, in future, the synthesis strategy can be further improved to yield a much better structured combination of microporous organic polymers with photocatalysts.
We have also mentioned the above discussions in the revised manuscript and supplementary information.
On Pages 4, "The elemental mapping images in Fig. 2f- Fig. S14) (a-c and g-h). Therefore, the TiO 2 crystals on the graphene sheets were not exposed outside but encapsulated by the ultrathin HCPs layer." Pore size distribution that calculated using DFT methods (slit pore models, differential pore volumes 2. The authors demonstrated that the photogenerated carriers of HCP-FG can be separated at the interface with TiO 2 . However, according to the "sandwich structure", there is no interface between HCP-FG and TiO 2 . Instead, the interface should be formed between FG and TiO 2 or HCP and TiO 2 . In addition, according to the "HCP-TiO 2 -FG sandwich structure", the TiO 2 intercalation somewhat restricted the aggregation of HCPs layers on graphene nanosheets, but also blocked the charge transfer from HCP to TiO 2 through graphene.
Response:
Since the proposed structure of HCP-TiO 2 -FG has been clarified in the above response, we are hoping that the interface between TiO 2 and HCP-FG could be clearly understandable now. As shown in Fig. 1, the TiO 2 -FG interface was first formed that served as "bridge" to favor the formation of interface between TiO 2 and HCP-FG. It should be noted that the HCP was covalently linked with FG for the formation of HCP-FG integrated structure instead of freestanding HCP blocks. Hence the interface we observed in Fig. 1-2 was actually the interface between TiO 2 and HCP-FG. In the absence of TiO 2 , the surface area and CO 2 uptake of HCP-FG were much lower than those of HCP-TiO 2 -FG (Supplementary Tab. S2). It was also found that the HCP-FG layers of TiO 2 /HCP-FG were much thicker than those of HCP-TiO 2 -FG ( Fig. 2 and Supplementary Fig. S13). The results implied that the TiO 2 intercalation somewhat restricted the aggregation of HCPs layers on graphene nanosheets. According to the charge separation pathway in Figure 4f, the photogenerated electron-hole pairs of the excited HCP-FG can move throughout the HCP-FG structure and then be separated at the interface with TiO 2 via their interfacial interaction. In the prerequisite of better understanding the structure, we can conclude that the graphene plays dual a role in the composite photocatalyst: (1) the interaction with TiO 2 serving as "bridge" to form well-defined porous HCP-TiO 2 -FG composite structure; (2) the covalent linking with HCPs improving the electronic conductivity of the HCPs and thus facilitating the electron transfer from HCP-FG to TiO 2 in the composite. For better understanding, here we would like to present a simple diagram illustrating the charge separation at the interface (Supplementary Fig. S31). We believe that given the above discussion, the query regarding "TiO 2 blocked the charge transfer from HCP to TiO 2 through graphene" is now better addressed.
Given below is the related explanation in the manuscript.
On Page 7, "The results implied the interaction of TiO 2 with graphene serving as "bridge" to the formation of well-defined HCP-TiO 2 -FG composite structure.
On Page 11, "the covalent linking with graphene effectively improves the electronic conductivity of the HCPs and thus facilitates the electron transfer in the composite.
The less efficient CH 4 production over HCP-TiO 2 photocatalyst can also reflect the influence of graphene on improving the charge separation efficiency ( Supplementary Fig. S27) 3. In the "sandwich structure", the catalytic sites are located on TiO 2 while the adsorptive sites are on HCP, as stated by the authors. This requires a short diffusion length for the transfer of CO 2 molecules from adsorptive sites to catalytic sites.
However, there is no direct evidence to support this argument.
Response:
In the HCP-TiO 2 -FG composite, the HCP outer layers serve as adsorptive sites for CO 2 molecules and the TiO 2 crystals function as catalytic sites for CO 2 reduction. We agree that the diffusion of CO 2 molecules from the adsorptive sites to the catalytic sites plays an important role in CO 2 conversion.
(1) The evidence on the role of diffusion The kinetic study of CO 2 adsorption and diffusion provided a convincing evidence to clarify the significant role of diffusion in such a gas-solid reaction system. The related discussion is available at pages 12-13. More detailed descriptions can also be found in the response letter of R2 (response to the Comment of Reviewer #3). In the following peer-review process, the Reviewer #3 made comments on our revision as "The careful revision of the authors is acknowledged. With regard to kinetic analysis and mass transfer, all parameters reasonable well accessible by experiments were investigated and a careful discussion was added. The presented additional data appear comprehensive." For your convenience, we have pasted the previous response at the bottom as reference.
(2) The evidence on the effect of diffusion length Since the gas diffusion has a crucial influence on the rate limiting for CO 2 conversion, an appropriate diffusion length should be beneficial for the diffusion of CO 2 molecules from the adsorptive sites to the catalytically active sites. According to the structural analysis, the TiO 2 crystals were encapsulated by ultrathin HCP outer layers with a thickness of 3~8 nm (Fig. 2), indicating a short diffusion length for CO 2 molecules diffusing from HCP-FG to TiO 2 photocatalysts. For better understanding, we present the CO 2 diffusion model in the diagram below (Supplementary Fig. S15). Figure S15. Diagram of CO 2 diffusion from adsorptive sites to catalytic sites for conversion.
In addition, we have prepared the HCP-TiO 2 -FG composite with different thickness of HCP outer layers to study the effect of the diffusion length on the CO 2 uptake and conversion efficiency. The results suggested that there is an appropriate thickness of HCP layers which balanced the CO 2 adsorption and diffusion. In this work, we tried to construct the HCP-TiO 2 -FG sandwich structure with ultrathin HCP layers to reduce the diffusion length. Of course, we expect that, in the future, the synthesis strategy can be further improved to yield a much better structure with more efficient CO 2 adsorption and diffusion.
Given below is the related explanation in the manuscript.
On Page 9, "The model of CO 2 diffusion and conversion was presented in Supplementary Fig. S15." On Page 9-10, "the HCPs obtained by this strategy are comprised of ultrathin layers with a thickness of 3~8 nm wrapping around TiO 2 crystals (Fig. 2d-f) (Supplementary Fig. S16), however the size of TiO 2 particles was decreased accompanied by the thickening of the HCP layers (Supplementary Fig. S17), which suggests that the HCP outer layers effectively suppress the growth of TiO 2 crystals. The distinct thickening of the outer layers was further verified from the characteristic morphology revealed in Fig. 1 Fig. S18a and Tab. S4), on the other hand, the diffusion length of CO 2 molecules also increased due to the thickening of the outer layer. As the CO 2 conversion efficiency increased initially and then decreased at higher amount (Supplementary Fig. S18b), there may be an appropriate thickness of HCP layers that balance the CO 2 adsorption and diffusion." Reference:
Query on diffusion from Reviewer #3
The authors were asked to provide further evidence for the governing nature of their two main Arguments, namely the superior CO 2 adsorption as pre-requisite of high substrate concentration close to or on the active site and their hypothesis on the shortend diffusion lengths. Indeed, a suitable kinetic analysis has been carried out illustrating that the investigated photocatalytic CO 2 reduction is not under intrinsic kinetic control of the catalyst but the observed rates of CO and CH 4 formation are rather determined by some transport effects. The observed limited dependence of rate on temperature may hind towards diffusion control. I fully agree that kinetic analyses is a yet under-represented aspect in photo-catalysis. Though, the little rate dependence on temperature appears to point towards film diffusion effects. Hast the stirring speed or the main particle size been varied? It remains unclear for me why the authors conclude on a reduced Diffusion length for the Optimum System, although they do not know which Diffusion is rate limiting: CO 2 from bulk to the film, through the fild, in/on the porous material or Charge charrier diffusion?
Response: Many thanks for appreciating our efforts on the kinetic analysis presented in the previous revision. The photocatalytic reactions were carried out in a gas-solid batch system without stirring the gas mixture. According to the suggestion, we studied the diffusion process by varying the stirring speed from zero to maximum. As shown in Supplementary Fig. S40, the increase in stirring speed greatly facilitates the photocatalytic conversion of CO 2 to CH 4 product, indicating that the diffusion plays a significant role in such a gas-solid reaction system. The related results and discussions have been added as a separate section "kinetic analysis" in the revised manuscript.
The particle size is another factor affecting the diffusion process, especially for internal diffusion. We would like to mention that the HCP-TiO 2 -FG composite produced through this strategy possesses the specific particle size. In the experience of optimizing synthesis conditions, TiO 2 crystals with larger or smaller size are inclined to form agglomerates, which cannot uniformly decorate on graphene or be fully wrapped by ultrathin HCPs layers. In the current system, we cannot achieve the varied particle size while keeping the designed structure with similar surface area, CO 2 uptake capacity and the number of active sites.
In order to reduce the diffusion length, we tried to construct the HCP-TiO 2 -FG sandwich structure with ultrathin HCP layers. The reduced diffusion length should be beneficial for the diffusion of CO 2 and photo-generated charges to the catalytically active sites, both of which may contribute to the improved CO 2 conversion efficiency.
Based on the gas diffusivity measurement, the diffusion coefficient of CO 2 in the HCP-TiO 2 -FG sandwich structure is calculated to be 1.8×10 -11 cm 2 s -1 at room temperature ( Supplementary Fig. S39). Typical polymers for photoconversion application, the exciton diffusion and charge transfer dynamics of poly(3-hexyl thiophene) (P3HT) and phenyl-C61-buryric acid methyl ester (PCBM) have been studied, giving the diffusion coefficient of 1.8×10 -3 and 2.7×10 -4 cm 2 s -1 , respectively (Adv. Mater. 2008, 20, 3516;Nanoscale 2011Nanoscale , 3, 2280. The diffusion of charge carrier is much faster than that of the adsorbed gas by several orders of magnitude, implying that the gas diffusion should have more crucial influence at the rate limiting rather than the charge carriers.
In the present study, we aim to provide new insights into the design and synthesis of well-defined porous photocatalysts for CO 2 uptake and conversion. The designed sandwiched structure is somewhat complicated and makes it impossible to establish individual kinetic models. Although the kinetic mechanism cannot be clearly clarified in the current study, we indeed have made much progress on the kinetic analysis of photocatalytic CO 2 conversion that is seldom discussed in the literature. Inspired by the reviewers' suggestions, we have realized that the kinetic analysis is indeed very important for photocatalytic CO 2 conversion and there are yet many challenges that need to be addressed. In future study, we will use the simple photocatalytic system such as pure TiO 2 photocatalyst to probe the kinetics model and reaction mechanism of CO 2 conversion, and then extend to the complicated models involving adsorption, diffusion and photocatalytic processes.
On pages 12-13, all results and discussions on kinetic analysis are included and displayed as a separate section "kinetic analysis" in the revised manuscript.
"Kinetic analysis. The kinetics experiments were carried out to understand the contribution of CO 2 adsorption and diffusion to the enhancement of photocatalytic efficiency. The relationship between the CO 2 adsorption and CH 4 production can be explored by varying the surface coverage of CO 2 on the active sites. The partial pressure of CO 2 is adjusted in CO 2 /N 2 mixture because of a high CO 2 /N 2 selectivity ratio of 25.8 over the HCP-TiO 2 -FG photocatalyst (Supplementary Fig. S36). Since the kinetic model and reaction mechanism of photocatalytic CO 2 conversion are ambiguous so far, the quantitative relationship between CO 2 coverage and CH 4 evolution rate is still unclear. Interestingly, it is observed that they show a similar trend of increase with CO 2 proportion, e.g. both of them dramatically increased at lower partial pressure and then displayed a slow increase at higher CO 2 concentration (Supplementary Fig. S37). Generally, the reaction rates that are normalized to the active sites allow the direct comparison of intrinsic reactivity on different catalysts [47][48][49] . For the catalytic system employing same catalyst, the reaction rate appears to be independent of the loading amount of catalyst after normalization to the same amount 50,51 . In this regard, the porous HCP-TiO 2 -FG photocatalyst possesses equivalent catalytic active sites to TiO 2 /HCP-FG due to the same content of TiO 2 photocatalyst. That is, the more efficient CH 4 production over HCP-TiO 2 -FG should not result from the difference in the number of catalytic sites but mostly come from the higher surface coverage of CO 2 on the active sites.
The temperature has a complicated influence on the rate of photocatalytic conversion from the aspects of adsorption and diffusion. By increasing the temperature, the surface coverage of CO 2 molecules on the catalyst surface was decreased due to the exothermic effect of adsorption process (Fig. 3e-f), while the diffusion rate was increased as a result of the increased thermal motion of CO 2 molecules (Supplementary Fig. S38). Based on Arrhenius plot, the adsorption activation energy for CO 2 adsorption is calculated to be 5.20 kJ mol -1 (Supplementary Fig. S39a) (Supplementary Fig. S39b). The diffusion process was further studied by varying the stirring speed. As shown in Supplementary Fig. S40 | 16,854.6 | 2019-02-08T00:00:00.000 | [
"Chemistry",
"Materials Science",
"Environmental Science"
] |
High-Density Dynamics of Laser Wakefield Acceleration from Gas Plasmas to Nanotubes
The electron dynamics of laser wakefield acceleration (LWFA) is examined in the highdensity regime using particle-in-cell simulations. These simulations model the electron source as a target of carbon nanotubes. Carbon nanotubes readily allow access to near-critical densities and may have other advantageous properties for potential medical applications of electron acceleration. In the near-critical density regime, electrons are accelerated by the ponderomotive force followed by the electron sheath formation, resulting in a flow of bulk electrons. This behavior represents a qualitatively distinct regime from that of low-density LWFA. A quantitative entropy index for differentiating these regimes is proposed. The dependence of accelerated electron energy on laser amplitude is also examined. For the majority of this study, the laser propagates along the axis of the target of carbon nanotubes in a 1D geometry. After the fundamental high-density physics is established, an alternative, 2D scheme of laser acceleration of electrons using carbon nanotubes
Introduction
Laser Wakefield Acceleration (LWFA) [1] is a compact method to accelerate charged particles to high energies that was first purposed by Tajima and Dawson [2] in 1979. While the accelerating electric field in a conventional linear accelerator is limited by the breakdown threshold of its device walls, the inherently broken-down nature of plasma allows plasma-based accelerators to access far higher electric fields. Consequently, plasmabased accelerators can access far higher accelerating gradients than those available to conventional accelerators, reaching potentially GeV per cm or higher. The development of Chirped Pulse Amplification (CPA) [3] allowed experimental access to the high laser intensities originally proposed for LWFA (10 18 W/cm 2 ), and LWFA was experimentally verified shortly thereafter [4,5]. Since then, many experiments have demonstrated this technique in different regimes, and the field has grown steadily.
Accelerators have many applications in our current society, one of the most important being their use in radiation therapy. Energetic beams composed of constituents such as of X-rays, electrons, or protons can be used to treat cancer. These energetic beams can ionize molecules and thus damage cellular DNA. Cells with damaged DNA can not reproduce and are eliminated through natural processes in the body. The type of beam used depends highly on the size and location of cancer being treated. For example, while X-rays and electrons deposit most of their energy in the surface layers, protons can be controlled to deposit their energy at a specific depth due to Bragg peak phenomenon [6,7], dramatically reducing damage to healthy cells. Proton therapy contends with other limitations, however [8]. For this study we are interested in electron beams, which can have shallow or deep penetration depths depending on energy.
Current accelerators used for radiation therapy use traditional linear accelerator technology. To produce an electron or X-ray beam, electrons from an electron gun are accelerated and guided through waveguides using electric fields and magnets. These electrons can eventually hit a target and produce X-rays. However, the material breakdown limits of linear accelerators tend to require that these machines be large and costly. The typical electron energy needed for radiation therapy is between 5 and 20 MeV. LWFA techniques can accelerate electrons to these energies in length scales between microns and millimeters. Such a high acceleration gradient reduces the size and cost of these machines, consequently increasing their availability.
Research in the use of LWFA to generate electron beams for medical applications has presently proceeded for more than two decades. Initially, these efforts focused on the generation of high-quality electron beams with energies roughly in the range of 6-25 MeV, as would be applicable for conventional, external sources of radiation for cancer therapy [9][10][11][12][13][14][15]. Recent innovations in the field of fiber lasers has produced a critical advancement for this effort: the Coherent Amplification Network (CAN) [16], in which many individual micron-scale fiber lasers are coherently combined and amplified to provide both high repetition rate and high power. In such a scheme, laser accelerators could possibly be further compactified as to be viable even for endoscopic applications. If electrons can be generated inside of a patient's body (or in an intraoperative [12,13] fashion), the desired energy of these accelerated electrons (and X-rays converted from them) is much lower than those of typical, high-energy LWFA (MeV and above), as they need not traverse healthy tissues before reaching the tissues to be treated.
In LWFA a clear path to the desired MeV-range electrons exists through utilizing high plasma densities. Consequently, we wish to study LWFA in the high-density regime. This regime has been less explored in detail than that of the more typical, low-density regime of LWFA. To establish a conceptual footing in this less understood regime, we exert our main focus on the fundamental physics of high-density electron acceleration. In doing so, we revive and take advantage of past work on sheath acceleration [17]. To this end, robust laser-plasma interaction is desired, and so we employ higher laser intensities than would likely be possible to achieve in a medical application based on fiber lasers, though CAN techniques may ultimately mitigate such concerns. Previous work [18] treated the practical considerations of fiber lasers and medical applications more explicitly.
Generally, gas plasmas are used as the electron source in LWFA. Indeed, as is described in more detail in Section 2, low-density plasmas are ideal for typical LWFA experiments. For medical applications, however, particularly for cases where the electron source is brought inside the body, a solid-state electron source is much more desirable for two chief reasons. First, as described above, the electrons produced from such a medium are of a desirably low energy. Second, a solid-state electron source potentially avoids the creation of gas plasma and the necessity of maintaining a vacuum, both of which are highly undesirable for endoscopic medical applications.
One possible electron source satisfying these requirements may be provided by an arrangement of carbon nanotubes (CNTs) such as those in Figure 1, which allows access to much high densities than those easily attained by gas plasmas. Various other advantageous properties of CNTs motivate such a scheme. Carbon nanotubes can be synthesized to have metallic properties by using the armchair configuration [19,20]. Though CNTs alone generally can have a lower conductivity than that of metals, the conductivity of composite materials such as CNTs embedded in copper nanotubes can reach or exceed that of metals [21,22]. Additionally, CNTs have been shown to have electron carrier mobility much higher than that of metals [23]. For example, metals like aluminum and copper have mobilities of order 10 1 to 10 2 cm 2 /(V·s) while single-wall CNTs can exhibit electron mobilities of order 10 4 cm 2 /(V·s). Other desirable properties of CNTs for the present study are a low work function (approximately 5 eV, similar to that of metals [24]) and an effective one-dimensional conductivity parallel to the CNT axis. We thus seek to assimilate our investigation of the physics of electron acceleration in the high-density regime to a possible CNT application. Specifically, the bulk of this work models electron acceleration from a laser propagating down the axis of a CNT bundle [? ], shown schematically in Figure 1b. Later, in Section 4, we consider an alternative arrangement of CNTs, shown in Figure 1b, that requires more advanced treatment.
The energy gain of electrons in LWFA is given by ∆E = 2g(a 0 )m e c 2 (n c /n e ), where a 0 = eE 0 /m e ω l c is the normalized vector potential of the laser pulse with E 0 and ω l representing the electric field and frequency of the laser. Here e, m e , and c are electron charge, electron mass, and speed of light, respectively. If the function g(a 0 ) takes the form of the ponderomotive potential, then g(a 0 ) = 1 + a 2 0 − 1 [26], but generally here g(a 0 ) is considered to be of order unity at a 0 = 1. The electron energy gain is proportional to the ratio of n c , the critical plasma density defined by the laser frequency, to n e , the plasma or electron density. If the value of this ratio is near unity, the electron energy gain is on the order of MeV or lower. For this work we assume a common 800-nm Ti:Sapphire laser, which has a critical density of n c ≈ 1.73 × 10 21 cm −3 . In comparison, a quick estimate for the average electron density of a CNT with a radius of 10 nm gives n e ∼ 10 22 cm −3 . As CNTs can flexibility possess radii both larger and smaller than that used in this estimation, CNTs readily allow access to both near-and super-critical densities as desired. In the following, we also study the scaling laws of electron energy gain ∆E over the parameters of plasma density and intensity a 0 in addition to investigating the mechanics of electron acceleration in the high-density regime.
This work is divided as follows. Section 2 examines the physics of wakefield acceleration in the high-density regime by modeling propagation of a laser down the axis of a CNT bundle. Section 3 elaborates this topic by examining the accelerating potential of different regimes of laser amplitude. Building on these results, Section 4 explores the use of a an alternative arrangement of CNTs (see Figure 1) as a source of low-energy electrons such as might be useful to medical applications. Finally, Section 5 offers concluding remarks.
Acceleration in the High-Density Regime
If the plasma density is near the laser critical density, the typical physics of LWFA transitions into a qualitatively distinct regime where analytic extensions of conventional wakefield physics [27] may become insufficient. Crucially, as n e approaches n c , the group velocity of the laser pulse, given by v g = c √ 1 − n e /n c , approaches zero. The wake phase velocity is approximately equal to the laser group velocity and thus also approaches zero in this regime. The laser pump depletion and dephasing lengths, which are on the order of L d ∼ L p ∼ λ p a 2 0 (n c /n e ), also diminish with v g until they become shorter than the plasma wavelength λ p = 2πc/ω p for a 0 = 1. The length scale of laser-plasma interaction then becomes better described by the plasma skin depth c/ω p . As a consequence of the low laser group velocity v g , the laser couples significantly to the bulk motion of the plasma, which is characterized by the plasma thermal velocity v T = √ T/m, where T and m here are most relevantly applied to electrons.
In contrast, wakefield physics in the low-density regime relies on a fast laser group velocity (v g ≈ c v T ). The laser penetrates deeply into the plasma without coupling to the bulk motion. The resulting wake phase velocity is then v ph = v g ≈ c v T , and L d ∼ L p λ p . This fast phase velocity and related long interaction length scale allow the laser to build a long and robust wakefield train. When electron injection occurs, the wakefield skims a small population of electrons from the bulk and accelerates them to high energies, unlike in the high-density case. This sharp divide in fundamental physics requires examination of the high-density regime on its own terms and a qualitative understanding apart from that of conventional wakefield acceleration.
The differences between the qualitative physics of the high-and low-density cases, which respectively represent waves of low and high phase velocity relative to the plasma thermal velocity, extends to many general features of plasma physics. For waves with v ph ∼ v T , the wave couples to the bulk thermal motion of the plasma, typically producing macro-instabilities and turbulence. Plasma structures are thus fragile to such waves, and may disintegrate from wave-induced transport. In contrast, waves with v ph v T do not couple to the bulk thermal motion of the plasma, and the plasma and wave are insulated from each other. With regard to the wave fields, the wave can then reach a robust saturation amplitude before particle trapping begins to occur. In this limit, the wave trapping velocity [28] becomes approximately equal to the wave phase velocity, leading to the characteristic Tajima-Dawson saturation amplitude E TD = mωv ph /q, where ω is the wave frequency and m and q are respectively the mass and charge of the relevant species. At this saturation amplitude, wave-particle interaction manifests as the acceleration of a tail of extremely fast particles while the thermal distribution remains intact. Indeed, under the influence of the free energy of such a wave, plasma structures can be built rather than destroyed; the plasma is durable against the wave, rather than fragile. Because the original LWFA concept was built upon this high phase-velocity paradigm and departs from the sheath-forming, high-density regime [17], most present works on LWFA have avoided the high-density (low phase-velocity) regime. Thus it is the purpose of this work to first qualitatively distinguish these two regimes and then quantitatively characterize the differences in their most important dynamics. To do so, we isolate the longitudinal spatial dynamics and show their overwhelming influence on the departure of the physical characteristics of the above two regimes.
The dynamics of tsunami waves in different regimes of water depth provides a convenient analogy for these contrasting regimes of acceleration in high-and low-density plasmas. The deep water of the open ocean allows tsunami waves to propagate with a fast phase velocity given by v ph = g/k with wavenumber k [29], where g is the constant of gravitational acceleration. This fast phase velocity causes only weak interaction with stationary objects (such as boats). Near the shore, however, the shallow water forces the wave to move with a slower phase velocity given by v ph = gh, where h is the water depth. As its phase velocity slows, the wave steepens and amplifies until breaking occurs. Two key related consequences follow. First, the slow phase velocity causes strong and catastrophic coupling to stationary objects. Second, the turbulent process of wave breaking causes dredging of sediment from the seabed. The sediment is then incorporated into the wave and transported forwards, creating a visibly black wave. The momentum transport imparted to the sediment can be considered to represent an effective viscosity caused by the turbulence of wake breaking. In contrast, the wave in the open ocean does not incorporate sediment and thus remains blue.
The typical case of wakefield acceleration in a low-density (n c n e ) plasma is analogous to that of the tsunami wave in the open ocean. The wakefield remains decoupled from the bulk electron population, leaving the wave ordered and "blue". In the case of highdensity (n c ∼ n e ) plasmas, the wake has sufficiently low phase velocity to begin "dredging" electrons from the bulk population, resulting in a more chaotic and "black" wave. We thus adopt the designations of "blue" and "black" waves to qualitatively distinguish the physics of wakefield acceleration in the low-and high-density regimes, respectively. Between these two extremes additionally lies a transitional "grey" state.
To study the distinct physics of the high-density regime and its transition from the low-density regime, we employ the particle-in-cell (PIC) code EPOCH to model the injection of a laser down the axis of a bundle of CNTs. For simplicity the laser wavelength is taken to be 1 micron. (The corresponding laser frequency is then 1884 THz.) The specification of a bundle is necessary because while a reasonably achievable laser spot size is on the order of microns, the upper range of CNT diameters is typically tens of nanometers.
Establishing a firm conceptual foundation in this physics first requires understanding of the case where one spatial dimension (and three velocity dimensions) are employed. This work is also primarily interested in the phase-space structure of accelerated electrons, rather than the real-space evolution of the laser pulse and wakefield. While two spatial dimensions are used in Section 4, the main focus of this work requires only a 1D treatment. This model also allows a rough representation of carbon nanotubes in one spatial dimension. More complex phenomena that occur in 2D, such as strong self-focusing [30] and holeboring of ions [26], are not examined. Such 2D effects beget other effects, such as collapse of the laser pulse [31], which can lead to an expanding cloud of electrons. These effects and others [32], such as magnetic vortex physics [33] and prominent ion motion, are also more typical of the regime of ultra-intense pulses, which is not an emphasis of this work. Peak ion energy achieved in this study is typically 0.1 MeV. Comparisons to ion-acceleration schemes, such as TNSA and RPA [34,35] are not addressed here. Indeed, ions are essentially stationary in this study.
For this simulation setup, the laser is injected from vacuum through an impedancematching boundary into a uniform plasma of electrons and protons with temperature T = 100 eV. Such a configuration represents a simple and idealized case that can be analyzed easily, yet contains the crucial physics. This scheme contrasts with some past efforts in which the laser was injected into a density ramp that peaked near the critical density [31]. In this case, the laser pulse collapsed before reaching the region of critical density owing to important 2D effects. Here a uniform density is used to examine the physics of laser-plasma interaction at the full critical density. Additionally, as opposed to initializing the laser inside the plasma, the vacuum injection scheme may better reflect the experimental reality for the high-density case near the critical density if we take as a target a porous nanomaterial [36? ,37], for which the injected laser has v g ∼ 0. Care is taken that the essential laser-plasma physics is unchanged between the cases of vacuum injection and laser initialization inside the plasma.
The laser is taken to have a resonant pulse length with functional dependence is a resonant flat-top profile, and φ is an optional phase, which can be identified as the carrier envelope phase (CEP). By default φ is set to zero. (The oscillatory component of E y thus grows from zero as the laser enters the simulation domain.) A resonant pulse is half the length of the plasma wavelength λ p = 2πc/ω p . The remaining laser and plasma quantities are then controlled through two parameters: the laser intensity a 0 and the critical density ratio n c /n e . Position in the simulation domain is indicated by the value x. The laser is injected at x = 0, and "forward" and "backward" correspond to the directions +x and −x, respectively.
The total 1D domain size is 16 micron, representing an equal number of laser and plasma wavelengths (16) for n e = n c . Similarly, the plasma frequency ω p is equal to the laser frequency. The domain is divided among 7187 cells to adequately resolve the Debye length. Each cell is initialized with 4000 electron and 40 ion pseudo-particles, the former being the physical interest and the latter being relevant for noise reduction.
The resonant pulse used in this case is motivated by a desire for simplicity and consistency with the approach typically used in the low-density regime. A resonant laser pulse in a plasma near the critical density (n c /n e ≤ 2) must necessarily be sub-cycle, or at most single cycle. While sub-cycle lasers have been demonstrated experimentally [38,39], such a setup would be generally difficult to implement, particularly in a fiber laser [16]. Another concern arising from a sub-cycle laser pulse is the influence of the initial laser phase φ. Care has been taken to ensure that choice of φ does not affect the qualitative physics, even for n c /n e = 1. One can show analytically that the initial ponderomotive kick felt by the electrons lies in the same direction as the laser Poynting vector, creating a tendency toward uniformity across various values of φ.
In the "blue" wave case, where n e n c , electrons that are trapped and accelerated form an ordered and repeating structure, with the highest-energy electrons reaching the theoretically expected momentum of p max x ≈ m e c (2g(a 0 )n c /n e ) 2 − 1 [2]. Similarly, the longitudinal electric field forms a coherent wake structure, with the field saturating near the expected value [40]. The "black" wave case shows qualitatively different behavior and invites closer inspection. For a plasma at the critical density n e = n c , snapshots during the early (Figure 2a) and late (Figure 2b) stages are shown. The phase space density is plotted in units of pseudo-particles per p x /mc × x/λ p . A run of this type was first made in prior work [18], and a similar run is produced here to examine the acceleration mechanism more closely. The group velocity of the laser is reduced to zero, v g = 0, and the dephasing the pump-depletion lengths are reduced to less than one plasma wavelength, L p,d λ p . This latter effect restricts the laser-plasma interaction to within one plasma wavelength. Streams of low-energy (∆E ∼ 100 keV) electrons ejected from the site of laserplasma interaction replace the long train of orderly trapped electrons seen in the "blue" wave case. Ejection of electrons occurs roughly every plasma period. The generation of low-energy electrons indicates strong coupling between the laser and the bulk population of electrons. The donation of a net bulk momentum to the electrons suggests the presence of an effective viscosity.
This behavior, applicable where n c /n e ≈ 1, clearly signals a departure in qualitative physics from that of the regime of typical wakefield acceleration, n c /n e 1, particularly where the laser enters the plasma medium. Rather than penetrating the plasma without significant hindrance as occurs in the low-density regime, in the high-density regime the laser has group velocity v g c and plows the bulk electron population forwards, forming a large spike in electron density (δn e /n e ≈ 3.5). As in the low-density case, ions essentially remain in place. This density spike creates a longitudinal electric field of approximately twice the strength of that in the low-density case and causes the reflection of a substantial portion of the laser. This powerful initial kick to the plasma establishes a strong longitudinal sheath oscillation of electrons in the range 0 ≤ x λ p . x and field structure of the high-density ("black") case n c /n e = 1 of a 1D carbon nanotube with laser intensity a 0 = 1 at early (a) and later (b) stages. The heatmap shows warmer colors for higher phase-space density. The longitudinal E x (green) and laser E y (translucent blue) fields are plotted according to the right axis. The plasma wavelength is equal to λ p = 1 micron. (a) is zoomed to 0 ≤ x ≤ λ p from (b). A similar run is made in previous work [18].
The formation of the sheath occurs when a strong restoring electric field then causes the density spike to rebound towards the left edge of the plasma (the entrance of the plasma domain). While this rebound occurs, a small population of electrons is accelerated to the energy ∆E expected from traditional 1D wakefield theory. Simultaneously, many electrons are expelled from the left edge of the plasma, establishing a sheath [17] at the plasma edge. The intensity of this sheath is comparable to that of the initial laser amplitude. This sheath then continues to oscillate longitudinally, with each oscillation accelerating a stream of electrons to low energy (<100 keV). These electrons are then ejected from the site of oscillation in the forward (right) direction. The presence of the sheath ensures that these electron streams travel nearly exclusively in the forward direction. (If the sheath is not located at the plasma edge, a significant number travel backwards.) Figure 2a, a snapshot of the electron phase space and fields zoomed to the range 0 ≤ x ≤ λ p , shows the beginning of this process, where the first streams of accelerated electrons are visible. As the oscillation continues, more streams accumulate, building up the phase-space distribution in Figure 2b, which shows the full simulation domain. In the later stages, the electron acceleration becomes increasingly turbulent until the oscillation is finally exhausted after about 30 plasma periods. The full evolution of the sheath and electron density is shown in Figure 3. While the individual energy of the accelerated electrons is low compared to that of the low-density case, the total energy imparted to the accelerated electrons can potentially be higher. This total imparted energy represents about 12% of the total injected laser energy, though it should be kept in mind that an such efficiency value is inherently a rough estimate in a 1D simulation. This understanding of the electron dynamics associated with sheath formation should also be useful for the understanding of related ion acceleration dynamics [1,6]. The sheath acceleration mechanism observed here is also reminiscent of that in cases examined previously [26].
The transition to sheath acceleration from typical wakefield acceleration represents a sharp division of qualitative regimes of wakefield physics. Pursuing this point further, we can attempt to find a quantitative means of discriminating these regimes. Comparing Figure 2 with that of the ordered structure of typical, low-density wakefield acceleration suggests a quantitative index related to the entropy of the phase-space structure; the electron phase space in the low-density case is highly ordered compared with that of the high-density case. In general however, comparing the entropy of two distributions also requires an accounting for the mean kinetic energy of the distributions. Thus, as an index for discriminating the "blue" and "black" regimes, we propose a "darkness" metric D. This quantity D is defined as the specific momentum entropy D = S/ K , where dP x is the differential Boltzmann entropy of the longitudinal momentum distribution f (P x ), where P x = p x /p T is the longitudinal momentum normalized to the thermal momentum p T = √ m e T e , and K = ∞ −∞ [ 1 + P 2 x /(m e c/p T ) 2 − 1] f (P x )dP x is the average electron kinetic energy per particle normalized to m e c 2 considering only the contribution from p x . The distribution f (P x ) is normalized according to ∞ −∞ f (P x )dP x = 1. This index D does not take into account the dependence of the total laser energy content on the plasma wavelength λ p ; as λ p increases for lower densities, the laser pulse length increases to maintain a resonant length. Instead, by keeping the laser always to a resonant pulse length, the plasma excitation mechanism is held constant.
For a scan over the density values n c /n e ∈ [0.5, 14] at a 0 = 1, Figure 4 shows the approximately final values for the index D normalized to the initial value D 0 , which is the same for each data point and has an analytic form for a Maxwellian distribution. One point in the overdense regime (n c /n e = 0.5) has been added as well for cautious comparison of the "black" and super-critical regimes. As n c /n e → ∞, s/s 0 → 0, while as n c /n e → 0, D/D 0 climbs to a large value. These limits reflect the substantive difference in each regime. For "blue" waves, the average electron energy grows much faster than the momentum entropy, owing to the development of a typical wakefield phase-space structure. For "black" waves in contrast, disorder in phase space dominates growth in average kinetic energy and becomes ever more severe for increasing plasma density. The "darkness" index D/D 0 for "blue" waves thus asymototes to zero while that for "black" waves is characterized by finite size tending to a large value. Between these two extremes, a "grey" wave state can exist, which shows both aspects of bulk flow and traditional wakefield acceleration.
(a) (b) Figure 3. The evolution in space and time of the longitudinal electric field E x (a) and electron density n (b). The electric field is normalized with respect to the Tajima-Dawson field E TD , and the electron density n is normalized to the initial uniform density n e . The downward arrow on the color bar of (b) reflects that n extends to zero in the deep blue areas. The time domain is normalized with respect to the period of plasma oscillation, τ p = 2π/ω p . This index may then provide a guide to the most appropriate regime in which to operate for a particular application. For the generation of a mono-energetic, high-energy electron beam, D/D 0 1 is desirable, as a "blue" wave will cleanly accelerate a small population of electrons to extremely high energy. Being mindful of the dephasing length, one can then ensure that the accelerated electrons are captured at peak energy. In contrast, for some medical applications, such as in a cancer-treatment scheme where a source of radiation is brought directly to the cite of a tumor, a significant dose of low-energy (shallow-penetrating) electrons is desirable, with less constraint on the beam quality and electron energy distribution. One is attracted in this case to the "black" regime, which has D/D 0 ∼ 1. For long, low-intensity laser pulses, as would be amenable to a fiber laser, this regime can also be accessed even at moderate plasma densities (n c /n e ≈ 10) due to Raman forward scattering [18].
Laser Intensity Scaling
Apart from plasma density, the second chief parameter determining the nature of the wakefield response is the laser intensity a 0 . To understand wakefield physics at high density, it is thus also necessary to understand the scaling of accelerated electron energy ∆E with respect to a 0 . For medical applications, it is also necessary to understand the electron energies available for various laser intensities, particularly a 0 < 1. Two cases are considered: the low-density "blue" case of n c /n e = 10 and the moderate-density "grey" case of n c /n e = 3. For each case a 0 is scanned logarithmically over the range a 0 ∈ [0.1, 10] and the maximum electron energy is recorded.
The expected functional dependence of ∆E (a 0 ) has thus far been represented simply by g(a 0 ). Here we compare the case g(a 0 ) = 1 + a 2 0 − 1 to the results of the scan over a 0 . Of particular interest for comparison with the simulation results is that this function has two slope regimes: ln g/ ln a 0 = 2 for a 0 1 and ln g/ ln a 0 = 1 for a 0 1. The results of the scan are shown in Figure 5. First for the low-density ("blue") case (Figure 5a), the transition in slope is indeed seen, and the simulation results are in general agreement with g(a 0 ). The moderate-density ("grey") case (Figure 5b) also shows rough agreement with g(a 0 ). Notably, for the low-density case, a sharp transition in maximum electron energy is seen around a 0 = 1. This transition may be indicative of the "switching on" of electron trapping that occurs once the laser amplitude enters the relativistic regime at a 0 = 1; for a 0 1, substantial electron trapping does not occur for typical LWFA. In contrast, at higher density (Figure 5b), the transition is less prominent, and electron energy for a 0 1 is higher than that given by g(a 0 ). Because the electron acceleration mechanism in this regime has shifted more to the sheath acceleration typified in Figure 2b, which does not have an intensity-based "switching on" transition, but can instead accelerate electrons even at very low intensities owing to the slow laser group velocity v g v T , a less abrupt transition around a 0 = 1 in this case is expected. As an additional consequence, the sheath acceleration is able to accelerate electrons with comparative efficiency in the regime a 0 1, leading to the apparent acceleration enhancement above g(a 0 ) in Figure 5b. In the regime of very large a 0 , it should also be noted that other work [41] has found that the scaling of electron energy should follow a 2 0 from ulta-relativistic effects.
(a) E max vs. a 0 for fixed ratio n c /n e = 10.
(b) E max vs. a 0 for fixed ratio n c /n e = 3. Figure 5. The maximum electron energy as a function of laser intensity a 0 for two density cases: n c /n e = 10 (a) and n c /n e = 3 (b). The maximum energies (red dots) are compared with the function g(a 0 ) (blue solid line). The blue dashed lines represent the asymptotic behavior of g(a 0 ) for a 0 1 and a 0 1.
These results suggest that an a 0 between 0.1 and 0.8 gives the best results for achieving electrons with ∆E < 1 MeV while still allowing the density ratio to be varied, such as would be desired for medical applications featuring shallow beam penetration.
High Density with Perpendicular Carbon Nanotubes
Thus far we have examined the mechanics of wakefield acceleration in the highdensity regime by modeling laser injection parallel to a bundle of CNTs. We now consider an alternative arrangement where the CNTs are oriented in the direction perpendicular to that of the laser propagation. To examine this case, we expand our simulation scheme to include two spatial dimensions. The properties of CNTs, particularly an effective onedimensional conductivity, allow for the straightforward modeling of a high-density target of perpendicularly oriented CNTs in the arrangement of Figure 1b in a PIC simulation. This arrangement is investigated using an implementation of the PIC code EPOCH with two spatial dimensions. An array of CNTs is modeled as periodic discrete bars of plasma with specified width and height in the x and y directions, respectively, as is shown schematically in Figure 6. The 2D domain size is 8 micron (4000 cells) in the x direction and 12 micron (6000 cells) in the y direction. The spatial resolution is thus 2 nm in each direction. The aperture size is 4 micron. A total of approximately one million pseudo-particles are used, each representing 10 12 real particles. The pseudo-particles are initially concentrated inside the nanotubes, with no particles initialized elsewhere.
Modifications to the code are made to enforce the one-dimensional conductivity of the CNTs by allowing electron motion and momentum change only in the y direction while an electron is inside a CNT. In order to emulate electron field emission, the boundary corresponding to the tip of each CNT is left open to allow electrons to spill out and leave the CNT as shown in Figure 6. This approximation is justified by the high laser fields of order 10 10 V/m or greater and the low work function of the CNT. These boundaries and restrictions on movement allow emission from the CNT tip only when the laser is polarized parallel to the CNT axis, a phenomenon found in previous experimental results [42]. The opposite boundary, where the CNTs touch the edge of the simulation domain in the y direction, is made periodic so that the upper and lower CNTs can exchange electrons. This boundary condition models the high parallel conductivity of the CNTs and mitigates space-charge effects that might result from the finite length of the CNTs used in the simulation. The CNTs are separated with equal spacing. The surplus space provided by this arrangement allows flexibility in the CNT spacing and consequently the effective electron density perceived by the laser while holding the total number of CNTs constant. The perceived electron density is calculated as the average electron density taking into account the CNTs and the vacuum gaps between them. The density of the CNTs themselves is taken to be 10 22 cm −3 , and the CNT width is 10 nm. As we wish to explore super-critical densities with this arrangement of CNTs, here we switch to the characterizing ratio n e /n c , where n e is the average perceived electron density accounting for the CNTs and the empty space between them. Figure 7 shows the change in this ratio with respect to CNT separation. The average density becomes equal to the laser critical density (and the ratio becomes unity) for a spacing of approximately 200 nm. By reducing the spacing, the perceived electron density can easily exceed the laser critical density, reaching up to n e /n c = 10 for the values surveyed.
To extract electrons from the CNTs, two lasers pulses (with a wavelength of 1 micron as before) are injected sequentially. The second laser pulse enters the simulation after the first pulse has fully exited (around 45 fs of total simulation time). Each has a Gaussian profile in time and width corresponding to a pulse length of 15 fs and a spot size of 10 micron, respectively. Each pulse has a 0 = 0.5. The first pulse extracts electrons to form an electron cloud between the rows of CNTs. The second pulse then accelerates the electrons in the cloud. We scan over various parameters of the system in order to obtain energy scaling laws. Figure 8 shows the locations of electrons overlaying the laser electric field for one simulation at different times to visualize the effects of two laser pulses. The number of extracted electron pseudo-particles in the space between the CNTs in Figure 8b suggests an estimated extracted electron density of 10 19 cm −3 . Although the first laser pulse is primarily intended to extract electrons from the CNTs, it also has some ability to accelerate electrons, as is shown by the energy distribution in Figure 9a, which corresponds to the moment that the first laser pulse has left the simulation and the second pulse has not yet entered. The momenta of these accelerated electrons lies mostly in the ±ŷ direction. As the second laser reaches midway through the domain, it couples with the freed electrons and ponderomotively accelerates them in the +x direction. This second stage of acceleration produces a bump in the energy distribution at around 20 keV and pushes the maximum energy to a higher value, as is shown in Figure 9b. The acceleration that occurs in the second stage requires some further remarks. Ponderomotive acceleration, as conceived in typical wakefield physics, is the result of a nonuniform and oscillating electromagnetic field and involves averaging of the accelerating field. In this case, however, acceleration in the +x direction can occur in a uniform laser field. This acceleration occurs via the instantaneous ponderomotive force given by p y B z , where p y for an electron is provided by the first laser pulse. In this manner, electrons with a favorable phase with respect to the laser can receive a kick in the +x direction. In a vacuum, such electrons cannot remain in phase with the laser (as is possible in typical wakefield acceleration) but nonetheless retain a positive p x .
Another consideration affecting electron acceleration is the perceived CNT electron density. Figure 10 shows the number and maximum energy of accelerated electrons with respect to the perceived ratio n e /n c . The ratio is varied by changing the CNT spacing. For n e /n c < 1, the laser is able to penetrate deep into the the CNT structure and extracts electrons in proportion to the total number of CNTs, as is shown in Figure 10a. When the perceived electron density exceeds the critical density, laser propagation through the CNT structure is impeded, and consequently fewer electrons are extracted. Note that electron recapture by the CNT boundaries causes a decrease in extracted electrons between roughly 20 and 60 fs. For the same simulations, maximum electron energy is shown in Figure 10b. Two regimes are evident; a significant transition in the maximum electron energy occurs for n e /n c > 1. In light of this observation and the preceding arguments, we propose an energy scaling law to roughly predict the energy gain ∆E based on instantaneous ponderomotive acceleration as follows: where ν ex is defined as the maximum velocity in the +x direction of all particles in the system, ∆τ = 15 fs, and ω = 2πc/λ ≈ 1.8 × 10 15 s −1 . The interaction interval ∆t is defined as Using Equation (2) in Equation (1), we find that: This scaling law compares well with simulation results as shown in Figure 11 for two different n e /n c density ratios on the extreme ends (0.48 and 10). An interesting idea to consider is that of resonance between the spacing and plasma wavelength of the CNTs. For the present CNT density of 10 22 cm −3 , the corresponding plasma wavelength is λ p ≈ 334 nm. This case is roughly represented by the red traces in Figure 10. The monotonic decrease in number of extracted electrons with CNT spacing in Figure 10a is interrupted for a spacing of 300 nm. A similar phenomenon is seen in Figure 10b. While the super-critical traces appear to follow different qualitative behavior, the case of a spacing of 300 nm gives the greatest electron energy among the critical and sub-critical traces. These observations suggest a possible resonance between the CNT plasma wavelength and spacing.
Conclusions
The majority of efforts involving plasma wakefield acceleration have focused on producing ever higher-energy electron beams, particularly for applications in particle accelerators. Notable experiments in this area include BELLA, FACET, and AWAKE (mentioned in such as [40,43]), which aim to reach TeV energies. To reach such high acceleration gradients, experiments typically use low-density plasmas (n c /n e 1) and a 0 > 1.
The opposite regime, that of LWFA near the critical density, remains comparatively unexplored. Nonetheless, this regime holds potential for innovative approaches in fields such as cancer therapy, in the form of LWFA-powered endoscopic electron therapy (or intraoperative radiation therapy). This regime also opens possibilities for highly localized, precise treatment of targets on the skin, such as for oncology or cosmetics, making use of extremely shallow-penetrating electrons. This latter case may be particularly tractable given the low electron energies required. Crucially in all of these applications, the source of radiation is brought close to the irradiation targets such as tissues to be treated, removing collateral damage to other tissues. Consequently the radiation need only have limited penetrative power. With electrons used as the source of radiation, the desired energies are then 1 MeV, which yields a penetration depth between microns and millimeters [18]. By tuning the laser intensity and plasma density, specific depths can be produced as desired. Here we have shown though a preliminary study that LWFA can indeed produce such electrons.
To do so, the plasma density must be close to the critical density (n c ∼ n e ), a regime that can be accessed via a solid-state target such as a bundle of carbon nanotubes. In this regime the group velocity of a laser pulse becomes increasingly slow, and the laser-plasma interaction range reduces nearly to a single wakefield oscillation. As a consequence of these properties, the wakefield, rather than skimming a small number of electrons from the bulk distribution and accelerating them to high energy, instead dredges somewhat more deeply from the bulk, creating an effective viscosity and momentum transport. This situation manifests as a "black tsunami" in analogy to beach wave physics and represents a qualitative departure from typical wakefield physics. Upon slowing down near the shore, the wave begins to break, creates turbulence, and dredges the sea floor, creating a visibly black wave. Wakefield physics in the limit of n c /n e = 1 manifests in a similar way, resulting in a churning wave of relatively low-energy electrons which can then be harnessed as a beam.
The gradual transition between the "black" and "blue" wakefield regimes, corresponding respectively to high and low plasma density, has been shown, along with the linear scaling of peak electron energy. The specific entropy metric D has been proposed as a quantitative index for the regime of wakefield physics under consideration. In the low-density limit ("blue" waves), D → 0, while near the critical density ("black" waves), D becomes finite, possibly tending to a large value. Furthermore, a scan of maximum electron energy ∆E over a range of intensities a 0 reveals a general agreement with the function g(a 0 ) = 1 + a 2 0 − 1, derived from the ponderomotive potential, despite additional complexities and the limitations of a 1D simulation geometry. The difference in the mechanism of acceleration between the high-and low-density regimes is also manifested in the maximum electron energies attained in the two cases in Figure 5.
The recent development of coherent networks of fiber lasers (CAN) [16] has allowed LWFA research to branch into new fields of medical applications. However, two chief limitations must be addressed for a medical fiber laser system: laser intensity and pulse length. Fiber lasers have stringent intensity limitations, with a maximum allowed individual fiber intensity likely less than 10 14 W cm −2 . This limitation can be mitigated through the use of many coherently added fibers and by retreating from the critical density to a more modest plasma density (such as n c /n e = 10). Even with these factors, the ultimate intensity would likely remain in the regime of a 0 < 1. Limitations on pulse length are also stringent; the shortest pulse length likely achievable in a fiber laser system is around 100 fs, which is several times longer than was used in Figure 2. Fortunately, Raman scattering effects and self-modulation may allow the "black", low-energy electron regime to be accessible for a long pulse, even at very low intensity (a 0 1) and low density (n c /n e = 10) [18,44]. The bulk of this work addressed a scheme were a laser is injected parallel to the axis of a modeled bundle of carbon nanotubes. With these limitations of fiber lasers in mind, however, exploratory simulations were also made to investigate an alternative, 2D arrangement of carbon nanotubes (CNTs), also allowing attainment of densities much higher than those possible in gas plasmas. CNTs were selected for various advantageous electrical properties, such as an effective one-dimensional conductivity. In this arrangement, two laser pulses travel through a gap between two sequences of CNTs with notably the laser electric field directed parallel to the CNT axis. The first laser pulse extracts electrons from the CNTs, and the second pulse accelerates the electrons by an instantaneous ponderomotive mechanism that is atypical of wakefield physics. Scaling for the number of electrons emitted and maximum electron energy with respect to the perceived electron density was investigated, leading to a proposed energy scaling law. These results suggest that such an arrangement of CNTs may be able to efficiently generate a large flux of low-energy electrons as would be useful in a medical application. Additionally, the high critical density of the laser and the high density of the CNTs compared to the background air density suggest that a device based on this scheme may not need to impose an internal vacuum, which is much more amenable to medical applications. We invite further investigation of using CNTs in this arrangement for generating large fluxes of low-energy electrons.
Other challenges remain. This work has addressed only the most fundamental aspects of LWFA near the critical density. The population of accelerated electrons generated by LWFA at high density is non-monoenergic and probably of high emittance. Additionally, treatment of higher-dimensional effects such as focusing and hole-boring will be necessary for any ultimate medical application, and thus must therefore await future work. However, we emphasize that the remarkable trend in specific entropy as the plasma density approaches the critical density may not have been noticed with the inclusion of higherdimensional effects in a mixed effort. In this sense, our study has followed in the spirit of Boltzmann [45] in his development of Boltzmann entropy. We may also strive to further increase energy efficiency. Toward such a purpose we may wish to employ a graded density of plasma to control the phase gradation of the wakefield [46,47]. Nonetheless, interesting physics has already emerged from these efforts, and the richness of a new regime is evident. Data Availability Statement: Not applicable (this study does not report any available data).
Acknowledgments:
The present paper arose from the term-project efforts of the students in the tri-campus (UCI, UCLA, UCSD) graduate physics course Special Topics in Plasma Physics PHY249, "Nonlinear Plasma Physics" (Winter, 2019), led by the instructor T. Tajima. We also tried to tie plasma physics with other disciplines such as medical physics and geophysics to broaden the students' experience in physics. The tri-campus plasma physics graduate course was launched in academic year 2018, and this course was one of three such courses. The materials are partially available on a Google Drive upon request. We are thankful for discussions with G. Mourou, D. Strickland, J. Wheeler, J.C. Chanteloup, D. Roa, X. Yan, N. Beier, and A. Nečas. | 11,597.6 | 2021-06-11T00:00:00.000 | [
"Physics"
] |
A Flavorful Factoring of the Strong CP Problem
Motivated by the intimate connection between the strong CP problem and the flavor structure of the Standard Model, we present a flavor model that revives and extends the classic ${m_u=0}$ solution to the strong CP problem. QCD is embedded into a $SU(3)_1\times SU(3)_2 \times SU(3)_3$ gauge group, with each generation of quarks charged under the respective $SU(3)$. The non-zero value of the up-quark Yukawa coupling (along with the strange quark and bottom-quark Yukawas) is generated by contributions from small instantons at a new scale $M \gg \Lambda_{QCD}$. The Higgsing of $SU(3)^3\to SU(3)_c$ allows dimension-5 operators that generate the Standard Model flavor structure and can be completed in a simple renormalizable theory. The smallness of the third generation mixing angles can naturally emerge in this picture, and is connected to the smallness of threshold corrections to $\bar\theta$. Remarkably, $\bar\theta$ is essentially fixed by the measured quark masses and mixings, and is estimated to be close to the current experimental bound and well within reach of the next generation of neutron and proton EDM experiments.
Introduction
The standard model contains two physical CP violating parameters: (1) the perturbative CKM phase, which originates in the misalignment of the eigenvectors of the Yukawa matrices y u and y d [1], and (2) the strong CP phaseθ = − arg det e −iθ y u y d , (1.2) which originates from the combination of the QCD θ angle and the determinant of the Yukawas. Although these two phases appear to be intimately related through their connection to the Yukawa matrices, δ CKM is observed to be O(1), while current limits giveθ 10 −10 [2][3][4]. This is the strong CP problem: how can such a small value ofθ be explained when the quark sector appears to feel O(1) CP violation? In view of the strong connection of the flavor sector with the strong CP problem, it is natural to explore its solutions in the context of models which also generate the flavor structure in the standard model [5][6][7]. We present such a mechanism in this work. One appealing class of solutions to this problem are those that contain a new anomalous U (1) P Q symmetry. The most economical possibility is the "massless up quark solution", where setting m u = 0 at a scale above the QCD scale leads to a U (1) P Q symmetry. This is not a priori inconsistent with current algebra since non-perturbative effects can generate an effective up-quark mass [8][9][10][11] (see [12] for a review). In the simplest extensions of the standard model, non-perturbative QCD effects are only relevant at the scale Λ QCD ∼ GeV, and the mechanism can therefore remove any contributions toθ generated above the scale Λ QCD . Unfortunately, the massless up-quark solution is now strongly disfavored by lattice results, which find a non-zero MS value [13,14], m u = 2.3 +0. 7 −0.5 µ=2 GeV . (1. 3) The significance with which this rules out m u = 0 solutions is more difficult to quantify. Refs. [12,15] have recently pointed out some ambiguities and suggested further direct lattice tests that can support this conclusion. In this work we consider an extension of the massless up quark solution into models where large non-perturbative effects are generated by embedding QCD as the diagonal subgroup of a SU (3) N gauge group. This mechanism for "factoring" the Strong CP problem was first presented in Ref. [16], where all of the quarks are charged under a single SU(3) factor, and the PQ symmetry is realized by a heavy axion in each sector. In this work, we instead give a flavorful embedding of the quarks in a SU (3) × SU (3) × SU (3) gauge group, with each quark generation charged under a separate factor. Each factor contains an independent PQ symmetry implemented by a perturbatively massless quark instead of a heavy axion, and the observed non-vanishing Yukawa couplings are generated entirely by non-perturbative effects at a high scale M . These non-perturbative effects can be sizable because although the SM QCD coupling is weak at high scales M Λ QCD , each individual SU (3) factor can easily be near strong coupling 1 . Higher dimension operators generate the quark mixing matrix upon the breaking to the diagonal group. Below the scale M the theory matches to the standard model with no additional matter. Since in the standard modelθ is very well sequestered from δ CKM [17][18][19][20], solving the strong CP problem at the scale M solves it at low energy as long as no new sources of flavor or CP violation are introduced [21]. Whileθ is suppressed in this model at tree-level, a non-vanishing radiative contribution is generated with a size directly connected to the observed quark masses and CKM angles. Remarkably, the model predictsθ ∼ 10 −10 , just below the sensitivity of current EDM experiments and within reach of proposed next generation neutron EDM [22,23] and proton storage ring experiments [24].
Other models that can explainθ = 0 at tree level in the UV typically require large discrete symmetries and extensions of the flavor structure, and do not preserve the radiative sequestering ofθ present in the SM. For example, in Nelson-Barr models [25][26][27][28], the radiative contributions ∆θ generally exclude the most appealing models unless some allowed couplings have unexplained suppressions or the symmetry structure of the SM is substantially extended [21,29]. There are also other mechanisms that introduce new non-perturbative PQ violating effects at higher energies M Λ QCD to solve the strong CP problem. Refs. [30][31][32][33][34] consider models where theθ of the SM is related by a Z 2 symmetry to a mirror copy of the standard model withθ =θ. Spontaneous Z 2 breaking [35] allows the states of the mirror sector to be decoupled, and non-perturbative mirror SU (3) effects to become strong at a scale Λ QCD Λ QCD and simultaneously relaxθ and θ either with a heavy-axion [30][31][32][33][34] or a heavy perturbatively massless quark [32]. These theories are significantly constrained by the cosmology of the mirror sector and new colored TeV-scale particles. Another possibility is that the SM QCD itself becomes embedded in a strongly coupled gauge group at high energies-Refs. [36][37][38][39][40] considered the possibility that extra matter causes QCD to run back to strong coupling at a scale M where it is embedded in a larger gauge group, e.g. SU (3 + N ). In general to obtain sizable effects these models also require the addition of new dynamics breaking the chiral symmetries, and contain new CP violating phases which cause a misalignment between the non-perturbative violations of the PQ symmetry at Λ QCD and Λ QCD , spoiling the solution to the strong CP problem [38].
Massless Quark Solution in QCD: the baby version
We start from a simpler version of the standard model with only a single generation of quarks -the SU (2) doublet q = (u, d) and two singlets u c , d c -charged as in the standard model. We include an SU (2) doublet Higgs H and assume a UV cut-off Λ U V . We make use of an anomalous U (1) P Q symmetry under which only u c transforms, which forbids an up Yukawa coupling at the perturbative level (more precisely, we assume that the dominant source of PQ breaking is from non-perturbative effects within the effective theory far below the scale Λ U V ). The relevant terms in the Lagrangian are The U (1) P Q symmetry and a chiral rotation of d c can be used to remove the topological phase θ and the phase of the non-vanishing Yukawa coupling y d . Therefore there is no physical CP violating parameter,θ = 0. This is effectively the massless up quark solution to the strong CP problem. Non-perturbative SU (3) effects violate the anomalous U (1) P Q , so non-perturbative effects suppressed as ∼ e −2π/αs will generate a non-vanishing effective y u coupling at energies below Λ U V . In the weak coupling limit, the dilute instanton gas approximation captures the leading non-perturbative effects, and the instantons can be integrated out to generate an effective Lagrangian for the fermions [9,41,42]. For SU (3) with two flavors of quarks, both four-fermion and bilinear terms are generated from single-instanton effects, where α, β are QCD indices and the dimensionless instanton density is which features the non-perturbative exponential suppression factor at weak coupling. The analytic constants are D 0 ≈ 0.02 and c 0 ≈ 1.79 [9]. The couplings in the integrand are evaluated at the scale ρ −1 (higher order corrections can be found in Ref. [12]). Higher dimension operators are suppressed by further powers of D[α] , and D[α] ∼ 1 signals the breakdown of the dilute instanton gas approximation. The effect of instantons on the Yukawa couplings can be conveniently described as a non-perturbative contribution to the running of the Yukawa couplings [9], Recall that the perturbative contributions to the running of Yukawas are multiplicative, and are negligible here. Now that non-perturbative effects are included, y u = 0 is generated and the PQsymmetry appears to be violated perturbatively in the low energy effective Lagrangian. However, the physical CP angleθ remains vanishing: the non-perturbatively generated y u has just the right phase to allow the θ angle and the phase in y d to be simultaneously rotated away, as is clear from eq. (2.3). Two-flavor QCD is asymptotically free and the instanton density grows in the IR. If SU (3) is Higgsed at the scale M , the instanton contribution to y u is cut-off and dominated by instantons of size comparable to the Higgsing, ρ −1 ∼ M (we will discuss the nature of the Higgsing sector in the following section). Using the one-loop running of the gauge coupling dα −1 = b 4π d ln µ, with b = 29/3 for 2-flavor QCD, the linear solution to the running eq. (2.5) gives where we have assumed α −1 (Λ U V ) 1 for the last equality, and Γ(n, x) is the upper incomplete Γ-function. Figure 1 shows the ratio |y u |/|y d | after integrating out effects above M as a function of the QCD coupling at the scale of Higgsing, α(M ). As |yu| |y d | approaches ∼ 1, multiple-instanton effects captured by higher order solutions to eq. (2.5) become important, and the ratio asymptotes to |y u |/|y d | = 1. For α(M ) ∼ 0.4 − 0.8 an O(1) ratio can be generated as required by the observed light quark masses. In this regime the dilute instanton gas approximation is only a qualitative picture of the non-perturbative QCD effects, but strongly suggests that they are O(1) and that a viable ratio |y u |/|y d | can be realized before the theory enters the chiral-symmetry breaking phase which would be expected to occur at α(M ) 0.7 − 1 [43,44]. As the theory flows to weak coupling at scales above M, the PQ violating effects are rapidly suppressed. For example for α ≈ 0.1, as in the SM near the weak scale, the non-perturbative contribution to y u is |y u |/|y d | 10 −16 .
This simple 2-flavor example shows that instanton effects can generate large non-perturbative contributions to a perturbatively vanishing Yukawa coupling. In fact such effects are known to be important near the scale of QCD confinement, Λ QCD , in the standard model, as reviewed in [12]. However, as mentioned above, lattice results strongly disfavor a massless up quark solution to the strong CP problem in the SM.
The suppression of this effect in the SM is partly due to the fact that the strange quark is also relevant at Λ QCD , and instanton contributions to m u are further suppressed by m s . In fact, 2+1 flavor lattice QCD results fully include all instanton configurations and can be interpreted as a calculation of the 2nd order term in the Chiral Lagrangian giving an effective up-quark mass proportional to m * d m * s /Λ QCD -these results suggest that the size of the desired non-perturbative effect is only ∼ 10-40% of the experimentally required value [12].
So, although qualitatively non-perturbative effects in the SM near the scale Λ QCD are nearly the right size to allow m u = 0 solution to the strong CP problem, quantitatively the possibility is strongly disfavored by precision lattice results. In the following section we will describe an extension to the SM in which non-perturbative effects can become important again at a high energy scale M Λ QCD , and these additional contributions allow a solution to the strong CP problem reminiscent of the massless up quark solution.
Massless Quark Solution in QCD: the real thing
Going beyond the illustrative two-flavor example, there are two challenges to generating a large nonperturbative contribution to the Yukawa couplings at a new scale M Λ QCD . The first is that QCD must be embedded in a strongly coupled theory at the scale M so that non-perturbative effects are important, but must match to the weak coupling of QCD in the standard model at high energies, e.g. α s (1000 TeV) ≈ 0.05. The second challenge is that at high energies in QCD, all three generations of quarks are relevant, leading to further Yukawa suppressions of high energy contributions from instantons at small sizes ρ −1 v. For example, as illustrated in fig. 2, the high energy contributions to y u in the 3-generation SM are further suppressed as because the explicit breaking of each non-anomalous U (1) P Q by the Yukawa couplings must be felt to generate y u = 0. Both these challenges can be solved by embedding the standard model 3 product gauge group above the scale M , as depicted in fig. 3. Each generation of quarks is charged under a separate SU (3) factor. The theory will be Higgsed at the scale M to the diagonal gauge group by bifundamental scalar fields, as discussed in more detail in the following section. The unbroken diagonal SU (3) c group's coupling is (3)3 theory, with one generation charged under each SU (3) factor. The link field Σ vevs break the gauge group down to the diagonal SU(3) of the standard model. One quark in each generation obtains its mass from non-perturbative effects, making theθ angle in each individual gauge factor unphysical. allowing to match to the weakly coupled SM QCD even when each individual factor is more strongly coupled.
Since there are now three separate SU (3) factors, there are now three separate θ problems! Fortunately, all the θ angles can be made unphysical if there is an independent anomalous U (1) P Q symmetry in each sector. The minimal realization of this PQ symmetry involves a perturbatively massless quark in each sector. Since the non-perturbatively generated Yukawa couping is always smaller than the unprotected Yukawa, a natural choice is to choose PQ symmetries that enforce y u = 0, y s = 0, y b = 0. Above the scale M of Higgsing, each site behaves as the two-flavor model of section 2. Schematically, the generation of the Yukawa couplings is depicted in fig. 4. From fig. 1, we can read off the size of the gauge couplings at the scale M that are necessary for the instantons in each factor to generate the observed Yukawa ratios: 2) then gives the coupling of the unbroken diagonal group at the matching scale α s (M ) = 0.12 − 0.22. Flavor constraints will require us to match to the SM at a scale M 1000 TeV where α s (1000 TeV) = 0.05, so it appears unlikely that this minimum SU (3) 1 × SU (3) 2 × SU (3) 3 model is viable unless our dilute instanton calculation significantly underestimates the size of non-perturbative effects.
One way to overcome this obstacle is to enlarge the product gauge group to SU where the extra gauge factors do not contain chiral matter and therefore can remain more weakly coupled. Removing the θ angle in these extra factors will involve introducing fig. 3 extended to contain an extra site with a more weakly coupled SU (3)4 factor. There is no chiral matter at this site, and the θ4 angle is removed by an anomalous U (1)P Q symmetry of a single vector-like quark species Ψ, Ψ c . While MΨ = 0 perturbatively, non-perturbative effects violating the PQ symmetry generate MΨ = 0. M generated by non-perturbative effects could be an interesting signature of this theory to study in further work, but for the remainder of this work we assume these states decouple and focus on the details of the Another alternative possibility to avoid enlarging the gauge group with extra SU (3) factors is to consider a model with PQ symmetries ensuring y d = 0 instead of y s = 0, so that smaller nonperturbative effects are required to generate the quark mass ratios. This possibility is appealing but is in tension with constraints onθ, as described in appendix B.
The scalar sector
The full description of the relevant particle content of the SU (3) 1 × SU (3) 2 × SU (3) 3 model is given in table 1. There are several possibilities for the scalar fields breaking the gauge group to the diagonal, here we take a simple choice motivated by CKM mixings as described in the following section.
We assume that the scalar link fields Σ 12 , Σ 23 , and Σ 31 get vevs f 12 ∼ f 23 ∼ f 31 to break the gauge group down to the diagonal, with M corresponding to the scale of Higgsing M ∼ gf (only two link fields are necessary to break the gauge group, but the simplest renormalizable flavor models will involve three link fields). The renormalizable potential allowed by the symmetries leads to spontaneous breaking of the gauge group without introducing any new CP phases or uneaten light Goldstone boson degrees of freedom. A standard renormalizable Higgs-like potential drives a vev for each field, The couplings λ ij , δ ij , and λ ij are independent real parameters for each field Σ. The phase of γ can be removed by a field redefinition, and causes the vacuum to align with vevs Σ 12 , Σ 23 , Σ 31 that can all consistently be chosen to be real. Taking γ to be a small perturbation for simplicity, we find [45,46] Σ ij = m Σij
CKM and noθ at tree level
The model we have introduced so far generates the diagonal Yukawa couplings and breaks the product gauge group down to the standard model SU (3) c , all while maintaining an accidental CP symmetry at the renormalizable level. After integrating out the non-perturbative effects near the scale M , the theory matches to the standard model with non-vanishing diagonal Yukawa couplings for all of the quarks and phases that preserveθ = 0.
The PQ symmetries and large non-perturbative effects are crucial to the accidental CP symmetry, since they allow the breaking of the quark chiral symmetries without introducing extra CP violating parameters. The next challenge is to introduce the CKM mixing without spoiling this protection. When we introduce additional off-diagonal Yukawa couplings, the accidental CP symmetry can no longer survive, since the observed CKM phase must be generated. However,θ SM will still vanish at tree level and remain highly suppressed even at loop level due to the residual approximate flavor symmetries. Introducing quark-mixing between generations requires higher dimensional operators involving the link fields, e.g.
generates the effective Yukawa matrices when the Σ fields acquire vacuum expectation values. We can write the off-diagonal Yukawa couplings below the scale of Higgsing, Since the off-diagonal entries in the Yukawa matrices can be small, the flavor scale Λ f M is possible, with a separation as large as Λ f 10 4 M consistent with unitarity and the size of the observed offdiagonal Yukawa elements. However, a natural assumption that the couplings λ of the UV completion are comparable to the non-vanishing diagonal Yukawa couplings would require e.g. Λ f ∼ f to generate the O(1) Cabibbo angle.
For general off-diagonal couplings, it is no longer true that the tree-levelθ vanishes after matching to the SM, (3.12) The first determinant factor is real, as shown above. For the other two factors, it is simple to see that we must require that the off-diagonal matrices O u,d can be put in a strictly triangular form (up to SU (3) rotations). We would like the quarks to transform under (possibly anomalous) U (1) symmetries that perturbatively protect this form, and in fact there are only two possible textures satisfying these constraints and giving viable CKM mixings. The texture we will focus on is: 14) and the assignment of PQ charges in table 2 protects this form of the Yukawa matrix. The other possible texture, described briefly in appendix B, gives a less natural realization of the CKM structure. The three anomalous U (1) P Q symmetries allow us to rotate away the θ angle in each SU (3) factor, and field redefinitions leave only two remaining physical CP phases in the Yukawa matrix, which we choose by convention to put in the Y d 23 and Y d 21 elements. Including non-perturbative instanton effects and for the moment ignoring all other radiative effects, below the scale M the theory matches to the SM with Yukawa matrices We can check explicitly thatθ SM = 0 at tree level, The real coefficients r 1,2,3 parameterize the size of the instanton suppression of PQ breaking in each SU (3) factor. The couplings Y can now be determined from the CKM matrix and the observed SM fermion masses. The only undetermined parameter is Y d 21 /Y d 11 , but we will be motivated shortly to focus on the limit Y d 21 Y d 11 . Then to leading order in the small Yukawa ratios y u,d /y c,s,t,b , y s /y b , and small CKM mixings |V 31 | = 0.0089, |V 32 | = 0.041 [14] we obtain where we have made a field definition choice to put the CKM phase entirely into Y d 13 and θ c is the Cabibbo angle. An alternative solution with the same texture but flipping the role of the strange and down quarks is discussed in appendix B. Now that the CKM elements are introduced, the gauge basis in the SU (3) × SU (3) × SU (3) theory is no longer aligned with the flavor basis, and four-fermion operators generated by gauge interactions at the scale M will introduces non-MFV contributions to CP-preserving flavor observables. The dominant constraint is due to the ∆C = 2 operator generated by exchange of the heavy broken SU(3) gauge bosons, given in the quark mass basis as Constraints on the D 0 splitting generated by this operator give M 1000 TeV [47]. The leading ∆B = 2 and ∆S = 2 operators are suppressed respectively by |V 13,23 | 2 and |V 12,23 y d /y s | 2 and give less stringent constraints. Figure 6. One of the leading diagrams generating a non-vanishing threshold correction to ∆θ. The offdiagonal Yukawa couplings appear in order to introduce a CP phase, and the instanton violates the anomalous PQ symmetry protecting the UV form of the Yukawa couplings as in eq. (3.14).
∆Θ from thresholds
With the two physical CP violating phases in the Y d 23 and Y d 12 elements, it is clear that at leading order in the Yukawa couplings, neither contributes to the low energy theta angle. However higher order perturbative corrections to the non-perturbative effects at M can give a non-vanishing threshold correction toθ SM .
At energies below M , the additional breaking of the SM flavor symmetry generated by the gauging of SU (3) 1 × SU (3) 2 × SU (3) 3 decouples and the theory is just the standard model, where the flavor symmetries suppress the running ofθ to negligible effects starting at 7-loops [17,20]. At energies far above M , the non-perturbative PQ violating effects are exponentially suppressed by the weak coupling of the gauge groups, and the PQ symmetry protects the form of the Yukawa matrices with θ = 0 manifest, eq. (3.14). Therefore the dominant effect onθ is a threshold effect at energies near M , where the non-perturbative violation of the PQ symmetries are still large and the extra breaking of the SM flavor symmetries through the gauging of SU (3) 1 × SU (3) 2 × SU (3) 3 has not decoupled.
The leading effects occur at third order in the Yukawa couplings, schematically generated from diagrams of the form of fig. 6. Roughly, these diagrams describe how the Yukawa elements closing the instanton diagrams depend on the scale of the instanton -there is a mismatch of the phase between instantons at different scales because of the perturbative running of the Yukawas. Taking the Σ fields as background fields, the 1-loop running of the effective Yukawa couplings eq. (3.10) takes the same form as in the SM [48], with the non-vanishing CP phases entering through the terms 3rd order in the Yukawa couplings: Since the phases entering in the instantons no longer align exactly with the low energy perturbative values of the Yukawa couplings, there is no longer an exact cancellation in phase between the nonperturbatively generated eigenvalues and the perturbative eigenvalues of Y u,d .
To obtain a parametric estimate of these effects, we iteratively solve the RGE including the perturbative running eq. (3.20) and non-perturbative running eq. (2.5) of the Yukawas, as described in detail in appendix A. We ignore the effects of perturbative gauge interactions and the propagation of the Σ fields -all effects that modifyθ must involve both an instanton and a Yukawa loop, so these higher order effects can give at most O(1) corrections to our estimate if these states are strongly coupled. Finite effects not captured by the RGE are also expected to be of comparable size. There are two leading contributions toθ. The size of the first is fixed by the experimentally determined elements of the Yukawa matrix, with this linear approximation holding well in the coupling region of interest α ∼ 0.2−1. The small size of ∆θ ∼ 10 −10 is due to the loop suppression and the smallness of the off-diagonal Yukawa elements. The form of ∆θ is consistent with the observation that Y 13 and Y 23 must appear as a product, since the physical phase can be rotated from one term to the other. The suppression by a factor of 1/b = 3/29 arises because there is only a small range of energies where instanton effects are important, controlled by how rapidly the gauge coupling runs. There is another contribution proportional to the undetermined Yukawa element Y 21 , If Y d 21 takes on a value ∼ y d with O(1) phase, this extra contribution is inconsistent with experimental limits. However, spurion arguments show that |Y d 21 | y d can be naturally obtained. Since Y d 21 breaks a different set of flavor symmetries, its natural size can be as small as making ∆θ subdominant.
We have checked these estimates numerically at the one-loop level.
UV Sensitivity
It is useful to discuss the degree to which this mechanism is insensitive to ultraviolet physics at some scale Λ U V where CP may be violated in a sector strongly coupled to the standard model. For CP violation to be communicated from this sector toθ, the anomalous breaking of the PQ symmetry must be active. There are two possible contributions: small instantons of scale Λ −1 U V interacting directly with the new UV physics, and the unsuppressed instantons at the scale M −1 interacting with the physics at Λ U V through higher dimensional operators.
The contributions of small instantons of size Λ −1 U V is suppressed by the exponentially small instanton density D(Λ −1 U V ) as long as the individual SU (3) factors have run back to weak coupling. For example, suppose the physics at Λ U V introduces an O(1) phase α in the non-vanishing Yukawas, e.g. y d (Λ U V ) ≈ e iα y d (M ). Then instantons at the scale generate a contribution to y u with a phase that will appear inθ, In a sector with two-flavors, this contribution is consistent with ∆θ 10 −10 if Λ U V 100M . The physics at the scale Λ U V can also generate higher dimensional operators consistent with the PQ symmetries and other approximate chiral symmetries that carry CP phases and can interact with the unsuppressed instantons at the scale M (such operators also interact with instantons at the scale Λ QCD and generate a shift inθ even in the standard PQ axion or massless up quark solution [49], but here these effects are subdominant by a factor Λ 2 QCD /M 2 ). The most dangerous operators are momentum dependent contributions to the phase of the perturbatively allowed diagonal Yukawas, Combined with instanton insertions at M , these give When Y ∼ Y and the phases are uncorrelated, this requires Λ U V 10 5 M to avoid generating ∆θ. Another dangerous d = 6 operator that can generate contributions toθ even in the absence of PQ breaking are mixed topological terms, for example gives a contribution ∆θ ≈θ 12 , again requiring Λ U V 10 5 M unlessθ 12 is suppressed.
A Flavor UV Completion
The d = 5 operators in eq. (3.9) generating the off-diagonal Yukawa elements require a UV completion at the scale Λ f . Unitarity of the d = 5 operator in eq. (3.9) generating the off-diagonal Yukawas requires Λ f 10 −4 M . Taking the effective action to d = 6 introduces operators consistent with the PQ symmetries that could allow the CP violation generating δ CKM to enter directly into ∆θ, as discussed in section 3.4.
In this section we give an example of a simple UV completion in which the higher dimension operators do not make large contributions to ∆θ and which can also explain the origin of the spurion argument giving |Y d 21 | y d . The model is extended to involve a set of vector-like fermions Q 3 ,Q 3 , U c 1 ,Ū c 1 , with charges under the gauge and PQ symmetries as given in table 3. Renormalizable mixings between heavy states and the SM-like fields generates the higher dimensional operators eq. (3.9) after integrating out the vector-like states.
The renormalizable terms in the Lagrangian consistent with the gauge and PQ symmetries are This term is also suppressed by the mixing of q 1 and q 2 with the vectorlike Q 3 . For Σ 13 ∼ Σ 23 ∼ M , the contribution to the theta angle is As long as the marginal couplings generating the q 1 and q 2 mixings are not too weakly coupled, x Q 13 , x Q 23 , z 33 0.2, this contribution is subdominant. This corresponds to a rough lower limit on the scale M Q 100M . Note that a hierarchy M Q M U ∼ M can naturally explain the small third-generation quark mixings and O(1) Cabibbo angle.
This flavor model has a similar structure to minimal Nelson-Barr models [25][26][27], which obtain CKM mixings through vector-like quarks [28], forbidding a tree-levelθ. However, in contrast to the present case where the U (1) symmetries are sufficient to protect the structure of the theory, in Nelson-Barr models discrete symmetries and additional UV structure are required [21,29]. In both cases, radiative contributions toθ limit the allowed parameter space, but in Nelson-Barr models these limits appear to generically require unexplained suppressions of allowed couplings [21].
Conclusions
The solutions to the strong CP problem and the origins of the flavor structure of the standard model may be intricately tied to each other. In this work, we constructed a model where embedding QCD in a SU (3) 3 gauge group with flavorful anomalous PQ symmetries can naturally explain the nonobservation of a neutron EDM, the smallness of the third generation CKM mixing angles, and the relative suppression of the down-like quark masses in the second and third generation. The theta angle in each SU (3) factor can be set to zero using an anomalous PQ symmetry. This symmetry is realized by forbidding a bare mass for the lighter quark in each generation (i.e. u, s, b). Their masses are generated through instantons, dominantly at the scale of SU (3) 3 breaking, M , which can be far above the weak scale. The instanton-generated mass terms have phases that are naturally aligned with the theta angle, and hence do not reintroduce a non-zeroθ.
There is a non-zeroθ generated at the threshold M through loop corrections that involve both the instanton vertex as well as the perturbative CKM phase. In fact, in our model the smallness of the CKM mixing angles is intimately tied to the smallness ofθ in this model, and the observed CKM elements give a predictionθ ∼ 10 −10 that can be probed at the next generation of neutron EDM [22,23] and proton storage ring experiments [24]. The solution to the strong CP problem is in the spirit of the massless up quark solution, and there are no axion-like states in the theory. An interesting future direction would be to study models which generate the full standard model flavor structure while also implementing our mechanism to solve the strong CP problem.
B Alternative Yukawa Structures
An alternative solution to the observed quark masses and CKM matrix is possible with the Yukawa texture of eq. (3.14) by switching the role of y d and y s . In this case the non-perturbative effects generate y d from y c , y u from y s , and y b from y t . This is an attractive possibility because it requires smaller nonperturbative effects, and therefore can more easily be accomodated without adding additional weakly coupled sites to the SU (3) × SU (3) × SU (3) model. However, the size of the radiative contribution to ∆θ is increased by a factor of (cot θ c ) 2 ≈ 20 in this model, which is excluded by current limits unless there is a ∼ 10% tuned cancellation with another contribution toθ.
While we focused on the Yukawa texture eq. (3.14), there is one other possibility for a viable Yukawa texture that can be protected by U (1) P Q symmetries and has a vanishing tree-level contribution toθ, The CKM structure emerges less naturally for this texture because of the right-handed dominant mixing structure in the down Yukawa matrix. Fitting the V 31 and V 32 CKM elements requires a cancellation between terms of order Y u 31 /y t and Y d 12 Y d 32 /Y 2 b . Nonetheless this texture remains an interesting possibility, and viable models can be realized and also generically predictθ ∼ 10 −10 from the radiative corrections. | 8,257.2 | 2017-12-15T00:00:00.000 | [
"Physics"
] |
Small angle neutron scattering data of polymer electrolyte membranes partially swollen in water
In this article, we show the small-angle neutron scattering (SANS) data obtained from the polymer electrolyte membranes (PEMs) equilibrated at a given relative humidity. We apply Hard-Sphere (HS) structure model with Percus–Yervick interference interactions to analyze the dataset. The molecular structure of these PEMs and the morphologies of the fully water-swollen membranes have been elucidated by Zhao et al. “Elucidation of the morphology of the hydrocarbon multi-block copolymer electrolyte membranes for proton exchange fuel cells” [1].
a b s t r a c t
In this article, we show the small-angle neutron scattering (SANS) data obtained from the polymer electrolyte membranes (PEMs) equilibrated at a given relative humidity. We apply Hard-Sphere (HS) structure model with Percus-Yervick interference interactions to analyze the dataset. The molecular structure of these PEMs and the morphologies of the fully water-swollen membranes have been elucidated by Zhao et al. "Elucidation of the morphology of the hydrocarbon multi-block copolymer electrolyte membranes for proton exchange fuel cells" [1].
& 2016 Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Subject area
Materials science More specific subject area
Soft matter
Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/dib The dry membranes with an average thickness of $ 50 μm were prepared by solution casting onto a flat glass plate from its dimethyl sulfoxide solution with a concentration of 5 wt%. Partially water swollen membranes were prepared by putting the dry membranes into a humility controller at 30% relative humidity and 25°C. Experimental features
Type of data
The incident neutron beam was monochromatized with a velocity selector to have the average wavelength (λ) of 5 Å with a wavelength resolution of Δλ/ λ¼ 20%. All of the measurements were done at 25 70.5°C. The scattering patterns were collected with a two-dimensional scintillation detector, and circularly averaged to obtain scattering intensity profiles as a function of q, where q is the scattering vector, defined as q ¼(4π/λ)sin(θ/2) with θ being the scattering angle. The scattering profiles were corrected for the instrument background, detector sensitivity, and scattering from empty cell, and finally calibrated on the absolute scale (cm À 1 ) using a Plexiglas secondary standard. Data source location SANS measurements were performed with KWS-2 at the neutron source Heinz Maier-Leibnitz (FRM II reactor) in Garching, Germany.
Data accessibility
Data is with this article
Value of the data
Hard-sphere structure model is introduced to elucidate the morphology of polymer electrolyte membranes.
Data of partially swollen membranes together with that of fully swollen membranes leads to a thorough understanding of the morphology.
The method and model analysis are worthy being applied to other types of membranes.
Data
Partially water swollen membranes were prepared by putting the dry PEMs into a humility controller at 30% relative humidity and 25°C. The SANS measurements were performed with KWS-2 at the neutron source Heinz Maier-Leibnitz (FRM II reactor) in Garching, Germany, and the scattering intensity profiles has been corrected and calibrated on the absolute scale (cm À 1 ). Fig. 1a and b show the SANS intensity profiles of the two membranes, PSP 14 -b-PAEK 14 and PSP 28 -b-PAEK 14 , as a function of scattering vector q, respectively. The profile of the corresponding fully D 2 Oswollen membranes is plotted in the same figure as a reference. Hard-Sphere (HS) structure model with Percus-Yervick interference interactions was applied to analyze these scattering profiles [1,2]. The best fitting parameters are listed in Tables 1 and 2. Note that the profiles at high-q range (0.08oqo0.45 Å À 1 ) can be fitted well by Eq. (6) below, and the best fitted curve is summed up with the fitting curve in the middle-q range and shown in the figure.
Materials
Two multiblock copolymer poly(sulfonate phenylene)-b-poly(arylene ether ketone) with different block ratios, designated as PSP 14 -b-PAEK 14 and PSP 28 -b-PAEK 14 for brevity, were synthesized by varying the stoichiometry of the sulfonated monomers and hydrophobic oligomers via the nickel-catalyzed polymerization [3,4]. The subscript 14 or 28 refers to the repeating unit number in each block. The molecular structure and characteristics of these two polymers can be found elsewhere [1,2]. The dry membranes with an average thickness of $ 50 μm were prepared by solution casting onto a flat glass plate from its dimethyl sulfoxide solution with a concentration of 5 wt% [3]. Partially water swollen membranes were prepared by putting the dry membranes into a humility controller at 30% relative humidity and 25°C.
Methods
SANS measurements were performed with KWS-2 at the neutron source Heinz Maier-Leibnitz (FRM II reactor) in Garching, Germany [5]. The incident neutron beam was monochromatized with a velocity selector to have the average wavelength (λ) of 5 Å with a wavelength resolution of Δλ/λ¼ 20%. All of the measurements were done at 257 0.5°C. The scattering patterns were collected with a two-dimensional scintillation detector, and circularly averaged to obtain scattering intensity profiles as a function of q, where q is the scattering vector, defined as q ¼(4 π/λ)sin(θ/2) with θ being the scattering angle. The scattering profiles were corrected for the instrument background, detector sensitivity, and scattering from empty cell, and finally calibrated on the absolute scale (cm À 1 ) using a Plexiglas secondary standard.
Analysis
We assume that the topology of the swollen membranes can be described by an almost random distribution of n particles in a homogeneous matrix. Let Δb be the contrast of the particle density with respect to the matrix density and v be the of average volume of a single particle, then the observed scattering intensity, I(q), is [6] IðqÞ ¼ ðΔbÞ 2 nv 2 PðqÞSðqÞ ¼ KPðqÞSðqÞ ð 1Þ where P(q) is the form factor of the particles, S(q) is an approximate interference factor and K is a constant in terms of Δb, n and v. We assume that the number of the particles per volume is high that S(q) must be considered despite the random arrangement of the particles. The contrast Δb¼b p À b m is defined by the difference between the scattering length density (SLD) of the particle phase, b p , and that of the matrix phase, b m . Thus, Δb is computable as long as the shape and composition of the particle phase and the matrix phase are well determined, and their SLDs are theoretically estimated below. SLD of a molecule of i atoms is related to its molecular structure and may be readily calculated from the simple expression given by Mw where b i is the scattering length of ith atom, d is the mass density of the scattering body, M w is the molecular weight, and N A is the Avogadoro constant [6].
Let us consider an ensemble of spheres with varying sizes that can be described by a Gaussian size distribution: with R being the average radius, and σ R being its standard deviation. Thus v ¼ 4πR 3 3 . We consider Percus-Yevick expression to account for interparticle interference [2,7], then S(q) is the interference factor, described for a random arrangement of spheres by the following expression: here A¼2qR and ϕ is the hard sphere volume fraction. F(A) is a trigonometric function of A and ϕ given by The distribution of the ionic clusters at high-q range can be fitted well by Gaussian distribution function, where the scattering intensity around the ionomer peak at 0.08 Å À 1 oq o0.45 Å À 1 , I ion (q), can be expressed by where I m,ion is the ionomer peak height, G(q) is Gaussian distribution function about the ionomer peak at q m,ion , given by G q ð Þ ¼ 1 ð2πÞ 1=2 σq exp À q À q m;ion À Á 2 =ð2σ q 2 Þ h i , with σ q being the standard deviation of q m,ion , and I inc is the incoherent scattering intensity, which can be determined by the average intensity of the flat part of the profile at q 40.4 Å À 1 in the high-q region. Eq. (6) is used to fit profiles in Fig. 1a and b and the fitting parameters are listed in Tables 1 and 2. | 1,916.6 | 2016-03-09T00:00:00.000 | [
"Materials Science"
] |
A Multiscale Visualization of Attention in the Transformer Model
The Transformer is a sequence model that forgoes traditional recurrent architectures in favor of a fully attention-based approach. Besides improving performance, an advantage of using attention is that it can also help to interpret a model by showing how the model assigns weight to different input elements. However, the multi-layer, multi-head attention mechanism in the Transformer model can be difficult to decipher. To make the model more accessible, we introduce an open-source tool that visualizes attention at multiple scales, each of which provides a unique perspective on the attention mechanism. We demonstrate the tool on BERT and OpenAI GPT-2 and present three example use cases: detecting model bias, locating relevant attention heads, and linking neurons to model behavior.
Introduction
In 2018, the BERT (Bidirectional Encoder Representations from Transformers) language representation model achieved state-of-the-art performance across NLP tasks ranging from sentiment analysis to question answering (Devlin et al., 2018). Recently, the OpenAI GPT-2 (Generative Pretrained Transformer-2) model outperformed other models on several language modeling benchmarks in a zero-shot setting (Radford et al., 2019).
Underlying BERT and GPT-2 is the Transformer model, which uses a fully attention-based approach in contrast to traditional sequence models based on recurrent architectures (Vaswani et al., 2017). An advantage of using attention is that it can help interpret a model by showing how the model assigns weight to different input elements (Bahdanau et al., 2015;, although its value in explaining individual predictions may be limited (Jain and Wallace, 2019). Various tools have been developed to visualize attention in NLP models, ranging from attention-matrix heatmaps (Bahdanau et al., 2015;Rush et al., 2015;Rocktäschel et al., 2016) to bipartite graph representations (Liu et al., 2018;Lee et al., 2017;Strobelt et al., 2018).
One challenge for visualizing attention in the Transformer is that it uses a multi-layer, multihead attention mechanism, which produces different attention patterns for each layer and head. BERT-Large, for example, which has 24 layers and 16 heads, generates 24 × 16 = 384 unique attention structures for each input. Jones (2017) designed a visualization tool specifically for multihead attention, which visualizes attention over multiple heads in a layer by superimposing their attention patterns (Vaswani et al., 2017(Vaswani et al., , 2018. In this paper, we extend the work of Jones (2017) by visualizing attention in the Transformer at multiple scales. We introduce a high-level model view, which visualizes all of the layers and attention heads in a single interface, and a lowlevel neuron view, which shows how individual neurons interact to produce attention. We also adapt the tool from the original encoder-decoder implementation to the decoder-only GPT-2 model and the encoder-only BERT model.
Visualization Tool
We now present a multiscale visualization tool for the Transformer model, available at https: //github.com/jessevig/bertviz. The tool comprises three views: an attention-head view, a model view, and a neuron view. Below, we describe these views and demonstrate them on the GPT-2 and BERT models. We also present three use cases: detecting model bias, locating relevant attention heads, and linking neurons to model behavior. A video demonstration of the tool can be found at https://vimeo.com/340841955.
Attention-head view
The attention-head view visualizes the attention patterns produced by one or more attention heads in a given layer, as shown in Figure 1 (GPT-2 1 ) and Figure 2 (BERT 2 ). This view closely follows the original implementation of Jones (2017), but has been adapted from the original encoder-decoder implementation to the encoder-only BERT and decoder-only GPT-2 models.
In this view, self-attention is represented as lines connecting the tokens that are attending (left) with the tokens being attended to (right). Colors identify the corresponding attention head(s), while line weight reflects the attention score. At the top of the screen, the user can select the layer and one or more attention heads (represented by the colored squares). Users may also filter attention by Figure 3: Examples of attention heads in GPT-2 that capture specific lexical patterns: list items (left); verbs (center); and acronyms (right). Similar patterns were observed in these attention heads for other inputs. Attention directed toward first token is likely null attention (Vig and Belinkov, 2019). Besides these coarse positional patterns, attention heads also capture specific lexical patterns, such as those as shown in Figure 3. Other attention heads detected named entities (people, places, companies), paired punctuation (quotes, brackets, parentheses), subject-verb pairs, and other syntactic and semantic relations. Recent work shows that attention in the Transformer correlates with syntactic constructs such as dependency relations and part-of-speech tags (Raganato and Tiedemann, 2018;Voita et al., 2019;Vig and Belinkov, 2019).
Use Case: Detecting Model Bias
One use case for the attention-head view is detecting bias in the model, which we illustrate for the case of conditional language generation using GPT-2. Consider the following continuations gen-erated 3 from two input prompts that are identical except for the gender of the pronouns (generated text underlined): • The doctor asked the nurse a question. She said, "I'm not sure what you're talking about." • The doctor asked the nurse a question. He asked her if she ever had a heart attack.
In the first example, the model generates a continuation that implies She refers to nurse. In the second example, the model generates text that implies He refers to doctor. This suggests that the model's coreference mechanism may encode gender bias (Zhao et al., 2018;Lu et al., 2018). Figure 4 shows an attention head that appears to perform coreference resolution based on the perceived gender of certain words. The two examples from above are shown in Figure 4 (right), which reveals that She strongly attends to nurse, while He attends more to doctor. By identifying a source of potential model bias, the tool could inform efforts to detect and control for this bias.
Model View
The model view ( Figure 5) provides a birds-eye view of attention across all of the model's layers and heads for a particular input. Attention heads are presented in tabular form, with rows representing layers and columns representing heads. Each layer/head is visualized in a thumbnail form that conveys the coarse shape of the attention pattern, following the small multiples design pattern (Tufte, 1990). Users may also click on any head to enlarge it and see the tokens. The model view enables users to quickly browse the attention heads across all layers and to see how attention patterns evolve throughout the model.
Use Case: Locating Relevant Attention Heads
As discussed earlier, attention heads in BERT exhibit a broad range of behaviors, and some may be more relevant for model interpretation than others depending on the task. Consider the case of paraphrase detection, which seeks to determine if two input texts have the same meaning. For this task, it may be useful to know which words the model finds similar (or different) between the two sentences. Attention heads that draw connections between input sentences would thus be highly relevant. The model view ( Figure 5) makes it easy to find these inter-sentence patterns, which are recognizable by their cross-hatch shape (e.g., layer 3, head 0). These heads can be further explored by clicking on them or accessing the attention-head view, e.g., Figure 2 (center). This use case is described in greater detail in Vig (2019).
Neuron View
The neuron view (Figure 6) visualizes the individual neurons in the query and key vectors and shows how they interact to produce attention. Given a token selected by the user (left), this view traces the computation of attention from that token to the other tokens in the sequence (right).
Note that the Transformer uses scaled dotproduct attention, where the attention distribution at position i in a sequence x is defined as follows: where q i is the query vector at position i, k j is the key vector at position j, and d is the dimension of k and q. N =i for GPT-2 and N =len(x) for BERT. 4 All values are specific to a particular layer / head. The columns in the visualization are defined as follows: • Query q: The query vector of the selected token that is paying attention. • Key k: The key vector of each token receiving attention. • q×k (element-wise): The element-wise product of the query vector and each key vector. This shows how individual neurons contribute to the dot product (sum of elementwise product) and hence attention. • q · k: The dot product of the selected token's query vector and each key vector. • Softmax: The softmax of the scaled dotproduct from previous column. This is the attention score.
Whereas the attention-head view and the model view show what attention patterns the model learns, the neuron view shows how the model forms these patterns. For example, it can help identify neurons responsible for specific attention patterns, as discussed in the following use case.
Use Case: Linking Neurons to Model Behavior
To see how the neuron view might provide actionable insights, consider the attention head in Figure 7. For this head, the attention (rightmost column) decays with increasing distance from the source token. This pattern resembles a context window, but instead of having a fixed cutoff, the attention decays continuously with distance.
The neuron view provides two key insights about this attention head. First, the attention weights appear to be largely independent of the content of the input text, based on the fact that all the query vectors have very similar values (except for the first token). Second, a small number of neuron positions (highlighted with blue arrows) appear to be mostly responsible for this distancedecaying attention pattern. At these neuron positions, the element-wise product q × k decreases as the distance from the source token increases (either becoming darker orange or lighter blue).
When specific neurons are linked to a tangible outcome, it presents an opportunity to intervene in the model (Bau et al., 2019). By altering the relevant neurons-or by modifying the model weights that determine these neuron values-one could control the attention decay rate, which might be useful when generating texts of varying complexity. For example, one might prefer a slower decay rate (longer context window) for a scientific text compared to a children's story. Other heads may afford different types of interventions.
Conclusion
In this paper, we introduced a tool for visualizing attention in the Transformer at multiple scales. We demonstrated the tool on GPT-2 and BERT, and we presented three use cases. For future work, we would like to develop a unified interface to navigate all three views within the tool. We would also like to expose other components of the model, such as the value vectors and state activations. Finally, we would like to enable users to manipulate the model, either by modifying attention (Lee et al., 2017;Liu et al., 2018;Strobelt et al., 2018) or editing individual neurons (Bau et al., 2019). | 2,525.6 | 2019-06-12T00:00:00.000 | [
"Computer Science"
] |
Synthesis, Characterization and Microstructure of New Liquid Poly(methylhydrosiloxanes) Containing Branching Units SiO4/2
Six liquid branched poly(methylhydrosiloxanes) of new random structures (PMHS-Q), containing quadruple branching units SiO4/2 (Q), both MeHSiO (DH) and Me2SiO (D) chain building units (or only mers MeHSiO), and terminal groups Me3SiO0.5 (M) were prepared by a hydrolytic polycondensation method of appropriate organic chlorosilanes and tetraethyl ortosilicate (TEOS), in diethyl ether medium at temperature below 0 °C. Volatile low molecular weight siloxanes were removed by a vacuum distillation at 150–155 °C. Yields of PMHS-Q reached from 55–69 wt%. Their dynamic viscosities were measured in the Brookfield HBDV+IIcP cone-plate viscometer and ranged from 10.7–13.1 cP. Molecular weights (MW) of PMHS-Q (Mn = 2440–6310 g/mol, Mw = 5750–10,350 g/mol) and polydispersities of MW (Mw/Mn = 2.0–2.8) were determined by a size exclusion chromatography (SEC). All polymers were characterized by FTIR, 1H- and 29Si-NMR, and an elemental analysis. A microstructure of siloxane chains was proposed on a basis of 29Si-NMR results and compared with literature data.
Twelve new liquid branched poly(methylhydrosiloxanes) with statistical structures (b-r-PMHS), containing triple branching units MeSiO 1.5 (T), both Me 2 SiO (D) and MeHSiO (D H ) chain building units (or only mers MeHSiO), and two b-r-PMHS containing five different structural units: D, D H , T and T H and trimethylsiloxy end groups Me 3 SiO 0.5 (M) were prepared by the hydrolytic polycondensation method of appropriate chlorosilanes in diethyl ether medium at temperature <0 • C. Yields of b-r-PMHS ranged from 57-84 wt% (after removal of low molecular weight oligosiloxanes by a vacuum distillation at 125-150 • C). All polymeric products were characterized by FTIR, 1 H-and 29 Si-NMR, and elemental analysis. Their dynamic viscosities were very low and usually ranged from 8-30 cP, which presumably resulted from their globular structure [9].
Methyl-substituted silica gels with Si-H functionalities were prepared by hydrolysis and condensation reactions of triethoxysilane and methyldiethoxysilane, used in various molar ratios [62]. They gave higher ceramic residue after pyrolysis than gels based only on MeSiO 1.5 branching units [63].
In the present work, we describe the hydrolytic polycondensation synthetic route to new liquid branched poly(methylhydrosiloxanes) of random structures (PMHS-Q), containing both MeHSiO (D H ) and Me 2 SiO (D) chain building units (or only mers MeHSiO), quadruple branching units SiO 4/2 (Q), and terminal groups Me 3 SiO 0.5 , from appropriate organic chlorosilanes and tetraethoxysilane.
An elementary analysis (% C and % H) was performed at the Centre of Molecular and Macromolecular Studies of the Polish Academy of Sciences in Łódź (CBMM PAN). The content of Si-H groups was calculated from an integration ratio of their signals to CH 3 signals in 1 H-NMR spectra, and compared to theoretical integration ratios of Si-H and CH 3 signals. The content of Si was determined by the gravimetric method with H 2 SO 4 (p.a.) [64].
The molecular masses and molecular mass distribution of polysiloxanes were analyzed by a size exclusion chromatography (SEC) in toluene solution, using LDC analytical chromatograph (Artisan Technology Group, Champaign, IL 61822, USA) equipped with refractoMonitor and a battery of two phenogel columns covering the MW range 10 2 -10 5 g·mol −1 . Calibration was made with polystyrene Ultrastyrogel standards with MWs: 10 2 , 10 3 , and 10 4 g·mol −1 .
Synthesis of Branched Polymethylhydrosiloxanes (PMHS-Q)
Branched polymethylhydrosiloxanes, containing only units D H and Q, terminated with Me 3 SiO 0.5 groups, with structures described by a general formula: (where: y = 1-3, m = n = 49-52, p = 2y + 2), were synthesized by the hydrolytic polycondensation of mixtures of tetraethoxysilane Si(OEt) 4 and appropriate chlorosilanes: dichloromethylsilane MeHSiCl 2 , dichlorodimethylsilane Me 2 SiCl 2 , and chlorotrimethylsilane Me 3 SiCl, in the medium of diethyl ether and water, at temperature ranged from −10-0 • C, within 3-5 h. Molar ratios of chlorosilanes were changed, depending on expected molecular formula of polysiloxane. Amounts of substrates used in syntheses of branched PMHS-Q and times of additions of chlorosilanes are presented in Table 1.
In the hydrolytic polycondensation reactions were used such amounts of distilled water, which were sufficient for a formation of hydrochloric acid with a final concentration about 20 wt%. Reaction mixture was allowed to warm to room temperature within 120-170 min, acid layer was separated, and organosilicon layer was washed with water until neutral, transferred to an Erlenmayer flask, and dried at~4 • C with anhydrous magnesium sulfate overnight. Magnesium sulfate was filtered through Schott funnel G-3 and washed with ether. Alternatively, instead of drying with anhydrous MgSO 4 traces of water were removed from products by cooling their ether solution in a refrigerator overnight, warming up the content of the flask to room temperature, and the ether solution of products was decanted from drops of water. The solvent was distilled off. In order to remove volatile cyclic and linear low molecular weight siloxane oligomers, the prepared products were heated at temperature 150-155 • C under reduced pressure (16-21 mm Hg, 2128-2793 Pa), and subsequently under a vacuum (3-5 mm Hg, 400-665 Pa).
In a second step of syntheses of Q 3 D H 50 M 8 and other poly(dimethyl-co-methylhydro)siloxanes, containing both mers D and D H , with a general formula: (where: y = 1-3, m = n = 49-52, p = 2y + 2), so called "extra blocking" of unreacted silanol groups Si-OH was applied: in reactions with (chloro)trimethylsilane, in the presence of triethylamine, which was used as an acceptor of hydrogen chloride with~5% excess with respect to a stoichiometric amount.
(4-Dimethylamino)pyridine (DMAP) was used as a nucleophilic catalyst in 1:10 mole ratio with respect to Et 3 N. Products untreated with extra amounts of TMCS and DMAP/Et 3 N showed increase of their viscosity after few months and a presence of small drops of water from a homo-condensation reaction of residual Si-OH groups.
The "extra blocking" reactions of silanol groups were carried out after drying step of ether solutions of products of the hydrolytic polycondensation, at room temperature within few hours. Precipitates of amines hydrochlorides were dissolved in diluted solution (5-10 wt%) of hydrochloric acid, a water layers were discarded and washed with distilled water until neutral, dried with anhydrous MgSO 4 , and filtered. Ether was distilled off under atmospheric pressure and final products were evacuated under vacuum at temperature 150-155 • C ( Table 2). A chemical composition of volatile siloxanes was not analyzed.
Synthesis of Branched Polymethylhydrosiloxanes (PMHS-Q)
Syntheses of poly(methylhydrosiloxanes) with statistical and branched structures containing quadruple branching points SiO 4/2 were carried out in the medium of diethyl ether at temperature below 0 • C. Solutions of chlorosilanes and Si(OEt) 4 in dry ether were added dropwise to water. In all syntheses were used such amounts of water which were necessary for hydrolysis reactions and dissolution of HCl, allowing to obtain hydrochloric acid with concentrations approximately 20 wt%.
Applying the hydrolytic polycondensation of mixtures of appropriate amounts of (tetraethoxy)-silane Si(OEt) 4 where y = 1-3, m = n = 49-52, p = 2y + 2. After addition of substrates stirring of obtained reaction mixtures was continued within next 2-3 h, in order to reach full conversion of substrates and full hydrolysis of Si-Cl and Si-OC 2 H 5 groups. In the case of syntheses of Q3, Q1D, Q2D, and Q3D termination reactions (so called "extra blocking" reactions) of unreacted silanol groups Si-OH in reactions with (chloro)trimethylsilane were applied, in the presence of: (1) triethylamine as the acceptor of hydrogen chloride (used with~5-10% excess with respect to stoichiometric amounts); and (2) (4-dimethylamino)pyridine (DMAP) as the nucleophilic catalyst (used in 1:10 mole ratio with respect to Et 3 N).
Products not treated with additional amounts of TMCS and DMAP/Et 3 N showed increase of their viscosity after few months and a presence of traces of water, which could originate from the homocondensation reaction of residual Si-OH groups. However, in the case of syntheses of Q1 and Q2 "extra blocking" was not applied, and no increase of their viscosity was observed during longer storage of these PMHS-Q. Ether solutions of products Q1, Q2, and Q3 were dried with anhydrous MgSO 4 , while polymers Q1D, Q2D, and Q3D were dried by freezing traces of water in the refrigerator overnight. Yields of prepared PMHS-Q ranged from 55-69 wt% ( Table 2). The highest yield was obtained for Q3.
The chemical structures of all PMHS-Q were confirmed by spectroscopic methods: FTIR and NMR ( 1 H and 29 Si) and the elemental analysis (% C, % H, and % Si) (see Table 3).
Dynamic viscosities (η 25 ) of PMHS-Q containing quadruple branching points SiO 4/2 , were very low and ranged from 10.7-13.1 cP. Low viscosities of PMHS-Q in comparison with linear polysiloxanes having similar molecular weights presumably may result from a globular structure of hyperbranched macromolecules. It is commonly known from a literature that dendrimers and hyperbranched polymers in solution and in melt have low viscosities. Their viscosities and molecular weights are much lower than those for linear analogs and depend on a degree of branching, a polarity of a solvent, a kind of functional group on their "surface", and also on pH of a polymer solution. Dendritic and hyperbranched polymers have a variable hydrodynamic radii depending on the property of solvents; they are smaller than those of their linear analogs with the same molar mass.
The values of molecular weights of prepared PMHS-Q determined by SEC method were lower than calculated values for predicted molecular formulas: QD 52 A polydispersity of molecular weights of PMHS-Q ranged from 2.0 to 2.8. The molecular weights of dendrimers and hyperbranched polymers determined by SEC using polystyrene standards are regarded with some scepticism. The hydrodynamic radii were also susceptible to the polarity of functional groups on the periphery [65][66][67]. Values of M n and M w determined by SEC method with polystyrene standards for hyperbranched polysiloxanes were much lower than MW obtained with application of MALLS detectors [68][69][70].
Köhler et al. used the SEC, 1 H-and 29 Si NMR, and MALDI-TOF-MS methods for characterization of a linear poly(dimethylsiloxane)-co-poly(hydromethysiloxane) (PDMS-co-PHMS) copolymer with respect to chain length distribution, heterogeneity of chemical composition, and sequence distribution [71].
Characterization of PMHS-Q by NMR
In 1 H-NMR spectra of copolymers, QD H 48M4, Q2D H 49M6 and Q3D H 50M8 were present signals at δ 0.01 -0.22 ppm, corresponding to hydrogen atoms of Si-CH3 groups and signals at δ about five parts per million, characteristic for hydrosilane groups Si-H. In the 1 H-NMR spectra of copolymers:
Characterization of PMHS-Q by NMR
In 1 H-NMR spectra of copolymers, QD H 48M4, Q2D H 49M6 and Q3D H 50M8 were present signals at δ 0.01 -0.22 ppm, corresponding to hydrogen atoms of Si-CH3 groups and signals at δ about five parts per million, characteristic for hydrosilane groups Si-H. In the 1 H-NMR spectra of copolymers: QD52D H 52M4, Q2D49D H 49M6, and Q3D50D H 50M8 were present signals at δ 0.0 -0.30 ppm, corresponding to hydrogen atoms of Si-CH3 groups and signals at δ about five parts per million, characteristic for Si-H groups. Examples of the 1 H-NMR and 29 Si-NMR spectra of branched poly(methylhydrosiloxanes) are presented in Figures 4-7. [8,9,52]. It was impossible to observe signals of quadruple silicon atoms of units SiO4/2 in 29 Si-NMR spectra, which were registered by the INEPT technique, so it was necessary to run 29 Si-NMR spectra with application of the INVGATE program. A summary of chemical shifts data in the 1 H-and 29 Si-NMR (INEPT and INVGATE) spectra of all PMHS-Q is presented in Table 5.
Characterization of PMHS-Q by NMR
In [8,9,52]. It was impossible to observe signals of quadruple silicon atoms of units SiO 4/2 in 29 Si-NMR spectra, which were registered by the INEPT technique, so it was necessary to run 29 Si-NMR spectra with application of the INVGATE program. A summary of chemical shifts data in the 1 H-and 29 Si-NMR (INEPT and INVGATE) spectra of all PMHS-Q is presented in Table 5.
In the 29 Si-NMR INVGATE spectra of branched random PMHS were present signals of silicon atoms corresponding to linear mers: In the 29 Si-NMR spectra (recorded by INEPT and INVGATE techniques) in the range of δ −33 -−37 ppm exist signals of middle silicon atoms of units D H , which undergo changes in pentades ( Table 5). Signals of silicon atoms in the range of δ −102 to −109 ppm, presumably correspond to Si atoms in the central units Q, in the following sequences of siloxane structures: Chemical shifts in the range of 7-11 ppm in the 29 Si-NMR spectra (INEPT and INVGATE) correspond to silicon atoms of the end groups M and change in tetrads (Table 5) [8,9,74].
Signals at δ −64 ppm of a very low intensity, registered both in INVGATE and INEPT 29 Si-NMR spectra of these three copolymers, probably come from Si atoms of units MeSiO1.5 (T), which were formed during syntheses of PMHS-Q from trace hydrolysis of Si-H bonds [74].
Signals at δ −64 ppm of a very low intensity, registered both in INVGATE and INEPT 29 Si-NMR spectra of these three copolymers, probably come from Si atoms of units MeSiO 1.5 (T), which were formed during syntheses of PMHS-Q from trace hydrolysis of Si-H bonds [74].
Assignments of all 29 Si-NMR signals resulting from the microstructure of siloxane chain of branched polymethylhydrosiloxanes are summarized in Table 6. | 3,127.6 | 2018-04-28T00:00:00.000 | [
"Materials Science"
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Auxin and Cell Wall Invertase Related Signaling during Rice Grain Development
Indole-3-acetic acid (IAA) synthesis is required for grain-fill in maize and appears to be regulated by cell-wall invertase (CWIN) activity. OsYUC12 is one of three IAA biosynthesis genes we previously reported as expressed during early rice grain development, correlating with a large increase in IAA content of the grain. This work aimed to investigate further the role of OsYUC12 and its relationship to CWIN activity and invertase inhibitors (INVINH). The analysis shows a brief peak of OsYUC12 expression early in endosperm development. Meta-analysis of microarray data, confirmed by quantitative expression analysis, revealed that OsYUC12 is coexpressed with OsIAA29, which encodes an unusual AUX/IAA transcription factor previously reported as poorly expressed. Maximum expression of OsYUC12 and OsIAA29 coincided with maximum CWIN activity, but also with a peak in INVINH expression. Unlike ZmYUC1, OsYUC12 expression is not reduced in the rice CWIN mutant, gif1. Several reports have investigated CWIN expression in rice grains but none has reported on expression of INVINH in this species. We show that rice has 54 genes encoding putative invertase/pectin methylesterase inhibitors, seven of which are expressed exclusively during grain development. Our results suggest a more complex relationship between IAA, CWIN, and INVINH than previously proposed.
Introduction
Several recent publications indicate key intersecting signaling roles for indole-3-acetic acid (IAA) and cell wall invertases (CWIN) during cereal grain development. The maize defective endosperm18 (de18) phenotype was recently shown to result from loss of expression of the IAA biosynthesis gene ZmYUC1 and related low levels of IAA in the developing grain [1]. The cell wall invertase miniature1 (mn1) mutant also shows poor grain fill, the low levels of cell wall invertase resulting in a defective basal endosperm transfer layer (BETL) with poorly developed wall in-growths [2]. Maize mn1 mutants have low levels of IAA and low expression of ZmYUC1; glucose was able to increase ZmYUC1 transcript levels in cultured kernels [3]. Forestan et al. [4] showed that IAA accumulates in the BETL, aleurone and embryo surrounding region (ESR) just before the endosperm starts to accumulate starch. In addition, both BETL and ESR showed a high level of auxin transporter ZmPIN1 transcript and protein. The rice ortholog of Mn1, GIF1/OsCIN2, also appears to be important for grain development, with gif1 mutants (that have much lower CWIN activity in developing grains) showing poor grain-fill; expression of GIF1 during grain development is localized to the vascular trace [5]. The relationship between IAA and invertase in rice has not been investigated.
In a previous paper on IAA synthesis in developing rice grains we showed that IAA accumulates more than 50-fold in developing kernels during endosperm cellularisation and early starch deposition [6]. The rise in IAA content was correlated with a large increase in expression of IAA biosynthesis genes OsYUC9, OsYUC11, and OsTAR1. We also obtained some rather inconsistent data on a third endosperm-specific YUCCA gene, OsYUC12. Preliminary results suggested that OsYUC12 was expressed only briefly during grain development and may have a distinct role from the more highly expressed OsYUC9 and OsYUC11. The aim of the work reported here was to clarify the expression of OsYUC12 in developing grains and to investigate its relationship to CWIN, as well as the unexpected observation that OsYUC12 is coexpressed with a putative invertase inhibitor (INVINH).
A number of reports, e.g., Jin et al. [7], indicate that invertases in dicots are regulated by INVINH. In addition, ZM-INVINH1 inhibited maize CWIN activity in vitro, bound to a glycoprotein fraction including CWIN, and was localized to the ESR of young developing maize kernels [8]. Several papers report on expression of CWIN in rice, e.g., [9], however the role of invertase inhibitors in rice has been neglected. Furthermore, extraction of invertase for assay of its activity has normally been carried out at pH 7.5, e.g., [10], conditions under which any bound inhibitor would be expected to dissociate from the enzyme [11]. In this work, we carried out a comprehensive phylogenetic analysis of invertase inhibitor homologs in rice; we investigated the expression of Os04g49720, a co-ortholog of ZM-INVINH1 previously designated as OsINVINH3 [8]; we extracted and assayed CWIN activity under conditions that have been shown to preserve an enzyme/inhibitor complex [8]. Our data on expression of OsYUC12 and OsINVINH3, as well as CWIN activity suggest that the relationship between IAA and CWIN is more complex than previously proposed.
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Invertase Inhibitor Phylogeny
A BlastP search of the rice proteome using query sequences ZM-INVINH1, ZM-INVINH2, and ZM-INVINH3 initially identified 20 homologous proteins. Additional rice homologs, as well as sequences from sorghum, were obtained using the homologous protein function in Phytozome. The phylogenetic tree shown in Figure 2 resulted from analysis of 54 protein sequences from rice, 34 sequences from sorghum, as well as experimentally characterized pectin methylesterase inhibitors (PMEIs) from wheat [15] and Arabidopsis [16], INVINHs from tomato [7], potato [17], and Arabidopsis [16] and F2DCS9 HORVD, an invertase inhibitor homolog from barley identified as up-regulated under heat stress by Mangelsen et al. [18]. The comprehensive set of homologs from the sorghum proteome was included to identify rice sequences that were conserved in more than one cereal species.
A number of bootstrap values for larger clades are low due to the highly diverse nature of the sequences. However, an examination of the multiple sequence alignment indicated that the four conserved cysteine residues previously shown to form disulfide bridges in PMEIs and INVINHs [19] were present in most sequences and were correctly aligned (Supplemental Figure and Os04g49720, as well as Os02g46360 are co-orthologous to ZM-INVINH1, the only characterized invertase inhibitor from a cereal [8]. Interestingly, characterized invertase inhibitors from dicot species are in separate clades from ZM-INVINH1. Arabidopsis invertase inhibitor, C/VIF1, as well as potato and tomato invertase inhibitors do not have any unambiguous cereal orthologs. On the other hand, C/VIF2 falls into a well-supported clade containing ZM-INVINH2, two rice sequences and four sorghum sequences. ZM-INVINH3 and Os01g20970 are orthologs of TaPMEI and are, therefore, likely to be PMEIs rather than invertase inhibitors. The Arabidopsis PMEIs appear in a separate branch from cereal PMEIs. The tree contains many orthologous pairs from rice and sorghum; however rice has many more sequences which appear to be due to recent gene duplication as evidenced by groups of tandem repeats, particularly on chromosome 8. The barley protein F2DCS9_HORVD, which has been given the name INVINH1 [18], is only distantly related to other characterized invertase inhibitors but has unambiguous orthologs in both rice and sorghum.
Analysis of OsCIN2/GIF1 and Putative INVINH Expression in Developing Caryopses Using Published Microarray Data
The extracellular invertase GIF1/OsCIN2 has been shown to be responsible for most of the CWIN activity in developing rice grains [5]. We mined microarray data for information on expression of GIF1 as well as the 54 invertase inhibitor homologs during grain development. Data was accessed via PLEXdb [14] from experiment accessions OS5 "Expression data for reproductive development in rice" [20], OS8 "Expression data from rice embryo, endosperm, root, leaf, and seedling" [21], OS16 "Genome-wide gene expression profiling of rice stigma" [22], OS44 "Rice expression atlas (3): Early embryogenesis" [23] and OS89 "Expression data from rice embryo and endosperm development" [24]. Arabidopsis are also included for comparison. The tree was produced in MEGA5.2 [25] using the Neighbor-Joining method [26]. MUSCLE [27] was used for multiple sequence alignment. The bootstrap consensus tree was inferred from 500 replicates [28]. Evolutionary distances were computed using the Poisson correction method [29]. All ambiguous positions were removed for each sequence pair. Highlighted sequences are encoded by genes expressed in endosperm during early caryopsis development.
Seven INVINH/PMEI homologs (Table 1) were found to be expressed exclusively during caryopsis development with expression highest in samples three to four days after pollination (DAP); expression appeared specific to the endosperm. Caryopsis-expressed INVINH/PMEI homologs included Os04g49720 which is co-orthologous with Os04g49730 and Os02g46360 to ZM-INVINH1. Os04g49730 and Os02g46360 appeared to be only weakly expressed; Os04g49720 has previously been designated as OsINVINH3 [8]. In contrast to the large changes in expression of OsINVINH3, there was little change in the expression of GIF1 from prior to anthesis until 20 DAP (Figure 3). Interestingly examination of endosperm-specific genes in Figure 2 showed them to be present in diverse clades. We also noted that the expression profiles of genes in Table 1 matched that of IAA biosynthesis gene OsYUC12 and the gene encoding putative AUX/IAA transcriptional regulator OsIAA29. [14] from experiment accessions OS5 "Expression data for reproductive development in rice" [26], OS8 "Expression data from rice embryo, endosperm, root, leaf, and seedling" [21], OS16 "Genome-wide gene expression profiling of rice stigma" [27], OS44 "Rice expression atlas (3): Early embryogenesis" [28], and OS89 "Expression data from rice embryo and endosperm development" [29].
Coexpression Meta-Analysis Using Bait Genes OsIAA29, OsYUC12 and OsINVINH3
Several on-line platforms are available for coexpression analysis including RiceNet [30], GeneCAT [31], and Rice Oligonucleotide Array Database [32]. Initial investigations indicated that the limited data set used in RiceNet led to the identification of some genes that had poorly correlated expression with our genes of interest in data sets, such as OS44 [28], which includes samples collected daily during the early stages after pollination. Rice Oligonucleotide Array Database contains more data sets but as most of these did not contain caryopsis tissue and the site does not allow for condition dependent selection of data sets, results were similarly unsatisfactory. We therefore downloaded RMA normalized datasets via PLEXdb for previously mentioned accessions OS5, OS8, OS16, OS44, and OS89 and calculated pairwise mutual coexpression ranks [33] for three bait genes: OsIAA29, OsYUC12, and OsINVINH3. Examination of the expression profiles of genes with a mutual co-expression rank <50 in individual experiments indicated very close correspondence with expression of bait genes. All appear to be expressed exclusively in the endosperm of developing grains with maximal expression at 3-4 DAP.
Genes with a mutual co-expression rank less than 20 (MR < 20) are shown in Table 2, with a larger set (MR < 50) shown in Supplemental Table S1. All database annotations have been manually checked against the literature; where the annotation differs from the literature, the published protein designation has been used. Table 2 includes two lipid transfer protein-like genes (LTPL) and four defensin/defensin like genes (DEF/DEFL). This group of genes encoding cysteine-rich peptides (CRPs) was also highly represented in the larger MR < 50 group, with a total of 13 genes present. Also present was a ZmEBElike (embryo sac/basal endosperm transfer layer/embryo surrounding region) gene; a further four homologs of this gene are found in the MR <50 group. A third group of homologous proteins found in the MR <50 group included two additional INVINH/PMEI homologs. Table 2 also includes genes encoding OsHAP3D/OsLEC1A (Leafy cotyledon1) [34] and a leucine-rich repeat receptor-like kinase. Genes with a likely signaling role in the MR <50 group also include OsRR33, a type-B response regulator [35] an ortholog of OBERON1/2 [36] and at least two other proteins with a predicted nuclear location.
Invertase Activity in Developing Rice Grains
Cell wall invertase activity during grain development is shown in Figure 5. Total cell wall invertase shown on a per grain basis increased to a maximum at 7 DAP; when calculated on a per g fresh weight basis, no significant difference was seen between samples from 1-7 DAP with a substantial decrease at 10 DAP.
Expression of IAA Related Genes, OsYUC12 and OsIAA29 Coincides with Endosperm Cellularisation
Previous research using maize and rice has suggested a key role for IAA and CWIN during early grain-fill however the exact roles of IAA and CWIN remain to be established. Our results indicated that the relationship between IAA and CWIN is complex, with differences in expression of three IAA biosynthesis genes OsYUC9, OsYUC11, and OsYUC12 during grain development. In this paper we explore the role of one IAA biosynthesis gene, OsYUC12. We chose to investigate this gene as to our knowledge there have been no other studies of it or its orthologs. We have shown that OsYUC12 has conserved orthologs in maize and sorghum, it is specifically expressed in endosperm for a short time during early grain development and this expression pattern also appears in maize. We, therefore, suggest that this gene has a specific and conserved signaling role during grain development. The aim of this work was to identify other possible components of the signaling network that could be investigated.
An examination of on-line accessible microarray data indicated that AUX/IAA gene OsIAA29 has a very similar expression pattern to OsYUC12; this was confirmed by qRT-PCR. Our quantitative expression data confirm that expression of OsYUC12 and OsIAA29 is limited to a short period during early grain-fill. The increase in expression coincided with our previously reported large increase in the IAA content of developing grains at 7 DAP in plants grown under the same conditions [6]. Examination of material under the light microscope indicated that, at 4 DAP, the endosperm syncytium contained many nuclei and a few small irregularly shaped cells. At day seven there were clearly defined endosperm cells containing amyloplasts, as well as differentiated outer cellular layers. The coexpression of OsYUC12 and OsIAA29 in the endosperm over a very limited period during grain development, suggests a specific role for IAA during this period. However, OsIAA29 is an unusual AUX/IAA protein that lacks domains I and II [40]. As domain II is responsible for interacting with the F-box protein, IAA co-receptor [41] it is unclear how OsIAA29 may interact with IAA. Dimerization domains III and IV, which mediate interactions between AUX/IAA proteins and ARFs are still present in OsIAA29 [40]. In work with seedling tissue, Jain et al. [40] reported very low expression of OsIAA29 and no expression of its tandem repeat OsIAA28. Our observations showing high expression at a very specific stage of development suggest that OsIAA29 may in fact play a key but as yet unidentified role. This is further supported by the existence of OsIAA29 orthologs in both sorghum and maize and our recent unpublished observation that the sorghum ortholog is also expressed during grain-fill.
Expression of OsINVINH3 Coincides with Maximum Extracellular Invertase Activity
LeClere et al. [42] have provided evidence that ZmYUC1 expression may be regulated by glucose levels produced as a result of CWIN activity. We therefore investigated the expression of GIF1 during grain development. Examination of microarray data indicated GIF1 expression appeared to change little from prior to pollination until 20 DAP. However, we were surprised to find that expression of Os04g49720 (OsINVINH3), a co-ortholog of ZM-INVINH1 [8] changed dramatically during early grain-development. Invertase inhibitor ZM-INVINH1 has been reported to bind CWIN during grain development in maize [8]; both ZM-INVINH1 and OsINVINH3 have predicted signal peptides. Quantitative expression analysis confirmed that Os04g49720 showed a large, short-lived increase in expression during early grain development. In plants grown under our conditions maximum expression was found in 7-DAP samples, also coinciding with the peak in OsYUC12 and OsIAA29 expression and rapidly increasing IAA levels [6]. We were surprised to also observe maximum invertase activity on a per grain basis at 7 DAP. The unexpected result was confirmed by repetition of the experiment by a second person in the laboratory. Clearly, further work is required to clarify the relationship between CWIN and OsINVINH3, however, our data support the suggestion by Wang et al. [5] that CWIN in developing grains may be tightly regulated.
Rice Has 54 INVINH Homologs Several of Which Are Expressed Specifically in Developing Endosperm
Invertase inhibitors have similar structure and are homologous to pectin methylesterase inhibitors [19]. A comprehensive search for members of this family revealed 54 diverse homologous proteins in rice. Sorghum homologs were also included to distinguish between species-specific proteins and those that have been conserved. Although the high sequence diversity resulted in some ambiguous relationships, both sorghum and rice have clear orthologs of ZM-INVINH1. In addition, a small well-supported clade containing the experimentally characterized wheat PMEI suggested that ZM-INVINH3, Sb03g012790, Os01g20970 and Os05g29740 are likely to be PMEIs. OsINVINH3 is not the only member from the family to be expressed exclusively during grain development. Os02g46290, Os03g43820, Os08g42890, Os08g04670, Os08g04710, and Os08g04740 are also grain specific and expressed maximally at 3-4 DAP. Exploration of data from OS8 [21], OS16 [27], and OS89 [29] indicated that expression is restricted to the endosperm. The seven endosperm-specific proteins are found in four clades; Os03g43820 is present in a large clade quite separate from the others, but including the barley protein F2DCS9 HORVD. Os08g04670, Os08g04710, and Os08g04740 are part of a cluster of nine genes found in tandem; Os08g42890 appears to be part of the same clade though this is not strongly supported. Os02g46290 is a possible ortholog of C/VIF1, an experimentally characterized vacuolar invertase inhibitor from Arabidopsis. The high diversity of these proteins in separate clades of a tree that is known to contain proteins of different biological functions raises the possibility that not all are invertase inhibitors or PMEIs. We suggest that some members of the INVINH/PMEI protein family may regulate other carbohydrate metabolizing enzymes. An investigation of the predicted subcellular locations of the gene products, using CELLO [43] and TargetP [44], suggests that all proteins have a signal peptide, however an examination of extracellular and vacuolar invertase inhibitors from potato [17] shows that domain prediction programs cannot reliably distinguish between these two subcellular destinations.
Putative Signaling Proteins Coexpressed with OsYUC12, OsIAA29 and OsINVINH3
The observation that OsYUC12, OsIAA29, and OsINVINH3 are expressed exclusively in endosperm samples from developing grains 3-10 DAP suggest they may be co-regulated and may be part of a common signaling pathway. A meta-analysis of microarray data indicated genes from three families, CRPs, ZmEBE-like, and INVINH/PMEI-like, all encoding putative extracellular proteins, are prominent among genes coexpressed with OsYUC12, OsIAA29, and OsINVINH1. The CRPs come from two distinct groups; the so-called lipid transfer protein-like group and the defensin/defensin-like group. We note that despite their reported antimicrobial activity, defensins have recently been shown to have a signaling role earlier in maize reproductive development [45]. In addition, the CRP MEG1 is essential for the differentiation of ETCs in maize [46]. OsLTPL29/OsPR602 and DEFL OsPR9a, as well as ZmEBE1, ZmEBE2, and ZM-INVINH1, are also expressed primarily in ETCs and ESR [38,47]. Differentiating transfer cells in maize kernels accumulate high levels of auxin transporter OsPIN1 transcripts [4]; the BETL and ESR also show high levels of PIN proteins as well as an accumulation of IAA itself. The specific localization of rice proteins found in Table 2 should be investigated to determine whether they are also restricted to the ETCs and/or ESR.
Genes with a mutual co-expression rank of <20 included also OsHAP3D [34] and Os05g07850, a putative leucine-rich repeat receptor-like kinase. OsHAP3D, also referred to as OsLEC1a, encodes a nuclear factor YC protein, homologous to Arabidopsis LEC1/L1L. These Arabidopsis proteins have a crucial role in embryogenesis [48] including the up-regulation of YUCCA10 [49]. Rice has two homologs of LEC1, OsHAP3D, and OsHAP3E. An examination of their expression profile via PLEXdb indicates that both are expressed in developing grains with a peak at 3-4 DAP. However, whereas OsHAP3D is expressed in endosperm, OsHAP3E expression appears to be restricted to the embryo. Os05g07850 encodes a leucine-rich repeat receptor-like kinase which has a predicted trans-membrane domain and serine/threonine kinase domain. It is homologous but not orthologous to the brassinolide receptor BRI1 and aligns in the same clade as Arabidopsis NSP interacting kinases. A partially homologous receptor-like kinase has been shown to form part of a signaling network that also includes a DEFL during fertilization in maize [50]. The identification of these coexpressed genes provides a framework for investigating protein-protein interactions that could form part of a signaling network.
Plant Material
Rice grains (ssp. Japonica cv. Jarrah) were direct sown into flooded soil-filled cylindrical plastic pots and thinned out to three plants per pot when the seedlings had reached the 2-3 leaf growth stage. Plants were grown in a glasshouse under a natural light with day/night temperatures 28 °C/18 °C. Plants were fertilized fortnightly using Aquasol ® (8 g/5 L). When spikelets in the top half of the panicle had reached anthesis, panicles were tagged to record the date; panicles were harvested at 1, 4, 7, 10, and 15 days after pollination (DAP). Grain samples were placed in microfuge tubes, the weight and number of grains recorded before freezing in liquid nitrogen and storage at −80 °C.
Quantitative Reverse Transcriptase PCR
Total RNA was extracted from 60-80 mg grain samples following instructions for the Bioline ISOLATE Plant RNA Mini Kit. RNA concentration and 260/280 ratio were determined using a NanoDrop ND-1000 Spectrophotometer (NanoDrop Technologies, Inc., Wilmington, DE, USA). Only samples with A 260 /A 280 of 1.8-2.0 were used for further analysis. The RNA quality was also checked using agarose gel electrophoresis for two clear bands of 18s and 28s rRNA [52].
Gene-specific primers (See Supplemental Table S2) were designed with melting points in the range 59-61 °C and product sizes between 100-150 bp. Primers were tested for amplification of a single product of the expected size using a QIAGEN OneStep RT-PCR kit (QIAGEN, Limburg, The Netherlands), with agarose gel analysis of products. To avoid the possibility of amplifying genomic DNA, either left or right primers were designed to span an exon-exon boundary. Controls (no reverse transcriptase) were included for INVINH1 and OsHAP3D genes, which had no introns; amplification was not detected in the controls. Quantitative RT-PCR was carried out following manufacturer's instructions using 50 ng RNA per 20 μL reaction, a final primer concentration of 0.5 μM and reagents from a Bioline SensiFAST™SYBR No-ROX RT-PCR kit (Bioline, London, UK). Reaction tubes were prepared by using a QIAgility robotic liquid handling system (QIAGEN). Reactions were monitored in a Rotor-Gene Q (QIAGEN) thermocycler fitted with a 100-tube gene disc rotor. The amplification program included 48 °C min, 95 °C 2 min and 45 cycles of 95 °C 5 s, 58 °C 10 s, and 72 °C 5 s. Expression was calculated relative to reference gene for ubiquitin-conjugating enzyme E2 (OsUBC) [53] using ROTORGENE software (QIAGEN). Melt curve analysis confirmed that a single product was obtained for each gene amplified.
Invertase Assay
Rice grain samples were extracted using a procedure modified from Tomlinson et al. [54]. Samples (200 mg) were ground to a fine powder in liquid N 2 in a mortar and pestle then transferred to a close fitting glass homogenizer and ground further with 1 mL of extraction buffer (pH 4.8, 100 mM acetic acetate buffer, containing 8 mM MgCl 2 , 2 mM EDTA and 12.5% (w/v) glycerol, 10 mM dithiothreitol and 1 mM phenylmethanesulfonyl fluoride). The homogenate plus a 400 μL wash were transferred to a 2 mL microfuge tube and centrifuged at 16,000 ×g for 10 min. The pellet was washed and re-centrifuged twice with 500 μL of extraction buffer before resuspending in two volumes of salt extraction buffer (pH 4.8 100 mM acetate buffer, 1 M NaCl). Samples were extracted for 1 h on ice with gentle agitation, as well as 3× sonication for 60 s. Following salt extraction, samples were centrifuged at 16,000 ×g for 10 min and the supernatant retained for assay of CWIN activity.
Reaction mixtures containing 80 μL of enzyme preparation, 10 mM sucrose and pH 4.8, 100 mM acetate buffer to a total volume of 440 μL were incubated at 37 °C for 30 min with gentle shaking. Three 40 μL aliquots were taken for glucose determination at 0 and 30 min. Glucose in the reaction mixture was measured using the Somogyi-Nelson method [55]; and calculated in comparison with a set of standards containing 5 to 100 μg glucose.
Conclusions
In conclusion, we have shown that the endosperm-specific IAA synthesis gene OsYUC12 and the AUX/IAA gene OsIAA29 are coexpressed, with expression limited to a short period during endosperm cellularisation. Extractable CWIN activity, as well as expression of putative invertase inhibitor OsINVINH3, also reached a maximum at 7 DAP, coinciding with maximal expression of OsYUC12 and OsIAA29. The possible regulation of CWIN activity by OsINVINH3 needs to be considered as part of any investigation of the role of CWIN during grain development. We have shown that rice has at least 54 genes encoding diverse proteins homologous to invertase inhibitors and PMEIs. In addition to OsINVINH3, a rice ortholog of ZM-INVINH1, six other INVINH/PMEI genes from widely divergent clades were specifically expressed in endosperm during early grain-fill. We explored other genes co-expressed with OsYUC12, OsIAA29, and OsINVINH3. Seven out of the nine genes with MR<20 appear to encode extracellular proteins homologous to molecules expressed exclusively in ETCs/ESR of other plants; these include six cysteine-rich proteins, some with similarity to BETL1 from maize. In addition, the presence of an endosperm-specific LEC1 ortholog, OsHADP3D and a receptor-like kinase gene suggests that these genes and their encoded proteins are a priority for experimental investigation in regard to a signaling network regulating differentiation of ETCs in rice. The expression of OsYUC12 is distinct from OsYUC9 and OsYUC11. It has orthologs in sorghum and maize; the maize ortholog is also expressed for a short time during grain development, suggesting conserved subfunctionalization. Expression of OsYUC9 but not OsYUC12 is reduced in the gif1 CWIN mutant. We suggest that further investigation of the specific roles of three IAA biosynthesis genes will be necessary to reveal the full extent of the relationship between CWIN and IAA. | 5,961.2 | 2014-02-07T00:00:00.000 | [
"Biology"
] |
Analysis of Mean Access Delay in Variable-Window CSM.
The paper addresses the problem of the mean access delay characteristics in termof the channel load for networked sensor/control systems in LonWorks/EIA-709 technology.The system modelling is focused on the Media Access Control protocol that provides theload prediction and determines the key network characteristics. The network model assumesthe consistency of load prediction between the nodes, and that the Transaction ControlSublayer does not introduce limitations on the data transmission. The latter means that thenumbers of concurrent outgoing transactions being in progress are unlimited. Furthermore, itis assumed that the destination addresses of transmitted messages are distributed rather thanconcentrated on particular nodes. The analytical approach based on Markov chains isapplied. The calculation of transition probabilities of the Markov chain is exemplified by theload scenario where all the transactions are acknowledged, unicast, and the optionalcollision detection is enabled. On the basis of the stochastic analysis, the probabilities of asuccessful transmission and collision, respectively, are computed. Furthermore, thenumerical results of the mean access delay are reported. The simulative validation ofanalytical results is provided.
Introduction
One of generic algorithms for random access control in networked systems is the p-persistent CSMA protocol. A node, contending for the shared channel according to the p-CSMA algorithm, transmits with the probability p, if the channel is idle, and defers a transmission with the probability (1-p) [12].
The evaluation of the random MAC performance is a complex task since an analytical model has to follow random protocol behavior. Therefore, the stochastic analysis presented in this study is carefully explained and includes all the necessary analytical derivations of analytical steps. This feature facilitates the adaptation of the analytical procedure developed in the paper to the other adaptive random access MAC protocols.
Several papers deal with performance analysis of the predictive p-persistent CSMA protocol. Main benefits of the predictive p-CSMA scheme have been displayed in LonWorks Engineering Bulletin [3]. The simulation analyses are carried out in [7,19]. The analytical approaches are reported in [4,10].
The latter follows the classical approach developed for p-CSMA by Kleinrock and Tobagi in the seventies [12]. The former is based on the queuing theory where the offered load is modelled by a number of stochastically distributed independent stimuli characterized by the corresponding packet arrival rates. The analysis developed in [4] includes the evaluation of the mean access delay and belongs to the node-centric approaches. In the present study, we have developed a channel-centric analysis with a model of an offered load different than that used in [4]. Namely, we define the offered load by a number of active nodes contending for the medium access. Such a model is widely used in CSMA performance analyses, e.g. in [5,6]. The motivation to use such a workload model is clear, since the purpose of the prediction built into the variable-window CSMA with collision avoidance is to reduce the contention among the nodes and to adapt the size of the contention window to the channel load, the number of nodes contending for the medium access is a more useful definition of the offered load for analyzing the protocol behavior. Roughly speaking, in order to recognize ability of the protocol to cope with congestion, we assume that a channel is heavily loaded since under light traffic workload the prediction mechanism is inactive. Furthermore, the backlog counting algorithm that we use in the protocol specification is slightly different than that analyzed in [4].
The paper is structured as follows. In Section 2, we present the predictive p-CSMA specification and the backlog counting algorithm. Section 3 describes the network model. The definition and the analytical derivation of the mean access delay characteristics is presented in Section 4. In Section 5, the analysis of a fixed window p-CSMA using the stochastic analysis, is carried out. The Markovbased extension of the analytical approach for the predictive p-CSMA is introduced in Section 6. The numerical results are reported in Section 7. The validation of the developed analytical approach by simulation with the comparison of sample results are reported in Section 8. Finally, the conclusions are drawn.
Packet Cycle
The predictive p-persistent CSMA belongs to slotted-CSMA protocols. The algorithm operates in the following way. A node (an intelligent sensor or actuator) attempting to transmit monitors the state of the channel. If the channel is busy, the node continues sensing. When the node detects no transmission during the minimum interpacket space of β 1 period, it delays a random number of contention slots of β 2 duration.
If the channel is still idle when the random delay expires, the node transmits. Otherwise, the node receives incoming packet and competes for the channel access again. If more than one node choose the same slot number, and when that slot has the lowest number selected by any node with a packet to send, then a collision happens. All the packets involved in a collision are corrupted.
The backoff time is expressed as a pseudorandom number of contention slots drawn from the uniform distribution between 0 and W, where W is the size of the contention window. The predictive p-CSMA is an adaptive version of p-CSMA, where a window size is dynamically adjusted to the current channel load. If the channel is idle, the contention window consists of 16 time slots. When the channel load increases, the number of slots grows by factor BL, called the estimated backlog. The backlog BL can range from 1 to 63 and the size of the window varies from 16 to 1008 slots, since where base W is the size of the basic contention window (16 slots In the predictive p-CSMA, the optional collision detection can be introduced. The aim of the collision detection in the control networked systems is that the sender does not have to wait for timeout before attempting to resend the messages. By comparison, a goal of the collision detection in data networks is to improve the total channel utilization by interrupting the transmission of packets involved in a collision. It is because the packet lengths in networked control systems are short and usually range from ten to twenty bytes.
Backlog Counting Algorithm
The backlog estimation is based on the calculation of the number of packets expected in a competition for the channel during the next packet cycle. The current value of the backlog counter BL varies from one to the next packet cycle and relies on the accumulation of consecutive backlog increments and decrements [1,2]. Backlog counting built in the node firmware, relies on the following principles [2]: -successive backlog increments are based on the information included in the header of each packet that is sent or successfully received by a particular node; this information is encoded in the 6-bit long field Delta_BL; -successive backlog decrements by one occurring at the end of successful or idle packet cycles. Both backlog modifications are independent of each other and occur in every cycle. Optionally, the backlog counter might be incremented by one in case of collision if the nodes are equipped with the collision detection [1,2]. Dedicated hardware in the transceiver is needed to detect collisions. A number encoded in the Delta_BL data field represents the number of acknowledgements that will be generated by receiver(s) as a result of packet reception. This number equals one for unicast messages. Similarly, for multicast messages the number encoded in the Delta_BL is greater than one, but does not exceed 63, so the maximum size of a group of receiving nodes addressed by a single message equals 63. In the predictive p-CSMA, acknowledgement packets are not privileged in the channel access, and compete for the channel jointly with messages. On the basis of the backlog counting algorithm we can conclude that after a successful transmission of a message the backlog BL is incremented by a number of (Delta_BL -1). It is a resultant of the increment by a number of Delta_BL, and the decrement by one at the end of a packet cycle. Comparing to the other congestion avoidance network protocols, the predictive p-CSMA uses a kind of additive increase/additive decrease window scheme (AIAD) [18], whereas IEEE 802.11 takes advantage of the truncated exponential backoff [17].
Backlog Consistency
Each node calculates the channel backlog autonomously based on the backlog counter implemented in LonWorks node firmware. To keep the consistency of backlog states, all the nodes in the network should modify their backlog counters in the same way.
The consistency is kept if each node is able to detect unsuccessful transmissions in the channel because all the recipients can increment their backlog counters by Delta_BL only if a received packet has correct CRC. Note that recipients mean all the nodes in a network segment where a packet is broadcasted, not only message destination nodes addressed by a sender. If transceivers, for example, enable only senders to detect possible packet collisions and increment their backlog counters, the backlog can lose its global character and becomes a local node-specific parameter. Any inconsistency in backlog counting among nodes causes unfairness in channel access.
Network Model
To recognize the predictive CSMA performance, we introduce some simplifications to the real network model. Below, we list the assumed simplifications in LonTalk/EIA-709.1 specification, and discuss how these simplifications may influence the obtained results.
Saturation Network Status
In our approach, we suppose that the network is at the saturation status where each node has a packet to send. To be precise, we assume that the network consists of n, a fixed number of nodes, and each node after the completion of a successful transmission immediately has a new packet available for sending. Thus, idle packet cycles do not occur in a saturated network. If an acknowledged message has been received by its recipient, this node generates an acknowledgement packet and places it in the
Link Layer Header Packet Body
Delta BL 0 … x output queue before messages waiting for a transmission. Throughout this paper the particular load scenario is considered, where the nodes are able to detect collisions, the acknowledged message service is used and all the transactions are unicast. The validity of saturation performance analysis can be extended and treated more generally. Namely, the results derived for saturation workload are valid also for the network that is at nonsaturated status but the number of transmitting nodes is constant.
Network Model
Unlike the classical p-CSMA, the predictive p-CSMA behavior is forced not only by the traffic rate but also by the structure of the traffic transmitted in the channel. In order to make the analysis tractable, we assume that each node is a source of messages unless it receives an acknowledged message. Then, it generates an acknowledgement packet and switches its status to the source of acknowledgements (i.e. schedules acknowledgement packet as the next packet for a transmission). According to the assumed load scenario all the messages are acknowledged and addressed to a single recipient (unicast). A key assumption we make is that the destination address(es) of transmitted messages are uniformly distributed in such a way that each message is sent to the node that currently possesses a status of a source of messages. The protocol performance analysis deals with the steady state of the network when the mean size of the contention window reaches asymptotically a constant value. The proportion between the number of sources of messages and the number of sources of acknowledgements in the steady state of the network determines the transition probabilities between backlog stages which are evaluated in Sect. 6.3. This proportion, however, does not influence the performance of the pure p-persistent CSMA because its behavior does not depend on the network traffic structure.
Network Segment
We assume that a network consists of a single segment that does not contain store-and-forward routers. The transceivers available on the market limit the segment size usually to 64 devices, although the LonTalk/EIA-709.1 can operate with segments containing hundreds of nodes [1].
Backlog as the Global Measure of Channel
We assume that either Physical Layer, or Link Layer of the protocol do not introduce the backlog inconsistency, i.e. either the transmitting node, or the receiver(s) modify their backlog counter(s) in the same way. It is achieved if the channel can be assumed to be noise-free and all the transceivers are able to detect collisions even if they are not senders of colliding packets. Then, backlog might be considered as a global channel measure. The similar assumption is adopted in [4].
The Number of Outgoing Transactions
We assume that the number of concurrent outgoing transactions being in progress is unlimited (i.e. each node tries to send a new packet even if acknowledgement(s) of previously sent packets have not been successfully received yet). As a result of this assumption, the number of contenders in each packet cycle equals the number of nodes in the network.
In the LonTalk/EIA-709.1 protocol, the number of active outgoing non-priority transactions is limited by the Transport Layer implemented on the top of the predictive CSMA and equals one. As a result, a node awaiting the acknowledgement packet after the successful message transmission does not try to send the next message until this acknowledgement is received. Consequently, in the saturated status of the real LON network the mean number of contenders is lower than the number of nodes in the network since some nodes do not compete for the channel due to awaiting the acknowledgement.
CPU Processing Power vs. Channel Bit Rate
We suppose that the processing speed of the node is infinite. In other words, we assume that the communication channel is not too fast for the node CPU. The limitation of transmitted packets due to finite CPU speed does not appear for relatively low channel bit rates or long packets [15].
Collision Detection
In LonTalk/EIA-709.1, the collision might be detected at the end of the packet preamble, or at the end of the packet transmission [1]. We assume that the collision is detected at the end of the packet transmission and the preamble preceding the packet transmission is assumed to be of zero length. Note that as a result of this assumption, the whole packets are in fact transmitted either in successful, or in unsuccessful packet cycles.
Mean Access Delay Definition
The mean access delay is defined as an average time from the instant the node starts trying to send a packet until the beginning of its successful transmission [14].
The channel access delay consists of the following components (see Fig. 2): -deferring transmission when the channel is busy as detected by carrier sense hardware, -delaying transmission by the fixed interval called the minimum interpacket gap (β 1 ) following any transmission in the channel to ensure that all the nodes can sense an idle channel, -deferring transmission for the random delay (from 0 to 1007 β 2 contention slots) to reduce the probability of packet collision during the contention, -deferring transmission before any of the transmission attempts if a packet is involved in collision(s).
Figure 2.
A packet access delay definition.
Method of Evaluating Mean Access Delay
We evaluate the mean access delay for the slotted CSMA basing on the estimation of an average time interval mean Δ between consecutive successful channel access attempts undertaken by a given node that always has packets to send. The time interval mean Δ can be found as: denotes the expected number of attempts in accessing the channel made by a selected node in order to transmit a packet successfully, and τ represents the mean length of a packet cycle in the channel access.
By the simplicity, we assume that the length of packets (i.e. messages and acknowledgements) sent via the channel is constant. This assumption is reliable if the application data field in the message is short comparing to the protocol overhead. This is the case when the brief explicit messages or network variable updates are exchanged between the nodes (see the application messages specification in [16] for details). Denote by PktLength the packet length in bits.
As follows from the definition presented in Sect. 3.1, the mean access delay mean t might be simply calculated as: As follows from (3) and (2), in order to evaluate the mean access delay mean t , both the expected number of transmission attempts ) ( X E and the mean length of a packet cycle τ have to be found.
Mean Number of Transmission Attempts
Let us suppose there are a number of n contenders. First, we will calculate the mean number of transmission attempts before winning the contention ) ( X E made by a selected node.
Following the notation, X represents a number of trials before a packet successful transmission is obtained. Denote by ) 1 ( succ p the probability that a certain node succeeds at any trial. The probability of the successful transmission of any packet in the channel with a number of n contenders, succ p , is given by: because each node may win the contention. Since the probability of failing during the first (i-1) tries is , the probability of succeeding at the ith attempt equals: The formula (5) defines the probability mass function of X. The mean number of transmission attempts ) ( X E is defined by the appropriate expectation: Multiplying both sides of the equation (6) Subtracting (7) from (6) gives: (8) Note that the right side of the (7) includes the infinity sum of a geometric series that equals one so: For example, if the probability ) 1 ( succ p that a given node transmits successfully equals 0.1, then a number of 10 successful packet cycles is needed on the average in order to transmit a packet with success. This result is not surprising since the transmission attempts are independent and may be modelled by the geometric distribution where the expected number of trials until the first success is the inverse of the probability of a success at any trial. The formula (9) defines the mean access delay as the average number of trials needed to win the channel contention. To express the mean access delay in bits or seconds, the mean length of a packet cycle τ has to be estimated.
Mean Length of Packet Cycle
The access to the shared channel is organized in packet cycles. Each packet cycle is an attempt of a packet transmission undertaken by node(s) that has data ready for sending. A packet cycle begins with an interpacket gap and a random number of contention slots followed by a packet transmission. The result of each transmission attempt is a successful transmission of a packet or a collision.
The mean length of a packet cycle, τ , is defined as a weigthed sum of the lengths of successful and unsuccessful packet cycles: where succ τ , coll τ denote the mean lengths of successful and unsuccessful packet cycles, respectively, where ) (n d succ denotes the mean slot number, at which a node winning the competition starts the transmission, ) (n d coll is the mean slot number at which a collision occurs, 1 β is the duration of the minimum interpacket gap, and 2 β is the contention slot width. All the parameters succ τ , coll τ , 1 β , 2 β , PktLength in the formulas (11) and (12) are specified in [bits].
Substituting (9), (10), (11), (12) and (2) in (3): The formula (14) is valid for any slotted-CSMA protocol where the size of the contention window maintained by each node is the same and the number of contenders is constant. This formula is essential for the content of the present study. The evaluation of the mean access delay given by (14) is consistent (excepting some differences in network models) with the corresponding formula included in [4] although both analytical derivations are obtained in different ways.
Under some constraints, the formula (14) can be further simplified. As will be shown in Sect. 5 The asymptotic limit defined by the formula (15) is exemplified in subsequent Fig. 3b for the 0.0625-persistent CSMA and in Fig. 7 for the predictive p-CSMA. As a result: since the interpacket space is negligible comparing with the packet length. Consequently, the mean access delay for large number of contenders can be approximated by the closed-form formula:
Input Parameters Required for Network Performance Evaluation
Summing up, in order to estimate the mean access delay mean t , the following measures have to be calculated (see formulas (14), (11), (12)): -the probability of a successful transmission ) (n p succ , or the probability of collision ) (n p coll , -the mean slot number when the successful transmission starts ) (n d succ , and the mean slot number when the collision occurs ) (n d coll .
All these measures might be evaluated using the standard probability calculus if the size of the contention window is constant, e.g. 16 slots for 1 = BL . If the randomizing window changes during the network operation, the analytical approach have to involve Markov chains to estimate the distribution of the window size in the network steady state. In Section 5, the stochastic analysis for the fixedwindow p-persistent CSMA is presented. Next, the Markov-based model for the variable-window predictive p-persistent CSMA will be shown in Section 6.
Stochastic Analysis of [1/(16k)]-Persistent CSMA
As stated, the backlog counter BL is responsible for dynamic adjustment of the contention window size to the current channel load. If the backlog equals k at some packet cycle, then the instantaneous persistence level of the predictive p-CSMA amounts to 1/(16k). Moreover, for some load scenarios the channel backlog BL permanently equals one or is closed to one. It is the case if the collision detection is absent, and no multicast messages are sent via the channel, or if the traffic rate is light regardless of the load scenario. respectively. Futhermore, in Fig. 4 the mean access delay versus the number of nodes, n, for 0.0625persistent CSMA is presented. As follows from Fig. 3 and Fig. 4, the 0.0625-persistent CSMA protocol presents a satisfactory performance if a network does not exceed a few nodes. For 20 active nodes, the probability of a successful transmission nearly equals the probability of a collision so only about half of the bandwidth is used for successful transmissions (Fig. 3a). For large networks ) ( ) 1 ( n p succ is degraded due to excessive collisions. The strong decrease of the probability of successful transmission succ p (Fig. 3a) causes the exponential lengthening of the mean access delay mean t versus the network size according to the equation (17) as is seen in Fig. 4.
Stochastic Analysis of Predictive CSMA
Now the analytical approach for the fixed-window p-CSMA will be extended for the variable contention window in the predictive p-persistent CSMA. The analytical approach based on Markov chains is applied.
Probability of Successful/Unsuccessful Transmission for Predictive p-CSMA
As follows from the predictive p-persistent CSMA specification, the contention window size varies from one to the next packet cycle following the random protocol behavior. Let us assume that the backlog BL equals k with the probability k π in the network steady state.
The mean channel backlog BL , defined as an expected backlog in the long-term prospect, is calculated as follows: The mean size of a randomizing window in the saturation steady state: The corresponding performance metrics for the variable-window CSMA can be found as appropriate expectations:
Analytical Model of Channel Backlog
In order to evaluate the performance measures given by the formulas (27) (1) an unsuccessful transmission due to a collision, which causes the channel backlog BL to increment by one in the next packet cycle: (2) a successful transmission of the message, when the channel backlog BL does not change in the next packet cycle: (3) a successful transmission of the acknowledgement packet, which decreases the channel backlog BL by one in the next packet cycle: Modelling the impact of backlog limitations, two additional conditions for the backlog minimum , remains at it even after successful transmission of an acknowledgement.
Transition Probabilities
The key approximation in our model is that the probability of a successful transmission of an acknowledgement is the same as the probability of the successful transmission of a message. The validity of this approximation will be checked in Sect. 8.2. According to this approximation, if the probability of a collision at a certain backlog stage k l BL = ) ( with n competing nodes amounts to ) ( ) ( n p k coll , then both the probability of a successful transmission of a message and of an acknowledgement are equal to 2 ) 1 ( . Suppose that the backlog enters the stage k at the lth packet cycle, that is, be the transition probability that the backlog enters the stage s k l BL in the (l+1)th packet cycle from the stage in the lth cycle. Let us denote the transition probabilities in short: Taking a specification of packet cycle types (1)-(5) into account, we can compute the probabilities of switching between the backlog stages:
Mean Backlog and Stationary Distribution
As is well-known, the stationary distribution of a Markov chain is an eigenvector of the transition matrix P , associated with the eigenvalue 1. The vector ] [ k π = π includes the long-term probabilities k π that the channel backlog will be at the stage k in the steady state, that is: The probability k π is the relative frequency that a channel enters the backlog stage k in the steady state. See [13] for the numerical methods of the stationary distribution computation. Here we calculate the stationary distribution directly as the appropriate eigenvector of the transition matrix. Namely, to compute the steady-state vector π of a Markov chain, the following linear system has to be solved: is a transition matrix 63 x 63; the elements j i p , of the matrix P are given by (35), is a vector, where 63 ,..., is a matrix 63 x 64, where the last column of this matrix is the vector e , ] is a vector, where 63 ,..., 1 ; 1 , According to (35), the transition matrix P for ACK/unicast/CD scenario is composed as follows:
Numerical Results for Predictive CSMA
Using the analytical approach presented in Section 6 we have obtained the following numerical results.
Mean Backlog and Probability of Successful/Unsuccessful Transmission
The plots presenting the mean channel backlog BL and the probability of collision versus the number of nodes n for a specified load scenario (ACK/unicast/CD) are shown in Fig. 6. Each point on the saturation backlog graph is found as a solution of the linear equation (37) Since we want to recognize the complete protocol behavior, the saturation backlog versus the wide range of a network size (from 2 to 2500 nodes) is presented. A typical network segment contains a few dozens of nodes although LonTalk protocol can operate with segments that consist of hundreds of devices [1].
The analysis of the results shows that the mean channel backlog is, as expected, a non-decreasing function of the network size. At the lower range the mean backlog increases linearly as the number of nodes grows and the slope of the curve is about 0.06 per node. It means in particular that adding a new node to the existing network causes the increase of the mean size of a competition window of about ) and decrease ( coll p ) are equal. Finally, for networks greater than 700 nodes, the influence of maximum size of a competition window appears, and the shape of both measures is close to that of the 0.0009-persistent CSMA.
Mean Slot Numbers Where the Successful/Unsuccessful Transmission Starts
The relationships between the mean slot numbers ) (n d succ , ) (n d coll and the number of nodes n according to (32), (33) for ACK/unicast/CD load scenario are shown in Fig. 7. The analysis of ) (n d succ versus the number of nodes allows to reply to the question how much the network bandwidth is wasted during the channel contention, that is, how many time slots 2 β are wasted in the average successful packet cycle in order to avoid the collision. As follows from Fig. 7, in the network containing 10 nodes about the third slot is drawn by the winning nodes in average, and for 100 nodes, about the second one. The next conclusion taken from Fig. 7 nodes with a few percent accuracy for typical packet lengths (e.g.
bytes).
Thus, we can conclude that the fraction of bandwidth wasted due to a randomization of the channel access is insignificant if the contention is high. This is the important advantage of the predictive ppersistent CSMA. (14) taking into account formulas (30), (32) and (33). The latency in accessing the channel increases nearly linearly with a growing number of contending devices up to about 700 nodes. This is the important qualitative difference compared with the mean access delay for the fixed window p-CSMA (see Fig. 4 For networks greater than 700 nodes, the shape of mean access delay plot starts to be nearly exponential since it is close to that of 0.0009-persistent CSMA. On the basis of the analytical formulas, the following conclusions can be drawn up: -if the channel is lightly loaded, the primary component of the latency is deferring transmission due to randomization of the channel access; the delay is then not greater than a few contention slots in average as is seen in Fig. 3b and Fig. 4 for the 0.0625-persistent CSMA, -if the channel is heavily loaded, the dominant component of the access delay is the probability of a successful transmission of a single node; this probability decreases due to two factors: first, because of decreasing the total channel bandwidth utilization as a result of collisions; second, since the channel bandwidth per a single node decreases because it is divided out among the growing number of contenders. Furthermore, since the asymptotic probability of a collision is bounded in the predictive p-persistent CSMA, the mean access delay grows almost linearly with the number of contending nodes.
It is worthy to emphasize that linear characteristic of the average access delay is the optimal delay relationship that can be achieved for heavy workload in MAC protocols based on the best-effort strategy and appears only for the range of workload where the channel throughput does not decrease with growing number of contenders. The linear access delay increase with the network load is the effect of dividing the bandwidth out among the increasing number of active nodes.
Simulative Validation of Analytical Approach
In order to verify the analytical approach we have run the simulations for the network containing selected number of nodes. The simulation model implemented in LabView corresponds to the analytical model specified in Section 3.
The simulation starts when the channel is idle. Next, the transient zone appears, when the nodes permanently try to access the channel and the mean channel backlog grows, but does not reach the steady-state value. Since the simulation model belongs to non-terminating systems and the steady state theoretically is never reached, we detect it with a finite accuracy. The detection relies on the search of the constant value of the mean backlog, rather than of the constant value of the current backlog. Therefore, we used the moving averages defined over a window of observations (i.e. a certain number of packet cycles, increasing with the number of nodes). Moving averages filter the higher frequency components in the mean backlog, arisen from the random behavior of the CSMA algorithm on the one hand, and remove also the influence of the transient zone on the estimation of saturation backlog on the other. The saturation backlog is found under quasi steady-state conditions when the moving average of the channel backlog is kept inside of 5% wide confidence interval.
Simulation outputs are the saturation channel backlog, the relative frequencies of successful/unsuccessful transmissions (as the experimental equivalents of the appropriate probabilities), and the mean access delay.
Validation of Transition Probabilities
The transition probabilities in Markov model have been derived basing on the equality of the probabilities of the successful transmission of a message and an acknowledgement (see Sections 6.3). This assumption is true if the mean number of nodes having a message waiting for a transmission (i.e. message sources) equals the mean number of nodes that possesses an acknowledgement ready for sending (i.e. acknowledgement sources).
A uniform distribution of destination addresses has been implemented in the simulation model as stated in Sect. 3.2. The assignment of recipient addresses is controlled by the simulator. First, the simulator tries to assign a recipient that is a source of messages to every message sender. In case of the lack of sufficient number of message sources, the sender sends a message to itself (by the way such transmissions occur sometimes in real LON systems during turnaround network variable updates, see [15]). Fig. 9 presents simulation results showing the mean number of message and acknowledgement sources in the network steady state. It is clear that both numbers are equal to 50% with finite simulation accuracy. It was checked that these results are independent of initial conditions, i.e. the proportion between the number of message and acknowledgement sources at the simulation beginning. Sources of messages Sources of acknowledgements Figure 9. Simulation results of the mean number of message/acknowledgement sources in the saturation network steady state
Simulation versus Numerical Results
The comparison of simulation and numerical results for the saturation backlog, the probability of collision coll p and its experimental measure (i.e. collision percentage coll p' ), and the mean access delay, are presented in Table 1. Since both results are very close to each other and the corresponding graphs overlap, they are not shown on the plots together. The comparison shows a good conformity of simulation and Markov chain-based analytical approach. The difference between the results obtained in both approaches stems from: -the finite accuracy of backlog estimation and the steady state detection in the simulation, -the inaccuracy (non-uniformity) of the pseudorandom generator in the simulation, -the finite precision of complex analytical computations. | 7,950.6 | 2007-12-01T00:00:00.000 | [
"Computer Science",
"Engineering"
] |
Predicting Adherence to Internet-Delivered Psychotherapy for Symptoms of Depression and Anxiety After Myocardial Infarction: Machine Learning Insights From the U-CARE Heart Randomized Controlled Trial
Background Low adherence to recommended treatments is a multifactorial problem for patients in rehabilitation after myocardial infarction (MI). In a nationwide trial of internet-delivered cognitive behavior therapy (iCBT) for the high-risk subgroup of patients with MI also reporting symptoms of anxiety, depression, or both (MI-ANXDEP), adherence was low. Since low adherence to psychotherapy leads to a waste of therapeutic resources and risky treatment abortion in MI-ANXDEP patients, identifying early predictors for adherence is potentially valuable for effective targeted care. Objectives The goal of the research was to use supervised machine learning to investigate both established and novel predictors for iCBT adherence in MI-ANXDEP patients. Methods Data were from 90 MI-ANXDEP patients recruited from 25 hospitals in Sweden and randomized to treatment in the iCBT trial Uppsala University Psychosocial Care Programme (U-CARE) Heart study. Time point of prediction was at completion of the first homework assignment. Adherence was defined as having completed more than 2 homework assignments within the 14-week treatment period. A supervised machine learning procedure was applied to identify the most potent predictors for adherence available at the first treatment session from a range of demographic, clinical, psychometric, and linguistic predictors. The internal binary classifier was a random forest model within a 3×10–fold cross-validated recursive feature elimination (RFE) resampling which selected the final predictor subset that best differentiated adherers versus nonadherers. Results Patient mean age was 58.4 years (SD 9.4), 62% (56/90) were men, and 48% (43/90) were adherent. Out of the 34 potential predictors for adherence, RFE selected an optimal subset of 56% (19/34; Accuracy 0.64, 95% CI 0.61-0.68, P<.001). The strongest predictors for adherence were, in order of importance, (1) self-assessed cardiac-related fear, (2) sex, and (3) the number of words the patient used to answer the first homework assignment. Conclusions For developing and testing effective iCBT interventions, investigating factors that predict adherence is important. Adherence to iCBT for MI-ANXDEP patients in the U-CARE Heart trial was best predicted by cardiac-related fear and sex, consistent with previous research, but also by novel linguistic predictors from written patient behavior which conceivably indicate verbal ability or therapeutic alliance. Future research should investigate potential causal mechanisms and seek to determine what underlying constructs the linguistic predictors tap into. Whether these findings replicate for other interventions outside of Sweden, in larger samples, and for patients with other conditions who are offered iCBT should also be investigated. Trial registration ClinicalTrials.gov NCT01504191; https://clinicaltrials.gov/ct2/show/NCT01504191 (Archived at Webcite at http://www.webcitation.org/6xWWSEQ22)
Introduction
Myocardial infarction (MI) afflicts more than 7 million individuals each year, making it the most common acute cardiac event caused by cardiovascular disease (CVD)-the leading cause of death in the world [1].After an acute MI, behavior changes are required in order to reduce the risk of reinfarction, stroke, and death.Important health-promoting behaviors include smoking cessation, regular physical activity, a healthy diet, and adherence to medications [2,3].
A substantial subgroup of patients with MI additionally also suffer from symptoms of anxiety, depression, or both (MI-ANXDEP).MI-ANXDEP patients have a higher risk factor burden and worse prognosis compared to MI patients in general [4,5].Alongside prescribed physical activity, psychological support is therefore suggested as treatment for MI-ANXDEP patients to reduce affective symptoms [6][7][8] and in turn facilitate health-promoting behavioral change toward cardiac risk reduction [2,9].Psychological support in the form of cognitive behavior therapy (CBT) has shown effectiveness on psychological symptoms for several common psychiatric disorders.Internet-delivered CBT (iCBT) is a cost-effective version of face-to-face CBT [10,11] that, however, places high demands on the reading and writing abilities of the patient.Patient dropout from iCBT in a meta-analysis for depression (n=40 studies) was 57%.Subanalyses showed 28% and 38% dropout from therapist-and administrator-supported iCBT, respectively.These attrition numbers are substantial, suggesting further research into adherence to iCBT.Although adherence to iCBT is not a guarantor for iCBT effectiveness, adherence is arguably a prerequisite for possible iCBT effect and thus worthwhile to study in its own right [12].
The multicenter Uppsala University Psychosocial Care Programme (U-CARE) Heart study was the first randomized controlled trial to test the effectiveness of a therapist-supported iCBT treatment for MI-ANXDEP patients [13,14].The U-CARE Heart trial design arguably had high ecological (clinical routine) validity [14] compared to other iCBT trials that have relied on self-referral and applied stricter inclusion/exclusion criteria [15,16].U-CARE Heart also featured relatively low adherence to iCBT, which in turn lacked effect at the group comparison level [13].For future dissemination of iCBT, it is crucial to assess the effect and practical utility of iCBT under ecologically valid conditions [17] such as in U-CARE Heart and explore factors that predict adherence if low adherence is a problem in such contexts.Adherence to treatment by cardiovascular patients has been thoroughly investigated with respect to medical compliance [18] but not with respect to iCBT offered to MI-ANXDEP patients.
Treatment adherence is in general a multifactorial phenomenon.Adherence to and effectiveness of iCBT has been associated with higher education, older age, and female sex [19,20].In addition to these background predictors, both patient motivation [12] and treatment credibility [19] have been found to substantially augment adherence to iCBT.Regarding MI-ANXDEP psychological symptomatology, patient motivation and belief in the iCBT treatment are probably also predicated on cardiac-related anxious and depressive symptom severity as well as placebo priors regarding iCBT effectiveness.The so-called therapeutic alliance, the patient-therapist bond sought to be developed during individual psychotherapy, has also been found to benefit adherence to iCBT [12].Furthermore, it is worthwhile to investigate the relative predictive power of some cardiovascular variables, as somatic disease severity might also influence adherence to iCBT among MI-ANXDEP patients.
The present iCBT U-CARE Heart study design offered a group of additional predictors that have not been assessed in this way, namely linguistic variables based on the texts that patients wrote in response to their standardized homework assignments.Syntactic structure and word use has to some extent been investigated before with regard to anxiety and depression [21][22][23], and number of words used when applying for Web-based depression treatment has been shown to correlate with adherence [24].In the U-CARE Heart study, the texts are logged at the start of treatment, and various quantitative variables can be extracted from these texts using linguistic procedures.These extracts were then modeled as additional linguistic predictors for adherence in our study.It is likely that more verbally oriented and engaged patients write longer and more complex texts and also adhere better to verbally demanding treatments such as iCBT.It is also possible that these linguistic predictors to some extent are proxies of other established predictors for adherence (eg, motivation, treatment credibility, and therapeutic alliance) and as proxies would thus hold predictive power.We propose that these linguistic predictors might contribute to the acuity of predictive models in addition to known predictors of iCBT adherence (eg, education, age, sex, and symptom severity).
The objective of our study was to investigate if predictors available up to the start of treatment (initial homework assignment response) would predict adherence to iCBT treatment at first follow-up in MI-ANXDEP patients.To this end, we applied a contemporary machine learning procedure to XSL • FO RenderX U-CARE Heart data to manage the relatively large amount of predictors and complex covariance structure.We hypothesized that symptom severity, age, sex, education, and linguistic behavior would predict adherence to treatment.We also hypothesized that more severe symptoms, younger age, being a woman, having a higher education, and using more words in the assignment response would be positively associated with adherence to iCBT.
Treatment and Study Sample
The recruitment, treatment, and follow-up of patients has been described in detail elsewhere [13,14,25].In summary, the trial recruited 239 patients from 25 Swedish hospitals and randomized 122 patients to a control group and 117 patients to therapist-guided and self-tailored 14-weeks of iCBT.Of these 117 patients, 27 did not respond to any homework assignments and were excluded due to lack of data on all linguistic variables.This rendered a study sample of 90 patients.The treatment modules consist of homework assignments to be completed by the patient on which the licensed psychologist provided feedback.The psychologist communicated with the patient through an in-portal message system.The first two homework assignments were standardized for all patients.This standardization removed the problem of complex patient-psychologist interactions that are inherently dynamic.After the first two assignments, the treatment was self-tailored.The treatment consisted of psychoeducation on principals for rational versus irrational thinking, graded exposure to fearful stimuli, the negative feedback loop in depressive behavior, as well as relaxation training, improving communication skills, additional behavioral change toward long-term goals, and relapse prevention.
Outcome and Initial Predictor Selection
The outcome variable was dichotomous: adherence was defined as completing 3 or more homework assignments (≥21% of total treatment), and nonadherence was defined as having completed less than that.This cutoff was chosen in part because it is clinically relevant to ascertain who continues with the self-tailored part of the U-CARE Heart treatment after completing the initial 2 standardized homework assignments versus who does not continue.Furthermore, the chosen cutoff rendered fairly balanced classes for the machine learning procedure, which is important for it to work properly with moderately sized data [26].Psychological (EO, JW, FN), cardiologic (CH), and linguistic (EG) experts selected an initial set of 34 possible predictors of psychometric, linguistic, clinical, and demographic type.See Table 1 for further details on the predictors.
Linguistic Predictors
The linguistic predictors were extracted from the patients' answers to the first standardized homework assignment, which consisted of an introductory text and 8 questions designed for the patient to describe their MI, associated psychological reaction, present psychological state, present social support, and what the patient wanted from iCBT treatment.In effect, patients had access to the same material prior to carrying out their homework assignment [13,14].Since the patients had read both example answers and an introductory text before writing their response, it is possible that the patients' choice of words would be substantially, but also equally, primed when answering the questions.The linguistic factors investigated were (1) the number of words used, (2) average sentence length, (3) normalized frequencies (results given as n/1000 words) of adjectives or adverbs, (4) normalized frequencies of possessive pronouns, (5) normalized frequencies of personal pronouns, (6) whether or not the patient mentions the MI, and the (7) frequency of mutual usage of a small set of prespecified key words (used both in a standardized question and in a patient answer).Predictors 1 through 7 were selected on the basis of them being possibly indicative of adherence to iCBT as probable proxies for verbal skill, socioeconomic status, and investment in therapy, all arguably important factors for iCBT adherence.See Multimedia Appendix 1 for further details on the linguistic predictors.
Imputation
Five of the 34 predictors had missing data, in the order of proportion missing: number of standard glasses of alcohol consumed per week, 11% (10/90); BMI, 10% (9/90); heart rate, 7% (6/90); systolic blood pressure (SBP), 7% (6/90); and the number of days between hospital admission for MI and study randomization, 4% (4/90).Missing values were thus relatively few and not considered missing completely at random (MCAR), instead their missingness was assumedly related to the other measured variables (MAR).We also did not impute the outcome.Thus, k nearest neighbor (k-NN) imputation was performed with number of nearest cases (k) set to 3 and all variables with missing values imputing the median of k values.The k-NN is a well-established algorithm for imputing both numerical and categorical variables based on a generalized distance metric [33,34].In this study, the Hower distance metric was used [35].If k, from which the algorithm borrows values for cases with missing values, is set low (eg, k ≤3), imputation with k-NN also preserves much of the underlying correlational structure of data.
Predictive Modeling
Adherence is a multifactorial problem [18,20], which suggested a multivariable prediction model.For testing the relative power of predictors, a useful method would be one that can weigh the variables according to their relative importance for solving the binary classification problem of predicting adherence versus nonadherence.The Breiman random forest model [36,37] is a well-established ensemble method which usually performs well with moderately sized data, is insensitive to multicollinearity and nuisance variables, and has previously worked well with MI patient data [38].These model characteristics are suitable for the multiple highly correlated psychometric measures and 90 MI-ANXDEP patients in this study.Random forest also models linear and higher-order effects automatically, which concurs with the main study objective to estimate the total relative importance of a range of predictors.Although random forest already has built-in cross-validation control for overfitting through its "out-of-bag" predictions, we added a second wrapper layer around the classifier in the form of backwards algorithmic predictor selection via recursive feature elimination (RFE) resampled with 3×10-fold cross-validation [39].This was done to further decrease the risk of overfitting and remove human bias from the final feature selection.Regular k-fold cross-validation partitions data into k parts and then trains the model k times, each time withholding data belonging to one of the folds and testing each trained model on the corresponding hold-out fold.Modeling results are thereafter usually averaged across resampling folds.Repeated cross-validation is an extension of regular k-fold cross-validation where data is again randomly partitioned into k-folds for each pass of regular cross-validation.Since random forest was used as the classifier within RFE resampling, the process optimized on classification accuracy, and predictors were ranked on their reduction in node impurity (Gini importance) across decision trees in the random forest ensemble.
Additional Statistics
If not stated differently, we report categorical variables as count (%), numerical variables as arithmetic mean (SD), P value for bivariate tests of significance set at 5%, and prediction accuracy for the binary outcome (adherent vs nonadherent) with 95% confidence intervals.
Coding
The linguistic data preprocessing was carried out with the corpus tool AntConc version 3.4.4m(Waseda University) [40], a corpus toolkit for concordancing and text analysis.Linguistic data was also annotated with a Part of Speech-tagger for Swedish called Stagger (Stockholm University) [41].Analysis was done in R version 3.4.0(The R Foundation for Statistical Computing) [42] using packages caret, data.table,foreign, ggplot2, ggpubr, ggthemes, mice, scales, tableone, and VIM.
Results
Descriptive data are available in Table 1.Patients who were adherent to iCBT were more frequently women and had higher self-rated cardiac anxiety and cardiac anxiety specifically related to fear and attention compared to those nonadherent.Adherent patients also used more words and more mutual words in their homework assignment.There was a tendency for adherence to increase with age and higher self-rated depression.There were no significant differences between adherers and nonadherers regarding educational attainment, whether Swedish-born or not, civil status, educational attainment, clinical characteristics, days from MI to treatment allocation, or preferred way of contact.
After imputation, the RFE feature selection procedure was applied to extract the most potent predictors for classifying adherers versus nonadherers.Figure 1 shows the resampled result optimized on prediction accuracy and the final optimal model as selected by RFE.This final model used 56% (19/34) of the provided predictors and performed significantly better than did a random model (Accuracy 0.64, 95% CI 0.61-0.68,P<.001) although with remaining room for acuity improvement.
Principal Findings
Our study tested and compared established and novel predictors for adherence to 14 weeks of therapist-supported iCBT using data from 90 MI-ANXDEP patients recruited from 25 hospitals in Sweden and randomized to treatment in the U-CARE Heart clinical trial.The time point of prediction was after completion of the first homework assignment, which therefore allowed the study of previously untested linguistic predictors extracted from actual written behavior together with previously established predictors.A robust machine learning procedure sifted out the most potent predictors for adherence assessed at the end of treatment, which were found to be self-assessed cardiac fear, sex, number of words, self-assessed general cardiac anxiety, average sentence length, and number of mutual words used.
Clinical Interpretation and Possible Implications
Both symptoms of general cardiac anxiety and specific cardiac fear were among the strongest predictors, and to the extent of symptom and mechanistic overlap, this corroborates previous findings that depression is associated with increased adherence to cardiac rehabilitation [43].It is even more likely that cardiac anxiety, which is directly linked to the present treatment, would trigger activity more strongly than depression, given the respective symptomatology.Depression and anxiety are highly interconnected, which might explain the result from the cited study.Thus, patients reporting high levels of depression and patients reporting high levels of anxiety have acknowledged that they have a problem.Overall, it seems reasonable given the strength of the anxiety-based predictors that those MI-ANXDEP patients who are relatively less worried, in general and specifically regarding their heart, are less likely to adhere to treatment that specifically targets such symptoms.Our study also found that female sex was an important predictor for adherence, in line with pooled iCBT trial data confirming that males have a higher drop-out rate from Web-based interventions for depression [20].Although not interchangeable, drop out is reasonably related to poor adherence.
On the other hand, our findings do not replicate other previously identified predictors for adherence to iCBT such as education and age [12,20], possibly due to the relatively old MI-ANXDEP patient population or the differing recruitment procedure in this study relative to the bulk of previous iCBT studies.Neither was alcohol a predictor, which might be due to a generally low level of problem drinking in the study sample.Although the U-CARE Heart inclusion had relatively high ecological validity compared to other iCBT studies, our patients were still selected, excluding, for instance, those with suicidal tendencies.Moreover, the weak predictive power of depression as gauged by the Hospital Anxiety and Depression Scale (HADS), especially compared to symptoms of anxiety and their strong predictive power, is puzzling.This may be due to exclusion of severe depressive symptoms on the basis of suicide risk, whereas no such screening was applied for very high anxious symptomatology.With that said, HADS anxiety was not a useful predictor, possibly suggesting psychometric shortcomings of the particular HADS scale.Consequently, the more cardiospecific anxiety scale CAQ seems more relevant for adherence in MI-ANXDEP patients.Furthermore, alternative ongoing treatment external to the trial (eg, psychoactive medication and third-party counseling) was not predictive of adherence to iCBT.Important to note is that there were no restrictions on patients seeking additional external treatment available from the relatively well-developed Swedish health care system.This could perhaps explain the null finding through the principle of homeostasis applied to symptom severity and sought treatment.In a relatively free and rich society, particularly severe symptomatology should be compensated for by such patients seeking and receiving multimodal treatment as needed.If so, these factors might cancel each other out with respect to both the need for and adherence to iCBT.
We also discovered that novel linguistic predictors based on written verbal responses predicted adherence.The number of words may be a proxy for verbal fluency and degree of patient effort in therapy, and the number of mutual words might be a proxy for the degree of therapeutic alliance, which in part corroborates previous research on therapeutic alliance and other interlinked concepts that promote adherence to iCBT [12,19,20,24,43].Together with previously known predictors, these linguistic predictors may enable improved risk stratification regarding which patients will likely adhere to treatment.This suggests a largely unexplored route for future clinical research seeking to lower iCBT treatment failure and might lead to further tailoring of limited therapeutic resources for augmenting cost-effectiveness and lowering human suffering in clinical care.
Although more work is arguably needed, the data collection, preprocessing, and analysis of written responses can be automated to a considerable degree so the current lack of off-the-shelf clinical utility might not be a future obstacle.An automated tool for predicting adherence can be constructed and then possibly used as a decision support tool by the clinician.Moreover, the tool could also determine the risk of low adherence in patients, which could possibly inform the tailoring of treatment for the MI-ANXDEP patient more objectivity and accurately compared to the guesswork and crude cutoffs often applied to counter low adherence in clinical research and care today.So-called artificial intelligence and the related supervised machine learning applications that are now being rapidly researched and implemented broadly would likely also be of benefit to better solve the clinically relevant problem of predicting adherence to internet-delivered treatments.
Limitations and Strengths
A limitation of this study is the sample size.Although the present U-CARE Heart study is the largest iCBT trial for MI-ANXDEP patients to date, it provides limited reliability estimates.The sample is too small to subdivide for more detailed analyses of those exclusively depressed or anxious.Within the limits of the present sample size not allowing for an external validation data set, the generalizability of findings is, however, quite good given that (a) applied predictive modeling procedure was robustly cross-validated, (b) national coverage was very good with recruitment from 25 hospitals, and (c) patients were recruited very similarly to routine clinical care.
Although we used expert content knowledge to select predictors and tested a range of common and domain specific predictors, there was still the possibility for using other predictors.This might explain the room for improvement in terms of classification acuity.Given that we studied a whole new class of predictors consisting of actual written behavior selected by domain experts, this study adds further novelty in that manner.The confirmation of some previously known predictors for adherence to psychotherapy with scarcely studied but very common MI-ANXDEP patients indicates potential clinical utility with MI-ANXDEP patients.The study was conducted in Sweden, and we cannot readily extrapolate our findings beyond our national and linguistic borders.The MI-ANXDEP population is also a distinct subgroup of MI patients, and the iCBT intervention is specifically tailored to these patients.Hence, replication outside of Sweden with different patients and for other psychotherapeutic treatments would be valuable.
There was also the limitation of operationalizing the outcome.This can be done in several ways, with the most strict adherence definition being to complete all treatment modules [44].However, since the U-CARE Heart trial had particularly high ecological validity but suffered from generally low adherence [13], this cutoff definition of adherence automatically had to be low to be able to model adherence since the moderate sample size inhibited us from modeling unbalanced classes.Defining adherence as those patients continuing treatment beyond the first two standardized modules is also arguably more clinically relevant on qualitative grounds compared to an arbitrary percentage cutoff.Considering clinical needs and data availability, the patients were selected on completion of the initial standardized homework module-the optimal time to predict treatment adherence if one wants to also use linguistic predictors derived from written treatment response to make early in-treatment prediction of treatment adherence.There are also qualitative approaches to investigate adherence to iCBT [25] that might augment our understanding of adherence if combined with the current data-driven approach.Furthermore, the purpose of studying linguistic predictors automatically excluded 27 patients who were randomized to treatment but did not complete any homework assignment.For obvious reasons, our prediction model cannot generalize to these patients, yet it seems likely that prediction accuracy would theoretically be higher if including these patients because they constitute extreme cases of low adherence.
Conclusions
For developing and testing effective iCBT interventions, investigating factors that predict adherence is important.Using a supervised machine learning approach, adherence to iCBT treatment in a multicenter trial for MI-ANXDEP patient was best predicted by a diverse set of predictors.The most potent predictors also included novel linguistic predictors from written patient behavior at the start of treatment.Our findings may improve the tailoring of iCBT for these high-risk patients.Future research should also investigate possible causal mechanisms and determine if these findings replicate outside of Sweden, in larger samples, and for other patient groups that might benefit from iCBT.
Figure 2
Figure 2 plots the main result with each of the 19 top predictors according to RFE by their resampled relative importance for classifying adherers versus nonadherers, showing that the 6 most potent predictors were Cardiac Anxiety Questionnaire (CAQ) fear, sex, number of words, CAQ total, average sentence length, and number of mutual words.
Figure 1 .
Figure 1.Predictor selection result with recursive feature elimination.
Figure 2 .
Figure 2. Relative importance of each predictor for adherence sorted by group.BADS: Behavioral Activation for Depression Scale-Short Form; BMI: body mass index; CAQ: Cardiac Anxiety Questionnaire; EQ5D: European Quality of Life Questionnaire-Five Dimensions; HADS: Hospital Anxiety and Depression Scale ; MI: myocardial infarction; VAS: visual analog scale.
Table 1 .
Descriptive statistics for all treated patients with myocardial infarction and stratified by adherence to internet-delivered cognitive behavioral therapy. | 5,656 | 2018-10-01T00:00:00.000 | [
"Medicine",
"Psychology",
"Computer Science"
] |
Osteocyte gene expression analysis in mouse bone: optimization of a laser-assisted microdissection protocol
Abstract Among bone cells, osteocytes are the most abundant, but also the most challenging to study because they are located inside a dense mineralized matrix. Due to their involvement in bone homeostasis, diverse tools are needed to understand their roles in bone physiology and pathology. This work was aimed at establishing a laser-assisted microdissection protocol to isolate osteocytes and analyze their gene expressions. The goal was to overcome the limitations of the technique currently most used: RNA extraction from the whole bone. To perform laser microdissection and subsequent gene expression analysis, the five main steps of the protocol have been adapted for the bone tissue. After testing many parameters, we found that the best options were (1) take unfixed snap-frozen tissue, (2) cryosection with a supported tape system to improve the tissue morphology if necessary, (3) microdissect regions of interest, and (4) recover the bone pieces by catapulting, if feasible, or by gravity. Finally, RNA extraction (5) was the most efficient with a precipitation method and allowed quantifying the expression of well described osteocyte genes (Gja1/Cx43, Phex, Pdpn, Dmp1, Sost). This work describes two protocols optimized for femur and calvaria and gives an overview of the many optimization options that one could try when facing difficulties with laser microdissection.
Protocol 1 (femur) STEP 1: Bone sample preparation
The protocol is designed based on experiments with adult mouse bones.The main goal of this step is to prepare the bone samples to allow for efficient cryosectioning and to preserve the RNA integrity.
1. Prepare molds for cryopreservation (1 mold/femur): add OCT (Optimal Cutting Temperature gel, TFM-C); avoid to introduce air bubbles.Let the molds at room temperature.
2. Prepare a container with liquid nitrogen.16.Adjust parameters depending on the section quality: objective 20x; laser beam energy: 78%; focus: 75%; speed: from 10% to 30%.17.Draw on the screen the areas that will be microdissected.We recommend to draw and dissect the areas one by one to adjust the number of cutting cycles if necessary.
18.The dissected areas will fall on the coverslip.It is possible to focus on the coverslip to confirm the presence of the bone pieces that were cut.19.Within 2 hours a total surface of 2.5 ± 0.1 mm 2 can be dissected.We have not tested the RNA quality with a longer period of time.
Protocol 2 (calvaria) STEP 1: Bone sample preparation
The protocol is designed based on experiments with adult mouse bones.The main goal of this step is to prepare the bone samples to allow for efficient cryosectioning and to preserve the RNA integrity.
2. Prepare a container of isopentane placed in liquid nitrogen.
3.
Euthanize mice by cervical dislocation and immediately dissect the femurs.There is no need to remove the periosteum or flush the bone marrow.4. Embed bones in OCT and immediately dive the molds in liquid nitrogen.5.When all the dissections are done, transfer the molds at -80 °C for storage.STEP 2: Cryosectioning 6. Adjust the cryostat temperature to -27 °C ± 1 °C and install a blade specifically designed for hard tissue.Clean all the instruments with RNase AWAY™.7. When the temperature is reached in the cryostat chamber, place the molds containing the bone samples in the chamber and let them equilibrate in temperature for 15 min.Position one sample on the tissue holder with OCT. 8. Adjust the tissue thickness to 5 µm and transfer the section to a PET FrameSlide; if possible, put 3 sections on the same FrameSlide.The sections should be as flat as possible to allow the laser beam to cut efficiently.Keep the slide in the cryostat chamber or continue to step 3. STEP 3: Dehydration and staining of sections 9. Prepare containers with ice-cold ethanol 50% (x2), 75% (x2), 95% (x2), and 100% (x2).10.Dive the FrameSlide successively in ethanol 95%, ethanol 75%, and ethanol 50% for 40 s in each bath.11.Put the FrameSlide on a paper and add a drop of the solution of Cresyl Violet (1% in ethanol 50%).Let stain for 10 s. 12. Transfer immediately the FrameSlide in the bath of ethanol 50 %, and proceed to dehydration with the successive baths of ethanol 75%, and twice 100% for 40 s in each bath.13.Let the FrameSlide dry completely at room temperature.STEP 4: Microdissection and collection of osteocyte-containing bone pieces 14.Immobilize a coverslip (0.13-0.16 mm) below the FrameSlide with a tape.The bone section should be between the PET membrane and the coverslip.15.Place this assembly on the slide holder of the P.A.L.M MicroBeam device with the coverslip below.
20 . 21 .
After 2 hours, take carefully the FrameSlide, remove the tape that immobilizes the coverslip and add lysis solution; use this solution to transfer the bone pieces into a microtube.Store the microtube containing the bone pieces at -80 °C until RNA extraction.STEP 5: Tissue lysis and RNA extraction 22. Use the MasterPure Complete DNA & RNA Purification Kit, and follow the protocol recommended for tissue samples.23.Add 1 µL of Proteinase K to the Tissue and Cell Lysis Solution.Homogenize the bone pieces in this solution.24.Incubate at 65 °C for 15 min, and regularly homogenize by vortexing after 5 and 10 min.Let the solution a few minutes on ice.25.Add 150 µL of the solution "MPC Protein Precipitation Reagent", and vortex for 10 s. 26.Centrifuge for 10 min at 4 °C at ≥ 10,000 g to discard the debris.Transfer the supernatant into a new microtube.27.Add 500 µL of isopropanol.Invert the microtube 30-40 times.28.Centrifuge for 10 min at 4 °C at ≥ 10,000 g to pellet the nucleic acids.29.Remove isopropanol without touching the nucleic acid pellet.30.Rinse with 70% ethanol and centrifuge.Remove all of the residual ethanol.Repeat this step.31.Resuspend the total nucleic acids in 15 μL of TE Buffer.Store at -80°C until the reverse transcriptase step.
3. Euthanize mice by cervical dislocation and immediately dissect the calvaria.Depending on the region of interest (ROI) in the calvaria, it may be interesting to cut the calvaria in the middle or near the ROI (with a scalpel blade) to present this region on an edge of the mold and to cut directly in the ROI after only a few sections.4. Embed bones in SCEM embedding medium and immediately dive the molds in liquid nitrogen.5.When all the dissections are done, transfer the molds at -80 °C for storage.STEP 2: Cryosectioning 6. Adjust the cryostat temperature to -27 °C ± 1 °C and install a blade specifically designed for hard tissue.Clean all the instruments with RNase AWAY™.7. When the temperature is reached in the cryostat chamber, place the molds containing the bone samples in the chamber and let them equilibrate in temperature for 15 min.Position one sample on the tissue holder with SCEM.8. Cut a few pieces of Kawamoto LMD film with scissors.The adhering part is in the center, framed by two non-adhering regions. | 1,582 | 2024-06-24T00:00:00.000 | [
"Medicine",
"Biology"
] |
FL* Interpretation of a Dichotomy in the Spin Susceptibility of the Cuprates
: We propose that some dichotomic Fermi liquid versus non-Fermi liquid behaviours of physical quantities in hole-doped cuprates can be explained in terms of the FL* fractionalized Fermi liquid concept, introduced some years ago, even beyond the region of underdoping. The particle excitations of this FL* system are the holon carrying charge, the spinon carrying spin 1/2, gauge fluctuations coupling them and the hole as a spinon–holon bound state or resonance due to gauge binding. In our proposal, physical responses have a Fermi-liquid-type behaviour if they are dominated by the hole resonance, whereas a non-Fermi liquid behaviour appears if they are dominated by spinon–spinon (and possibly also holon–holon) gauge interactions. The specific case of spin susceptibility in the so-called "strange metal phase" is discussed. The uniform susceptibility turns out to be hole-dominated, the spin-lattice relaxation rate in the Cu sites is spinon-dominated.
Introduction
A peculiar feature of hole-doped cuprates is that in the same range of (in-plane) doping and temperature some quantities have a Fermi liquid (FL)-type behaviour and others exhibit a clearly non-Fermi liquid (NFL) behaviour.
Let us mention some examples in two regions of the phase diagram. In the "pseudogap phase" (see, e.g., [1]), i.e., roughly in the underdoped low-temperature region, ARPES experiments prove the existence of gapless Fermi arcs (see, e.g., [2] and references therein) and the Fermi liquid paradigm would suggest a metallic resistivity with a temperature dependence T α , with α = 2 for standard FL, and more generally greater than 1. Instead, the in-plane resistivity exhibits a metal-insulator crossover (see, e.g., [3]) and, if suitably normalized, a universal behaviour [4] which appears hardly compatible with an explanation of the crossover in terms of disorder localization.
In the so-called "strange metal phase" [1], i.e., roughly for moderate dopings and temperatures, the uniform spin susceptibility at large T almost approaches a constant behaviour [5], as expected for a Fermi liquid. In the same range of parameters, the spin-lattice relaxation time of the Cu sites, 63 T 1 , involving the spin susceptibility at the antiferromagnetic wave vector, is such that 63 T 1 T never approaches the Fermi liquid constant behaviour, growing up instead linearly in T [6].
We propose that such dichotomic FL versus NFL behaviours of physical quantities in hole-doped cuprates can be explained in terms of the FL* fractionalized Fermi liquid concept, introduced in [7,8] and briefly recalled below, within a description of the lowenergy physics of the cuprates in terms of the t-t -J model for the Cu sites. Of course, it is known that this model is insufficient to explain some phenomena appearing in the cuprates, such as charge density waves and fluctuations (see, e.g., [9]), and a more complete description is needed including doubly occupied sites, oxigen, phonons and disorder. However, apparently these phenomena are qualitatively irrelevant for the issue of the present paper, where we briefly discuss the above-mentioned dichotomy for the spin susceptibility.
An FL* is an exotic fractionalized Fermi liquid which has conventional excitations, either electron-like or hole-like as in the hole-doped cuprates, near a Fermi surface satisfying a generalization of Luttinger theorem, together with fractionalized excitations emerging from a topological order, in particular holons (h) charged spinless and spinons (s) neutral of spin½, interacting via gauge fields (a). The electron or hole is a bound state or resonance arising from holon-spinon binding generated by the gauge attraction. There have been several proposals of an FL* nature of the "pseudogap phase" [10,11] (and references therein), but to our knowledge not of the "strange metal phase" as claimed here.
The proposed FL* interpretation of the above-cited FL versus NFL dichotomies is as follows: if some physical response is dominated by the hole excitations (spinon-holon interaction), then its behaviour is close to that of a Fermi liquid; if instead it is dominated by a spinon-spinon (and possibly also holon-holon) interaction, then it has a clear non-Fermi liquid character.
In this paper, we show that indeed an interpretation of the above quoted dichotomy for the spin susceptibility can be achieved according to this line of thought.
Emergence of FL* Structure in the t-t -J Model
In the description of the low-energy physics of the cuprates in terms of a twodimensional (2D) t-t -J model, the sites correspond to the Cu sites of a CuO plane in the cuprates and the Zhang-Rice singlets to the empty sites. The Hamiltonian is given by where n.n.n. denotes next-nearest-neighbor sites and α the spin index which is assumed to be summed up in the following if repeated. P G denotes the Gutzwiller projection implementing the no-double occupation and describing the Mott physics of the system. It can be tackled with a spin-charge decomposition of the hole field c α = hs * α where the holon h is a spinless fermion, so that by the Pauli principle the no-double occupation is implemented, and the spinon s is a boson, satisfying in each site the constraint s * α s α = 1. However, for the t-J model in 1D, the above statistics of holon and spinon are not able to reproduce the critical exponents obtained in the exact solution by means of Bethe ansatz or conformal field theory techniques [12,13]. To reproduce such exponents, both the holon and the spinon should be semions (see e.g., [14]), i.e., an equal time exchange of their fields introduces a factor ±i, the sign depending on their order on the time 0 real line, instead of the +1 factor for boson and −1 factor for fermion fields. In 1D, this change of statistics can be obtained by a generalized Jordan-Wigner transformation dressing the fermionic holon by a "charge string" with coefficient ½ (with respect to standard Jordan-Wigner) and the bosonic spinon by a "spin ½ string" [15,16].
To obtain the same change of statistics in the 2D model, one adds a charge ½ flux, Φ h , to the spinless fermion h and an SU(2) spin ½ flux, Φ s , to the spin ½ boson s. The gradient of such fluxes is the potential of a vortex (similar to Laughlin vortices in the fractional quantum Hall effect) modifying the statistics of the holon and spinon, converting them into semions as in 1D, still keeping the hole c fermionic [17,18]. These fluxes do not modify the dynamics, and the statistics changes of U(1) and SU(2) compensate each other, thus providing an exact rewriting of the model. This is rigorously proved in the t-J model in the previous references using the euclidean path integral approach, where the introduction of the charge and spin fluxes is implemented by minimally coupling the fermions of the t-J model to Chern-Simons gauge fields. The proof is based on the representation of partition and correlation functions in terms of quantum mechanical paths of the fermions, where the Chern-Simons gauge fields appear in phase factors associated to the fermion worldlines. Since the Chern-Simons gauge theory is topological, the only effect of the U(1) and SU(2) gauge fields is the introduction of phase factors, i for U(1) and −i for SU(2), for each undercrossing and the opposite factors for each overcrossing of the fermion worldlines. Therefore, the two contributions cancel in every crossing among each other, thus providing an exact rewriting of the model. The crucial ingredients for such rewriting are the existence of a global U(1) charge and SU(2) spin symmetries of the model, allowing the gauging by Chern-Simons gauge fields and, for lattice models, the no-double occupation constraint, forbidding finite intersections in the worldlines of fermions, so that the crossings are well defined. Therefore, this procedure can be applied to any model with the above features and in particular the extension to the t-t -J model considered here is straightforward. As a bonus, the additional SU(2) degree of freedom for s turns out to be more efficient in optimizing both t and J terms in the mean field, with respect to the standard abelian slave-boson treatment, as in 1D.
The spin-charge decomposition of the hole in terms of spinon and holon brings up an emergent local U(1) slave-particle gauge symmetry, whose parameter we denote by Λ:h j → h j e iΛ j , s jα → s jα e iΛ j . In the large-scale continuum limit, this local gauge-invariance can be made manifest with the introduction of a gauge field a µ transforming as a µ (x) → a µ (x) + ∂ µ Λ(x). Such slave-particle gauge fields generate an attraction between the spinon and holon giving rise to a hole resonance at low energy. Analogously, an attraction between a spinon and antispinon gives rise to a magnon resonance. Furthermore, this gauge interaction introduces a new scale into the theory: the Reizer momentum [19]. In fact, the dynamic of the transverse mode of the gauge field is dominated by the contribution of the gapless holons, and their Fermi surface (FS) produces an anomalous skin effect, with the momentum scale being given by the Reizer momentum Q ≈ (Tk 2 h ) 1/3 , where k h is the (average, in our approximation) holon Fermi momentum. As a consequence of the T-dependence of the Reizer momentum, the hole and the magnon resonances have a strongly T-dependent life time, leading to a behaviour of these excitations that is less coherent than in a standard Fermi liquid. In particular, in the "strange metal phase" it behaves as T −4/3 . To take into account the effect of gauge fluctuations beyond perturbation theory as a very rough approximation, we apply a kind of eikonal resummation. This resummation is obtained by treating first a µ as an external field, expanding the correlation function in terms of quantum mechanical paths of spinons and, for the hole, also of holons, then integrating out the leading transverse component of a µ to obtain an interaction between paths, controlled by the Reizer momentum. The interaction is then treated in the eikonal approximation. Finally, a Fourier transform is performed to obtain the retarded correlation function, treating the short scales via a multiplicative scale-renormalization, assuming as UV cutoff the Reizer momentum, see [18] and references therein.
Let us turn to the effects generated by spin and charge fluxes. Neglecting the spinon fluctuations in the spin flux one obtains x, y, z denoting the Pauli matrices. Physically then Φ s attaches U(1) antiferromagnetic (AF) spin vortices at the holon positions with opposite (−1) |i| chirality in the two Néel sublattices. These vortices are in the U(1) subgroup of the spin group SU(2) complementary to the two-sphere of spin directions, therefore they do not modify the AF background, but still, as discussed below, they have a physical dual role.
In the large scale continuum limit, the interaction of the AF vortices with the spinons is described by the term with J ≈ J(1 − 2δ) representing the coupling of the large-scale spinon action, where δ corresponds to in-plane doping in the cuprates. Then, on one hand, a quenched average, denoted < · >, of (∇Φ s ) 2 in (2) yields a mass term m 2 s ≡< (∇Φ s ) 2 > providing a gap J m s ≈ J (δ| ln δ|) 1/2 to the originally gapless spinon of the O(3) sigma model describing the low energy of the undoped system, thus generating a phase transition from a long-range AF order to a short-range one.
On the other hand, averaging s * s in (2) produces a term J < s * s > ∑ i, where ∆ is the 2D lattice laplacian. This term describes at large scales a 2D Coulomb attraction between holons in different Néel sublattices due to a Kosterlitz-Thouless interaction between the AF spin-vortices [20]. As a consequence at the BKT temperature T ph ≈ J < s * s >, there is the formation of a finite density of incoherent holon pairs, the corresponding order parameter ∆ h being obtained by solving a BCS-like gap equation. Its doping dependence turns out to be of the form where J e f f = J(1 − 2δ)( 1 + m 2 s − m s ) and c ≈ 1.25 in units of J. The spin degrees of freedom are still unpaired above a lower crossover spin-pairing temperature (with a dome structure in the phase diagram, above the superconducting dome [21]).
In our approximation, we keep the modulus of ∆ h (up to its d-structure) constant near the Fermi surface, but its phase is strongly fluctuating, since the charge pairs are not condensed. The field describing the phase fluctuations of the pairs has a gap, denoted by m φ (T), decreasing with T, that modifies the standard BCS form of self-energy near the hole Fermi surface [22] to where ∆ h ( k) is the d-wave holon pair order parameter, ω h ( k) the holon dispersion and Γ the scattering rate of the hole without charge pairing. This d-wave charge-pairing produces a reduction of the hole spectral weight away from diagonals in the Brillouin zone giving rise to what one may call a high pseudogap phenomenon. Qualitatively, it has some analogy to the one advocated by Uemura [23], and in fact the pairing temperature has a somewhat similar doping dependence. The charge-flux companion of the spin flux is given by and it has also a double role. On one hand, the uniform term corresponding to 1 in (5) produces a π flux per plaquette at low δ, T in a region that we identify as low pseudogap (PG); such π lattice is screened by spinon fluctuations above a crossover temperature, denoted T * , and the region above can be identified as the "strange metal phase" (SM).
The π flux produces small hole Fermi surfaces near (±π/2, ±π/2) with linear dispersion and a reduced spectral weight in the outer boundary, giving rise for the holes to a phenomenology of Fermi arcs for strong underdoping. The destruction of the π lattice in SM allows the recovery of a large " tight-binding" hole FS, but still with a suppression of the spectral weight away from the diagonal below T ph (where in this approach holons have two small nodal Fermi surfaces and a small antinodal one due to folding), induced by the charge pairing [22].
On the other hand, the non-uniform term in (5) (which is analogous to the Jordan-Wigner "charge string" in 1D) acts by modifying the exchange statistics of holons, turning them into semions, and also changing their occupation statistics, giving to them Haldane 1/2 statistics [24,25] (as in 1D), so that the area of the FS of semionic spinless holons is equal to the area of the FS of spin ½ fermions [26].
From the above description, one can see that we have all the ingredients for an FL*: holons, spinons and holes. In this approach in PG we have a Z2 topological order, as suggested in somewhat different frameworks by several authors [10,11] and a generalized Luttinger theorem proves that the area of the four hole FS pockets is given by δ/2. Additionally, in SM a generalized Luttinger theorem proves that the area of the FS of the holes is given by (1 + δ)/2. This has been shown [27] using topological arguments of the kind considered in [8], starting from an insulator at half-filling in PG and from the fully occupied band in SM. Hence, both in PG and in SM we have an FL* in our approach to the t-t -J model.
FL* Solution of FL vs. NFL Dichotomy in the Spin Susceptibility in SM
The relation between spinons s, holons h and the electron spin S a (j) = c * j σ a c j at the site j is given by S a (j) = (1 − h * j h j )(−1) |j| s * j σ a s j , and the low-energy continuum limit of s * j σ a s j is described by a magnon field Ω, behaving as a spinon-antispinon resonance. From the above formula, it follows that the spinon's contribution to the spin susceptibility is peaked at the AF wavevector Q AF . In SM at Q AF , the hole/electron contribution is subleading because there is no nesting of the FS. Therefore, through the magnon resonance, the spinon's contribution to the spin susceptibility at Q AF is dominating.
The spin-lattice relaxation time 63 T 1 of Cu sites is known to be controlled by the spin susceptibility at Q AF (see, e.g., [28]). The spinon dependence can explain its NFL-like behaviour, with 63 T 1 T growing linearly with T at high temperatures, instead of approaching a constant behaviour expected for a standard Fermi liquid.
More concretely, the calculation is performed using the formula where χ s ( q, ω) is the spin susceptibility and F( q) is the hyperfine field which for the Cu sites is peaked around Q AF = (π, π), thus probing the AF spin fluctuations. We can use this fact and the representation of the spin in terms of spinons to approximate the above formula. We treat in mean field the term h * h in S a and use the relevant Kubo formula obtaining The right hand side of Equation (7) is then treated with the techniques and approximations sketched in the previous section and discussed in [18], with the q-integration cutoff by the Reizer momentum and considering k h arising from the t-t -J model. In our approach, the physics of 63 T 1 is dominated by the dissipation proportional to T 4/3 of the gauge fluctuations binding the spinon and antispinon in a magnon resonance together with the scale set by the Reizer momentum, producing for 63 T 1 T a large-T behaviour linear in is the diamagnetic susceptibility of the holons with "large Fermi surface". δ 1 is an effective hole doping corresponding to the holon FS which is slightly smaller than the hole Fermi surface; numerically, for values of t, t , J adopted for LSCO, one finds δ 1 ≈ δ − 0.04 (modification essentially irrelevant not considered in [18]).
It turns out that the above coefficient of the T behaviour for intermediate dopings is almost doping-independent, as observed also in the slope of the experimental data of 63 T 1 T in LSCO [6]. As a side remark, we notice that with the same formalism a linear T contribution to the in-plane resistivity is reproduced in SM, but with the slope decreasing with doping, as in the experiments [18]. In the above calculation of 63 T 1 T, the upward shift with doping of the experimental curves is not reproduced, but one can conjecture that it might arise from a contribution of weak antiferromagnetism of the hole resonance. Notice that, as in the experimental data, there is no effect of the high pseudogap, which in our theoretical framework is naturally explained by the fact that spinons are not affected by the charge pairing responsible for the high pseudogap.
In the uniform spin susceptibility in SM, the effect of the spinons is instead negligible, precisely because the spectral weight due to spinons is peaked at Q AF . Therefore the uniform susceptibility is dominated by the hole resonance and, taking into account the effect of the high pseudogap causing its suppression for low T, it is more FL-like.
The calculation is performed using the standard procedure for FL, but taking into account the anomalous gauge-induced dissipation and the charge pairing. In fact, contrary to 63 T 1 , the uniform susceptibility feels the effect of the high pseudogap, because the charge pairing of holons is also reflected in the holes, as shown in the contribution to the hole self-energy given in (4).
More in detail, in the calculation the doping dependence of the order parameter at T = 0 is given by solving numerically the BCS gap equation mentioned in the previous section (as in [20]). The extension of the order parameter to finite temperature is achieved using a standard d-wave BCS approximate formula [29]: The scale of the holon pairing temperature T ph (δ) is fixed by identifying it in two doping values with the experimental high-pseudogap temperature in LSCO. This gives a reasonable result because the doping dependence of T ph derived from the BCS gap equation is approximately the one found experimentally in [5] for the high pseudogap. For the mass of the phase of the charge pairs, m φ (T), we use an approximate ansatz of the kind suggested in [30], setting the pair condensation temperature to 0 (since holon pairs by themselves never condense in our approach): The result for the temperature dependence of the uniform spin susceptibility with the above approximate calculation is qualitatively consistent with experimental data for LSCO at intermediate dopings. Decreasing the temperature, it exhibits for moderate δ a slow increase up to the pairing temperature T ph , instead of a constant behaviour of a standard Fermi liquid, due to the enhanced scattering rate of the electron generated by the gauge fluctuations. Then, it falls rapidly due to the high-pseudogap phenomenon generated by charge pairing. If above T ph one assumes a renormalization of the scattering rate of the hole with respect to that of the magnon proportional to the square of the ratio between the holon and spinon velocity (∼1/(1 − 2δ)), the calculated behaviour also agrees qualitatively in doping dependence with the experimental data (see Figure 1), in spite of the big approximations made. Let us remark that within such approximations, the doping and temperature dependences are completely determined by the theory only up to the scales involved, which have been optimized for one doping and then never changed.
Discussion
In this paper, we have presented evidence that one can extend the proposal of an FL* nature of hole-doped cuprates from the pseudogap, where it was advocated by several authors, to the strange metal phase, SM, and we prove that such a proposal is able to explain, at least qualitatively, some FL versus NFL dichotomies appearing in the experimental data.
As an example, we analyzed the case of spin susceptibility. We find a qualitative agreement with data for the doping and temperature behaviour of the the uniform susceptibility, dominated by the hole resonance and exhibiting at high temperatures an essentially FL-type behaviour, modified at low temperatures by high-pseudogap effects which we attribute to charge pairing. Actually, one can recover an improvement of the comparison at small dopings and temperatures, where it is worse, by considering a crossover to the low pseudogap "phase" PG [27]. A qualitative agreement with experimental data is also exhibited by the spin-lattice relaxation rate for the Cu sites, involving the spin susceptibility at the AF wave vector, which in our approach is dominated by the spinon response and shows a clear NFL behaviour. Following the strategy advocated here for the spin susceptibility, the FL* approach presented allows one to solve FL vs NFL dichotomies appearing for several physical quantities and in different regions of the phase diagram of the cuprates, such as the dichotomy between in-plane resistivity and ARPES in PG quoted in the introduction. Computations in this direction are in progress, with positive preliminary results [27]. | 5,437.6 | 2023-03-23T00:00:00.000 | [
"Physics"
] |
Morphisms and order ideals of toric posets
Toric posets are cyclic analogues of finite posets. They can be viewed combinatorially as equivalence classes of acyclic orientations generated by converting sources into sinks, or geometrically as chambers of toric graphic hyperplane arrangements. In this paper we study toric intervals, morphisms, and order ideals, and we provide a connection to cyclic reducibility and conjugacy in Coxeter groups.
Introduction
A finite poset can be described by at least one directed acyclic graph where the elements are vertices and directed edges encode relations. We say "at least one" because edges implied by transitivity may be present or absent. The operation of converting a source vertex into a sink generates an equivalence relation on finite posets over a fixed graph. Equivalence classes are called toric posets. These objects have arisen in a variety of contexts in the literature, including but not limited to chip-firing games [Eri94], Coxeter groups [EE09,Shi01,Spe09], graph polynomials [Che10], lattices [ES09,Pro93], and quiver representations [MRZ03]. These equivalence classes were first formalized as toric posets in [DMR15], where the effort was made to develop a theory of these objects in conjunction with the existing theory of ordinary posets. The name "toric poset" is motivated by a bijection between toric posets over a fixed (undirected) graph and chambers of the toric graphic hyperplane arrangement of that graph. This is an analogue to the well-known bijection between ordinary posets over a fixed graph G and chambers of the graphic hyperplane arrangement of G, first observed by Greene [Gre77] and later extended to signed graphs by Zaslavsky [Zas91].
Combinatorially, a poset over a graph G is determined by an acyclic orientation ω of G. We denote the resulting poset by P (G, ω). A toric poset over G is determined by an acyclic orientation, up to the equivalence generated by converting sources into sinks. We denote this by P (G, [ω]). Though most standard features of posets have elegant geometric interpretations, this viewpoint is usually unnecessary. In contrast, for most features of toric posets, i.e., the toric analogues of standard posets features, the geometric viewpoint is needed to see the natural proper definitions and to prove structure theorems. Once this is done, the definitions and characterizations frequently have simple combinatorial (non-geometric) interpretations.
To motivate our affinity for the geometric approach, consider one of the fundamental hallmarks of an ordinary poset P : its binary relation, < P . Most of the classic features of posets (chains, transitivity, morphisms, order ideals, etc.) are defined in terms of this relation. Toric posets have no such binary relation, and so this is why we need to go to the geometric setting to define the basic features. Perhaps surprisingly, much of the theory of posets carries over to the toric setting despite the absence of a relation, and current toric poset research strives to understand just how much and what does carry over. As an analogy from a different area of mathematics, topology can be thought of as "analysis without the metric." A fundamental hallmark of a metric space is its distance function. Many of the classic features of metric spaces, such as open, closed, and compact sets, and continuous functions, are defined using the distance function. However, once one establishes an equivalent characterization of continuity in terms of the inverse image of open sets, many results can be proven in two distinct ways: via epsilon-delta proofs, or topologically. When one moves from metric spaces to topological spaces, one loses the distance function and all of the tools associated with it, so this first approach goes out the window. Remarkably, much of the theory of real analysis carries over from metric spaces to topological spaces. Back to the poset world, one can prove theorems of ordinary posets using either the binary relation or the geometric definitions. However, upon passing to toric posets, the binary relation and all of the tools associated with it are lost, so one is forced to go to the geometric setting. Remarkably, much of the theory of ordinary posets still carries over to toric posets. This analogy is not perfect, because toric posets are not a generalization of ordinary posets like how topological spaces extend metric spaces. However, it should motivate the reliance on geometric methods throughout this paper.
An emerging theme of toric poset structure theorems, from both the original paper [DMR15] and this one, is that characterizations of toric analogues, when they exist, usually have one of two forms. In one, the feature of a toric poset P (G, [ω]) is characterized by it being the analogous feature of the ordinary poset P (G, ω ′ ), for all ω ′ ∈ [ω]. In the other, the feature of P (G, [ω]) is characterized by it being the analogous feature of P (G, ω ′ ) for some ω ′ ∈ [ω]. Several examples of this are given below. It is not obvious why this should happen or which type of characterization a given toric analogue should have a priori. Most of these are results from this paper, and so this list provides a good overview for what is to come. The "For All " structure theorems: A set C ⊆ V is a toric chain of P (G, [ω]) iff C is a chain of P (G, ω ′ ) for all ω ′ ∈ [ω]. The "For Some" structure theorems: A partition π ∈ Π V is a closed toric face partition of P (G, [ω]) iff π is a closed face partition of P (G, ω ′ ) for some ω ′ ∈ [ω]. (Theorem 4.7) A set A ⊆ V is a (geometric) toric antichain of P (G, [ω]) iff A is an antichain of P (G, ω ′ ) for some ω ′ ∈ [ω]. (Proposition 5.17) If a set I ⊆ V is a toric interval of P (G, [ω]), then I is an interval of P (G, ω ′ ) for some ω ′ ∈ [ω]. (Proposition 5.14) A set J ⊆ V is a toric order ideal of P (G, [ω]) iff J is an order ideal of P (G, ω ′ ) for some ω ′ ∈ [ω]. (Proposition 7.3) Collapsing P (G, [ω]) by a partition π ∈ Π V is a morphism of toric posets iff collapsing P (G, ω ′ ) by π is a poset morphism for some ω ′ ∈ [ω]. (Corollary 6.2) If an edge {i, j} is in the Hasse diagram of P (G, ω ′ ) for some ω ′ ∈ [ω], then it is in the toric Hasse diagram of P (G, [ω]). (Proposition 5.15) This paper is organized as follows. In the next section, we formally define posets and preposets and review how to view them geometrically in terms of faces of chambers of graphic hyperplane arrangements. In Section 3, we translate well-known properties of poset morphisms to this geometric setting. In Section 4, we define toric posets and preposets geometrically in terms of faces of chambers of toric hyperplane arrangements, and we study the corresponding "toric face partitions" and the bijection between toric preposets and lower-dimensional faces. In Section 5, we define the notion of a toric interval and review some features of toric posets needed for toric order-preserving maps, or morphisms, which are finally presented in Section 6. In Section 7, we introduce toric order ideals and filters, which are essentially the preimage of one element upon mapping into a two-element toric poset. The toric order ideals and filters of a toric poset turn out to coincide. They form a graded poset J tor (P ), but unlike the ordinary case, this need not be a lattice. In Section 8, we provide a connection of this theory to Coxeter groups, and then we conclude with a summary and discussion of current and future research in Section 9.
2. Posets geometrically 2.1. Posets and preposets. A binary relation R on a set V is a subset R ⊆ V × V . A preorder or preposet is a binary relation that is reflexive and transitive. This means that (x, x) ∈ R for all x ∈ V , and if (x, y), (y, z) ∈ R, then (x, z) ∈ R. We will use the notation x R y instead of (x, y), and say that x ≺ R y if x R y and y R x. Much of the basics on preposets can be found in [PRW08].
An equivalence relation is a preposet whose binary relation is symmetric. For any preposet P , we can define an equivalence relation ∼ P on P by saying x ∼ P y if and only if x P y and y P x both hold. A partially ordered set, or poset, is a preposet P such that every ∼ P -class has size 1. We say that a preposet is acyclic if it is also a poset.
Every preorder P over V determines a directed graph ω(P ) over V that contains an edge i → j if and only if i P j and i = j. Not every directed graph arises from such a preorder, since edge transitivity is required. That is, if i → j and j → k are edges, then i → k must also be an edge. However, any directed graph can be completed to a transitive graph via transitive closure, which adds in all "missing" edges. Note that the graph ω(P ) is acyclic if and only if P is a poset. The strongly connected components are the ∼ P -classes, and so the quotient ω(P )/∼ P is acyclic and P/∼ P inherits a natural poset structure from P .
If R 1 and R 2 are preorders on V , then we can define their union R 1 ∪ R 2 as the union of the subsets R 1 and R 2 of V × V . This need not be a preorder, but its transitive closure R 1 ∪ R 2 will be.
Another way we can create a new preorder from an old one is by an operation called contraction. Given a binary relation R ⊆ V × V , let R op denote the opposite binary relation, meaning that (x, y) ∈ R op if and only if (y, x) ∈ R. If P and Q are preposets on V , then Q is a contraction of P if there is a binary relation R ⊆ P such that Q = P ∪ R op . Intuitively, each added edge (x, y) ∈ R op forces x ∼ Q y because (y, x) ∈ P ⊆ Q by construction. Note that in this context, contraction is a different concept than what it often means in graph theory -modding out by a subset of vertices, or "collapsing" a set of vertices into a single vertex.
2.2. Chambers of hyperplane arrangements. It is well known that every finite poset corresponds to a chamber of a graphic hyperplane arrangement [Wac07]. This correspondence will be reviewed here. Let P be a poset over a finite set V = [n] := {1, . . . , n}. This poset can be identified with the following open polyhedral cone in R V : It is easy to see how the cone c determines the poset P = P (c): one has i < P j if and only if x i < x j for all x in c. Each such cone c is a connected component of the complement of the graphic hyperplane arrangement for at least one graph G = (V, E). In this case, we say that P is a poset over G (or "on G"; both are used interchangeably). Given distinct vertices i, j of a simple graph G, the hyperplane H ij is the set Under a slight abuse of notation, at times it is convenient to refer to A(G) as the set of points in R V on the hyperplanes, as opposed to the actual finite set of hyperplanes themselves. It should always be clear from the context which is which.
Each point x = (x 1 , . . . , x n ) in the complement R V −A(G) determines an acyclic orientation ω(x) of the edge set E: direct the edge {i, j} in E as i → j if and only if x i < x j . Clearly, the fibers of the mapping α G : x −→ ω(x) are the chambers of the hyperplane arrangement A(G). Thus, α G induces a bijection between the set Acyc(G) of acyclic orientations of G and the set Cham A(G) of chambers of A(G): We denote the poset arising from an acyclic orientation ω ∈ Acyc(G) by P = P (G, ω). An open cone c = c(P ) may be a chamber in several graphic arrangements, because adding or removing edges implied by transitivity does not change the poset. Geometrically, the hyperplanes corresponding to these edges do not cut c, though they intersect its boundary. Thus, there are, in general, many pairs (G, ω) of a graph G and acyclic orientation ω that lead to the same poset P = P (G, ω) = P (c). Fortunately, this ambiguity is not too bad, in that with respect to inclusion of edge sets, there is a unique minimal graphĜ Hasse (P ) called the Hasse diagram of P and a unique maximal graphḠ(P ), where (G, ω) −→ (Ḡ(P ),ω) is transitive closure.
Given two posets P, P ′ on a set V , one says that P ′ is an extension of P when i < P j implies i < P ′ j. Geometrically, P ′ is an extension of P if and only if c(P ′ ) ⊆ c(P ). Moreover, P ′ is a linear extension if c(P ′ ) is a chamber of A(K V ), where K V is the complete graph.
2.3. Face structure of chambers. Let π = {B 1 , . . . , B r } be a partition of V into nonempty blocks. The set Π V of all such partitions has a natural poset structure: π ≤ V π ′ if every block in π is contained in some block in π ′ . When this happens, we say that π is finer than π ′ , or that π ′ is coarser than π.
Intersections of hyperplanes in A(G) are called flats, and the set of flats is a lattice, denoted L(A(G)). Flats are partially ordered by reverse inclusion: If X 1 ⊆ X 2 , then X 2 ≤ L X 1 . Every flat of A(G) has the form D π := {x ∈ R V : x i = x j for every pair i, j in the same block B k of π} , for at least one partition π of V . Note that D π ≤ L D π ′ if and only if π ≤ V π ′ ; this should motivate the convention of partially ordering L(A(G)) by reverse inclusion.
Given a poset P = P (G, ω) over G = (V, E), a partition π of V defines a preposet P π := (π, ≤ P ) on the blocks, where B i ≤ P B j for x ≤ P y for some x ∈ B i and y ∈ B j (and taking the transitive closure). This defines a directed graph ω/∼ π , formed by collapsing out each block B i into a single vertex. Depending on the context, we may use P π or ω/∼ π interchangeably. If this preposet is acyclic (i.e., if P π is a poset, or equivalently, the directed graph ω/∼ π is acyclic), then we say that π is compatible with P . In this case, there is a canonical surjective poset morphism P → P π . We call such a morphism a quotient, as to distinguish it from inclusions and extensions which are inherently different.
Compatibility of partitions with respect to a poset can be characterized by a closure operator on Π V . If P π = (π, ≤ P ) is a preposet that is not acyclic, then there is a unique minimal coarsening cl P (π) of π such that the contraction (cl P (π), ≤ P ) is acyclic. This is the partition achieved by merging all pairs of blocks B i and B j such that B i ∼ P B j , and we call it the closure of π with respect to P . If P is understood, then we may write this as simplyπ := cl P (π). A partition π is closed (with respect to P ) ifπ = π, which is equivalent to being compatible with respect to P . Geometrically, it means that for any i = j, there is some x ∈ c(P ) ∩ D π such that x bi = x bj for some b i ∈ B i and b j ∈ B j . If π is not closed, then the polyhedral face c(P ) ∩ D π has strictly lower dimension than D π . In this case,π is the unique coarsening that is closed with respect to P and satisfies c(P ) ∩ Dπ = c(P ) ∩ D π .
Still assuming that P is a poset over G = (V, E), and π is a partition of V , define (3)F π (P ) := c(P ) ∩ D π .
If D π is a flat of A(Ḡ(P )), thenF π (P ) is a face of the (topologically) closed polyhedral cone c(P ).
In this case, we say that π is a face partition of P . Since it is almost always clear what P is, we will usually writeF π instead ofF π (P ). If D π is not a flat of A(G), then the subspace D π still intersects c(P ) in at least the line x 1 = · · · = x n . Though this may intersect in the interior of c(P ′ ), it is a face of c(P ′ ) ⊆ c(P ), for at least one extension P ′ of P .
To characterize the facial structure of the cone c(P ), it suffices to characterize the closed face partitions. This is well known -it was first described by Geissinger [Gei81], and also done by Stanley [Sta86] in the characterization of the face structure of the order polytope of a poset, defined by Clearly, if π is a closed face partition of P , then the subposets induced by the individual blocks are connected (that is, their Hasse diagrams are connected). We call such a partition connected, with respect to P . To summarize Theorem 2.1, characterizing the faces of O(P ) amounts to characterizing which face partitions π are closed. If π is not compatible with P , then it is not closed. On the other hand, if π not connected, then it is either not closed, or the flat D π cuts through the interior of O(P ) (and hence of c(P )), in which case π is not a face partition.
Example 2.2. Let P be the poset shown at left in Figure 1; its lattice of closed face partitions is shown at right. In this and in later examples, we denote the blocks of a partition using dividers rather than set braces, e.g., π = B 1 /B 2 / · · · /B r .
The partition σ = 1/23/4 is closed but not connected; it is not a face partition because D σ = H 23 intersects the interior of c(P ). The partition π = 124/3 is connected but not closed. Finally, the partition π ′ = 14/23 is neither connected nor closed. However, both π and π ′ are face partitions because the subspaces D π and D π ′ intersect c(P ) in the line x 1 = x 2 = x 3 = x 4 , which is the flat D V . Therefore, both of these partitions have the same closure: cl P (π) = cl P (π ′ ) = 1234. Ifπ = π = {B 1 , . . . , B r } is a closed face partition of P , then D π is an r-dimensional flat of A(G), and the closed faceF π is an r-dimensional subset of D π ⊆ R V . The interior ofF π with respect to the subspace topology of D π will be called an open face. So as to avoid confusion between open and closed faces, and open and closed chambers, we will speak of faces as being features of the actual poset, not of the chambers. It should be easy to relate these definitions back to the chambers if one so desires.
Definition 2.3. A set F ⊆ R V is a closed face of the poset P if F =F π = c(P ) ∩ D π for some closed face partition π = cl P (π) of V . The interior ofF π with respect to the subspace topology of D π is called an open face of P , and denoted F π . Let Face(P ) and Face(P ) denote the set of open and closed faces of P , respectively. Finally, define the faces of the graphic arrangement A(G) to be the faces of the posets over G: Face(P (G, ω)) .
Faces of co-dimension 1 are called facets.
Remark 2.4. The dimension of the face F π (P (G, ω)) is the number of strongly connected components of ω/∼ π . As long as G is connected, there is a unique 1-dimensional face of A(G), which is the line x 1 = · · · = x n and is contained in the closure of every chamber. There are no 0dimensional faces of A(G). The n-dimensional faces of A(G) are its chambers. Additionally, R V is a disjoint union of open faces of A(G): If P is a fixed poset over G, then there is a canonical isomorphism between the lattice of closed face partitions and the lattice of faces of P , given by the mapping π → F π . Recall that since π is closed, P π = (π, ≤ P ) is an acyclic preposet (i.e., poset) of size |π| = r. This induces an additional preposet over V (i.e., of size |V | = n), which is ≤ P with the additional relations that x ∼ π y for all x, y ∈ B i . We will say that this is a preposet over G, because it can be described by an (not necessarily acyclic) orientation ω π of G. The notation reflects the fact that this orientation can be constructed by starting with some ω ∈ Acyc(G) and then making each edge bidirected if both endpoints are contained in the same block of π. Specifically, ω π orients edge {i, j} as i → j if i ≤ P j and as i ↔ j if additionally i ∼ π j. Let Pre(G) be the set of all such orientations of G that arise in this manner. That is, When working with preposets over G, sometimes it is more convenient to quotient out by the strongly connected components and get an acyclic graph ω π /∼ π . Note that this quotient is the same as ω ′ /∼ π for at least one ω ′ ∈ Acyc(G). In particular, ω ′ = ω will always do. In summary, a preposet over G can be expressed several ways: (i) as a unique orientation ω π of G, where π is the partition into the strongly connected components; (ii) as a unique acyclic quotient ω/∼ π of an acyclic orientation ω ∈ Acyc(G). Note that while the orientation ω π and acyclic quotient ω/∼ π are both unique to the preposet, the choice of representative ω is not. Regardless of how an element in Pre(G) is written, it induces a canonical partial order (π, ≤) on the blocks of π. However, information is lost by writing it this way; in particular, the original graph G cannot necessarily be determined from just (π, ≤).
(2) can be extended to all of R V by adding both edges i → j and j → i if x i = x j . This induces a bijection between the set Pre(G) of all preposets on G and the set of faces of the graphic hyperplane arrangement: Consequently, for any preposet ω π over G, we can let c(ω π ) denote the open face of A(G) containing any (equivalently, all) x ∈ R V such that α G (x) = ω π . Moreover, if we restrict to the preposets on exactly r strongly connected components, then the α G -fibers are the r-dimensional open faces of A(G). If x lies on a face F π (P ) = Fπ(P ) for some poset P and closed face partitionπ = cl P (π), then the preposet P π = (π, ≤ P ) has vertex set π = {B 1 , . . . B r }; these are the strongly connected components of the orientation α G (x).
Morphisms of ordinary posets
Poset isomorphisms are easy to describe both combinatorially and geometrically. An isomorphism between two finite posets P and P ′ on vertex sets V and V ′ is a bijection φ : • geometrically by the equivalent condition that the induced isomorphism Φ on R V → R V ′ maps c(P ) to c(P ′ ) bijectively. By "induced isomorphism," we mean that Φ permutes the coordinates of R V in the same way that φ permutes the vertices of V : Morphisms of ordinary posets are also well understood. The "combinatorial" definition is easiest to modify. If P and P ′ are as above, then a morphism, or order-preserving map, is a function The geometric characterization is trickier because quotients, injections, and extensions are inherently different. These three types of order-preserving maps generate all poset morphisms, up to isomorphism. Below we will review this and give a geometric interpretation of each, which will motivate their toric analogues.
3.1.1. Contracting partitions. Roughly speaking, a quotient morphism of a poset P (G, ω) is described combinatorially by contracting ω by the blocks of a partition π = {B 1 , . . . , B r } while preserving acyclicity. Geometrically, the chamber c(P ) is orthogonally projected toFπ := c(P ) ∩ Dπ, whereπ = cl P (π). This is the mapping By construction, the image of this map is Fπ, which is a face of P if π is a face partition. Though the map d π extends to the closure c(P ), it does not do so in a well-defined manner; the image d π (x) for some x on a hyperplane depends on the choice of P , and each hyperplane intersects two (closed) chambers along facets, and intersects the boundary of every chamber.
Example 3.1. Let G = K 3 , the complete graph on 3 vertices. There are six acyclic orientations of G, and three of them are shown in Figure 2. The curved arrows point to the chamber c(P i ) of A(G) for each P i := P (G, ω i ), i = 1, 2, 3. The intersection of each closed chamber c(P i ) with [0, 1] 3 is the order polytope, O(P i ).
To see why the map d π from Eq. (7) does not extend to the closure of the chambers in a welldefined manner, consider the point y shown in Figure 2 that lies on the hyperplane x 1 = x 2 , and the same partition, π = 1/23. The orthogonal projection d π : c(P 3 ) → D π as defined in Eq. (7) and extended continuously to the closed chamber maps c(P 3 ) onto the line x 1 = x 2 = x 3 . However, if c(P 4 ) is the other closed chamber containing y (that is, the one for which x 3 ≤ x 2 ≤ x 1 ), then d π : c(P 4 ) → D π extended to the closure maps c(P 4 ) onto a 2-dimensional closed faceF π (P 4 ) = c(P 4 ) ∩ D π . The point y is projected orthogonally onto the plane D π , and does not end up on the line Despite this, there is a natural way to extend d π to all of R V , though not continuously. To do this, we first have to extend the notion of the closure of a partition π with respect to a poset, to a preposet P over G. This is easy, since the original definition did not specifically require P to actually be a poset. Specifically, the closure of π with respect to a preposet P is the unique minimal coarseningπ := cl P (π) of π such that (π, ≤ P ) is acyclic. The map d π can now be extended to all of R V , as Figure 2. The hyperplane arrangement A(G) for G = K 3 . Three orientations in Acyc(G) are shown, along with the corresponding chambers of A(G), and the preposet that results when contracting where α G is the map from Eq. (5) sending a point to the unique open face (i.e., preposet over G) containing it. Let us return to the case where P is a poset over G, and examine the case when π is not a face partition of P . Indeed, for an arbitrary partition π of V withπ = cl P (π), the subset F π := c(P ) ∩ Dπ need not be a face of P ; it could cut through the interior of the chamber. In this case, it is the face of at least one extension of P . Specifically, let G ′ π be the graph formed by making each block B i a clique, and let G/∼ π be the graph formed by contracting these cliques into vertices, with loops and multiedges removed. Clearly, D π is a flat of the graphic arrangement A(G ′ π ) (this choice is not unique, but it is a canonical one that works). Thus, the setFπ =F π = c(P ) ∩ D π , forπ = cl P (π), is a closed face of A(G ′ π ), and hence a face of some poset P ′ over G ′ π for which π = cl P ′ (π).
Whether or not π is a face partition of a particular poset P over G, the map d π in Eq. (8) projects a chamber c(P ) onto a flat Dπ of A(G ′ π ), whereπ = cl P (π). From here, we need to project it homeomorphically onto a coordinate subspace of R V so it is a chamber of a lower-dimensional arrangement. Specifically, for a partition π = {B 1 , . . . , B r }, let W ⊆ V be any subset formed by removing all but 1 coordinate from each B i , and let r π : R V −→ R W be the induced projection. The r π -image of A(G) is the graphic arrangement of G/∼ π . The following ensures that r π is a homeomorphism, and that the choice of W does not matter. We omit the elementary proof.
Moreover, all such projection maps for a fixed π are topologically conjugate in the following sense: i , then the following diagram commutes: with Σ and Σ ′ being the induced linear maps as defined in Eq. (6).
By convexity, d π induces a well-defined map δ π : Face A(G) −→ Face A(G ′ π ) making the following diagram commute: The map δ π is best understood by looking at a related mapδ π on closed faces. LetF = c(P )∩D σ be a closed face of A(G), for some closed face partition σ ∈ Π V . Then the mapδ π is defined bȳ The map δ π is between the corresponding open faces. These faces are then mapped to faces of the arrangement A(G/∼ π ) under the projection r π | Dπ : D π −→ R W . [Alternatively, we could simply identity the quotient space R V /D ⊥ π with R W .] To summarize, the open faces of A(G) arise from preposets ω = ω σ in Pre(G), where without loss of generality, the blocks for σ ∈ Π V are the strongly connected components. The contraction of this preposet formed by adding all relations (edges) of the form (v, w) for v, w ∈ B i yields a preposet ω ′ π over G ′ π . Then, modding out by the strongly connected components yields an acyclic preposet, i.e., a poset. This two-step process is a composition of maps , the closure of π with respect to the preposet P σ , which we have been denoting by ω σ under a slight abuse of notation.
Putting this all together gives a commutative diagram that illustrates the relationship between the points in R V , the open faces of the graphic arrangement A(G), and the preposets over G. The left column depicts the acyclic preposets -those that are also posets.
3.1.2. Intervals and antichains. Poset morphisms that are quotients are characterized geometrically by projecting the chamber c(P ) onto a flat Dπ of A(G ′ π ) for some partitionπ = cl P (π), and then homeomorphically mapping this down to a chamber of a lower-dimensional graphic arrangement A(G/∼ π ). Equivalently, contracting P (G, ω) byπ yields an acyclic preposet Pπ = (π, ≤ P ). It is well known that contracting a poset by an interval or an antichain yields an acyclic preposet. Verification of this is elementary, but first recall how these are defined.
Definition 3.3. Let P be a poset over V . An interval of P is a subset I ⊆ V , sometimes denoted [i, j], such that I = {x ∈ P : i ≤ P x ≤ P j}, for some fixed i, j ∈ P . An antichain of P is a subset A ⊆ V such that any two elements are incomparable.
We will take a moment to understand how contracting an interval or antichain fits in the partition framework described above, which will help us understand the toric analogue. Given a nonempty subset S ⊆ V , define the partition π S of V by where |B i | = 1 for i = 2, . . . , r.
Contracting an interval I ⊆ V in a poset P yields the poset P πI = (π I , ≤ P ). In this case, π I = cl P (π I ) is a face partition and F π is a (|V | − |I| + 1)-dimensional face of P . Similarly, collapsing an antichain A ⊆ V yields the poset P πA = (π A , ≤ P ). Note that D πI is a flat of A(G) and lies on the boundary of c(P ), but the (|V | − |A| + 1)-dimensional subspace D πA cuts through the interior of c(P ). For both of these cases, S = I and S = A, the subspace D πS is trivially a flat of A(G ′ πS ). 3.2. Extension. Given two posets P, P ′ on a set V , one says that P ′ is an extension of P when i < P j implies i < P ′ j. In this case, the identity map P −→ P ′ is a poset morphism. Geometrically, P ′ is an extension of P if and only if one has an inclusion of their open polyhedral cones c(P ′ ) ⊆ c(P ). Each added relation i < P ′ j amounts to intersecting c(P ) with the half-space 3.3. Inclusion. The last operation that yields a poset morphism is an injection φ : P ֒→ P ′ . This induces a canonical inclusion Φ : R V ֒→ R V ′ . Note that i < P j implies i < P ′ j, but not necessarily vice-versa. Thus, up to isomorphism, an inclusion can be decomposed into the composition P ֒→ P ′′ → P ′ , where the first map adds the elements {n + 1, . . . , m} to P but no extra relations, and then the map P ′′ → P ′ is an extension. This gives an inclusion of polyhedral cones: 3.4. Summary. Up to isomorphism, every morphism of a poset P = P (G, ω) can be decomposed into a sequence of three steps: (i) quotient : Collapsing G by a partition π that preserves acyclicity of ω (projecting c(P ) to a flat D π of A(G ′ π ) for some closed partition π = cl P (π)). (ii) inclusion: Adding vertices (adding dimensions). (iii) extension: Adding relations (intersecting with half-spaces). In the special case of the morphism P −→ P ′ being surjective, the inclusion step is eliminated and the entire process can be described geometrically by projecting c(P ) to a flat D π and then intersecting with a collection of half-spaces.
Toric posets and preposets
4.1. Toric chambers and posets. Toric posets, introduced in [DMR15], arise from ordinary (finite) posets defined by acyclic orientations under the equivalence relation generated by converting maximal elements into minimal elements, or sources into sinks. Whereas an ordinary poset corresponds to a chamber of a graphic arrangement A(G), a toric poset corresponds to a chamber of a toric graphic arrangement A tor (G) = q(A(G)), which is the image of A(G) under the quotient is called a toric chamber for G, or simply a chamber of A tor (G). Let Cham A tor (G) denote the set of all chambers of A tor (G). A toric poset P is a set c that arises as a toric chamber for at least one graph G. We may write P = P (c) or c = c(P ), depending upon the context.
If we fix a graph G = (V, E) and consider the arrangement A tor (G), then each point in R V /Z V naturally determines a preposet on G via a mapᾱ G : x → ω(x). Explicitly, for x = (x 1 mod 1, . . . , x n mod 1) in R V /Z V , the directed graph ω(x) is constructed by doing the following for each edge {i, j} in E: If x i mod 1 ≤ x j mod 1, then include edge i → j; If x j mod 1 ≤ x i mod 1, then include edge j → i. The mappingᾱ G is essentially the same as α G from Eq. (5) except done modulo 1, so many of its properties are predictably analogous. For example, the undirected version of ; in this case ω(x) describes a poset. Otherwise it describes a preposet (that is not a poset). Modding out by the strongly connected components yields an acyclic graph ω(x)/∼ x that describes a poset.
Definition 4.2. When two preposets ω(x) and ω(y) are such that the directed graphs ω(x)/∼ x and ω(y)/∼ y differ only by converting a source vertex (equivalence class) into a sink, or vice-versa, we say they differ by a flip. The transitive closure of the flip operation generates an equivalence relation on Pre(G), denoted by ≡.
In the special case of restricting to preposets that are acyclic, we get Acyc(G) ⊆ Pre(G) and a bijective correspondence between toric posets and chambers of toric graphic arrangements. This is Theorem 1.4 in [DMR15]. A generalization of this to a bijection between toric preposets and faces of the toric graphic arrangement appears later in this section (Proposition 4.11). Theorem 1.4) The mapᾱ G induces a bijection between Cham A tor (G) and Acyc(G)/≡ as follows: When G is understood, we will say that the order polytopes O(P (G, ω)) and O(P (G, ω ′ )) are torically equivalent whenever ω ′ ∈ [ω]. Under the natural quotient q : [0, 1] V → R V /Z V , each order polytope O(P (G, ω)) is mapped into the closed toric chamberc [ω] . Moreover, by Theorem 4.3, the closed chambers of A tor (G) are unions of q-images of torically equivalent order polytopes.
) be a toric poset, and q : The closure of the chamber c(P ) is
4.2.
Toric faces and preposets. Let P = P (c) be a toric poset over G = (V, E). To define objects like a face of P or its dimension, it helps to first lift c up to a chamber of the affine graphic arrangement which lies in R V : The affine chambers are open unbounded convex polyhedral regions in R V , the universal cover of R V /Z V . The path lifting property guarantees that two points x and y in R V /Z V −A tor (G) are in the same toric chamber if and only if they have liftsx andŷ that are in the same affine chamber. Moreover, since Corollary 4.4 characterizes the closed toric chamber c(P ) as a union of torically equivalent order polytopes under a universal covering map, each closed affine chamber is a union of translated copies of torically equivalent order polytopes in R V . We usually denote an affine chamber byĉ or c aff . Each hyperplane H tor ij has a unique preimage containing the origin in R V called its central preimage; this is the ordinary hyperplane Thus, the set of central preimages of A tor (G) is precisely the graphic arrangement A(G) in R V . Each closed affine chamberc aff contains at most one order polytope O(P (G, ω)) for ω ∈ Acyc(G). Affine chambers whose closures contain precisely one order polytope O(P (G, ω)) are central affine chambers.
We will call nonempty sets that arise as intersections of hyperplanes in A aff (G) affine flats and nonempty sets that are intersections of hyperplanes in A tor (G) toric flats. Since the toric flats have a nonempty intersection, they form a lattice that is denoted L(A tor (G)), and partially ordered by reverse inclusion.
Since a toric flat of A tor (G) is the image of a flat of A(G), it too is determined by a partition π of V , and so it is of the form Since R V q −→ R V /Z V is a covering map, it is well-founded to declare the dimension of a toric flat D tor π in R V /Z V to be the same as the dimension of its central preimage D π in R V .
Recall that a partition π = {B 1 , . . . , B r } is compatible with an ordinary poset P if contracting the blocks of π yields a preposet P π = (π, ≤ P ) that is acyclic (also a poset). The notion of compatible partitions does not carry over well to toric posets, because compatibility is not preserved by toric equivalence. Figure 2 shows an example of this: the preposets (π, ≤ P1 ) and (π, ≤ P2 ) are acyclic but (π, ≤ P3 ) is not. Despite this, every set D tor π , whether or not it is a toric flat of A tor (G), intersects the closed toric chamber c(P ) in at least the line x 1 = · · · = x n . We denote this intersection by (15)F tor π (P ) := c(P ) ∩ D tor π . If D tor π does not intersect c(P ), then we say that π is a toric face partition, since it intersects the closed toric chamber along its boundary. Compare this to the definition of face partitions of an ordinary poset P (G, ω), which are those π ∈ Π V characterized by D π being a flat of the graphic arrangement of the transitive closure, or equivalently, by D π ∩ c(P (G, ω)) = ∅. The transitive closureḠ(P (G, ω)) is formed from G by adding all additional edges {i, j} such that H i,j ∩ c(P (G, ω)) = ∅. Similarly, we can define the toric transitive closure of P (G, [ω]) as the graph G along with the extra edges {i, j} such that H tor i,j ∩ c(P ) = ∅. This was done in [DMR15], and we will return to it in the Section 5.3 when we discuss toric Hasse diagrams. Now, let π ∈ Π V be an arbitrary partition. Since flats of A tor (K V ) are closed under intersections, there is a unique maximal toric subspace D tor π (that is, of minimal dimension) for which F tor π = c(P ) ∩ D tor π . The partitionπ is the unique minimal coarsening of π for whichF tor π =F tor π , and it is the lattice-join of all such partitions. We call it the closure of π with respect to the toric poset P , denoted cl tor P (π), and we define dim(F tor π ) := dim(D tor π ). A partition π is closed with respect to the toric poset P if π = cl tor P (π). Note that the closure is defined for all partitions, not just toric face partitions. Toric faces of co-dimension 1 are called facets.
The following remark is the toric analogue of Remark 2.4.
Remark 4.6. Let P = P (G, [ω]) be a toric poset. The dimension ofF tor π (P ) := c(P ) ∩ D tor π is simply the maximum dimension of c aff (P ) ∩ D π taken over all affine chambers that descend down to c(P ). Since closed affine chambers are unions of translations of order polytopes, this is the maximum dimension of c(P (G, ω ′ )) ∩ D π taken over all ω ′ ∈ [ω]. In other words, dim F π (P (G, ω ′ )) .
On the level of graphs, this is the maximum number of strongly connected components that ω ′ /∼ π can have for some ω ′ ∈ [ω]. In particular, a partition π is closed with respect to P (G, [ω]) if and only if ω ′ /∼ π is acyclic for some ω ′ ∈ [ω].
As long as G is connected, there is a unique 1-dimensional face of A tor (G), which is the line x 1 = · · · = x n and is contained in the closure of every chamber. There are no 0-dimensional faces of A tor (G). The n-dimensional faces of A tor (G) are its chambers. Additionally, R V /Z V is a disjoint union of open faces of A tor (G): As in the case of ordinary posets, there is a canonical bijection between the closed toric face partitions of P and open faces (or closed faces) of P , via π → F tor π . To classify the faces of a toric poset, it suffices to classify the closed toric face partitions. The proof of Theorem 4.7 will be done later in this section, after the following lemma, which establishes that cl tor P is a closure operator [War42] on the partition lattice Π V and compares it with cl P .
Conversely, suppose that π is connected and compatible with respect to P (G, ω ′ ) for some ω ′ ∈ [ω]. By Theorem 2.1, π is a closed face partition of P (G, ω ′ ). Since π is connected, D π is a flat of A(G). Therefore, D tor π is a toric flat of A tor (G), and soF tor π := c(P ) ∩ D tor π is a face of the toric poset P (G, [ω ′ ]) = P (G, [ω]) = P . Therefore, π is a toric face partition. Closure of π with respect to P = P (G, [ω]) = P (G, [ω ′ ]) follows immediately from Lemma 4.8(a) applied to the fact that π is closed with respect to P (G, ω ′ ).
Unlike the ordinary case, where faces of posets are literally faces of a convex polyhedral cone, it is not quite so "geometrically obvious" what subsets can be toric faces. The following example illustrates this. The subtlety in Example 4.10 does not arise for ordinary posets, because distinct ordinary posets never have chambers with the same topological closure. In contrast, if G = (V, E) and G ′ = (V, E ′ ) are both forests, then A tor (G) and A tor (G ′ ) both have a single toric chamber. This is because the number of chambers is counted by the Tutte polynomial evaluation T G (1, 0), which is always 1 for a forest; see [DMR15]. In this case, the closures of both chambers will be all of R V /Z V . A more complicated example involving a toric poset over a graph with three vertices, will appear soon in Example 4.13.
Recall the mapᾱ G from Eq. (11) that sends a point x in R V /Z V to a preposet ω(x). By Theorem 4.3, when restricted to the points in R V /Z V −A tor (G), this map induces a bijection between toric posets and toric chambers. Toric faces F tor π that are open in D tor π are chambers in lower-dimensional arrangements that are contractions of A tor (G), namely by the subspace D tor π . Thus, the bijection between toric equivalence classes of Acyc(G) (n-element preposets) and toric chambers (n-dimensional faces) extends naturally to a bijection between toric preposets over G and open faces of A tor (G).
Proposition 4.11. The mapᾱ G induces a bijection between Face A tor (G) and Pre(G)/ ≡ as follows: In other words, given two points x, If x lies on a toric face F tor π of P , where (without loss of generality) π = cl tor P (π), then the strongly connected components of the preposetᾱ G (x) are π = {B 1 , . . . B r }.
Example 4.13. Let G = K 3 , as in Example 3.1. The six acyclic orientations of G fall into two toric equivalence classes. The three orientations shown in Figure 3.1 comprise one class, and so the corresponding toric poset is P = P (G, [ω i ]) for any i = 1, 2, 3. Equivalently, the closed toric chamber is a union of order polytopes under the natural quotient map: This should be visually clear from Figure 3.1. The two chambers in A tor (G) are the threedimensional faces of P . Each of the three toric hyperplanes in A tor (G) = {H tor 12 , H tor 13 , H tor 23 } are two-dimensional faces of P , and these (toric preposets) correspond to the following toric equivalence classes of size-2 preposets ω π /∼ π over K 3 : The toric flat D {V } is the unique one-dimensional face of P , and this corresponds to the unique size-1 preposet over K 3 ; when x 1 = x 2 = x 3 , which is trivially in its own toric equivalence class.
Toric intervals and antichains
Collapsing an interval or antichain of an ordinary poset defines a poset morphism. This remains true in the toric case, as will be shown in Section 6, though the toric analogues of these concepts are trickier to define. Toric antichains were introduced in [DMR15], but toric intervals are new to this paper. First, we need to review some terminology and results about toric total orders, chains, transitivity, and Hasse diagrams. This will also be needed to study toric order ideals and filters in Section 7. Much of the content in Sections 5.1-5.3 can be found in [DMR15]. Throughout, G = (V, E) is a fixed undirected graph with |V | = n, and coordinates x i of points x = (x 1 , . . . , x n ) in a toric chamber c(P ) are assumed to be reduced modulo 1, i.e., x i ∈ [0, 1). 5.1. Toric total orders. A toric poset P ′ is a total toric order if c(P ′ ) is a chamber of A tor (K V ). If P (G, [ω]) is a total toric order, then P (G, ω ′ ) is a total order for each ω ′ ∈ [ω], and thus [ω] has precisely |V | elements. Since each P (G, ω ′ ) has exactly one linear extension, total toric orders are indexed by the (n − 1)! cyclic equivalence classes of permutations of V : [w] = [(w 1 , . . . , w n )] := (w 1 , . . . , w n ), (w 2 , . . . , w n , w 1 ), . . . , (w n , w 1 , . . . , w n−1 ) .
Recall that if P and P ′ are toric posets over G, then P ′ is an extension of P if c(P ′ ) ⊆ c(P ). Moreover, P ′ is a total toric extension if P ′ is a total toric order. Analogous to how a poset is determined by its linear extensions, a toric poset P is determined by its set of total toric extensions, denoted L tor (P ).
5.2.
Toric directed paths, chains, and transitivity. A chain in a poset P (G, ω) is a totally ordered subset C ⊆ V . Equivalently, this means that the elements in C all lie on a common directed path i 1 → i 2 → · · · → i m in ω. Transitivity can be characterized in this language: if i and j lie on a common chain, then i and j are comparable in P (G, ω). Geometrically, i and j being comparable means the hyperplane H i,j does not cut (i.e., is disjoint from) the chamber c(P (G, ω)).
The toric analogue of a chain is "essentially" a totally cyclically ordered set, but care must be taken in the case when |C| = 2 because every size-two subset C ⊆ V is trivially totally cyclically ordered. Define a toric directed path in ω, to be a directed path i 1 → i 2 → · · · → i m such that the edge i 1 → i m is also present. We denote such a path by i 1 → tor i m . Toric directed paths of size 2 are simply edges, and every singleton set is a toric directed path of size 1. A fundamental property of toric directed paths is that up to cyclic shifts, they are invariants of toric-equivalence classes. That is, i 1 → tor i m is a toric directed path of ω if and only if each ω ′ ∈ [ω] has a toric directed path j 1 → tor j m , for some cyclic shift (j 1 , . . . , j m ) in [(i 1 , . . . , i m )]. This is Proposition 4.2 of [DMR15], and it leads to the notion of a toric chain, which is a totally cyclically ordered subset.
The following is a reformulation of Proposition 6.3 of [DMR15] using the language of this paper, where notation such as P (G, ω) and P (G, [ω]) is new. Having the concept of a toric chain leads to the notion of toric transitivity, which is completely analogous to ordinary transitivity when stated geometrically.
Proposition 5.5. Let i, j ∈ V be distinct. Then the hyperplane H tor i,j does not cut the chamber c(P (G, [ω])) if and only if i and j lie on a common toric chain.
Toric Hasse diagrams.
One of the major drawbacks to studying toric posets combinatorially, as equivalences of acyclic orientations (rather than geometrically, as toric chambers), is that a toric poset P or chamber c = c(P ) generally arises in multiple toric graphic arrangements A tor (G) over the same vertex set. That is, one can have P (G, [ω]) = P (G ′ , [ω ′ ]) for different graphs, leading to ambiguity in labeling a toric poset P with a pair (G, [ω]) consisting of a graph G and equivalence class [ω] in Acyc(G)/≡. Toric transitivity resolves this issue. As with ordinary posets, there is a well-defined notion for toric posets of what it means for an edge to be "implied by transitivity." The toric Hasse diagram is the graphĜ torHasse with all such edges removed. In Section 5.3, we encountered the toric transitive closure, which is the graphḠ tor with all such edges included. In other words, given any toric poset P = P (G, [ω]), there is always a unique minimal pair (Ĝ torHasse (P ), [ω torHasse (P )]) and maximal pair (Ḡ tor (P ), [ω tor (P )]) with the property that the set c(P ) is in Cham A tor where ⊆ is inclusion of edges. In this case, ω can be taken to be the restriction to G of any orientation in [ω tor (P )].
Geometrically, the existence of a unique toric Hasse diagram is intuitive; it corresponds to the minimal set of toric hyperplanes that bound the chamber c(P ), and the edges implied by transitivity correspond to the additional hyperplanes that do not cut c(P ). The technical combinatorial reason for the existence of a unique Hasse diagram (respectively, toric Hasse diagram) follows because the transitive closure (respectively, toric transitive closure) A −→Ā is a convex closure, meaning it satisfies the following anti-exchange condition; also see [EJ85]: Edges {i, j} in the Hasse diagram (respectively, toric Hasse diagram) are precisely those whose removal "change" the poset (respectively, toric poset), and the geometric definitions make this precise. Though the ordinary and toric cases are analogous, there are a few subtle differences. For example, consider the following "folk theorem." Since toric posets are defined geometrically as subsets of R V /Z V that are chambers of a graphic hyperplane arrangement, the equivalence (i)⇔(ii) is immediate for toric posets. Condition (iii) says that the edges {i, j} of the Hasse diagram are precisely the size-2 intervals, and Condition (iv) says these are the closed face partitions having two blocks of the form π = {{i, j}, V −{i, j}}. Finally, note that the implication (i)⇒(v) in Proposition 5.6 trivially fails for toric posets. For a simple counterexample, take any tree G with at least one edge. Since A tor (G) has only one chamber, removing any H tor i,j will never increase the number of chambers. Since adding or removing edges implied by toric transitivity does not change the toric poset, it does not change which sets are toric chains. Thus, to characterize the toric chains of P (G, [ω]), it suffices to characterize the toric chains of P (Ḡ tor (P ), [ω tor (P )]). The following is immediate.
Remark 5.7. Let P be a toric poset. A size-2 subset C = {i, j} of V is a toric chain of P if and only if {i, j} is an edge ofḠ tor (P ). In particular, if C is a maximal toric chain, then {i, j} is an edge inĜ torHasse (P ).
Toric intervals.
To motivate the definition of a toric interval, it helps to first interpret the classical definition in several different ways. We will define toric intervals geometrically, motivated by Condition (i), and show how it is equivalent to the toric version of Condition (ii). In contrast, Condition (iii) has a small wrinkle - the property of lying on a directed path from i to j does not depend on the choice of (G, ω) for P . Specifically, if P (G, ω) = P (G ′ , ω ′ ) and k lies on an ω-directed path from i to j, then k lies on an ω ′ -directed path from i to j. This is not the case for toric directed paths in toric posets, as the following example illustrates. As a result, we will formulate and prove a modified version of Condition (iii) for toric intervals.
Example 5.9. Consider the circular graph G = C 4 , and ω ∈ Acyc(C 4 ) as shown at left in Figure 3. Let P = P (C 4 , [ω]), which is a total toric order. Therefore, the toric transitive closure of (C 4 , [ω]) is the pair (K 4 , [ω ′ ]), where ω ′ is shown in Figure 3 on the right. Therefore, Now, let i = 1 and j = 3. The set {i, j} lies on a toric directed path from 1 to 3 in ω ′ (which also contains 2). However, none of the 4 representatives in [ω] contain a toric directed path from 1 to 3.
Another obstacle to formulating the correct toric analogue of an interval is how to characterize which size-2 subsets should be toric intervals. This ambiguity arises from the aforementioned "size-2 chain problem" of all size-2 subsets being totally cyclically ordered. Since ordinary intervals are unions of chains, we will require this to be a feature of toric intervals. Remark 5.11. If i, j, k are distinct elements of the toric interval I = [i, j] tor of P = P (G, [ω]), then for each x in c(P ), exactly one of the following must hold: By Theorem 5.1, we can rephrase Remark 5.11 as the toric analogue of Definition 5.8(ii): the toric interval [i, j] tor in P is the set of elements between i and j in the cyclic order of any total toric extension of P . Finally, the toric analogue of Definition 5.8(iii) can be obtained by first passing to the toric transitive closure.
Proposition 5.13. Fix a toric poset P = P (G, [ω]). An element k is in [i, j] tor if and only if k lies on a toric directed path i → tor j inω ′ , for someω ′ ∈ [ω tor (P )].
Proof. Throughout, let C = {i, j, k}. Assume that |C| ≥ 3; the result is trivial otherwise. Suppose k is in [i, j] tor , which means that P | C = [(i, k, j)]. Take any ω ′ ∈ [ω] for which i is a source. By Proposition 5.3, the elements of C occur as a subsequence of a toric directed path in ω ′ , ordered (i, k, j). Since this is a toric chain, the edges {i, k}, {k, j}, and {i, j} are all implied by toric transitivity. Thus, k lies on a toric directed path i → tor j inω ′ , the unique orientation of [ω tor (P )] whose restriction to G is ω ′ .
Conversely, suppose that k lies on a toric directed path i → tor j inω ′ , for someω ′ ∈ [ω tor (P )]. Then C is a toric chain, ordered P | C = [(i, k, j)], hence k is in [i, j] tor .
Proposition 5.14. Let P = P (G, [ω]) be a toric poset. If a set I ⊆ V is a toric interval I = [i, j] tor , then there is some ω ′ ∈ [ω] for which the set I is the interval [i, j] of P (G, ω ′ ). The converse need not hold.
Proof. Without loss of generality, assume that G =Ḡ tor (P ). The statement is trivial if |I| < 2. We need to consider the cases |I| = 2 and |I| ≥ 3 separately. In both cases, we will show that one can take ω ′ to be any orientation that has i as a source.
First, suppose |I| = 2, which means that I = {i, j} is an edge of G. Take any ω ′ ∈ [ω] for which i is a source. Since |I| = 2, there is no other k ∈ {i, j} on a directed path from i to j in ω ′ , as this would form a toric directed path. Therefore, the interval [i, j] in P (G, ω ′ ) is simply {i, j}.
Next, suppose |I| ≥ 3. As before, take any ω ′ ∈ [ω] such that i is a source in ω ′ . Since G =Ḡ tor (P ), the directed edge i → j is present, and so by Proposition 5.13, [i, j] tor consists of all k ∈ V that lie on a directed path from i to j. This is precisely the definition of the interval [i, j] in P (G, ω ′ ).
Proof. Given the toric Hasse diagram of P (G, [ω]), the ordinary Hasse diagram of P (G, ω) is obtained by removing the edge {i 1 , i m } for each toric directed path i 1 → tor i m in P (G, ω) of size at least m ≥ 3. This establishes the first inequality in Eq. (21). The second inequality is obvious. Loosely speaking, the final equality holds because edges in the toric transitive closure are precisely the size-2 toric chains, which are precisely the subsets that are size-2 chains in every representative poset. We will prove each containment explicitly. For "⊆", take an edge {i, j} ofḠ tor (P ), which is a size-2 toric chain. By Proposition 5.3, {i, j} is a toric chain of P (G, ω ′ ) for all ω ′ ∈ [ω], which means that it is an edge of the transitive closurē G(P (G, ω ′ )). The "⊇" containment is analogous: suppose {i, j} is an edge ofḠ(P (G, ω ′ )) for each ω ′ ∈ [ω]. Then by Proposition 5.3, it is a toric chain of P , and hence an edge ofḠ tor (P ).
Toric antichains. An antichain of an ordinary poset P is a subset A ⊆ V characterized
• combinatorially by the condition that no pair {i, j} ⊆ A with i = j are comparable, that is, they lie on no common chain of P , or • geometrically by the equivalent condition that the (|V | − |A| + 1)-dimensional subspace D πA intersects the open polyhedral cone c(P ) in R V . As shown in [DMR15], these two conditions in the toric setting lead to different notions of toric antichains which are both easy to formulate. Unlike the case of ordinary posets, these two definitions are non-equivalent; leading to two distinct versions of a toric antichains, combinatorial and geometric. The following is the geometric one which we will use in this paper. Its appearance in Proposition 5.17, which is one of the "For Some" structure theorems listed in the Introduction, suggests that it is the more natural toric analogue of the two. Proposition 5.17. Let P = P (G, [ω]) be a toric poset. Then a set A ⊆ V is a geometric toric antichain of P if and only if A is an antichain of P (G, ω ′ ) for some ω ′ ∈ [ω].
Morphisms of toric posets
Morphisms of ordinary posets have equivalent combinatorial and geometric characterizations. In contrast, while there seems to be no simple or obvious combinatorial description for morphisms of toric posets, the geometric version has a natural toric analogue.
Firstly, it is clear how to define a toric isomorphism between two toric posets P and P ′ on vertex sets V and V ′ : a bijection φ : V → V ′ such that the induced isomorphism on R V /Z V → R V ′ /Z V ′ maps c(P ) to c(P ′ ) bijectively. The other types of ordinary poset morphisms have the following toric analogues: quotients that correspond to projecting the toric chamber onto a flat of A tor (G ′ π ) for some closed toric face partition π = cl tor P (π); inclusions that correspond to embedding a toric chamber into a higher-dimensional chamber; extensions that add relations (toric hyperplanes). Since every poset morphism can be expressed as the composition of a quotient, an inclusion, and an extension, it is well-founded to define a toric poset morphism to be the composition of the toric analogues of these maps. In the remainder of this section, we will describe toric morphisms in detail. Most of the difficulties have already been done in Section 3, when interpreting the wellknown concept of an ordinary poset morphism geometrically. In contrast, this section is simply an adaptation of this geometric framework from R V to R V /Z V , though there are some noticeable differences. For example, there is no toric analogue of intersecting a chamber with a half-space, because the torus minus a hyperplane is connected.
6.1. Quotient. In the ordinary poset case, a quotient is performed by contracting P (G, ω) by a partition π = {B 1 , . . . , B r }. Each B i gets collapsed into a single vertex, and the resulting acyclic graph is denoted by ω/∼ π , which is an element of Acyc(G/∼ π ). This does not carry over to the toric case, because in general, contracting a partition will make some representatives acyclic and others not. However, the geometric definition has a natural analogue. Now, let P = P (G, [ω]) be a toric poset, and π be any partition of V closed with respect to P , i.e., π = cl tor P (π). By construction, D tor π is a flat of A tor (G ′ π ), and so the subset F tor π (P ) is a face of A tor (G ′ π ). First, we need a map that projects a point x in c(P ) onto this face, which is relatively open in the subspace topology of D tor π . This can be extended to the entire torus, by taking the unique mapd π that makes the following diagram commute, where d π is the mapping from Eq. (9): Explicitly, the mapd π takes a point x ∈ R V /Z V , lifts it to a pointx in an order polytope in R V , projects it onto the flat D π as in Eq. (9), and then maps that point down to the toric flat D tor π . In light of this, we will say that the mapd π is a projection onto the toric flat D tor π . After projecting a chamber c(P ) onto a flat D tor π of A(G ′ π ), we need to project it homeomorphically onto a coordinate subspace of R V /Z V so it is a chamber of a lower-dimensional toric arrangement. As in the ordinary case, let W ⊆ V be any subset formed by removing all but 1 coordinate from each B i , and letr π : R V /Z V −→ R W /Z W be the induced projection. Ther π -image of A tor (G) will be the toric arrangement A tor (G/∼ π ). As before, the following easily verifiable lemma ensures that our choice of W ⊆ V does not matter.
Moreover, all such projection maps for a fixed π are topologically conjugate in the following sense: and projection mapr ′ π | Dπ : D tor π −→ R W ′ /Z W ′ , and σ is the permutation of V that transposes each b i with b ′ i , then the following diagram commutes: withΣ andΣ ′ being the induced linear maps as defined in Eq. (6), but done modulo 1.
By convexity (in the fundamental affine chambers), two points in the same face of A tor (G) get mapped to the same face in A tor (G/∼ π ). In other words,d π induces a well-defined mapδ π from Face A tor (G) to Face A tor (G ′ π ) making the following diagram commute: Explicitly, the mapδ π is easiest to defined by the analogous map on closed faces: The open faces of A tor (G ′ π ) are then mapped to faces of the arrangement A tor (G/ ∼ π ) under the projectionr π | Dπ : D tor Combinatorially, the open faces of A tor (G) are toric preposets [ω] over G (i.e., in Pre(G)/≡). These are mapped to toric preposets over G/∼ π via the composition The following commutative diagram illustrates the relationship between the points in R V /Z V , the faces of the toric graphic arrangement A tor (G), and the toric preposets over G. The left column depicts the toric preposets over G that are also toric posets.
To summarize, toric poset morphisms that are quotients are characterized geometrically by projecting the toric chamber c(P ) onto a flat of A tor (G ′ π ), for some closed toric face partition π = cl tor P (π). Applying Theorem 4.7 gives a combinatorial interpretation of this, which was not a priori obvious.
The following is now immediate from Propositions 5.14 and 5.17. Corollary 6.3. Let P be a toric poset over V . Then contracting a toric interval I ⊆ V or a geometric toric antichain A ⊆ V defines a toric morphism.
6.2. Inclusion. Just like for ordinary posets, a toric poset can be included in larger one. Let P be a poset over V and let V V ′ . The simplest injection adds vertices (dimension) but no edges (extra relations). In this case, the inclusion φ : P ֒→ P ′ defines a canonical inclusion Φ : This sends the arrangement A tor (G) in R V , where G = (V, E), to the same higher-dimensional arrangement: The toric chamber c = c(P ) is sent to the chamber More generally, an injection P → P ′ can have added relations in P ′ either among the vertices in P or those in V ′ −V . Such a map is simply the composition of an inclusion described above and a toric extension, described below.
6.3. Extension. Extensions of ordinary posets were discussed in Section 3.2. A poset P ′ is an extension of P (both assumed to be over the same set V ) if any of the three equivalent conditions holds: The first of these conditions does not carry over nicely to the toric setting, but the second two do. A toric poset P ′ is a toric extension of P if and only one has an inclusion of their open polyhedral cones c(P ′ ) ⊆ c(P ) in R V /Z V , which is equivalent toĜ torHasse (P ) ⊆Ĝ torHasse (P ′ ).
Note that in the special case of the morphism P −→ P ′ being surjective, the inclusion step is eliminated and the entire process can be described geometrically by projecting c(P ) to a toric flat D tor π and a then adding toric hyperplanes.
Toric order ideals and filters
Let P be a poset over a set V of size at least 2, and suppose φ : P → P ′ is a morphism to a poset over a size-2 subset V ′ ⊆ V . This is achieved by projecting c(P ) onto a flat D π of A(G ′ π ) such that π = cl P (π) has at most two blocks, and henceF π = c(P ) ∩ D π is at most 2-dimensional. A point x = (x 1 , . . . , x n ) on F π has at most two distinct entries. Thus, the partition π = {I, J} of V satisfies The set I is called an order ideal or just an ideal of P and J is called a filter.
Ideal/filter pairs are thus characterized by closed partitions π of V such that D π intersects c(P ) in at most two dimensions. The set of ideals has a natural poset structure by subset inclusion. Allowing I or J to be empty, this poset has a unique maximal element I = V (corresponding to J = ∅) and minimal element I = ∅ (corresponding to J = V ). Moreover, the order ideal poset is a lattice; this is well-known [Sta01]. Similarly, the set of filters is a lattice as well.
Toric order ideals and filters can be defined similarly.
Definition 7.1. Let P be a toric poset over V , and suppose φ : P → P ′ is a morphism to a toric poset over a size-2 subset V ′ ⊆ V . This projects c(P ) onto a toric flat D tor π of A tor (G ′ π ) for some π = cl tor P (π) such thatF tor π = c(P ) ∩ D tor π is at most 2-dimensional. For the partition π = {I, J} of V , each point x = (x 1 , . . . , x n ) on F tor π satisfies x i k mod 1 = x i ℓ mod 1 for all i k , i ℓ in I; x j k mod 1 = x j ℓ mod 1 for all j k , j ℓ in J. The set I is called a toric order ideal of P .
Remark 7.2. By symmetry, if I is a toric order ideal, then so is J := V −I. A toric filter can be defined analogously, and it is clear that these two concepts are identical. Henceforth, we will stick with the term "toric filter" to avoid ambiguity with the well-established but unrelated notion of a toric ideal from commutative algebra and algebraic geometry [Stu96].
By construction, toric filters are characterized by closed toric partitions π of V such that D tor π intersects c(P ) in at most two dimensions -either a two-dimensional face of P or of an extension P ′ over G ′ π . Proposition 7.3. Let P (G, [ω]) be a toric poset. The following are equivalent for a subset I ⊆ V .
Proof. The result is obvious if I = ∅ or I = V , so assume that ∅ I V , and π = {I, V −I}. This forces D tor π to be two-dimensional (rather than one-dimensional). (i)⇒(ii): If I is a toric filter of P (G, [ω]), then D tor π intersects c(P (G, [ω])) in two-dimensions, and so D π intersects an order polytope O(P (G, ω ′ )) in two-dimensions, for some ω ′ ∈ [ω]. Therefore, D π intersects the chamber c(P (G, ω ′ )) in two-dimensions, and hence I is an ideal of P (G, ω ′ ).
(ii)⇔(iii): Immediate by Remark 7.2 upon reversing the roles of I and V −I.
(ii)⇒(iv): If I is a size-k ideal of P (G, ω ′ ), then by a well-known property of posets, there is a linear extension of the form (i 1 , . . . , i k , v k+1 , . . . , v n ), where each i j ∈ I. The cyclic equivalence class [(i 1 , . . . , i k , v k+1 , . . . , v n )] is a total toric extension of P (G, [ω ′ ]) = P (G, [ω]) in which the elements of I appear in consecutive cyclic order.
(iv)⇒(ii): Suppose [(i 1 , . . . , i k , v k+1 , . . . , v n )] is a toric total extension of P (G, [ω]). This means that for some x ∈ R V /Z V , The unique preimagex of this point in [0, 1) V under the quotient map q : Given a toric poset, we can define the characteristic function χ I of a toric filter similarly. However, one must be careful because under the canonical quotient to the torus, the vertices of every order polytope get identified to (0, . . . , 0). Therefore, we will still identify χ I with a point in R V , not R V /Z V . Let J tor (P ) denote the set of toric filters of P . This has a natural poset structure by subset inclusion. Once again, there is a unique maximal element I = V and minimal element I = ∅.
Proposition 7.6. With respect to subset inclusion and cardinality rank function, J tor (P ) is a graded poset.
Proof. Let P = P (G, [ω]) be a toric poset over G = (V, E). It suffices to show that every nonempty toric filter J contains a toric filter J ′ of cardinality |J ′ | = |J| − 1. By Proposition 7.3, the set J is an order ideal of P ′ = P (G, ω ′ ) for some ω ′ ∈ [ω]. Choose any minimal element v ∈ V of P ′ , which is a source of ω ′ . Let ω ′′ be the orientation obtained by flipping v into a sink. The set J ′ := J−{v} is an ideal of P (G, ω ′′ ), and so by Proposition 7.3, it is a toric filter of P (G, [ω ′′ ]) = P (G, [ω]).
Example 7.7. Let G = C 4 , the circle graph on 4 vertices, and let ω ∈ Acyc(G) be the orientation shown at left in Figure 4. The Hasse diagram of the poset P = P (G, ω) is a line graphĜ Hasse (P ) = L 4 , and the transitive closure isḠ(P ) = K 4 . Since V is a size-4 toric chain, it is totally cyclically ordered in every ω ′ ∈ [ω], and the dashed edges are additionally implied by toric transitivity. Thus, The 4 torically equivalent orientations are shown in Figure 4. The only total toric extension of (1, 2, 3, 4) , (2, 3, 4, 1) , (3, 4, 1, 2) , (4, 1, 2, 3)] , and this is shown at right in Figure 5. The toric filters are all subsets of V that appear as an initial segment in one of these four total orders. The poset J tor (P (C 4 , [ω])) is shown at left in Figure 5. Note that unlike the ordinary poset case, it is not a lattice.
Example 7.8. Let G = C 4 , as in Example 7.7, but now let ω ′ ∈ Acyc(G) be the orientation shown at left in Figure 6. The only nonempty toric chains are the four vertices (size 1) and the four edges (size 2). Since ω ′ has no toric chains of size greater than 2, the Hasse diagram and the transitive closure of the toric poset P (G, [ω ′ ]) are both C 4 . Note that the transitive closure of the (ordinary) poset P (G, ω ′ ) contains the edge {1, 3}, and so as graphs,Ḡ(P (G, ω ′ )) =Ḡ tor (P (G, [ω ′ ])). The 6 torically equivalent orientations of ω ′ are shown in Figure 6. There are four total toric extensions of P (G, [ω ′ ]) which are shown on the right in Figure 7, as cyclic words. The toric filters are all subsets of V that appear as a consecutive segment in one of these four total orders. The poset J tor (P (C 4 , [ω ′ ])) of toric filters is shown at left in Figure 7. In this particular case, the poset of toric filters is a lattice. In fact, it is isomorphic to a Boolean lattice, because every subset of {1, 2, 3, 4} appears consecutively (ignoring relative order) in one of the four cyclic words in Figure 7.
Application to Coxeter groups
A Coxeter system is a pair (W, S) consisting of a Coxeter group W generated by a finite set of involutions S = {s 1 , . . . , s n } with presentation W = S | s 2 i = 1, (s i s j ) mi,j = 1 where 2 ≤ m i,j ≤ ∞ for i = j. The corresponding Coxeter graph Γ has vertex set V = S and edges {i, j} for each m i,j ≥ 3 labeled with m i,j (label usually omitted if m i,j = 3). A Coxeter element is the product of the generators in some order, and every Coxeter element c ∈ W defines a partial ordering on S via an acyclic orientation ω(c) ∈ Acyc(Γ): Orient s i → s j iff s i precedes s j in some (equivalently, every) reduced expression for c. Conjugating a Coxeter element by an initial generator (note that s i = s −1 i ) cyclically shifts it: s x1 (s x1 s x2 · · · s xn )s x1 = s x2 · · · s xn s x1 , and the corresponding acyclic orientation differs by reversing the orientations of all edges incident to s x1 , thereby converting it from a source to a sink vertex. In 2009, H. and K. Eriksson showed [EE09] that two Coxeter elements c and c ′ are conjugate if and only if ω(c) ≡ ω(c ′ ). Thus, there are bijections between the set C(W ) of Coxeter elements and Acyc(Γ), as well as between the corresponding conjugacy classes and the toric equivalence classes: The toric equivalence class containing ω(c ′ ) has six orientations, which were shown in Figure 6. Each of these describes a unique conjugate Coxeter element: s 1 s 2 s 4 s 3 s 2 s 4 s 1 s 3 s 4 s 1 s 3 s 2 s 2 s 1 s 3 s 4 s 1 s 3 s 2 s 4 s 3 s 2 s 4 s 1 = s 1 s 4 s 2 s 3 = s 2 s 4 s 3 s 1 = s 4 s 3 s 1 s 2 = s 2 s 3 s 1 s 4 = s 1 s 3 s 4 s 2 = s 3 s 4 s 2 s 1 = s 4 s 2 s 3 s 1 = s 3 s 1 s 4 s 2 = s 4 s 2 s 1 s 3 = s 3 s 1 s 2 s 4 These are listed above so that the Coxeter element in the i th column corresponds to the i th orientation in Figure 6. The linear extensions of each orientation describe the reduced expressions of the corresponding Coxeter element, which are listed in the same column above. The toric poset P (G, [ω(c ′ )]) has four total toric extensions, and these were shown on the right in Figure 7 (replace k with s k ). The toric filters of P (G, [ω(c ′ )]) correspond to the subsets that appear consecutively in one of these cyclic words. The poset J tor (P (C 4 , [ω ′ ])) of toric filter appears on the left in Figure 7.
Concluding remarks
In this paper, we further developed the theory of toric posets by formalizing the notion of toric intervals, morphisms, and order ideals. In some regards, much of the theory is fairly analogous to that of ordinary posets, though there are some noticeable differences. Generally speaking, the one recurring theme was the characterization of the toric analogue of a feature in P (G, [ω]) by the characterization of the ordinary version of that feature in P (G, ω ′ ) either for some ω ′ ∈ [ω], or for all ω ′ ∈ [ω].
One question that arises immediately is whether there is a toric order complex. While there may exist such an object, there are some difficulties unique to the toric case. For example, a Figure 8. Two non-torically equivalent orientations ω ≡ ω ′ in Acyc(C 5 ) for which P (C 5 , [ω]) and P (C 5 , [ω ′ ]) have the same set of toric chains. poset is completely determined by its chains, in that if one specifies which subsets of V are the chains of P , and then the toric order of the elements within each chain, the entire poset can be reconstructed. This is not the case for toric posets, as shown in Figure 8. Here, two torically non-equivalent orientations of C 5 are given, but the toric posets P (C 5 , [ω]) and P (C 5 , [ω ′ ]) have the same sets of toric chains: the 5 vertices and the 5 edges.
The fact that an ordinary poset is determined by its chains just means that once one specifies the total order between every chain of size k ≥ 2, then the entire partial order is determined. The problem for toric posets, which we encountered in this paper, is that every size-2 subset is trivially cyclically ordered, whether it lies on a toric chain or not. In other words, a total order can be defined on two elements, but a cyclic order needs three. The analogous statement for toric posets would be that specifying the total cyclic order between every toric chain of size k ≥ 3 specifies the entire toric order. Such a statement would establish the intuitive idea that knowing all total cyclic orders should determine the toric partial order "modulo the size-2 toric chains." Current works suggests that there is an analogue of the aforementioned properties for toric posets, but it requires a new generalization of the concept of a chain. The details are too preliminary and complicated to describe here, and it is not clear whether it will lead to a combinatorial object such as a toric order complex. Without this, there might not be a natural way to study toric posets topologically.
Another important feature of ordinary posets that does not seem to have any obvious toric analogue are Möbius functions, and this is vital to much of the theory of ordinary posets. Recall the analogy from the Introduction about how topology is like "analysis without the metric." Similarly, many of the basic features of ordinary posets have toric analogues, despite the fact that toric posets have no binary relation. However, much of the more advanced theory is likely to fail because one also seems to lose valuable tools such as an order complex and a Möbius function. Even the theory that does carry over has its shortcomings. For example, morphisms have a simple combinatorial characterization using the binary relation: i < P j implies φ(i) < P ′ φ(j). The geometric definition requires a patchwork of quotients, extensions, and inclusions. It would be desirable to have a more "holistic" characterization of toric poset morphisms, though it is not clear that that such a description should exist.
Finally, the connection of toric posets to Coxeter groups is the subject of a paper nearing completion on cyclic reducibility and conjugacy in Coxeter groups. Loosely speaking, reduced expressions can be formalized as labeled posets called heaps. This was formalized by Stembridge [Ste96,Ste98] in the 1990s. The fully commutative (FC) elements are those such that "long braid relations" (e.g., sts → tst) do not arise. Equivalently, they have a unique heap. The cyclic version of the FC elements are the cyclically fully commutative CFC elements, introduced by the author and collaborators in [BBE + 12]. In 2013, T. Marquis showed that two CFC elements are conjugate if and only if their heaps are torically equivalent [Mar14]. These elements were further studied by M. Pétréolle [Pét14]. In our forthcoming paper, we will formalize the notion of a toric heap, which will essentially be a labeled toric poset. This allows us to formalize objects such as cyclic words, cyclic commutativity classes, and develop a theory of cyclic reducibility in Coxeter groups using the toric heap framework. | 21,718.2 | 2015-01-09T00:00:00.000 | [
"Mathematics"
] |
Realisation of the metre by using a femtosecond laser frequency comb : applications in optical frequency metrology
The appearance of the frequency comb technology, awarded the Nobel Prize in Physics 2005, has enormously revolutionized the metrology of optical frequencies, eliminating the need for complicated frequency chains. By direct linking to the unit of time, the second, through frequency standards (Cs, Rb), by using femtosecond mode-locked lasers and frequency comb technology, the Spanish Centre of Metrology (CEM) has established a new way of practical realisation of the National Standard of Length, the metre. By stabilising and characterising two free parameters – the repetition frequency fr and the offset frequency f0, the frequency comb generator thereby was successfully put into operation. After such realization, the accuracy of the length unit will be increased in two orders of magnitude, that is 2 10 13 instead of 2.1 10 . In this paper we present the results of applying comb generator to the absolute measurement of the three Zeeman stabilized He–Ne lasers operating at 633 nmwith a nominal frequency of 473.612THz. A comparison of these results with those obtained by the current system based on standard iodine stabilized lasers is in good compatibility. A treatment for the evaluation of measurement uncertainty of laser frequency in calibration using a comb in accordance with Guide of Uncertainty Measurement ISO/BIPM is also presented.
Introduction
The definition of the unit of length and its practical realisation are based on the adopted value of the speed of light, c 0 = 299 792 458 m/s, and the frequency of an optical transition.Thus, length measurements are intrinsically related to the unit of time.It was adopted by the 17th Conference Générale des Poids et Mesures in 1983 [1].At the same time, the Comité International des Poids et Mesures (CIPM) made recommendations for the practical realization of the metre, referred to as the mise en pratique (in later text referenced as MeP) of the definition.The metre should be realized by one of the following methods [2]: (a) by means of the length l of the path travelled in vacuum by a plane electromagnetic wave in a time t; this length is obtained from the measured time t, using the relation l = c 0 • t and the value of the speed of light in vacuum c 0 = 299 792 458 m/s; (b) by means of the wavelength in vacuum l of a plane electromagnetic wave of frequency f; this wavelength is obtained from the measured frequency f using the relation l = c 0 /f and the value of the speed of light in vacuum c 0 = 299 792 458 m/s; (c) by means of one of the radiations from a given list, whose stated wavelength in vacuum or whose stated frequency can be used with the uncertainty shown, provided that the given specifications and accepted good practice are followed.
Various sources of radiation have been recommended as standards of wavelength and have been updated by the CIPM over time [2,3].One of the most important recommended radiations in the field of length metrology and worldwide precision measurements is that at 474 THz (633 nm) from a He-Ne laser, stabilized on an absorbing hyperfine component in 127 I 2 .This laser is used in many laboratories around the world as a practical means of realizing the SI metre and is commonly used for calibrating the frequency of lasers employed in length measurement and precision measurement in atomic physics.The lasers standards work according to method (c) of the Comité consultatif de Longueurs (CCL)/CIPM recommendation for the realization of SI of the metre definition.
To check the values of the standards and the possible improvement of uncertainty, one needs to absolutely measure laser frequency (hundreds of terahertz) relative to caesium clocks (realizing SI definition of the second).This measurement (method b in MeP) was made easier by the invention of optical frequency comb technique [4][5][6] awarded the Nobel Prize in Physics 2005.
With this system (frequency comb), the Spanish Centre of Metrology (CEM) is establishing a new practical realization of the metre improved accuracy in two orders of magnitude (i.e. 2 Â 10 À13 instead of 2.1 Â 10 À11 ) with respect to the current system based on iodine stabilized lasers [7,8].
In this paper, the state of art of femtosecond optical frequency comb, including a theoretical background study, is briefly described.The absolute frequency measurement of Zeeman-stabilized He-Ne lasers operating at 633 nm by the frequency comb and the comparison of the results obtained by the current method of beating frequency, using a standard iodine stabilized lasers (CEM2) have been reported.In both cases, a stability study of the signal beat frequency is presented.Finally, we estimate the measurement uncertainty for comb and laser frequency under calibration using the Guide of Uncertainty Measurement (GUM) ISO/BIPM.
Theoretical background
Optical frequency combs are routinely used to generate optical radiation with a frequency uncertainty limited only by the uncertainty of the master clock that sets the repetition frequency of the combs.These frequency combs, working in mode-lock regime, have to be designed so that the round trip time for all longitudinal modes is the same.To understand the mode structure of a femtosecond frequency comb and the techniques applied for its stabilization one can look at the idealized case of a pulse circulating in a laser cavity with length L and carrier frequency f c as shown in Figure 1.The output of this laser is a sequence of pulses that are essentially copies of the same pulse separated by the round trip time given by: where v g is the cavity mean group velocity defined by the round trip time and the cavity length.The pulses however are not quite identical.This is because the pulse envelope A(t) propagates with v g while the carrier wave travels with its phase velocity.As a result, the carrier shifts with respect to the pulse envelope after each round trip by a phase angle Df as shown in Figure 1.The shape of the pulse train in time domain is related to the amplitude and phase spectra by complex Fourier transform.
Let us describe the time evolution of the electric field at one point in space by carrier frequency f c and periodic amplitude/envelope A. Unlike the envelope function, which provides us with a more rigorous definition of the pulse repetition time f r = 1/T by demanding A(t) = A (t + T), the electric field is, in general, not expected to be periodic in time.If the periodicity of the envelope function is assumed, the electric field at a given place outside the laser resonator can be written as, Because the envelope is periodic where A n are Fourier components of A(t).This equation shows that, under the assumption of a periodic pulse envelope, the resulting spectrum consists of a comb of laser modes that are separated by the pulse repetition frequency.Since f c is not necessarily an integer multiple of f r , the modes are shifted with respect to the exact harmonics of the repetition frequency by an offset which can be selected in such a way that f 0 < f r simply by renumbering the modes: where n is a large integer of order 10 6 that indexes the comb line.This equation maps two radio frequencies (RF) f r and f 0 onto the optical frequencies f n .Although the detection of f r is rather effortless and usually lies between a few ten MHz and a few GHz depending on the length of the laser resonator, the determination of f 0 is far more challenging to access unless the frequency comb contains more than an optical octave.f 0 then is detected by the selfreferencing technique (Fig. 2) with an f-2f interferometer setup [9,10].Therefore, a mode, with mode number n at the red wing of the comb, whose frequency is given according to equation ( 4), is frequency doubled in a nonlinear crystal.If the frequency comb covers a full optical octave, a mode with the number 2n should oscillate simultaneously at The beat note between the frequency doubled mode and the mode at 2n yields the offset frequency The frequency of a laser under calibration (continuous wave), f cw , is determined by observing a beat frequency, f beat , with the nearest mode of the frequency comb system.Therefore, the f cw is expressed as The signs of the equation ( 5) depend on the measurement conditions and can be determined by changing f 0 and f r while monitoring the resulting change in the beat signal.
If the visible cw lasers are measured after second harmonic generation (SHG), that is our case, equation (5) has to be modified to take the SHG process into consideration.The f 0 has to be multiplied by a factor of two: The repetition rate remains unchanged due to the fact that the dominant process in the SHG is sum frequency generation.
Experimental setup
The details on experimental arrangements of the femtosecond laser frequency comb were published elsewhere [7,8].In this paper, a brief summary is presented.The experimental arrangement employed is sketched in Figure 3.The version of the femtosecond laser frequency comb, the FC1500, developed by Menlo Systems GmbH, is based on a 250 MHz repetition rate mode-locked erbium fibre-ring laser and a non-linear microstructured fibre.
The heart of the frequency comb generator is a fibre laser head with internal erbium doped fibre amplifier (EDFA) for generating high power IR light at 1500 nm with power up to 2 mW.The femtosecond laser output power is split into two branches and fed to the monitor port and the external parts of the system.One branch is amplified in an external EDFA and spectrally broadened in a highly nonlinear fibre to cover a spectrum of one octave in frequency space, and which will later be doubled in frequency.The beat of the offset frequency f 0 is detected by means of a nonlinear interferometer.The other branch for generating high power IR light at 1560 nm for subsequent frequency doubling at 780 nm radiation, and a photonic crystal fibre setup for subsequent broadening of the SHG output to (530-1000) nm with power up to 60 mW.
We use a fast p-i-n junction (PIN) diode to detect the offset frequency.
The laser head features an internal fast PIN photo diode to detect the 4th harmonic of the repetition frequency which increases the phase sensitivity.
Two phase locked loops to lock the repetition rate and offset frequency in RF standard allow to transfer the accuracy and stability between the RF and optical domain and are part of the electronics.Frequency counters without dead time are used to measure beat signals with cw lasers and to control the phase locked loops for cycle slips.An oscilloscope and a spectrum analyzer are also included for monitoring purposes.
The beat detection unit (Fig. 4) consists of a series of silver/gold coated mirrors, polarized beam splitters, l/2 or l/4 waveplates, which aim to place the beams from both the laser comb and calibration in the same polarisation plane, and lead them to a photodetector.
The repetition rate frequency, f r , and the carrierenvelope offset frequency (20 MHz), f 0 , and f beat were referenced to a primary frequency standard, a Cs atomic clock (Symmetricom, model 5071A), integrated into the network of atomic clocks of the Navy Observatory, ROA, in charge of maintaining the Spanish time and frequency standards.
To measure the beat note between Zeeman-stabilized He-Ne lasers emitting at a nominal wavelength of 633 nm and the frequency comb mode, a grating (2100 lines/mm) for spectral filtering was used.The primary difficulties with measuring f beat arise from the fact that only a very small fraction signal of the comb power is in the mode that gives rise to a beat signal.Several strategies are needed to maximize signal to noise relation and reduce detector saturation effects.Probably the most important single step is simply to take great care in aligning the beam from the test laser with the beam from the comb.To be more precise, what is ideally needed is perfect matching of the wavefrontstwo coaxial Gaussian beams with the same waist position and same size, travelling in the same direction.It is very important to assure that the beams overlap very well, travel accurately in the same direction and have similar waist size to obtain a good beat signal.Such beat note frequency was detected by an avalanche photodetector APD210.All relevant frequencies in the experiment have been analyzed and counted by a spectrum analyzer (Hameg, HM5510 model) and frequency counters (Menlo Systems, FXM50 model), respectively, which have been referenced to a primary frequency standard (Symmetricom, 5071A model) with a relative stability of 1 Â 10 À12 at short time, which is worse than real uncertainty of combs and reference RF signals.However, this stability value is definitely sufficient for length measurements.Therefore, the stability of our system is predetermined by the reference source.Currently, to achieve long-term stability it is possible to use H-Masers and fountains based on cold atoms.In our case, we are using both Cs clock and Rb clock disciplined to the previous one, thus ensuring long and short term stability.
During the process of measurement, the frequency comb system as well as the remaining phase is very reliably locked.The frequency counters used for these measurements count continuously every second without dead time for more than 5 h.In our case, the S/N ratio over 30 dB is sufficient for counting without cycle slips.
Results and discussions
At CEM we count with several Zeeman-stabilized He-Ne lasers operating at 633 nm.These lasers are traceable to the primary standard (CEM2) He-Ne laser stabilized to hyperfine spectral components of the transition 11-5 R (127) of 127 I 2 vapour in internal cell with a nominal wavelength at 633 nm with third harmonic locking technique [8].In this section we present results of absolute frequency measurement of three Zeeman stabilized He-Ne laser at 633 nm, using a frequency comb.A comparison of these results with those obtained with primary standard CEM2 laser has been treated.
The f beat of Zeeman-stabilized He-Ne lasers deviation measurements from the mean value are shown in Figures 5 and 6.It can be seen that the standard deviations of these measurements are in agreement with the acceptance and rejection criteria established for obtaining reliable results.
The stability of the measured absolute frequency of our wavelength standard is limited by the stability of the reference Cs clock and Rb clock disciplined to the previous one, for ensuring long and short term stability.
In previous study we calculated the Allan deviation (square root of the Allan variance) the stability of the femtosecond comb reaches 8.38 Â 10 À11 at 1 s averaging and improves to 3.54 Â 10 À15 after 10 000 s [8].Figures 7 and 8 show the Allan deviation of frequency beat obtained with the comb system.The beat note and the Allan deviation of HP5519A laser look like the frequency beat and Allan deviation of HP5517D.
It can be seen that Allan deviation of beat frequency obtained with the Tesa laser against the frequency comb describes the typical behaviour with white noise common in the caesium and rubidium time/frequency standards [11,12].However, the stability of HP5517D and HP5519A lasers (Fig. 8) at the longer averaging times is degraded.In particular, the stability plot has a t [11,12] slope (time = t) beyond 250 s that corresponds to the drift (i.e., about 5.6 Â 10 À9 at 5000 s).Evaluating the compatibility coefficient C, using the formula where X 1 and X 2 are the frequency values of lasers under measurement obtained with CEM2 and frequency comb respectively.U 1 and U 2 are expanded uncertainties (k = 2) of lasers under measurement using a CEM2 and frequency comb respectively.We obtained C values less than 0.34, this result indicates the compatibility of these measurements using two different standards (CEM2 and frequency comb).
Table 1 shows a summary of these measurements' results.
Evaluating measurement uncertainty
Estimating measurement uncertainty via studying the repeatability of the measurement is a well-established technique often used in dimensional metrology at many National Metrology Institutes.However, it often requires years of data to truly sample all sources of error in a typical dimensional measurement system.
Every GUM [13] compliant uncertainty calculation must start with the definition of the measurand and the formulation of the model equation for it.In frequency metrology, special mathematical tools have been developed to deal with time series of correlated data.In addition, the use of relative uncertainties is common practice in this field.However, we stay at a more traditional treatment [14]; we start with the comb equation ( 6) which relates the laser frequency (the measurand) to the repetition, offset frequencies of the comb, and the beat frequency with the nth comb mode, respectively.
where f 0 and f beat are calculated as the mean value of the offset and beat frequencies found in the measurement process, then Applying the law of propagation of uncertainty, the corresponding expression is obtained by using combined standard uncertainty u c (y) (assuming the absence of correlations).
In our case, By collecting everything and substituting, we end up with the model equation for a laser calibration using a comb Next we analyse each of the uncertainty contributions.
Uncertainty associated to the reference standard (frequency comb)
The uncertainty of the frequency comb depends on the uncertainty in determining the offset frequency, f 0 and the repetition frequency, f r .However, both frequencies depend on two common contributions due to the stability of the synthesizer, and to the time reference is given by the Cs atomic clock.The uncertainty of the parameters that define the frequency comb is included within the stability of the frequency comb, characterized by the Allan variance, which is the internal counter of the comb synthesizer.Using the Allan variance as a contribution to the uncertainty avoids the correlations because the stability considers the direct contribution of servos, PLLs (Phase Locked Loops) and system electronics.For an integration time of 1000 s, the Allan deviation is u s = 9.5 Â 10 À14 [8].In each calibration performed it has been verified that the stability value is less than or equal to u s .Furthermore, the frequency comb is referenced to a primary frequency standard, a Cs atomic clock integrated into the network of atomic clocks of the Navy Observatory, ROA The certificate value emitted by ROA, which is for 24 h, is u Cs = 0.32 Â 10 À13 .Finally, the uncertainty of the reference standard frequency comb is, U(k = 2) = 2 Â 10 À13 .
Uncertainty due to beat contribution
The uncertainty associated with the measured value of the beat signal is estimated using a type B evaluation of uncertainty.To do so, we consider a type of rectangular distribution, with an amplitude (f max Àf min ), where the first is the maximum value and the second is the minimum one of the frequencies found Assigning a number of degrees of freedom v i = 100, this is a conservative approach established in Length Area of CEM by which the rectangular distributions are associated with an effective number of degrees of freedom equal to 100, to avoid an "infinite" number of degrees, which would suppose a total security as regard to the limit's values of distribution.Therefore, equation ( 14) is written as The expanded uncertainty, U is obtained by multiplying the combined standard uncertainty u(f cw ) by a coverage factor k where k is a function of the effective degrees of freedom obtained by Welch-Satterthwaite formula [13], from the values and the degrees of freedom of the partial uncertainties, for the desired confidence value, typically 95%.If it can be assumed a normal distribution the factor k = 2 is often used.In Table 2 we summarise the uncertainty budget.
Conclusions
Optical frequency combs have received much attention in recent years due to their enormous potential in optical frequency metrology applications, taking advantage of the continuous breakthroughs in the field of time and frequency metrology.The absolute frequency measurements of Zeeman-stabilized He-Ne lasers with our femtosecond laser frequency comb are in good compatibility with previous studies using a CEM2 as primary standard.In addition, the stability of beat frequency of Tesa RSD/SD is dominated by the typical white noise; while the stability of beat frequency of HP5517D and HP5519A at longer averaging times is degraded and corresponds to the drift.By using Allan variance analysis, we estimate a CMC of frequency comb in 2 Â 10 À13 .We evaluate the measurement uncertainty for comb-based laser frequency calibrations in accordance with GUM analysis.Finally, this realisation of metre based on femtosecond comb improves measurement accuracy more than 100 times compared to current method based on iodine-stabilized lasers.
A very serious contribution of anonymous referees to the improvement of this manuscript is gratefully acknowledged.Author wish also, to thank the Spanish CEM, and the Ministry of Industry, Energy and Tourism, MINETUR, for their support to this work in the period of 2009-2013.
Fig. 1 .
Fig. 1.Representation of the output field of a mode-locked laser in domain time and the corresponding spectrum.
Fig. 2 .
Fig. 2. The self-referencing technique of the optical frequency comb used for the measurement of the carrier-envelope-offset frequency.
Fig. 3 .
Fig. 3. Experimental setup used to measure the absolute frequency of different Zeeman-stabilized He-Ne lasers operating at 633 nm with a femtosecond comb generator.
Fig. 4 .
Fig. 4. Beat detection unit used for to measure the absolute frequency of different Zeeman-stabilized He-Ne lasers operating at 633 nm with a femtosecond comb generator.
Fig. 7 .
Fig. 7. Allan deviation of f beat between Tesa RSD/SR and femtosecond comb.Error bars corresponding to the standard uncertainty are shown for longer averaging times, where the error is large enough to be significant.
Fig. 8 .
Fig. 8. Allan deviation of f beat note between HP5517D and femtosecond comb.Error bars corresponding to the standard uncertainty are shown for longer averaging times, where the error is large enough to be significant.
Table 1 .
Frequencies of lasers under calibration measured by CEM2 and frequency comb printed as a difference from nominal frequency values.All values in MHz.
Table 2 .
The expanded uncertainty sources values involving in the measurement of frequency laser. | 5,175.8 | 2017-01-01T00:00:00.000 | [
"Physics"
] |
Recreating mineralogical petrographic heterogeneity within microfluidic chips : assembly , examples , and applications †
Micromodels have been used for decades to visualize multiphase flow through porous media by earth scientists, groundwater hydrologists, and petroleum engineers interested in the physical processes that govern the flow of immiscible fluids through soil, sediment, and rock. The earliest micromodels were of uniform pore geometry etched in resin or glass or silicon. In the past decade, researchers have begun creating micromodels with more complex pore geometry by transferring via photo lithography and then etching thin section or X-ray microcomputed tomography images of real rock into a single acid-etchable material such as silicon, quartz, glass, or calcite. These models allow dynamic imaging of pore-scale processes, but because they are etched from a single material they do not capture the scope of the variation seen in the mineralogical composition of rock (petrographic variation), nor the corresponding variations in rock/fluid chemical interaction, grain texture, and grain size and shape. In rock, such variations occur at all scales, from nm (sub-pore scale) to km. For example, random variations in the hydrophilicity and elasticity over length scales as small as 50 nm have been reported in Danish North Sea chalk. Rocks often display mm-scale variations in mineralogy which result from the sequential deposition of laminae that possess distinctive mineralogy. For different types of sedimentary rock (different lithologies), variation at the mm-scale may be slow and gradational (e.g., from the base to the top of a lamination) or clearly defined and sharp depending on the depositional process. Accordingly, such variations are fundamental in classifying petrographic features as important as mineralogy. Furthermore, because sedimentary successions can often be described in terms of facies models – conceptual models that explain the occurrence of different types of rock in both time and space – hydraulic properties of much larger sedimentary units can be extrapolated from smaller observations. Rock/fluid interaction and grain size, shape, and texture – and their spatial variation – determine the distribution of fluids over a wide range of scales and consequently their displacement. Sub-pore scale heterogeneity in hydrophilicity due to differential exposure to non-aqueous phase liquids (NAPL), commonly referred to as mixed wettability, is associated with dramatically protracted recovery of non-aqueous phases from oil reservoirs and NAPL-contaminated aquifers. Similarly, pore size and topology largely determine permeability, and their variation at the reservoir scale give rise to bypassing and poor oil recovery. Despite the long history of microfluidic studies, previous work has not addressed the consequences of the varied surface properties of the different mineral components of sedimentary rocks at the pore scale and lamina scale. This is remarkable when mineralogical composition is an inherent and fundamental rock property used for classification (e.g., QFL-scheme of siliciclastic rocks). One reason for this may be the previous monolithic composition of micromodels. To explore the impact of lamina-scale heterogeneities in mineralogy on two-phase flow through porous media under conditions representative of the subsurface, we developed a technique for rapid, low-cost assembly of single-use “micromodels” that recreate mineralogical heterogeneities at the OIJ100) μm to OIJ1) mm scale. This paper reports oil recovery measurements on uniform and layered micromodels which, combined, demonstrate the complex flow behaviour that emerges in the presence of structured variations. Our micromodels are unconsolidated, quasi-2.5dimensional beds of mineral grains packed into custom-
Micromodels have been used for decades to visualize multiphase flow through porous media by earth scientists, groundwater hydrologists, and petroleum engineers interested in the physical processes that govern the flow of immiscible fluids through soil, sediment, and rock.The earliest micromodels were of uniform pore geometry etched in resin or glass or silicon. 1 In the past decade, researchers have begun creating micromodels with more complex pore geometry by transferring via photo lithography and then etching thin section [2][3][4][5] or X-ray microcomputed tomography 6,7 images of real rock into a single acid-etchable material such as silicon, quartz, glass, or calcite.
These models allow dynamic imaging of pore-scale processes, but because they are etched from a single material they do not capture the scope of the variation seen in the mineralogical composition of rock (petrographic variation), nor the corresponding variations in rock/fluid chemical interaction, grain texture, and grain size and shape.In rock, such variations occur at all scales, from nm (sub-pore scale) to km.For example, random variations in the hydrophilicity and elasticity over length scales as small as 50 nm have been reported in Danish North Sea chalk. 8Rocks often display mm-scale variations in mineralogy which result from the sequential deposition of laminae that possess distinctive mineralogy.For different types of sedimentary rock (different lithologies), variation at the mm-scale may be slow and gradational (e.g., from the base to the top of a lamination) or clearly defined and sharp depending on the depositional process.Accordingly, such variations are fundamental in classify-ing petrographic features as important as mineralogy.Furthermore, because sedimentary successions can often be described in terms of facies modelsconceptual models that explain the occurrence of different types of rock in both time and space 9 hydraulic properties of much larger sedimentary units can be extrapolated from smaller observations. 10ock/fluid interaction and grain size, shape, and textureand their spatial variationdetermine the distribution of fluids over a wide range of scales and consequently their displacement.2][13] Similarly, pore size and topology largely determine permeability, and their variation at the reservoir scale give rise to bypassing and poor oil recovery. 14Despite the long history of microfluidic studies, previous work has not addressed the consequences of the varied surface properties of the different mineral components of sedimentary rocks at the pore scale and lamina scale.This is remarkable when mineralogical composition is an inherent and fundamental rock property used for classification (e.g., QFL-scheme of siliciclastic rocks). 15One reason for this may be the previous monolithic composition of micromodels.
To explore the impact of lamina-scale heterogeneities in mineralogy on two-phase flow through porous media under conditions representative of the subsurface, we developed a technique for rapid, low-cost assembly of single-use "micromodels" that recreate mineralogical heterogeneities at the OIJ100) μm to OIJ1) mm scale.This paper reports oil recovery measurements on uniform and layered micromodels which, combined, demonstrate the complex flow behaviour that emerges in the presence of structured variations.
Our micromodels are unconsolidated, quasi-2.5dimensionalbeds of mineral grains packed into custom- Grains.For silica, commercially available soda lime glass spheres (White House Scientific, UK) are used. 16Suitable products are not commercially available for other minerals and, accordingly, we prepare these grains by crushing rock (e.g., marble 17 ) or single crystals (e.g., orthoclase).Further details are provided in ESI, † along with the characterisation of materials used in the experiments presented below.Two key advantages of using crushed rock are the partial conservation of surface roughness and grooves (e.g., Fig. S1 and S2 †) and intra-grain heterogeneities in mineral composition.Both influence in situ, pore-scale contact angles [18][19][20] and hence the distribution and displacement of fluids within a porous medium.][23] Assembly of layered beds.Packed beds are assembled by wet-packing, i.e., by flushing suspensions of grains.A gap filter comprised of 100 μm-diameter, semi-circular channels retains the grains in the channel (Fig. 1).Micron-to mm-scale structures are assembled by sequentially injecting suspensions of grains of different mineralogy until a pack or a lamina of the desired length assembles behind the gap filter (Fig. 2).The carrier phase is chosen to be non-aqueous and chemically inert with respect to the mineral phase being used to suppress cohesion; n-hexane was used in all experiments presented below.The of grains in the suspension is kept low (1 : 7 to 1 : 9 v/v unconsolidated particles to liquid phase) to avoid blockages in ancillary tubing.
Fig. 3 and 4 illustrate the application of this technique to recreating a finely laminated siltstone from the top of the Poll a'Mahuillt member of the Stoer Group in NW Scotland. 24he siltstone comprises alternating laminae of fine grained silica and coarser grained orthoclase feldspar and quartz.The packed beds assembled within a microfluidic chip similarly comprise sub-mm laminae of orthoclase and silica (e.g., Fig. 4b).The key difference between the two packs is the thickness of the orthoclase lamina, which is 890 μm (or 14 grain diameters, cf.Table S3 †)-thick in the first analogue (Fig. 3) and 200 μm (3 grain diameters)-thick in the second (Fig. 4).
Displacement experiments.The experimental procedure employed to study the flow of immiscible fluids in these beds closely follows that presented previously for uniform beds. 16,17In short: syringe pumps are used to dispense fluids into the packed bed, and a high-speed 24 bit colour camera coupled to an optical microscope is used to capture the packed bed in a sequence of still images.The acquired images are converted to gray scale and segmented to determine the distribution of the fluids within the packed bed at a given instance.
The segmentation threshold is determined from the gray value histograms of two images during the waterflood: one at the onset of waterflood (e.g., red squares, Fig. 5) and one towards the end of the waterflood (blue circles).As waterflood progresses and water content in the packed bed increases, the frequencies of lower gray values (darker pixels) decrease and those of higher gray values (brighter pixels) increase.The between the two distributions, i.e., the lowest gray value whose frequency increases as waterflood progresses, is taken as the threshold (arrow, Fig. 5).Water saturation at a given instance is then given by the fraction of pixels within the region of interest with gray values larger than this threshold.Because refractive properties vary between different minerals (e.g., calcite generates double refractions) and with crystallographic orientation, a segmentation threshold is determined for each lamina separately.
The displacement sequence itself is designed to mimic that in the application of interest.The packed bed is first cleaned with a sequence of solvents that finishes with a solvent that can be easily solubilised by the primary phase.For model oil reservoirs, the primary phase is a brine representative of the water present in the reservoir prior to the invasion of oil.Next, a volume of the primary phase equivalent to 100 times the pore volume (pv) of the packed bed is flushed through the chip.The test oil is then injected into the packed bed to mimic buoyancy-driven oil invasion; a high flow rate is used to create back pressure to facilitate the establishment of a uniform oil saturation.The chip may then be left at elevated temperature ('aged') so that adsorption and other surface chemistry processes can reach equilibrium.Finally, an aqueous phase is dispensed to displace the oil in the packed bed to mimic waterflood oil recovery.
To demonstrate the impact of lamina-scale structure on oil distribution and recovery, waterflood experiments were undertaken on four packed beds: a uniform silica bed, a uniform orthoclase bed, and the two laminated siltstone analogues in Fig. 3 and 4, respectively (Table 1).The test oil was a topped (light components removed) medium crude oil.The aqueous phase was either 5.0 wt% NaCl, 1.0 wt% KCl in deionised water (hereafter referred to as synthetic brine) or coastal seawater; further details can be found in ESI.† The packed beds were aged at 45 °C for 40 minutes at initial oil saturation, after which they were allowed to cool to ambient temperature before water was injected at constant flow rate.§ Fig. 6 (top row) presents images captured at different stages of the waterflood for the two heterogeneous beds: (i) prior to water injection, (ii) after the injection of a moderate volume analogous to a mature oil field (1-2 pv), and (iii) after the injection of a greater pore volume (40 pv).
The contrast in flow behaviour between the two laminated beds is readily seen.Oil was displaced uniformly from the entire packed bed when the orthoclase-rich lamina was relatively thick (Fig. 6, left).In contrast, oil was preferentially recovered from the silica-rich regions of the packed bed when the orthoclase-rich region was thin.Indeed, the water saturation within the orthoclase-rich region increased only marginally to 25% after 30 pv of water injection (bottom row, right).
The observed differences may be attributed to differences in grain roughness and lamina thickness.Silica grains are both smooth and of uniform grain size (Fig. S3 †), so water tends to invade the pores uniformly, displacing oil from them.In contrast, the grooves on the rough orthoclase surfaces (Fig. S1 †) provide a pathway for water to flow through the orthoclase-rich lamina without displacing the oil in the bulk of the pore space.However, the permeability of these thin pathways is very low, so if the orthoclase-rich lamina is sufficiently long, the pressure gradient required to accommodate the imposed injection rate will drive the water into the centers of the pores, thereby displacing the oil in them and giving rise to a more efficient recovery.
The lamina-averaged water saturation (Fig. 6, bottom row) indicates that oil recovery from the main silica zone in the two laminated beds (cyan circles) were more efficient, with water saturation reaching 75% after 30 pv in both cases, than that from the uniform bed (blue solid line).This discrepancy highlights the influence of the orthoclase lamina on the upstream silica layer, and indicates that the impact of mineralogical discontinuities can extend upstream.This may have important implications not only for laminated rock but for other systems with capillary discontinuities, e.g., fractured reservoirs.
A further strength of the method is that the distribution of the fluids can be visualized at the pore scale and sub-pore scale.To illustrate, Fig. 7 presents a uniform bed of crushed marble, † our microfluidic analogue of carbonate rock, at the later stages of a waterflood.It can be seen that water has displaced the oil completely from the center of the large pore captured in the inset, while a small volume of oil remains as a thin film along the surface of the grains surrounding it.This observed pore-scale distribution is direct evidence that the grains have been rendered oil-wet from exposure to the oil.This conclusion is corroborated by pore-scale observations: the water preferentially invaded the largest pores first.The largest pores are associated with the lowest capillary entry pressure to the non-wetting phase, so this invasion pattern indicates that oil has become the wetting phase.Also, Table 1 Experimental conditions.Only the lengths of the dominant silica and orthoclase-rich laminae are reported below for the heterogeneous packs (cf.Fig. 3 and 4).The aqueous phase was synthetic brine for the uniform silica bed, and seawater for all others much of the oil remains connected even after tens of pv of water injection which, as discussed earlier, is a salient feature of mixed wet systems.Microscaled porous media experiments permit a wide range of geological variables to be investigated and mineralogical composition is clearly at the forefront of underinvestigated parameters.The experiments presented here illustrate that measurable differences in recovery result from not only global differences in wetting preference, but also from petrographic variables and factors such as the type of minerals involved and their architecture (e.g., lamination style).These findings highlight the importance of considering mineralogical heterogeneity when using microfluidic experiments to evaluate oil recovery.Packed beds assembled from key rock forming minerals are a novel tool for this purpose.
Fig. 2
Fig. 2 Assembly of a laminated packed bed.Grains are moved using gently pulsed flow (pulses are created by tapping the syringe plunger).Resolution is 2.4 μm per pixel.
Fig. 1
Fig.1Plan view of the microfluidic channel in which the packed bed is assembled.Fluids are dispensed from two ports on the right 14 or 18 mm upstream of the gap filter, and expelled from a single port on the left (not shown).
Fig. 4 A
Fig. 4 A second siltstone analogue: (a) photomosaic and (c) an interpretation of its mineralogy; (b) view of the feldspathic zone in cross polarised light (commonly used in petrography to identify different mineral components in rock and sediment) in which orthoclase exhibits bright birefringence colours but silica, which is glass-like, does not.
Fig. 5
Fig. 5 Histogram of gray values at the onset of waterflood (red square) and towards the end of the experiment (blue circle) in a region of interest; the dashed box demarcates the analyzed region in the corresponding raw images.Vertical arrow indicates the intersection of the two frequency distributions.Packed bed is the same as that shown in Fig. 3.
Fig. 6
Fig.6Selected raw images (top row) and lamina-averaged water saturation (bottom row) in the upstream silica-rich region (cyan solid circle) and the subsequent orthoclase-rich (red solid square) region during a waterflood experiment on the packed beds shown in Fig.3(left) and 4 (right).Superposed are mean water saturations in uniform beds of orthoclase (red dotted line) and silica (blue solid line).Vertical bars depict the difference between two regions (typically the two half-widths of the channel) within the lamina of interest.Flow is right to left in the images.
Lab Chip, 2016, 16, 4677-4681 | 4677 This journal is © The Royal Society of Chemistry 2016 a Dept.Geology and Petroleum Geology, University of Aberdeen, Aberdeen AB24 3UE, UK b School of Engineering, University of Aberdeen, Aberdeen AB24 3UE, UK. | 3,929.8 | 2016-11-29T00:00:00.000 | [
"Geology"
] |
Valuing Mobile Health: An Open-Ended Contingent Valuation Survey of a National Digital Health Program
Background Changing population demographics and technology developments have resulted in growing interest in the potential of consumer-facing digital health. In the United Kingdom, a £37 million (US $49 million) national digital health program delivering assisted living lifestyles at scale (dallas) aimed to deploy such technologies at scale. However, little is known about how consumers value such digital health opportunities. Objective This study explored consumers’ perspectives on the potential value of digital health technologies, particularly mobile health (mHealth), to promote well-being by examining their willingness-to-pay (WTP) for such health solutions. Methods A contingent valuation study involving a UK-wide survey that asked participants to report open-ended absolute and marginal WTP or willingness-to-accept for the gain or loss of a hypothetical mHealth app, Healthy Connections. Results A UK-representative cohort (n=1697) and a dallas-like (representative of dallas intervention communities) cohort (n=305) were surveyed. Positive absolute and marginal WTP valuations of the app were identified across both cohorts (absolute WTP: UK-representative cohort £196 or US $258 and dallas-like cohort £162 or US $214; marginal WTP: UK-representative cohort £160 or US $211 and dallas-like cohort £151 or US $199). Among both cohorts, there was a high prevalence of zeros for both the absolute WTP (UK-representative cohort: 467/1697, 27.52% and dallas-like cohort: 95/305, 31.15%) and marginal WTP (UK-representative cohort: 487/1697, 28.70% and dallas-like cohort: 99/305, 32.5%). In both cohorts, better general health, previous amount spent on health apps (UK-representative cohort 0.64, 95% CI 0.27 to 1.01; dallas-like cohort: 1.27, 95% CI 0.32 to 2.23), and age had a significant (P>.00) association with WTP (UK-representative cohort: −0.1, 95% CI −0.02 to −0.01; dallas-like cohort: −0.02, 95% CI −0.03 to −0.01), with younger participants willing to pay more for the app. In the UK-representative cohort, as expected, higher WTP was positively associated with income up to £30,000 or US $39,642 (0.21, 95% CI 0.14 to 0.4) and increased spending on existing phone and internet services (0.52, 95% CI 0.30 to 0.74). The amount spent on existing health apps was shown to be a positive indicator of WTP across cohorts, although the effect was marginal (UK-representative cohort 0.01, 95% CI 0.01 to 0.01; dallas-like cohort 0.01, 95% CI 0.01 to 0.02). Conclusions This study demonstrates that consumers value mHealth solutions that promote well-being, social connectivity, and health care control, but it is not universally embraced. For mHealth to achieve its potential, apps need to be tailored to user accessibility and health needs, and more understanding of what hinders frequent users of digital technologies and those with long-term conditions is required. This novel application of WTP in a digital health context demonstrates an economic argument for investing in upskilling the population to promote access and expedite uptake and utilization of such digital health and well-being apps.
Introduction Background
Globally, more than 50% of the world population owns a mobile device, rising to nearly 90% in the developed world [1]. Digital technology use is becoming integrated into our daily lives and clearly has potential to promote physical and psychological well-being [2]. Digital health is seen as having the potential to transform health care [3] at a time when changing population demographics and rising levels of chronic illness and multimorbidity (the presence of 2 or more long-term conditions) make change imperative [4]. However, this opportunity presents a number of challenges as developers must tackle a current underuse of readily available digital health innovations and there is a need for more evidence to aid understanding of what is of value to users [5]. In recent years, the United Kingdom has prioritized developing a digital health strategy to be implemented nationally [3,6]. A key driving force behind digital health is the need to move to more cost-effective health care delivery models, with the National Institute for Health and Care Excellence (NICE) announcing plans to develop a new digital health apps evaluation system to respond to the recent growth in digital health. Digital health, particularly mobile health (mHealth), refers to raising awareness of health information via mobile or wireless devices and has the potential to provide an alternative, less resource-intensive delivery of health to a changing population [7,8]. In their most recent communications report, Ofcom declared the United Kingdom to be a smartphone society, with more than 60% of the population owning a smartphone [9]. The number of mHealth apps continues to grow at an ever-increasing pace, with as many as 325,000 health apps available in 2017 and 78,000 new health apps added to major app stores in the last year [10]. However, existing studies have demonstrated the complex and highly variable nature of implementing successful well-being digital technologies and tools [11][12][13][14][15]. mHealth technology should be flexible and accessible for both users and practitioners [7]. Using digital devices also enables users to create platforms for support and self-management, providing opportunities for wider aspects of one's well-being to be improved. Looking beyond health to include nonhealth aspects of quality of life, such as one's sense of empowerment and ability to participate in community activities, has increasingly become a focal point of health service interventions [16,17]. Furthermore, NICE has emphasized the need for successful community engagement initiatives by health services to produce positive health gains and tackle health inequalities [18,19]. However, the personalization of digital health technologies and their focus on seeking to improve multiple broader aspects of health pose a number of challenges for economic evaluations in determining the value of their delivery and outcomes [20]. Issues include the need for wider measurement of costs and benefits as well as the handling of development costs [21].
In this paper, we present a contingent valuation (CV) willingness-to-pay (WTP) study for a hypothetical mHealth app that would deliver against 6 well-being outcomes alongside any other health services or treatments. The study examines the value the public places on improving broader well-being outcomes with mHealth. This was part of a wider program delivering assisted living lifestyles at scale (dallas). The dallas program launched in 2012 and funded by Innovate UK established 4 multiagency communities across the United Kingdom, who were to show "how independent living technologies, services and systems can be used to promote wellbeing, and provide integrated top quality health and care, enabling people to live independently" [22]. These communities worked in collaboration with a number of stakeholders, including health care services, industry, third sector voluntary organizations, and academic and government bodies, to explore how digital health can be delivered successfully for preventative care and to promote well-being across the United Kingdom [14]. Further details of the communities and their associated partnerships have previously been reported [14,23].
Existing Studies
Research on WTP for specific treatment or disease management using digital health technologies has been conducted but is still in its infancy. In Ireland, they have examined women's valuation of an integrated app and stand-alone app for postoperative monitoring post cesarean section [24]. WTP levels were considerably smaller than anticipated, and this was attributed to the participant's experiences of paying small amounts for mobile phone apps previously [24]. In Bangladesh, a country where health care is provided on a fee for service basis, WTP for mobile phone short message service text messaging to promote diabetes self-management was explored [25]. The researchers found that participants were generally willing to pay for the service and that those males with higher household income and higher levels of education reported higher WTP levels. However, research on WTP for mHealth apps looking at improving broader lifestyle well-being outcomes is currently an understudied area. This study seeks to build on previous studies such as that by Callan and O'Shea [18], which focused on determining societal values for different telecare solutions for older people. Their study demonstrates that there is a preference for developing supportive technologies, which seek to keep older people in their community, and that above telecare for physical or cognitive care needs, strongest preferences were for telecare that sought to improve user's social connections. This potential for mHealth as an individual's own tailored health service is further emphasized by researchers such as Klasnja and Pratt [24] who argue that if delivered in a sensitive and appropriate manner, mHealth could be effective in managing both specific diseases and general health while also enabling communities to support one another. This would allow virtual networks or communities of users with similar goals or location to connect to one another [26]. Reviews of mHealth interventions have demonstrated that few evaluations have captured data that allow for consideration of economic outcomes and overall effectiveness and cost-effectiveness of interventions [27][28][29][30][31]. The lack of standardization in the delivery of mHealth programs means that currently full societal outcomes are not being captured and decision makers cannot make fully informed decisions when comparing the cost-effectiveness of different programs [32]. The potential to understand the value the public places on aspects of broader well-being, lifestyle, or other measures of individual autonomy is important and a much-needed advance in evaluations of these types of person-centered digital health and wellness products and services. Indeed, guidelines for producing high-quality evidence of digital health programs have emphasized the need for appropriate analytical methodology that can capture these noncost-related outcomes [30,33].
Broader Lifestyle Outcomes (The 6Cs)
As the name of dallas explicitly highlights, the program from the outset had an emphasis on making a positive impact on citizens' lifestyles, moving away from a purely medical model.
As the dallas communities' implementation plans included specific targets on recruitment number, the program funder, Innovate UK, took steps to ensure that impact on lifestyles could also be objectively measured as part of the broader dallas initiatives' deployment. For this purpose, it proposed the use of 6 key concepts that could demonstrate commonality of purpose for the broader program regardless of the details of each of the many communities' interventions. These key concepts were called the 6Cs, namely, connectedness, control, choice, collaboration, community, and contribution. To achieve some degree of consensus on how these key concepts could be applied to each community implementation plan, a workshop was organized at the outset of the program by Innovate UK in June 2012 (Birmingham). Key representatives from the program funder, the 4 dallas communities, and the program evaluation team (ie, University of Glasgow) attended this workshop. During the workshop, a series of focus groups was undertaken to develop and iteratively refine a detailed mapping of how the 6Cs applied to each community's specific implementation plan [13,14,34]. Being provided with a suite of alternative apps to manage symptoms at home Choice in terms of products, services, and systems available to suit needs Choice Can share health data with others and contribute to forums to raise issues and share experiences Organizations and communities collaborating together to develop and deliver products, systems, and services Collaboration Can share to and link with Web-based and local communities through social media and can gain information about local community resources that might be helpful for individuals or their caregivers Individuals that are part of a community rather than living in isolation, connected to others with shared needs, interests, and aims Community By selecting their home location and their interest areas, individuals can receive alerts about local happenings and can also organize their own events or groups Individuals' ability to contribute to their local community
Contingent Valuation
CV is a form of stated preference methodology used to estimate welfare gains or losses. CV allows researchers to value nonmarket commodities [35]. In the absence of a market for a good, such as that occurring in publicly funded health care systems, surveys can be used to directly ask participants to report their WTP or willingness-to-accept (WTA) the gain or loss of a hypothetical good or service. Values elicited are then regarded as a value indicator and measure of the demand for the good [36]. This allows a direct valuation for the 6Cs, which could be used within a cost-benefit analysis (CBA). The application of WTP methodology can provide insights into what people value (or not) in future digital health services and, therefore, inform both commercial endeavors to provide what the market wants and will pay for and also the planning of health and care services in a future where health care will most certainly be supported by digital products. In this study, the approach provides an indication of people's valuation of a change in the 6Cs.
The study design was a self-complete, stated preference, open-ended WTP survey embedded within a questionnaire, which also asked respondents to self-report sociodemographic information, their general health status, and details of any existing health conditions as well as report their current app-and digital-device and services ownership and usage. Data were collected through the use of Web-based survey panels accessed through the survey host, ResearchNow. In exchange for completing surveys, members were offered e-currency (points). For a 10 minute survey, they receive approximately £0.50 (US $0.66). Panelists accrue this as e-currency and can exchange it for goods.
Sample
Data were collected from 2 cohorts of participants. First, ResearchNow contacted UK-based panel members to create a representative sample based on age, gender, and income demographics. Second, a subsample whose characteristics mirror those of dallas communities (a dallas-like sample) gave the opportunity to generate a WTP estimation for those citizens currently being targeted by dallas and similar National Health Service (NHS) initiatives.
Following guidance on optimal sample sizes for CV open-ended questions, it was predicted that a sample size of no less than 400 was required [37]. To undertake subgroup analyses by including a cohort dallas-like sample and to take into consideration the prevalence of multimorbidity in the UK population, advice was sought from a statistician and existing literature and the sample size was increased to approximately 2000 [4,38].
Contextual Information
Pivotal to the success and accuracy of valuations derived from CV studies is the development of realistic, plausible scenarios, which are then presented to individuals. Poorly designed, cognitively burdensome surveys, which respondents find unrealistic, can generate biased responses and can undermine the reliability of their WTP or WTA estimates [35,39]. Before completing the WTP task, respondents were presented with contextual information (see Multimedia Appendix 1).
Respondents were then presented with a hypothetical mHealth app called Healthy Connections that was designed to describe the broader lifestyle and well-being outcomes (the 6Cs) that were embedded as part of the dallas program, as described in Table 1.
Willingness-to-Pay Questions
A key consideration of a stated preference WTP study is the type of hypothetical payment vehicle used to generate monetary values. The payment vehicle must be realistic to avoid provoking a rejection of the task [40]. For the purpose of this study, a monthly subscription fee was used. Both absolute and marginal WTP questions were included [41]. An open-ended WTP question confirmed the participants' absolute WTP for access to the app and their marginal WTP. The absolute WTP question was framed with participants asked to consider their WTP in relation to what they currently pay to stay connected to others (ie, mobile broadband charges) and for health benefits (ie, mHealth apps or gym memberships). This was to ensure that WTP for the physical mHealth features was similar to that for the current mHealth and health service markets. However, the research team acknowledged that such framing could introduce bias into the WTP results by asking respondents to state a WTP linked to their current spending on similar health or digital services and would not fully capture the respondents' valuation of the health benefits of an improvement in their sense of the 6Cs. Therefore, the marginal WTP question asked participants to consider the maximum they would be willing to pay for improved levels of 6Cs from their current 6Cs' situation. Capturing both these results allows for the researchers to understand the value placed on the health improvement expected and the value for the product or service needed to produce these.
Sociodemographic and Economic Characteristics
Our hypothesis was that general health (complete physical, mental, and social well-being) and experiences of living with long-term health conditions were likely to affect valuations for the 6Cs and that participants' familiarity with mobile technology and mHealth apps may lead to a higher WTP for the Healthy Connections app. Respondents were asked to rate their overall general health and well-being from excellent to poor. When referring to long-term conditions, the examples of asthma, diabetes, cancer, psoriasis, lung disease, heart disease, and depression were provided to respondents to demonstrate the diversity of conditions they should consider when describing their own health. In addition, we hypothesized that younger users could have a higher WTP (more risk taking and more familiar with newer technologies); however, we acknowledged that this had to be balanced with the likelihood that their incomes will likely be lower. Finally, we expected an income effect, with those with higher incomes and with more disposable income reporting a higher WTP.
To examine these possible influences, questions on health (self-reported general health, long-term health conditions, and medication history); ownership of, and accessibility to, technologies (computers, smartphones, internet, previous health apps' history, and total monthly spending on technology); age; and total annual income were included in the survey.
Validity Testing: Pilot Survey
To test the face validity of the survey and the suitability of the open-ended question format, a soft pilot survey was conducted (n=52) before the main Web-based survey. From these results, we were able to test the validity of our survey and whether our open-ended WTP question format was suitable and understood by participants. No respondents were reported to have struggled with the task or were unable to complete.
Analysis
Stata/12SE software (Stata Corp)was used to analyze the data [42]. To estimate a demand function for the 6Cs and the mean WTP, linear regression analyses were used. The open-ended WTP was used as the continuous, dependent variable. Socioeconomic characteristics of the participants were used as predictor independent variables. This allowed for the opportunity to test and profile WTP. Furthermore, the pilot study data demonstrated the wide range of WTP responses and prevalence of zero responses. Zero valuations are common in this form of study as the good or service in question is a UK health app and would be part of the suite of NHS services, which are all free at point of use (covered by taxation), and thus, there would be an assumption that this mHealth app should not differ. Indeed, all apps on the NHS digital library are free for use. Thus, to reduce the large skew in the results and learning from the pilot study, the WTP values were converted into natural logarithms (LN) before running regressions with the main survey data. It should be noted that before taking the natural log, a value of 1 was added to WTP values to avoid the problem of 0 values. Thus, in each of the models presented, the dependent variable used was LN(WTP)=log(1+WTP). The same calculation was conducted for the marginal WTP values.
Ethics Approval and Consent to Participate
The survey and project received confirmation of University of Glasgow ethics approval (July 29, 2015).
Absolute and Marginal Willingness-to-Pay
Summary statistics of both cohorts' respondents' absolute WTP and marginal WTP are shown in Table 2. When compared with the WTP figures of the UK general population sample, dallas-like respondents reported lower mean WTP and marginal WTP than that estimated in the general population survey, whereas both samples' marginal WTP estimates had a range of £600 (US $793). Furthermore, among both cohorts, there was a high prevalence of zeros for both the absolute WTP (UK general population sample: 467/1697, 27.52% and dallas-like cohort: 95/305, 31.15%) and marginal WTP (UK-representative cohort: 487/1697, 28.70% and dallas-like cohort: 99/305, 32.5%) estimates. Table 3. The results illustrate that for the general UK population cohort, respondents who felt they disagree, were neutral, or agree to the statement that they feel connected to health care providers were more likely to pay more (P<.05) for the optimal scenario presented to them than the reference group (strongly disagree). Furthermore, feeling connected to social care services or providers was shown to act as a predictor of higher WTP. The dallas-like cohort demonstrated that the only potential predictor was the sense of control responses. Higher levels of control over health management acted as an inverse indicator of WTP as respondents (relative to the reference level of strongly disagree) were more likely to pay less for the improvement provided by Healthy Connections. Standard linear regression conducted and, therefore, coefficients show the difference between the variable category and "Strongly Disagree" as reference category. Strongly disagree P values are not applicable.
Sociodemographic and Economic Characteristics
Both cohorts indicated that respondents' age has a significant (P<.05) relationship with WTP (UK population cohort: −0.1, 95% CI −0.02 to −0.01; dallas-like cohort: −0.02, 95% CI −0.03 to −0.01), illustrating that younger respondents will pay more for the health connections app. In the general UK population cohort, relative to the reference level group (≤£14,999/US $19,819), £15,000 to £29,999 (US $19,821 to $39,641), income level acts as a significant, positive predictor of higher WTP (0.21, 95% CI 0.14 to 0.4). This is the theoretically expected result. However, this trend is not shown in the income earning brackets of £30,000 to £49,999 (US $39,642 to $66,069) or ≥£50,000 (≥US $66,070), and no relationship between income and WTP is estimated in the dallas-like cohort. Gender differences were statistically significant only in the dallas-like cohort where females had a lower WTP relative to the male reference level (−0.35, 95% CI −0.69 to −0.01). For both cohorts, general health was a positive predictor of WTP, with those respondents who describe themselves in better health being more likely to spend more for the Healthy Connections app.
However, only in the general UK population sample, there was a statistically significant positive relationship between regularly taking medication and higher WTP (0.16, 95% CI −0.01 to 0.32). This trend was not statistically significant in the dallas-like cohort, and neither cohort illustrated that long-term illness was a factor influencing WTP. These results suggest that individuals who are currently in better health value the mHealth app the most. The full analysis can be found in Multimedia Appendix 3.
In the general UK population cohort, higher WTP values were positively associated with current total monthly payments on phone, internet, and additional features (ie, app subscriptions), with respondents who reported they currently spent more on these services monthly stating larger WTP for the Healthy Connections app. Respondents who described themselves as having the internet yet never use it had a significant (P<.05), positive relationship with WTP (1.18, 95% CI 0.34 to 2.01) and were more likely to pay a higher amount than the reference group who have no access to the internet at home. In addition, those who have access to the internet at home and use it regularly demonstrated a negative association with WTP (−0.5, 95% CI −0.93 to −0.07) relative to the reference group. Finally, owning a computer but rarely using it acted as a statistically significant predictor of an inverse WTP (−0.5, 95% CI −0.95 to −0.05), paying less than those who do not own a computer. Results from the dallas-like cohort highlighted that owning a computer or smartphone, having regular access to the internet, and the total monthly payment for phones and internet usage (and additional features) were not indicators for higher WTP. For both cohorts, previous amount spent on health apps acted as a significant positive predictor of WTP, yet the effect was minimal (0.01). These linear regression results on familiarity and accessibility to mHealth and technology demonstrate that aside from the UK population cohort's positive association between current payments for phone, internet, and additional features and higher WTP, having access to a computer and internet is not a clear indicator of higher value and WTP for mHealth and was shown to be a negative indicator of WTP in the UK population cohort (see Multimedia Appendix 3 for further details).
Principal Findings
Drawing on data from 2 cohorts, we have demonstrated that both the general UK population and a cohort whose characteristics are similar to those already receiving a large-scale digital health program valued both the access to improved broader well-being (6Cs) and the development of an mHealth app such as Healthy Connections. This WTP study revealed a positive valuation of the 6Cs of £196 (US $258) per annum for the general UK population cohort's absolute WTP values and a value of £160 (US $211) for the marginal WTP (ie, to move participants from their current 6Cs' position to the highest level of 6Cs). In addition, the dallas-like cohort's absolute WTP valued the 6Cs mHealth app at £162 (US $214) and a value of £151 (US $200) for the marginal WTP. By incorporating questions about both these forms of WTP, we were able to evidence positive valuations for both the possibility of the improvement in their sense of each of the 6Cs' lifestyle components from their current 6Cs' experience (marginal WTP) and also for the value for the app itself (absolute WTP). Therefore, the study's results lend themselves to a wider evidence base than just mHealth apps and solutions and can demonstrate that investment in other activities or services, which seek to foster improvement in 6Cs lifestyle components, may also be a worthwhile investment in resource allocation.
Furthermore, the study illustrates that for the general UK population cohort, this WTP was positively affected by participants' existing sense of connection to social care services and having current connections to health care services or staff. Conversely, dallas-like respondents who felt they already had a sense of control in their health and well-being management demonstrated an inverse relationship to WTP. Such sensitivity to individual needs and preferences may represent a costly or time-consuming development process, yet these results further evidence the challenges associated with obtaining consistent, homogenous preferences from WTP surveys of digital health programs.
In addition, the valuations are based on the understanding that the Healthy Connections mHealth app was a generalizable (not disease specific) mHealth service suitable for the whole population. The research team envisaged that the 6Cs lifestyle components were aspects of health and well-being that could be valuable for all users, not just those currently suffering from an illness. The results highlighted that for both cohorts, better self-reported health was positively associated with WTP, and long-term illness was not a factor that influenced respondents' WTP, whereas regular medication was associated with higher WTP in the general UK population cohort. The lack of clarity on the relationship between a person's health, health behaviors, and WTP for an app such as Healthy Connections in the results suggest that the true value of an app such as Healthy Connections could be investigated further with a more detailed focus on types of health (physical and mental well-being) and disease types. The strength of this study is that it shows there is an inherent value for the 6Cs for multiple types of users with differing health needs and status and, thus, provides initial evidence of the need for further investigation of the role of mHealth to improve lifestyle. Examination of sociodemographic and economic factors and familiarity with mHealth technology demonstrated some user traits that may help inform future development of similar mHealth apps. Age was shown to act as a predictor of higher WTP in both cohorts, with younger respondents being willing to pay more for the app. Female respondents were shown to have a lower WTP than their male counterparts in the dallas-like cohort. Beyond higher current spending on digital devices and health apps as indicators of higher WTP, no clear trends were shown across internet, computer, or smartphone access and use. In fact, although the dallas-like cohort results showed no statistically significant trends, the general UK population results showed owning a home computer and using it rarely and being regular users of internet as negatively associated with WTP. This variability in the results highlights a clear need for more research on how type of digital platform or accessibility options may impact the success of mHealth apps and the investment in upskilling of users required. Importantly, it suggests that it is incorrect to assume that levels of access to smartphones or the internet can be used to reliably predict uptake of digital health services. Surprisingly, despite other cost indicators acting as indicators of WTP, an increase in total household income was not shown to have the expected significant trend on WTP. There was an increase in WTP, relative to the reference level of less than £14,999 (US $19,819); however, this was not significant beyond £15,000 to 29,999 (US $19,821 to $39,641). Such confounders suggest that although our study demonstrates that there is clear evidence to support the rationale for developing mHealth as a new supporting method for health care delivery, inherently their use or appropriateness may not be solely reliant on income but perhaps existing familiarity and acceptance for these forms of health-related technologies as a norm or part of daily routine.
Limitations
A limitation of the dallas evaluation is that impact on health and social care resource use was not captured. We can, however, compare our WTP results with both the cost of a dallas-type product and also the cost of the dallas program. The cost of an app can range from free to £1, £10s, and £100s [43], dependent on the type of app. The dallas program included costs of recruiting and reaching users and interoperability costs (ie, enabling work to integrate the apps with health records and social care systems). Further research would enable these WTP results to be used in a CBA framework [20]. To do this, longer-term follow-up would be required to capture impact on health and social care resource use and any potential cost-savings, for example, an attributable reduction in hospital admissions in addition to the cost of an app itself.
The open-ended WTP approach is typically associated with large values, skewed data, and zeros [44]. We have found this to be the case in this study; however, through the decision to capture data on both absolute and marginal WTP, we were able to mitigate the effect of anchoring bias. The study was able to determine value of both the development of mHealth apps and of users' improving their sense of the 6Cs [45].
Another limitation of this study is the UK context, an environment in which there is free universal access to health care. WTP might be quite different in a fee-paying environment, for example, the United States, where use of mHealth apps to avoid attending traditional health care professionals might be valued differently.
Researchers such as Klasnja and Pratt [24] have highlighted how advancements in mHealth technology could, if delivered in a sensitive and appropriate manner, not only be effective for solely specific disease management or general health improvement but could also leverage social networks and communities to support one another. This would allow virtual networks or communities of users with similar goals or location to connect to one another.
Conclusions
This study demonstrates that although consumers value mHealth solutions that promote well-being, social connectivity, and health care control, mHealth is not universally embraced, and more research is needed to understand the relationship between health status of the potential user and how to tailor an app such as Healthy Connections to suit their needs. Furthermore, the study evidences that accessibility and use of smartphones, internet, or computers do not equate to WTP for mHealth apps. For mHealth to achieve its potential, apps need to be tailored to the accessibility and health needs of the user and more understanding of what hinders the use or acceptability of mHealth apps to even the most frequent users of multiple digital technologies is required. A key challenge is how to engage people with long-term conditions to encourage uptake of mHealth apps. This novel application of WTP in a digital health context presents a compelling economic argument for further research and future investment in both improving the accessibility and, where necessary, upskilling the population to | 7,445.2 | 2019-01-01T00:00:00.000 | [
"Medicine",
"Economics",
"Computer Science"
] |
Accurate Sparse Recovery of Rayleigh Wave Characteristics Using Fast Analysis of Wave Speed (FAWS) Algorithm for Soft Soil Layers
: This paper presents a novel fast analysis of wave speed (FAWS) algorithm from the waveforms recorded by a random-spaced geophone array based on a compressive sensing (CS) platform. Rayleigh-type seismic surface wave testing is excited by a hammer source and conducted to develop the phase velocity characteristics of the subsoil layers in Shenyang Metro line 9. Data are filtered by a bandpass filter bank to pursue the dispersive profiles of phase velocity at various frequencies. The Rayleigh-type surface-wave dispersion curve for the soil layers at each frequency is conducted by the (cid:96) 1 -norm minimization algorithm of CS theory. The traditional frequency-wavenumber transform technique and in-site downhole observation are employed as the comparison of the proposed technique. The experimental results indicate the proposed FAWS algorithm has a good agreement with both the results of conventional even-spaced geophone array and the in-site measurements, which provides an effective and efficient way for accurate non-destructive evaluation of the surface wave dispersion curve of the soil.
Introduction
In recent decades, with rapid urban population growth, underground constructions which extend human activities into underground spaces have attracted increasing attention [1,2]. A metro system is a kind of underground construction in an urban region to perfect alternative transportation in order to overcome traffic congestion, road accidents and environmental pollution caused by vehicles in the modern international metropolis [2,3]. A metro project faces significant challenges of construction for the complex conditions, e.g., soft soil layers, interaction caused by the urban infrastructures, vibration issues, accidents during the construction phase, etc. Thus, the safety level and durability of metro construction are of critical importance [4]. The constant need to improve the operational safety of construction has driven the development of non-destructive evaluation techniques and in-site monitoring methods aimed at the ongoing assessment of the metro rail corridors and near-surface soil layers [5,6].
The most important step of the underground construction in geotechnical evaluation is in situ identification of soil properties. The soil is a kind of multiphase, particulate medium with complex mechanical profiles. The analysis of wave propagation is an essential tool for the identification of the elastic and dissipative characteristics of soil layers in dynamic conditions. The mechanical properties of the soil are obtained by analyzing dynamic problems as important parameters for site response evaluation, vibration control, earthquake engineering, etc. [3,7]. The compressional and shear waves propagating in the subsoil has been widely used for the evaluation for various purposes with a great number of techniques: seismic reflection and refraction technique, downhole testing, seismic tomography, surface wave detection technique and so on [8].
In recent decades, as a non-destructive in situ evaluation technique, the surface wave method has been attracting increasing attention from both geophysicists and geotechnical engineers. In the 1960s, after being introduced by seismologists, Jone [9] developed a prototype for the surface wave measurement system. Multiple stations were employed to estimate the characterizations of the subsurface of the Earth. Jongmans and Demanet [10] studied the surface wave technique for the evaluation of the dynamic parameters of the subsoil. Foti et al. [8] discussed the applications of various wave modes (Rayleigh wave, Stoneley wave, and Love wave) for real engineering problems.
Because of the complex mechanical properties of the subsoil, the shallow shear wave velocity is a function witnessed from the characteristics of the soil layers and the frequency of ground motion. To obtain the wave velocity map, an on-site surface wave method has been proposed to involve multiple geophones to acquire the ground motion signals for the benefit of non-intrusive testing, effectiveness, and reliable data. The multiple channel data will be analyzed by interpretation algorithms (such as, the two-receiver spectral analysis of surface wave (SASW) method [11] and the multichannel analysis of surface waves (MASW) method [12,13], etc.) to achieve an experimental multimode dispersive image.
In spite of the demonstration of accurate, high-resolution dispersion image, the application of a large number of geophones becomes a bottleneck to widespread use of the technique from the laboratory to large scalar engineering applications. Thus, in order to reduce the redundant geophones used in conventional measurements, this paper contributes to this objective by exploring a novel in-site technique based on compressive sensing (CS) to reduce the number of required geophone and measurements for the estimation of surface wave velocity of the subsoil. CS has been applied to recover the multimodal and dispersive properties of Lamb wave from observed data in the laboratory for analysis, reconstruction, and prediction of guided waves [14][15][16][17][18][19][20]. Jiang et al. applied CS to ultrasonic computerized tomography to reduce observation times for estimation of a steel tube slab structure [21,22]. This paper is organized as follows: Section 2 deals with the CS theoretical framework, wave field imaging, and the proposed fast analysis of the wave speed (FAWS) algorithm. Three actual experimental applications are implemented and analyzed in Section 3. Finally, conclusions and further developments are summarized in Section 4.
Materials and Methods
This section describes the process for constructing maps of local phase velocity estimates. The first part will introduce the compressive sensing methodology to apply a novel measurements strategy for evaluation. The second part will explain how the lower measurements approach to transfer the raw geophone data into local wave velocity estimates. The processing is performed with the optimized picking of the frequency-wavenumber spectral maxima by the 1 -norm minimization algorithm, which is then transformed to the dispersion curve of surface wave velocity.
Compressive Sensing Framework
Compressive sampling is a new theory of information acquisition proposed by Donoho [23], Candès [24] and Tao et al. [25,26]. The fundamental mathematical theory of compressive sensing (CS) states that if a real-valued, finite-length, one-dimensional, discrete-time signal x ∈ R N is S-sparse, i.e., only S (S N) components of x are non-zero, this signal can be exactly recovered from far fewer randomly chosen samples or linear measurements with an overwhelming probability. In addition, a compressible signal can also be treated as sparse if most of the transform coefficients are zeros or near zero in transform domains (e.g., Fourier, wavelet bases, spatial domain, etc.). CS is a theoretical framework that stands upon two pillars: sparsity and incoherence. Sparsity indicates that a signal's information content can be represented in terms of a proper basis. The proper basis which transfers a compressible signal into sparse is called a "sparsifying basis", Ψ ∈ R N×N , which can be expressed as: where x is the compressible signal, α is the transform coefficients vector with S nonzero elements (S-sparse) and Ψ is the sparsifying basis in a specific domain.
The general under-sampling measurements can be expressed as: where y ∈ R m is the measurement vector, Φ ∈ R m×N is the under-sampling linear measurement matrix (m < N), n represents the noise during the measuring process, and Θ = ΦΨ is defined as the final transfer matrix. The under-sampling measurement is the number of linear measurements y smaller than the number of unknown variables in compressible signal x. It is an ill-posed problem to estimate the unknown variables in x from few measurements y [27,28]. As we mentioned above, because the unknown signal x is compressible and sparse, the sparse vector α which contains information of signal x could be reconstructed by solving an 1 -norm optimization problem. In order to reconstruct the unknown compressible signal x, the second principle: incoherence is introduced due to its robustness in the presence of measurement noise [29]. Thus, the transfer matrix Θ is required to satisfy the following restricted isometry property (RIP) with an isometric constant δ smaller than unity [24]: where δ is the RIP constant which is defined as the smallest value that meets the requirement of Equation (3), v ∈ R N is all S-sparse vector. RIP constant δ is a parameter representing the character of the nearly orthogonal matrices operating on sparse vectors. δ ≈ 0 indicates that the transfer matrix is a nearly orthonormal matrix, while δ ≈ 1 indicates that the vectors in the transfer matrix Θ are redundant. Random selected matrices have been proven to meet the requirement of RIP [24], which guarantees that the CS problem can be reconstructed with an overwhelming probability. In addition, the sampling number should be larger than the required number m > µ·S· log(N/S) where µ is a constant (generally, µ = 4) dependent on the basis. Thus, as a random matrix (e.g., random Gaussian, Bernoulli and the partial Fourier matrix), it has the benefits of accurate reconstruction, good compatible with data, easy to apply, etc. Considering the noise, the sparsest solution is solved by the l 1 -norm optimization algorithm using a toolbox embedded in MATLAB (developed by M. Grant and S. P. Boyd, available at: http://cvxr.com/cvx/download/): where,α is the reconstructed transform coefficients vector, λ is the Lagrangian multiplier, · 1 is the 1 -norm and · 2 is the 2 -norm.
Wave Field Imaging
The speed of a Rayleigh wave propagating in the elastic Earth's surface is dispersive which means the velocity of the Rayleigh wave depends on its frequency. In addition, multiple modes of Rayleigh wave are involved at any frequency. Thus, it is difficult to analyze the real-world dataset with the interference of a multi-mode Rayleigh wave to obtain an accurate, high-resolution dispersion image.
A geophone array containing hundreds of geophones was used to pursue the wave speed and to distinguish the involved modes of Rayleigh wave for technicians and engineers (see in Figure 1).
In order to rapidly estimate the velocity of a surface wave from multiple channel data, a CS platform is proposed to improve the conventional geophone array assignment and analysis method. A randomly allocated geophone array is assigned in a line instead of the traditional uniformly spacing geophone linear array in this study. The signal measured by each geophone in the frequency domain is a sum of frequency dispersive modes of Rayleigh waves: where G j (ω) is the complex-valued amplitude of each wave mode, k j (ω) represents the real-valued frequency dependent wavenumber of each mode, ω represents the angular frequency, and r is the distance from the source to the received sensor. spacing geophone linear array in this study. The signal measured by each geophone in the frequency domain is a sum of frequency dispersive modes of Rayleigh waves: where is the complex-valued amplitude of each wave mode, represents the real-valued frequency dependent wavenumber of each mode, represents the angular frequency, and is the distance from the source to the received sensor.
where indicates the actual wavenumber in the Earth's surface, which contains the roots of total S modal Rayleigh wave of the wave equation.
Considering the randomly allocated geophone array of m geophones, the signal received by the geophone array is the superposition of all modal components of the Rayleigh waves: where is a × transfer matrix. In addition, the condition for the RIP is satisfied due to the random allocation of the geophone array. represents the solution to a discrete inverse problem and a discretized approximation of . For most frequency and wavenumber , , is zero based on the theoretical dispersion image and wave equation. Thus, its discretization is Based on the character of dispersion, for each mode j = 1, 2, 3,· · · , N, the complex-valued amplitude G j (ω) and wavenumber k j (ω) in Equation (5) are continuous functions of frequency ω and wavenumber κ in the Rayleigh wave equation: k j (ω) = κ for some j at special frequencies 0 otherwise (7) where κ indicates the actual wavenumber in the Earth's surface, which contains the roots of total S modal Rayleigh wave of the wave equation.
Considering the randomly allocated geophone array of m geophones, the signal received by the geophone array is the superposition of all modal components of the Rayleigh waves: where A is a m × N transfer matrix. In addition, the condition for the RIP is satisfied due to the random allocation of the geophone array. α(ω) represents the solution to a discrete inverse problem and a discretized approximation of G(ω). For most frequency ω and wavenumber k(ω), G(ω, k) is zero based on the theoretical dispersion image and wave equation. Thus, its discretization α(ω) is sparse as well. These imply that the acquired signal y(ω) could be recovered by chasing the sparse solution for α(ω) based on the CS theory from the underdetermined inverse problem: It is noted that G(ω) is a two-dimensional function across frequency and wavenumber, thus, a filter bank is proposed to estimate the dispersion image in the various frequency bands. The benefit of the filter bank is to solve Equation (10) in each certain narrow band to focus on the sparsest representation of the wavenumber (velocity) from measurements. The dispersion curves of the wavenumber (phase velocity) are obtained from one frequency range to another.
The filter bank is established by a family of bandpass filters which are used to separate the information according to their frequency components. Second-order bandpass filters with tuned frequencies are employed to assemble the bandpass filter bank to separate the information at various interested frequencies (see in Figure 2). The central frequency and the spacing are the most important parameters for the parallel bandpass filter bank. The basic bandpass transfer function of the filter is expressed as Equation (11): where s is the complex variable, ω is the angular frequency in rads −1 , that is, ω = 2π f , ω p is the central angular frequency, and Q p is the the quantity Q-factor of the filter; higher Q p produces narrower bandwidth.
The 3dB bandwidth of the bandpass filter is defined as: where ω BW is the bandwidth of the bandpass filter, ω +3dB and ω −3dB are the half-power frequencies, which are defined as: In summary, the proposed FAWS is divided into five steps to carry out for the on-site experimental testings: (1) preparing step, determining the detection range and the measurement number; (2) arrangement step, generating random Bernoulli matrix and allocating the geophones based on the random matrix; (3) acquiring step, generating surface wave and recording the raw data of the ground-motion waveforms by the ununiformed geophone array; (4) processing step, filtering the raw data by a narrow-bandpass filter bank to decompose and extract the information of the surface wave from the recorded data at various interested frequencies; (5) inversion step, computing the wavenumber or velocity of surface wave at each frequency and assembling the inversed information as the final dispersive mapping of the surface wave of the subsoil to evaluate its mechanical properties. Figure 3 shows a summary flow diagram that describes the transformation process in detail. the raw data by a narrow-bandpass filter bank to decompose and extract the information of the surface wave from the recorded data at various interested frequencies; (5) inversion step, computing the wavenumber or velocity of surface wave at each frequency and assembling the inversed information as the final dispersive mapping of the surface wave of the subsoil to evaluate its mechanical properties. Figure 3 shows a summary flow diagram that describes the transformation process in detail.
Results and Discussion
A real-world experiment was employed to study the effectiveness of the proposed FAWS algorithm.
The experiment was carried out on a station of the metro system for the city of Shenyang, Liaoning province, China. Olympic Metro Station is a transfer station of Shenyang metro line 9 and line 2 in the downtown of Shenyang city. The property of the super shallow buried soil layer should be tested on site to make sure the load-carrying capacity of the underground construction. The transfer station is oriented in a west-east direction as shown in Figure 4a. For metro line 2, the station was built in 2016, thus, a tunnel is constructed to connect the previous station (line 2) to the new one of metro line 9. To estimate the mechanical properties of the soil layer, a linear array of 50 geophones with the spacing of 0.5 m was used to acquire the site response of ground under the impact. The testing site is flat, free of obstacles, and of one-dimensional geometry. The total length of 25 m test array ran through the west-east direction of the metro line 9 before the construction of the new metro station, as shown in Figure 4a. The in-site testing were conducted in summer with daily temperature from 20 to 30 ℃.
A sledgehammer with a 4 kg weight was employed to excite the vertical ground motion. The impact source caused by the hammer blow is located at the offset distance of 0.5 m. The locations of the first and last geophones are 0.5 m and 25 m, respectively. The data were recorded by multiple geophones with 5 Hz resonant frequency and a digital geometrics seismography to save as a .dat file with a sampling frequency of 1000 Hz. The record length of the multiple channel data is 600 ms. A schematic of the experimental setup is shown in Figure 4b.
Results and Discussion
A real-world experiment was employed to study the effectiveness of the proposed FAWS algorithm.
The experiment was carried out on a station of the metro system for the city of Shenyang, Liaoning province, China. Olympic Metro Station is a transfer station of Shenyang metro line 9 and line 2 in the downtown of Shenyang city. The property of the super shallow buried soil layer should be tested on site to make sure the load-carrying capacity of the underground construction. The transfer station is oriented in a west-east direction as shown in Figure 4a. For metro line 2, the station was built in 2016, thus, a tunnel is constructed to connect the previous station (line 2) to the new one of metro line 9. To estimate the mechanical properties of the soil layer, a linear array of 50 geophones with the spacing of 0.5 m was used to acquire the site response of ground under the impact. The testing site is flat, free of obstacles, and of one-dimensional geometry. The total length of 25 m test array ran through the west-east direction of the metro line 9 before the construction of the new metro station, as shown in Figure 4a. The in-site testing were conducted in summer with daily temperature from 20 to 30 ℃.
A sledgehammer with a 4 kg weight was employed to excite the vertical ground motion. The impact source caused by the hammer blow is located at the offset distance of 0.5 m. The locations of the first and last geophones are 0.5 m and 25 m, respectively. The data were recorded by multiple geophones with 5 Hz resonant frequency and a digital geometrics seismography to save as a .dat file with a sampling frequency of 1000 Hz. The record length of the multiple channel data is 600 ms. A schematic of the experimental setup is shown in Figure 4b.
Results and Discussion
A real-world experiment was employed to study the effectiveness of the proposed FAWS algorithm. The experiment was carried out on a station of the metro system for the city of Shenyang, Liaoning province, China. Olympic Metro Station is a transfer station of Shenyang metro line 9 and line 2 in the downtown of Shenyang city. The property of the super shallow buried soil layer should be tested on site to make sure the load-carrying capacity of the underground construction. The transfer station is oriented in a west-east direction as shown in Figure 4a. For metro line 2, the station was built in 2016, thus, a tunnel is constructed to connect the previous station (line 2) to the new one of metro line 9. To estimate the mechanical properties of the soil layer, a linear array of 50 geophones with the spacing of 0.5 m was used to acquire the site response of ground under the impact. The testing site is flat, free of obstacles, and of one-dimensional geometry. The total length of 25 m test array ran through the west-east direction of the metro line 9 before the construction of the new metro station, as shown in Figure 4a. The in-site testing were conducted in summer with daily temperature from 20 to 30 • C.
A sledgehammer with a 4 kg weight was employed to excite the vertical ground motion. The impact source caused by the hammer blow is located at the offset distance of 0.5 m. The locations of the first and last geophones are 0.5 m and 25 m, respectively. The data were recorded by multiple geophones with 5 Hz resonant frequency and a digital geometrics seismography to save as a .dat file with a sampling frequency of 1000 Hz. The record length of the multiple channel data is 600 ms. A schematic of the experimental setup is shown in Figure 4b.
Conventional Even-Spaced Array Results
As a comparison, the data were sampled by regular geophones and stored without any filtering or filter bank. The raw data acquired with the impulsive sledgehammer source and the 50 vertical geophones are demonstrated in Figure 5a. In addition, the time-domain signal recorded by the number 10 geophone with a 5-m distance from the impact source was transformed to a timefrequency spectrogram using Gabor wavelet transform, as shown in Figure 5b. It is noted that the energy in the measured wave field concentrates in the frequency band of 40-80 Hz. (a)
Conventional Even-Spaced Array Results
As a comparison, the data were sampled by regular geophones and stored without any filtering or filter bank. The raw data acquired with the impulsive sledgehammer source and the 50 vertical geophones are demonstrated in Figure 5a. In addition, the time-domain signal recorded by the number 10 geophone with a 5-m distance from the impact source was transformed to a time-frequency spectrogram using Gabor wavelet transform, as shown in Figure 5b. It is noted that the energy in the measured wave field concentrates in the frequency band of 40-80 Hz.
Conventional Even-Spaced Array Results
As a comparison, the data were sampled by regular geophones and stored without any filtering or filter bank. The raw data acquired with the impulsive sledgehammer source and the 50 vertical geophones are demonstrated in Figure 5a. In addition, the time-domain signal recorded by the number 10 geophone with a 5-m distance from the impact source was transformed to a timefrequency spectrogram using Gabor wavelet transform, as shown in Figure 5b. It is noted that the energy in the measured wave field concentrates in the frequency band of 40-80 Hz.
(a) To address the dispersion curve of phase velocity of the near-surface earth, waveform analysis is processing using frequency-wavenumber transform (f-k transform) by two-dimensional fast Fourier transform (2D-FFT). This technique is extensively used for many near-surface applications as a full-waveform inversion approach. All the time-domain signals recorded by the even-spaced array were transformed to a wavenumber-frequency spectrogram and a dispersion image using 2D-FFT as a function of two variables: time and offset.
The reference wavenumber-frequency spectrogram of the conventional technique is obtained by applying 2D FFT on the even-space signals transferring them from the time domain into the frequency (f-) domain, from spatial domain (offset) into wavenumber (k-) domain. The transform of the multi-sensed surface wave data is aimed at identifying the wavenumber with the energy propagating at each frequency. The f-k transform provides an obvious image of the multiple modal propagations, as shown in Figure 6. The fundamental mode and the first higher mode could be clearly separated at the different dominant ranges. The resulting image represents the energy density as functions of the wavenumber: one wave mode is focused on 50 Hz with a wavenumber of 1 m , and the other one is around 60 Hz with a wavenumber of 2 m (Figure 6a). Similarly, the phase velocityfrequency image of the soil layers yields two main dispersion curves: one mode ranges between 150 to 200 m/s with a central frequency of 60 Hz, the other curve is about 400 m/s with 50 Hz frequency, as shown in Figure 6b. To address the dispersion curve of phase velocity of the near-surface earth, waveform analysis is processing using frequency-wavenumber transform (f-k transform) by two-dimensional fast Fourier transform (2D-FFT). This technique is extensively used for many near-surface applications as a full-waveform inversion approach. All the time-domain signals recorded by the even-spaced array were transformed to a wavenumber-frequency spectrogram and a dispersion image using 2D-FFT as a function of two variables: time and offset.
The reference wavenumber-frequency spectrogram of the conventional technique is obtained by applying 2D FFT on the even-space signals transferring them from the time domain into the frequency (f-) domain, from spatial domain (offset) into wavenumber (k-) domain. The transform of the multi-sensed surface wave data is aimed at identifying the wavenumber with the energy propagating at each frequency. The f-k transform provides an obvious image of the multiple modal propagations, as shown in Figure 6. The fundamental mode and the first higher mode could be clearly separated at the different dominant ranges. The resulting image represents the energy density as functions of the wavenumber: one wave mode is focused on 50 Hz with a wavenumber of 1 m −1 , and the other one is around 60 Hz with a wavenumber of 2 m −1 (Figure 6a). Similarly, the phase velocity-frequency image of the soil layers yields two main dispersion curves: one mode ranges between 150 to 200 m/s with a central frequency of 60 Hz, the other curve is about 400 m/s with 50 Hz frequency, as shown in Figure 6b. To address the dispersion curve of phase velocity of the near-surface earth, waveform analysis is processing using frequency-wavenumber transform (f-k transform) by two-dimensional fast Fourier transform (2D-FFT). This technique is extensively used for many near-surface applications as a full-waveform inversion approach. All the time-domain signals recorded by the even-spaced array were transformed to a wavenumber-frequency spectrogram and a dispersion image using 2D-FFT as a function of two variables: time and offset.
The reference wavenumber-frequency spectrogram of the conventional technique is obtained by applying 2D FFT on the even-space signals transferring them from the time domain into the frequency (f-) domain, from spatial domain (offset) into wavenumber (k-) domain. The transform of the multi-sensed surface wave data is aimed at identifying the wavenumber with the energy propagating at each frequency. The f-k transform provides an obvious image of the multiple modal propagations, as shown in Figure 6. The fundamental mode and the first higher mode could be clearly separated at the different dominant ranges. The resulting image represents the energy density as functions of the wavenumber: one wave mode is focused on 50 Hz with a wavenumber of 1 m , and the other one is around 60 Hz with a wavenumber of 2 m (Figure 6a). Similarly, the phase velocityfrequency image of the soil layers yields two main dispersion curves: one mode ranges between 150 to 200 m/s with a central frequency of 60 Hz, the other curve is about 400 m/s with 50 Hz frequency, as shown in Figure 6b.
Results of the Proposed Fast Analysis of Wave Speed (FAWS) Method
To validate the capability of the proposed FAWS method in the CS framework, geophones were randomly chosen to acquire the data based on the Bernoulli matrix. Figure 7a shows the random distribution of the active geophones. The total number of the geophones in the non-even-spaced array is 20 instead of 50 geophones in the whole 25-m measurement length. The locations of the activated geophones are randomly selected based on Bernoulli matrix as mentioned in the previous section. The black block represents a geophone at the corresponding location; by contrast, the white block means no geophone is arranged there. The bandwidth and the filter spacing of the bandpass filter bank is 0.5 Hz and 1 Hz, respectively. Thus, there are 98 filters in the desired range of 3 to 100 Hz.
Considering the impulsive wave propagation admits only a few modal wave number at each frequency in the dispersion image, the sparse f-k spectrogram is reconstructed based on the ℓ1-norm minimization algorithm of CS theory (Equation (10)). The reconstruction results are shown in Figure 7. The two modes can be obviously separated in the wavenumber-frequency spectrum. The reconstructed results are demonstrated in an image whose amplitudes is mapped by a white-red colortable: the higher magnitude, the darker red color. It can be seen the wavenumber-frequency spectrum have two peaks: one peak is observed at 50 Hz with the wavenumber of 1 m , the other is in the range of 50 Hz to 60 Hz with the wavenumber around 2 m , which are in good agreement with the conventional 2D-FFT algorithm.
Meanwhile, as shown in Figure 7c, the two dispersion curves of the phase velocity of surface wave are accurately identical in the whole range, which means the proposed method transform can be used to identify the properties of the two modes. Thus, in the application of Shenyang metro line 9, a total number of 20 geophones are random selected from 50 geophone space array for measuring the seismic wave to evaluate the mechanical properties of the soil. This proposed technique reduces the acquisition time to achieve high speed in characterization of the shallow subsurface by removing 60% of the Nyquist sampling grid. (a)
Results of the Proposed Fast Analysis of Wave Speed (FAWS) Method
To validate the capability of the proposed FAWS method in the CS framework, geophones were randomly chosen to acquire the data based on the Bernoulli matrix. Figure 7a shows the random distribution of the active geophones. The total number of the geophones in the non-even-spaced array is 20 instead of 50 geophones in the whole 25-m measurement length. The locations of the activated geophones are randomly selected based on Bernoulli matrix as mentioned in the previous section. The black block represents a geophone at the corresponding location; by contrast, the white block means no geophone is arranged there. The bandwidth and the filter spacing of the bandpass filter bank is 0.5 Hz and 1 Hz, respectively. Thus, there are 98 filters in the desired range of 3 to 100 Hz.
Considering the impulsive wave propagation admits only a few modal wave number at each frequency in the dispersion image, the sparse f-k spectrogram is reconstructed based on the 1 -norm minimization algorithm of CS theory (Equation (10)). The reconstruction results are shown in Figure 7. The two modes can be obviously separated in the wavenumber-frequency spectrum. The reconstructed results are demonstrated in an image whose amplitudes is mapped by a white-red colortable: the higher magnitude, the darker red color. It can be seen the wavenumber-frequency spectrum have two peaks: one peak is observed at 50 Hz with the wavenumber of 1 m −1 , the other is in the range of 50 Hz to 60 Hz with the wavenumber around 2 m −1 , which are in good agreement with the conventional 2D-FFT algorithm.
Meanwhile, as shown in Figure 7c, the two dispersion curves of the phase velocity of surface wave are accurately identical in the whole range, which means the proposed method transform can be used to identify the properties of the two modes. Thus, in the application of Shenyang metro line 9, a total number of 20 geophones are random selected from 50 geophone space array for measuring the seismic wave to evaluate the mechanical properties of the soil. This proposed technique reduces the acquisition time to achieve high speed in characterization of the shallow subsurface by removing 60% of the Nyquist sampling grid.
Results of the Proposed Fast Analysis of Wave Speed (FAWS) Method
To validate the capability of the proposed FAWS method in the CS framework, geophones were randomly chosen to acquire the data based on the Bernoulli matrix. Figure 7a shows the random distribution of the active geophones. The total number of the geophones in the non-even-spaced array is 20 instead of 50 geophones in the whole 25-m measurement length. The locations of the activated geophones are randomly selected based on Bernoulli matrix as mentioned in the previous section. The black block represents a geophone at the corresponding location; by contrast, the white block means no geophone is arranged there. The bandwidth and the filter spacing of the bandpass filter bank is 0.5 Hz and 1 Hz, respectively. Thus, there are 98 filters in the desired range of 3 to 100 Hz.
Considering the impulsive wave propagation admits only a few modal wave number at each frequency in the dispersion image, the sparse f-k spectrogram is reconstructed based on the ℓ1-norm minimization algorithm of CS theory (Equation (10)). The reconstruction results are shown in Figure 7. The two modes can be obviously separated in the wavenumber-frequency spectrum. The reconstructed results are demonstrated in an image whose amplitudes is mapped by a white-red colortable: the higher magnitude, the darker red color. It can be seen the wavenumber-frequency spectrum have two peaks: one peak is observed at 50 Hz with the wavenumber of 1 m , the other is in the range of 50 Hz to 60 Hz with the wavenumber around 2 m , which are in good agreement with the conventional 2D-FFT algorithm.
Meanwhile, as shown in Figure 7c, the two dispersion curves of the phase velocity of surface wave are accurately identical in the whole range, which means the proposed method transform can be used to identify the properties of the two modes. Thus, in the application of Shenyang metro line 9, a total number of 20 geophones are random selected from 50 geophone space array for measuring the seismic wave to evaluate the mechanical properties of the soil. This proposed technique reduces the acquisition time to achieve high speed in characterization of the shallow subsurface by removing 60% of the Nyquist sampling grid. (a)
In-Site Downhole Testing Results
In addition, the conventional in-site downhole testing method was also employed to directly obtain the measurements of compression (P-) and shear (S-) wave velocity as a comparison. Figure 8 shows the prepared borehole with a diameter of 127 mm for downhole testing according to the ASTM standard test method [30]. Four boreholes were drilled 15 m on the ground to put the downhole receivers. A 14-bit ADC measurement equipment (XG-1 type 3-axis receiver manufactured by Langfang Dadi corporation, Ltd. Langfang, China) was employed to acquire the wave velocities through a sampling frequency of 1000 Hz. After the 3-axis receiver were placed at the desired test locations in the downhole, the energy source is activated to generate ground motion, the waves were recorded three times by the receivers to improve the signal-to-noise ratio (SNR). The experimental results are listed in Table 1. There are 3 kinds of soil layers: topsoil layer, silt and clay layer, and sand layer with various depths at different locations. The S-wave velocities of the top two layers are identified in the ranges between 150 to 200 m/s, and the P-wave velocity is in the range of 400-500 m/s, as shown in Table 1. The results of in-site observation provide sufficient evidence to the surface wave identification methods for both the proposed FAWS method and the conventional even-spaced geophone array. As we can see, the results are in good agreement with the previous estimation results obtained by the proposed method. Considering the time-consuming drilling, complicated implement, and redundant observations, the proposed FAWS technique is an effective and efficient game-changing technique with accurate estimation of the wave velocities of soil properties in actual engineering applications.
In-Site Downhole Testing Results
In addition, the conventional in-site downhole testing method was also employed to directly obtain the measurements of compression (P-) and shear (S-) wave velocity as a comparison. Figure 8 shows the prepared borehole with a diameter of 127 mm for downhole testing according to the ASTM standard test method [30]. Four boreholes were drilled 15 m on the ground to put the downhole receivers. A 14-bit ADC measurement equipment (XG-1 type 3-axis receiver manufactured by Langfang Dadi corporation, Ltd. Langfang, China) was employed to acquire the wave velocities through a sampling frequency of 1000 Hz. After the 3-axis receiver were placed at the desired test locations in the downhole, the energy source is activated to generate ground motion, the waves were recorded three times by the receivers to improve the signal-to-noise ratio (SNR). The experimental results are listed in Table 1. There are 3 kinds of soil layers: topsoil layer, silt and clay layer, and sand layer with various depths at different locations. The S-wave velocities of the top two layers are identified in the ranges between 150 to 200 m/s, and the P-wave velocity is in the range of 400-500 m/s, as shown in Table 1. The results of in-site observation provide sufficient evidence to the surface wave identification methods for both the proposed FAWS method and the conventional even-spaced geophone array. As we can see, the results are in good agreement with the previous estimation results obtained by the proposed method. Considering the time-consuming drilling, complicated implement, and redundant observations, the proposed FAWS technique is an effective and efficient game-changing technique with accurate estimation of the wave velocities of soil properties in actual engineering applications.
Conclusions
In this study, an accurate FAWS algorithm is proposed based on compressive sensing theory. Fewer measurements of a random-spaced geophone array are needed to provide the desired dispersion curve of surface wave velocity for the non-destructive evaluation of the soil layers. In-site experimental testing is deployed in Shenyang metro line 9 to validate the capability of the proposed technique. A bandpass filter bank is introduced to reconstruct the multi-modal dispersion characters of wavenumber and surface wave velocities at various frequencies. According to the sparse features of the Rayleigh-type seismic surface wave of the Earth, an -norm optimization algorithm is employed to reconstruct the dispersion curve of the velocity and wavenumber-frequency spectrum.
As comparisons, both a conventional even-spaced geophone array and in-site downhole testing are carried out to evaluate the soils in Shenyang metro line 9 for the future construction. The dispersion curve identified by the FAWS method was picked up with a good agreement with the trend of the dispersion image of surface wave processed by the comparison technique. In addition, the experimental results indicate the proposed technique can identify both the wavenumberfrequency distribution and velocity-frequency image of the surface wave of subsoil with very good accuracy. Considering the measurements required are fewer than the traditional method, the proposed approach is a game-changing technique with the advantage of being low cost, rapid, and safe for the identification of the soil properties for both geotechnical research and engineering construction.
It should be emphasized that the FAWS technique has its own specific requirements and limitations, which might need comparisons and supplements from other in-situ testing for a complete, accurate evaluation of deeper soil properties.
In future work, the proposed technique requires additional study for the optimization of the arrangement of the geophones and the filter bank. In addition, the proposed in-situ FAWS technique
Conclusions
In this study, an accurate FAWS algorithm is proposed based on compressive sensing theory. Fewer measurements of a random-spaced geophone array are needed to provide the desired dispersion curve of surface wave velocity for the non-destructive evaluation of the soil layers. In-site experimental testing is deployed in Shenyang metro line 9 to validate the capability of the proposed technique. A bandpass filter bank is introduced to reconstruct the multi-modal dispersion characters of wavenumber and surface wave velocities at various frequencies. According to the sparse features of the Rayleigh-type seismic surface wave of the Earth, an l 1 -norm optimization algorithm is employed to reconstruct the dispersion curve of the velocity and wavenumber-frequency spectrum.
As comparisons, both a conventional even-spaced geophone array and in-site downhole testing are carried out to evaluate the soils in Shenyang metro line 9 for the future construction. The dispersion curve identified by the FAWS method was picked up with a good agreement with the trend of the dispersion image of surface wave processed by the comparison technique. In addition, the experimental results indicate the proposed technique can identify both the wavenumber-frequency distribution and velocity-frequency image of the surface wave of subsoil with very good accuracy. Considering the measurements required are fewer than the traditional method, the proposed approach is a game-changing technique with the advantage of being low cost, rapid, and safe for the identification of the soil properties for both geotechnical research and engineering construction.
It should be emphasized that the FAWS technique has its own specific requirements and limitations, which might need comparisons and supplements from other in-situ testing for a complete, accurate evaluation of deeper soil properties.
In future work, the proposed technique requires additional study for the optimization of the arrangement of the geophones and the filter bank. In addition, the proposed in-situ FAWS technique will be applied to evaluate the soil properties on a larger scale for both engineering applications and geophysical research. More efficient and powerful algorithms, e.g., orthogonal matching pursuit (OMP), CoSaMP, and subspace-pursuit (SP), will be investigated in future work. Also, the characteristics of deep soil layer properties will also be studied to pursue the tomography of the subsoil.
Author Contributions: Z.C., B.J. and W.W. conceived and designed the method; Z.C., B.J. and J.S. analyzed the data; Z.C. and W.W. wrote the paper.
Funding: This study is financially supported by the project supported by the Scientific Research Fund of Institute of Engineering Mechanics, China Earthquake Administration with grant No. 2018A01, key special project of national key R&D plan, international scientific and technological innovation cooperation with grant No. 2016YFE0105500, and natural science foundation of Heilongjiang province with grant No. QC2017037. | 9,730 | 2018-07-23T00:00:00.000 | [
"Geology"
] |
Immobilization of urease from Phaseolus vulgaris L. seeds using calcium alginate as a support matrix
. Exploration of urease from various sources continues because of its many industrial uses. This research aimed to isolate urease from kidney bean ( Phaseolus vulgaris L.) seed and immobilize it using a Ca-alginate support matrix and a trapping technique. Eight days were devoted to germinating kidney bean seeds to begin the investigation. Isolation of crude urease extract from kidney beans was carried out using phosphate buffer pH 7. It was then immobilized with Ca-alginate at different concentrations of Na-alginate and contact times The crude free and immobilized urease extract was further characterized including pH, temperature and stability of repeated use. The urease activity was determined using the Nessler method using a spectrophotometer. The results demonstrated that urease immobilization from kidney bean seeds with a Ca-alginate matrix was most effective at a concentration of 5% Na-alginate and a contact period of 60 minutes, yielding a value of 5.92 U/mL. The optimal pH of free and immobilized urease was 7 and 8, respectively, and temperatures of 35 and 40 °C, respectively. The immobilization of urease from kidney bean seeds using a Ca-alginate support matrix increased the stability of recurrent use by fivefold, while the relative urease activity remained at 52%.
INTRODUCTION
Urease is an enzyme that functions as a catalyst for the hydrolysis of urea into ammonia and carbon dioxide [1]. This enzyme is of the hydrolase class, a component of amidohydrolase [2]. Urease has been identified in bacteria, fungi, and plants that play a significant part in the natural nitrogen cycle [3]. Nuts contain high levels of protein so they can be used as a source of urease. Nut seeds that have been used as urease producers include peas (Pisum sativum L.) [2], Kayo beans (Cajanus cajan) [4], and long beans (Vigna unguiculata ssp sesquipedalis L.) [5]. Urease is an enzyme that plays a crucial function in nitrogen metabolism during plant germination [2].
Urease has been utilized as an antifungal [6], a method for detecting heavy metals in milk [7], and in industrial sewage treatment [2]. Due to the inclusion of an imported component, the price of urease stays high. Therefore, it is vital to obtain urease from readily available basic materials. Kidney bean (Phaseolus vulgaris L) seeds can be a source of urease due to their high protein content of 20 to 27% [8]. Furthermore, they belong to the same family as P. sativum L. and Vigna unguiculata ssp sesquipedalis L. This study used kidney bean seeds as a urease source to enhance their value.
The use of free enzymes as biocatalysts can usually only be used for one reaction. This issue can be remedied by immobilizing the enzyme [9]. Enzyme immobilization is the attachment of enzymes to an insoluble matrix in water. Immobilization can be done through several methods such as cross-linking, adsorption, and entrapping method [10]. Each technique has its benefits. This study used the entrapping method as its methodology. In the entrapping method, the enzyme does not bind to the matrix. Therefore, the enzyme's native structure and catalytic function are preserved [11] .
Ca-alginate was used as the immobilization matrix in this investigation. Ca-alginate immobilization has the advantages of forming a solid gel, being non-toxic, and inexpensive [3]. The purpose of the investigation was to isolate urease from kidney bean seeds. The crude *Corresponding Author<EMAIL_ADDRESS>extract produced was immobilized using Caalginate and then analyzed.
Instruments and Materials
The equipments and tools used in this research include centrifuge (Quantum), UV-Vis spectrophotometer (Shimadzu UV-1800 Spectrophotometer), pH meter (Hanna Instrument), incubator (Memmert), Scanning Electron Microscopy (JSM-6510LA) and analytical balance (Ohaus). This study utilized urea, acetic acid, commercial-grade Naalginate, CaCl2, Na2HPO4, NaH2PO4, H2SO4, Na-tungsten, and Nessler's reagent. All the chemicals used were of analytical grade and were acquired from Merck Chemical Company (Merck, Germany). The kidney bean seeds are used as the source of urease (Wage market, Purwokerto).
Isolation of urease from kidney bean seeds
The isolation of urease from kidney bean seeds began with germination and continued through the extraction procedure. Germination was accomplished as follows: kidney bean seeds were steeped in distilled water for six hours, then drained, placed in a plastic container with wet cotton, and then covered with plastic. Germination was performed in the dark at room temperature [12]. The resulting sprouts were harvested as follows: 10 grams of kidney bean sprouts were crushed using a mortar and pestle and cooled in the freezer, followed by adding 40 mL of phosphate buffer pH 7 at 4 °C. The solution was agitated with a stirrer for three hours until two layers, the filtrate and the precipitate, developed. The filtrate and precipitate were separated by using a muslin cloth. Fifteen minutes were spent centrifuging the resulting filtrate at 4 °C and 12,000 rpm. The supernatant obtained was an extract of crude urease. The crude extract was subsequently evaluated for urease activity using Nessler's technique and immobilized using a Ca-alginate matrix.
Free Urease Activity Examination [5] A sample tube containing 1.90 mL of a pH 7 phosphate buffer solution was filled with 1 mL of 1000 ppm urea. The sample tube was filled with 0.1 mL of urease solution, incubated for 15 minutes at 35 °C, and cooled. To inhibit the urease enzyme activity, 1 mL of 2/3 N H2SO4 was added to the sample solution in the test tube, followed by 1 mL of Na-Wolframate. The control test tube was filled with 2 mL of pH 7 phosphate buffer, followed by 1 mL of 2/3 N H2SO4 and 1 mL of Na-Wolframate. After 15 minutes of incubation at 35 °C, the solution was cooled. Then, 1 mL of urea at 1000 ppm was added to the control tube. The sample and control tubes were centrifuged for 15 minutes, after which the supernatant was collected. The 250 μL of Nessler's reagent was added to approximately 1.5 mL of each solution. The absorbance of the solution was then measured with a UV-Vis spectrophotometer at a maximum λ of 500 nm. Ammonium sulfate standard solutions with 20, 30, 40, 50, and 60 ppm were applied to determine the standard curve. By using the standard curve of ammonium sulfate, urease concentration was determined. One unit of urease activity (U) was defined as the amount of ammonia produced per minute for every 1 ppm of urea hydrolyzed by the urease in the sample.
Optimization of immobilized urease matrix Ca-alginate
The concentration of sodium alginate and the contact period between immobilized urease beads and CaCl2 solution were varied to optimize immobilized urease. Alginate beads are used to immobilize urease by entrapping it. The 4 mL of Na-alginate solution with varying concentrations of 2; 3; 4; 5; and 6% (w/v) in phosphate buffer pH 7 was combined with 1 mL of crude kidney bean urease extract and stirred at 4 °C using a magnetic stirrer. The resulting solution was dropped into 30 mL of 0.2 M CaCl2 solution. Before filtering, the produced beads were soaked for one hour in a 0.2 M CaCl2 solution. Bead pores were analyzed using SEM. The activity of beads was assessed, and the concentration of Na-alginate with the highest activity was used to immobilize urease under varying contact times of 20, 40, 60, 80, and 100 minutes.
Measurement of immobilized urease activity was carried out by taking as much as 5 mL of 1000 ppm urea substrate in a pH 7 buffer and then adding as many as beads of immobilized urease beads formed in one formulation. A duration of 15 minutes was then spent to incubate the solution at 35 o C. The Nessler method was used to determine the ammonia concentration in the supernatant after the filtered beads. The same procedure was performed as control by using beads devoid of urease.
Characterization of free urease and immobilized urease
The characterization of urease was conducted at various pH levels and incubation temperatures to identify the optimal conditions. The activity test was utilized to determine the optimal pH for free urease and immobilized urease activity. However, it was conducted at different pH levels for the urea substrate solution, including Immobilization of urease from Phaseolus vulgaris L. seeds using calcium alginate as a support matrix (Zusfahair, Dian Riana Ningsih, Amin Fatoni, Ely Setiawan) ___________________________________________________________________________________________________ pH 5, 6, 7, 8, and 9. The urease activity was measured at the optimal pH at several incubation temperatures ranging from 30, 35, 40, 45, and 50 °C. The characterization of immobilized urease also included repeated usage experiments. This experiment was repeated until it was observed that the relative urease activity dropped by approximately 50%. Under optimal conditions, the reaction was conducted. The reaction was terminated by filtering the beads via filter paper, and the beads were then reused for urea hydrolysis. On the initial use of the beads, the activity was set to 100%.
Enzyme isolation from kidney bean seeds
Germination is the initial stage in separating urease from kidney bean seeds. Germination is accomplished by soaking kidney bean seeds in water to absorb water into the plant tissue's cavities so that the plant tissue's cells become actively growing [13]. The soaked kidney bean seeds are then placed on moist cotton and kept in the dark to prevent sunshine from interfering with the auxin hormone's effectiveness. Auxin contributes to the growth and elongation of plant cells. The auxin concentration is more significant in the portion of the plant that is not exposed to light than the lit portion [14].
The activity test was carried out by measuring the amount of ammonia produced from the reaction of urea with urease from kidney bean seeds. The activity test was carried out using the Nessler method. The principle of measuring ammonia using the Nessler method is that Nessler's reagent (K2HgI4) when reacted with ammonia in an alkaline environment will form a colloidal dispersion with a yellowish brown color [HgOHg(NH2)I]. The intensity of the color that occurs is directly proportional to the concentration of ammonia present in the sample. The absorbance of the solution was measured using a UV-Vis spectrophotometer at 500 nm. The results of the urease activity test obtained a value of 11.84 U/mL. Figure 1 shows the activity test using Nessler method: a) blank (aquades) b) control (urea without the addition of enzymes) c) reaction of urea with urease. from kidney beans.
Ca-alginate matrix immobilization of urease Effect of alginate concentration on urease immobilization
Urease from kidney bean was immobilized by utilizing a trapping approach with an alginate matrix. Using a micropipette, urease was immobilized by dropping a mixture of Naalginate solution and urease enzyme into a 0.2 M CaCl2 solution. Ca-alginate beads subsequently formed, trapping the enzyme inside. The pores in the beads are formed as a result of cross-linking between the carboxyl anion (COO−) of guluronic acid in alginate and the bivalent cation Ca 2+ produced from CaCl2 ( Figure 2) [15].
Meanwhile, the test results of immobilized urease activity with variations in the Naalginate solution can be seen in Figure 3. Figure 3 demonstrates that the optimal concentration of Na-alginate was achieved at a concentration of 5% with an activity value of 4.74 U/mL. When the concentration of the Na-alginate solution was less than 5%, the pores of the produced beads were prominent, making it more straightforward for the trapped enzymes to escape the matrix, which resulted in low activity. If the concentration of the Na-alginate solution is above 5%, the pores of the beads formed will be more tightly packed, this is because the cross-links formed are also increasing so that the substrate diffusion process becomes inhibited and the product will Immobilization of urease from Phaseolus vulgaris L. seeds using calcium alginate as a support matrix (Zusfahair, Dian Riana Ningsih, Amin Fatoni, Ely Setiawan) ___________________________________________________________________________________________________ be difficult to form so that its activity decreases [3].
Effect of contact times on urease immobilization
The effect of contact time on urease activity can be seen in Figure 4. As presented in Figure 4, the optimal contact duration was 60 minutes, with an activity level of 5.92 U/mL. A lack of urease activity resulted from beads coming into contact with CaCl2 before the optimal time. Ca-alginate beads can only form on the surface. Bead formation would continue in the deep section until the optimal contact time, at which point the beads would be homogeneous and solid. After exceeding the optimum contact time, the activity of the urease beads decreased because the enzyme was exposed to Ca metal for a more extended period, thereby denatured [11].
Effect of pH on enzyme activity
The study results on the effect of pH on urease activity can be seen in Figure 5. The optimal pH for free urease is pH 7, with an activity value of 15.45 U/mL. In contrast, the optimal pH for immobilized urease is pH 8, with an activity value of 6.68 U/mL, as shown in Figure 5. Under low pH conditions, the enzyme would undergo protonation and lose its negative charge. Under high pH conditions, the substrate would undergo ionization and lose its positive charge, making the formation of the enzymesubstrate complex more challenging. The enzyme can be denatured if the pH conditions are excessively high or low. At the optimal pH, the conformation of the enzyme's active site corresponds to the shape of its substrate [16]. The difference between the optimal pH for free urease and immobilized urease is that, after immobilization, the supporting matrix would influence changes in environmental conditions [17].
Effect of temperature on the activity of urease
The research results on the effect of temperature on urease activity can be seen in Figure 6. Figure 6 shows that the optimal temperature difference between free urease and immobilized urease is 35 °C and 40 °C, with 17,18 U/mL and 7.25 U/mL. The interaction of the enzyme structure with the immobilization matrix led to the formation of secondary and tertiary hydrophobic interactions, resulting in a change in the enzyme's conformation. It necessitates higher temperatures to attain the proper conformation for optimal activity [17]. The support matrix can absorb a certain amount of heat and prevent the denaturation of the enzymes. It may increase the optimal temperature of immobilized urease. The majority of industrial applications of enzymes are carried out at room temperature or higher Immobilization of urease from Phaseolus vulgaris L. seeds using calcium alginate as a support matrix (Zusfahair,
temperatures.
Typically, immobilization increases the enzyme's resistance to higher temperatures, making the immobilized enzyme more valuable and cost-effective in the industry [18].
Effect of repeated use of immobilized enzymes
With optimal bead conditions, repeated use of immobilized urease was conducted. At the end of the activity test reaction, the immobilized enzyme was collected by filtration using filter paper, washed with buffer, and added back into the new substrate to start a new cycle. The results can be seen in Figure 7. Figure 7 shows that urease beads can be reused up to five times with a 52% relative residual activity. Reduced activity after repeated use because the beads become very brittle and the surface of the beads is harmed, causing the enzymes to become inactive and consequently reducing their activity. Immobilized urease from chickpea with alginate maintained 60% of its initial activity at the end of five cycles [19]. Immobilized urease from jack bean using alginate can also be used up to 5 times with an activity of about 40% [20] CONCLUSION Kidney bean seeds' urease activity was significantly affected by the concentration of Na-alginate and the contact time between immobilized beads and CaCl2. The obtained beads can be reused up to five times with a remaining activity of 52%. | 3,641.4 | 2022-10-31T00:00:00.000 | [
"Materials Science",
"Environmental Science"
] |
ANSWERS TOOLS FOR UNCERTAINTY QUANTIFICATION AND VALIDATION
ANSWERS is developing a set of uncertainty quantification (UQ) tools for use with its major physics codes: WIMS/PANTHER (reactor physics), MONK (criticality and reactor physics) and MCBEND (shielding and dosimetry). The Visual Workshop integrated development environment allows the user to construct and edit code inputs, launch calculations, postprocess results and produce graphs, and recently uncertainty quantification and optimisation tools have been added. Prior uncertainties due to uncertainties in nuclear data or manufacturing tolerances can be estimated using the sampling method or using the sensitivity options in the physics codes combined with appropriate covariance matrices. To aid the user in the choice of appropriate validation experiments, the MONK categorisation scheme and/or a similarity index can be used. An interactive viewer has been developed which allows the user to search through, and browse details of, over 2,000 MONK validation experiments that have been analysed from the ICSBEP and IRPhE validation sets. A Bayesian updating approach is used to assimilate the measured data with the calculated results. It is shown how this process can be used to reduce bias in calculated results and reduce the calculated uncertainty on those results. This process is illustrated by application to a PWR fuel assembly.
INTRODUCTION
When calculating best estimate reactor parameters of interest it is not only important to provide an accurate estimated value of a given parameter, but also to provide a reliable estimate of the uncertainty on that estimated value. The move in recent years from pessimistic estimates to BEPU (best estimate plus uncertainty) requires the use of sophisticated tools for uncertainty quantification (UQ) [1]. The aim of an ongoing strand of ANSWERS [2] development work is to establish UQ tools for use with the major ANSWERS' physics codes, including: WIMS/PANTHER (reactor physics), MONK (criticality and reactor physics) and MCBEND (shielding and dosimetry). For some years ANSWERS has been developing Visual Workshop, an Integrated Development Environment to accompany the physics codes. This allows the user to construct and edit code inputs, launch calculations, post-process results and produce graphs, and recently uncertainty quantification and optimisation tools have been added.
Initial UQ tool development focused on the sampling method in which the user can specify statistical distributions rather than numerical values for user-specified input parameters [3]. We have also produced sampled nuclear data libraries in which the data on the evaluated nuclear data files are selected from statistical distributions, rather than using the reported central values. Monte Carlo sampling or Latin hypercube sampling can be chosen by the user. Additionally, capabilities have been included in the physics codes to calculate sensitivities which can be combined with a covariance matrix for the input parameters as an alternative way of undertaking UQ. These methods are described and results for a PWR fuel assembly are presented.
The above approaches do not account for evidence obtained from plant measurements or validation experiments, which can be used to refine best estimate values for parameters and their uncertainties. When using validation data, a major concern is what constitutes appropriate data. Two main tools are provided to aid the user in the choice of appropriate experiments: the MONK categorisation scheme (see ref [4] for details) and a similarity index described in Section 5. To aid this an interactive viewer has been developed which allows the user to search through details of roughly 2,000 MONK validation experiments that have been analysed from the ICSBEP and IRPhE validation sets.
ANSWERS has investigated a number of methods for combining plant calculations and validation data including: data assimilation, Bayesian updating, maximum likelihood estimation and extreme value theory. In this paper we concentrate on the Bayesian updating approach and describe how this is implemented in ANSWERS software. It is shown how this process can be used to reduce bias in calculated results and reduce the uncertainty on the estimated quantities. This process is illustrated by application to a PWR fuel assembly.
VISUAL WORKSHOP
Visual Workshop is the ANSWERS' IDE (integrated development environment) for preparing and verifying models, launching calculations, post-processing results and graphical display, see Figure 1. It is designed to work with ANSWERS' physics codes, including WIMS, MONK ® , MCBEND and RANKERN. Visual Workshop also contains tools to help the user undertake uncertainty analyses with ANSWERS' codes, as described in Sections 3 to 6 below.
SAMPLING TOOL FOR UNCERTAINTY QUANTIFICATION
Tools have also been implemented in Visual Workshop for uncertainty quantification and optimization [5]. A sampling methodology is available for estimating prior uncertainties, by running a number of calculations in which uncertain input parameters are varied by choosing values from user-specified distributions; Monte Carlo, stratified and Latin hypercube sampling options are currently available [3]. Wilks method [6] is also available for user-defined probability and confidence levels [3]. Figure 2 shows an example input for the sampling tool, for estimating prior uncertainties due to uncertainties arising from manufacturing tolerances (geometry, composition and density). In this simple, illustrative example, a 19 x 19 UO2 fuel assembly partially immersed in water is investigated. The uncertainty in the calculated value of k-effective (using MONK's "K(THREE)" estimator) arising from uncertainties in fuel enrichment, fuel density, length of fuel pins, pitch of the fuel pins, fuel pellet diameter and clad thickness, is estimated. This is achieved by sampling the uncertain parameters from normal distributions in this instance; truncated-normal, uniform and beta distributions are also available. Only five sampled calculations are requested in order to keep the output to manageable proportions for display in Figure From the output it is a simple matter to estimate the mean and standard deviation and such basic statistics are saved in the runref.statistics.csv file.
The nuclear data used by the codes are themselves subject to uncertainty. The values of the cross-sections etc. in the evaluated nuclear data files, such as the JEFF, ENDF/B, CENDL and JENDL series of evaluations, are provided with uncertainties by the evaluators. The cross-sections etc. must be processed to produce the continuous energy (BINGO) nuclear data libraries required by the MONK and MCBEND Monte Carlo codes and also to produce the multigroup libraries required by WIMS/PANTHER. In order to propagate the evaluated nuclear data uncertainties through the physics calculations, sets of nuclear data libraries have been produced in which the evaluated parameters are drawn from statistical distributions chosen to represent the nominal values and their associated uncertainties. These are processed into sets of sampled BINGO and WIMS libraries as described in [5]. Sets of 25, 60 and 120 Latin hypercube sampled libraries have been produced. In addition a set of 1,000 Monte Carlo sampled libraries has been generated in the WIMS energy group scheme as a reference set. These libraries can be chosen for use with the UQ calculations to allow the uncertainty resulting from nuclear data to be evaluated. The sampled libraries can also be used in combination with variations in the geometric and compositional data to estimate the total uncertainty [3].
VALIDATION DATABASE VIEWER
Once the prior uncertainty has been estimated the next task is to choose measured data for validation. Here "validation" is defined to be the process by which measured data are combined with calculated results to refine the calculated values for parameters of interest; i.e. to remove calculation bias and update the estimated uncertainty. At the time of writing, the ANSWERS' criticality database contains 828 Tier 1 (independently checked) experimental configurations and 1205 Tier 2 (self checked) configurations for use with the MONK reactor physics and criticality code, see ref [5] for more details. The Tier 1 and 2 validation cases are displayed in Figure 3 To assist with the choice of measured data for MONK analysis, a validation database viewer has been implemented in Visual Workshop. The viewer allows the user to search and browse the Tier 1 and 2 cases in the MONK validation database, and click on individual cases to display details, as shown in Figure 4. This gives a value that indicates how similar the nuclear data sensitivities of systems B and S are, that essentially ranges from 0 (no similarity) to 1 (complete similarity). A Similarity Index tool evaluates the similarity indices for each of the validation experiments appropriate to the chosen application and displays the results in descending order of magnitude.
Figure 5. Screen Shot from the Similarity Index Tool
An example is shown in Figure 5. In this case, the top 20 matches all have ESUM similarity indices between 0.94 and 0.95. (Also given are the total sensitivity and two quantities, AVALS and DSUM, associated with an alternative similarity measure not discussed here.)
VALIDATION
A number of methods are being made available within Visual Workshop to combine the measured data with the calculated results to improve the estimated value of keffective and its uncertainty. The UK Working Party on Criticality (WPC) produced a summary of general techniques available to derive the safety criterion used in criticality assessments [8],including (where EPD = error in physical data and USL = upper sub-critical limit): EPD -standard error method; EPD -standard deviation method; Systematic bias and uncertainty -subtraction; Systematic bias and uncertainty -addition; USL method 1 -H to fissile material ratio; USL method 1 -mean log of exponential energy of neutrons causing fission (MLENCF); USL method 1 -mean log of exponential energy of neutrons causing capture (MLENCC).
In addition, a Bayesian updating scheme is available based on the method discussed in ref [9] and also the generalized linear least squares (GLLS) method described below. The estimated bias for application case α, kα,bias, is given by (using the Einstein summation convention over repeated suffices): where , is the sensitivity of the application (α), experiment (ε), respectively to nuclear data item i, is the nuclear data covariance matrix, is the covariance between experiments ε and δ resulting from uncertainties in dimensions and compositions etc. and (∆ )/ is the relative code bias for experiment δ.
The posterior uncertainty, , , is related to the prior uncertainty, , , by:
EXAMPLE CALCULATION
An example calculation has been performed for a GBC-32 flask holding PWR fuel elements with a burnup of 45 GWd/te and five years of cooling; actinide only compositions were transferred from the reactor to the flask using the COWL material transfer facility in MONK [10]. The similarity to 1967 experimental configurations was evaluated and those with similarity index > 0.78 were chosen, giving 175 experiments for consideration. The prior uncertainty was estimated using the sensitivity matrix and the nuclear data covariance matrix ( ). The MONK calculations were run using 5,000 superhistories per stage with a target standard deviation of 0.0002 on keffective.
The results of the GLLS analysis are displayed in Table I. Note that the use of the experimental data has more than halved the estimated uncertainty on the calculated result. Also the bias corrected value of keffective plus three standard deviations is less than 0.95. Note, however, that the correlation between experiments within an experimental series has been neglected. Estimating such correlations is a complex and time-consuming process. A way to approach this is described in [11,12]. A simple approach to get around this is discussed below. Note that, although the posterior estimate of keffective is higher than the prior estimate, the posterior estimate of keffective plus three standard deviations is lower than the prior estimate. For comparison, results for two of the methods listed in Section 6 are displayed in Table II. Both of the methods indicate that the maximum allowable value for the prior keffective is less than the value of 0.9241 arrived at above. Hence the operation would be not be considered safe despite the GLLS analysis indicating that the posterior best estimate value of keffective is nearly nine standard deviations below 0.95. Neglecting correlations in the uncertainties of experiments in a single series can lead to an underestimate of the uncertainty. One way to address this is to use only a single experiment from each series. In this case the experiment with the highest similarity index was chosen from each series. This reduced the number of experimental configurations used to 13. The results of the revised analysis are shown in Table III. Again the use of the experimental data leads to a significant reduction in the estimated uncertainty. In this case 0.95 is more than seven standard deviations above the posterior best estimate value for keffective.. Although the posterior estimate of keffective is higher than the prior estimate, the posterior estimate of keffective plus three standard deviations is again lower than the prior estimate. For comparison, results for two of the methods listed in Section 6 are displayed in Table IV. In this case use of the EPD methods would again indicate that the operation is not safe, but the USL method would suggest that it is safe. This illustrates some of the issues associated with establishing safe critical limits, but also shows that the ANSWERS tools available for uncertainty analysis can greatly assist in providing increased confidence, or when used carefully could potentially support a less conservative approach.
CONCLUSIONS
ANSWERS is developing a coherent set of tools to aid the user in the estimation of uncertainty on predicted values. The tools are implemented in the Visual Workshop IDE so that they are available for use with ANSWERS' WIMS/PANTHER, MONK and MCBEND physics codes. The tools have been applied to the criticality safety of irradiated PWR fuel elements in a flask. More traditional approaches are compared to the best estimate plus uncertainty (BEPU) approach. The BEPU approach is shown to provide a higher degree of confidence in the criticality safety of the configuration studied. | 3,162.6 | 2021-01-01T00:00:00.000 | [
"Physics"
] |
POSSIBILITIES OF LOGISTICS POLICY IMPROVEMENT
The paper presents the strategic logistics management with emphasis on clear, accurate and effective material flow from the suppliers and internally, as well as an outline of the logistics policy for continuous improvement. The implementation of a complete Supplier Logistics Performance System is essential to support internal processes efficiency and establish a continuous improvement system according to the main logistics policy. Every company should consider such a system in order to win in the challenging field of current industry.
INTRODUCTION
Public policies aim to create an operating environment that fosters the competitiveness of trade and industry.Regulation is the necessary part of mixed economies in logistics supply chains but it must be intelligent and further development.The harmonisation of policies and regulations and the investments into infrastructure are preconditions for eliminating the barriers of common market.
Logistics policy is an essential document in a company.It should be focused on the main topics which lead to the best stock management, reliable supplies and accurate material flow at the lowest expenses.
One segment of the problem in logistics companies is the absence of logistics agreement on the actual problem causing that nobody is responsible for negotiating logistics conditions and lack of integration between supplier and manufacturing procurement.
To establish a competitive condition in a plant and among suppliers, it is essential to build up a consistent assessment system to allow benchmarking and strong management.For this purpose it is necessary to create a fixed logistics policy which also provides a solution for regular evaluation.A group of powerful indicators should act as a measurement tool.
LOGISTICS POLICY IN THE FUNCTION OF LOGISTICS CONTINUOUS IMPROVEMENT SYSTEM
The objective of the Logistics Policy in the function of Logistics Continuous Improvement System is to provide high quality service to customers, to integrate suppliers in logistics processes in order to pull flows and reduce lead time and to optimize logistics processes with reduction of costs and increased reactivity.
This system is based on three tools: common improvement system for all facilities; common language for all our logistics people: GLOBAL MMOG/LE (global MMOG/LE is a continuous improvement and self-assessment tool with a format aligned with ISO/TS 16949:2002 to provide automotive suppliers with a means to measure and streamline their material planning and logistics processes); common structure to share and to define best practices: working group meetings.Logistics policy is the essential document in a company.It should be focused on the main topics which lead to best stock management, reliable supplies and accurate material flow at the lowest expenses.The manufacturing companies generally use four times larger space, twice more human resources and ten times more time than they really need [6].The management should always be able to see opportunities for cost reduction and quality improvement and take all the possible steps to bring them alive.
The Logistics Policy shall be built on: -respect of customer requirements through systematization of self-assessment of logistics processes, -transparency through a procurement strategy based on supplier partnership, -professionalism through skilled logistics people, -trust through a performing and reliable information system, -ambition through the optimization of Physical Logistics Flows, -profitability through the control and optimization of production capacity.
To achieve the goals mentioned above, it is necessary to involve the suppliers using a Supplier Logistics Performance System which consists of implementing of several tools and concepts (Figure 1).
Diagnosis of the procurement system using logistics global MMOG
The starting step of logistics performance system implementation should be focused on self-assessment.This is an opportunity to find any non-conformance or non-standard processes in the company (Figure 2).
Self-assessment will enable: -identification of the lack of performance in procurement process, -inadequate stock level, -inadequate packaging, -heavy receipt control procedure, -poor inventory accuracy.
Logistics agreement implementation
The logistics agreement is an essential document between the supplier and the customer defining the basic requirements such as delivery condition, packaging condition, communication escalation opening windows, etc.The logistics agreement implementation can be done in three steps (Table 1).
A few issues can be met during the implementation phase:
Making the Logistics agreement a dynamic process
A logistics agreement is efficient if it is not only a "law table", but a real tool to manage the day-to-day issues and to optimize the logistics.The key to success is responsibilization of all actors with the ability to have a multi-level agreement (global level, site level, reference level).
Electronic Data Interchange (EDI or XML data interchange) implementation
The next step of the logistics performance system implementation is data interchange system implementation.Electronic data interchange is the organization-to-organization, computer-to-computer exchange of business data in a structured, machine-processable format.The purpose of EDI is to eliminate duplicate data entry and to improve the speed and accuracy of the information flow by linking computer applications between companies.The system should enable a quick and accurate exchange of forecast and material order data with each supplier.
There are three basic keys of success during EDI implementation: 1. Use of standard messages and automotive certified solutions (WebEDI).
To go faster, to mutualize cost for suppliers and to make the message mapping easier.2. Develop an internal culture of EDI.
EDI has an important impact on part controller practices; involvement of the purchasing department is required.3. Implement message per message with a test period.Each message must be tested previously with a few suppliers.
Logistics Key Performance Indicators (LKPI) Implementation
Introduction of LKPI is essential for the improvement activity, and it is a standardized tool for measurement of the main characteristics and timely evaluation.The standardized characteristics enable benchmarking activity among all suppliers thus challenging the conditions for their improvement.Six basic LKPIs are proposed as an evaluation basis: The implementation of LKPI with suppliers enables the achievement of Logistics objectives.
Example of benefits by LKPI implementation: improving the supplier delivery accuracy, increases customer delivery accuracy; improving the supplier delivery accuracy, facilitates reduction of stock level; improving the quality of ASN, reduces receiving costs; improving the quality of labels, increases inventory accuracy (mislabelling…); improving conformity to packaging specifications, reduces labour on-costs (repackaging…).Benefits for the suppliers are in the standardization of requirements in terms of logistics performance within the industry and benefits for the customers are
Table 1 -Three steps of logistics agreement implementation
Define and implement a common procurement process GOALS: to implement a common and consistent procurement process to clarify our requirements and our commitments to suppliers Diffuse and explain the Logistics Agreement to suppliers GOALS: to obtain the involvement of the suppliers and quick results to negotiate common terms of agreement (lead time, incoterm, ordering system…) Update and optimize the logistics agreement GOALS: to sort the day-to-day issues quickly and locally to negotiate local terms of agreement (packaging, delivery time slot…) in the development or the enhancement of a supplier appraisal system.The recommendation enables a common understanding between the trading parties for part supply, compliance with Global MMOG/LE recommendation and compliance with other automotive standards (Trading Partners Agreement, messages…).
The scope of the LKPI recommendation includes the logistics processes between supplier & customer, regardless of their level in the supply chain: between OEMs and suppliers, between suppliers (between tier N and tier N+1) and internal supply (between 2 plants of the same company).
Out of the scope are logistics service providers, performance indicators, internal logistic indicators and "customer" logistics performance indicators.
LKPI recommendation defines the standard indicators measuring the effectiveness of the supplier's delivery processes.It also measures the adherence to the trading partner's agreement.
LKPI analysis and diffusion can be provided monthly by the part controllers, delivery accuracy.every two months with all the part controllers, pur-
CONCLUSION
Innovative and intelligent regulation is needed but unnecessary regulation must be avoided.The authorities must ensure competition in transport market.Regulatory changes should have long-term perspective so that actors have sufficient time to adjust.Impact assessment of new regulations must consider also logistics.Efficient logistics is also cost-efficient.
The implementation of a complete Supplier Logistics Performance System is essential to support internal processes efficiency and to establish a continuous improvement system according to the main logistics policy.If it concerns the suppliers, the implementation requires high involvement of all internal actors and must also be considered as a change management issue.The reliability from suppliers can be obtained with two essential values: CONSISTENCE: of the logistics agreement, of the procurement practices, of the means to animate, and of the indicators measured.
PARTNERSHIP: in order to evaluate we must be ready to be contested and be able to improve also the internal organization.
The paper is published as output of the project VZ-MSM 0021627505 "The transport systems theory". | 1,976.8 | 2009-03-01T00:00:00.000 | [
"Business",
"Engineering"
] |
Structure-Function Analysis of Escherichia coli DNA Helicase I Reveals Non-overlapping Transesterase and Helicase Domains*
TraI (DNA helicase I) is an Escherichia coli F plasmid-encoded protein required for bacterial conjugative DNA transfer. The protein is a sequence-specific DNA transesterase that provides the site- and strand-specific nick required to initiate DNA strand transfer and a 5 (cid:1) to 3 (cid:1) DNA helicase that unwinds the F plasmid to provide the single-stranded DNA that is transferred from donor to recipient. Sequence comparisons with other transester-ases and helicases suggest that these activities reside in the N- and C-terminal regions of TraI, respectively. Com-puter-assisted secondary structure probability analysis identified a potential interdomain region spanning residues 304–309. Proteins encoded by segments of traI , whose N or C terminus either flanked or coincided with this region, were purified and assessed for catalytic activity. Amino acids 1–306 contain the transesterase activity, whereas amino acids 309–1504 contain the helicase activity. The C-terminal 252 amino acids of the 1756-amino acid TraI protein are not required for either helicase or transesterase activity. Protein and nucleic acid sequence similarity searches indicate that the oc-currence of both transesterase- and helicase-associated motifs in a conjugative DNA transfer initiator protein is rare. Only two examples (other than R100 plasmid TraI) were found: R388 plasmid
TraI (DNA helicase I) is an Escherichia coli F plasmidencoded protein required for bacterial conjugative DNA transfer. The protein is a sequence-specific DNA transesterase that provides the site-and strand-specific nick required to initiate DNA strand transfer and a 5 to 3 DNA helicase that unwinds the F plasmid to provide the single-stranded DNA that is transferred from donor to recipient. Sequence comparisons with other transesterases and helicases suggest that these activities reside in the N-and C-terminal regions of TraI, respectively. Computer-assisted secondary structure probability analysis identified a potential interdomain region spanning residues 304 -309. Proteins encoded by segments of traI, whose N or C terminus either flanked or coincided with this region, were purified and assessed for catalytic activity. Amino acids 1-306 contain the transesterase activity, whereas amino acids 309 -1504 contain the helicase activity. The C-terminal 252 amino acids of the 1756-amino acid TraI protein are not required for either helicase or transesterase activity. Protein and nucleic acid sequence similarity searches indicate that the occurrence of both transesterase-and helicase-associated motifs in a conjugative DNA transfer initiator protein is rare. Only two examples (other than R100 plasmid TraI) were found: R388 plasmid TrwC and R46 plasmid (pKM101) TraH, belonging to the IncW and IncN groups of broad host range conjugative plasmids, respectively. The most significant structural difference between these proteins and TraI is that TraI contains an additional region of ϳ650 residues between the transesterase domain and the helicase-associated motifs. This region is required for helicase activity.
Bacterial conjugation is the primary mechanism by which many plasmids and conjugative transposons are spread throughout a bacterial population. The process begins with the formation of a stable mating pair involving a donor cell that contains a conjugative plasmid (or transposon) and a recipient cell that lacks the plasmid. This establishes the close cell-cell contact required for physical transfer of single-stranded DNA (ssDNA) 1 from the donor to the recipient. A site-and strand-specific nick is then introduced in oriT (origin of transfer), and the DNA is unwound to provide ssDNA for transfer to the recipient. Upon entering the recipient cell, the transferred ssDNA is converted into double-stranded DNA by host enzymes and either circularized to form a plasmid or recombined into the recipient chromosome. This stabilizes the transferred DNA in the recipient and ensures the transfer of genetic traits (for review, see Ref. 1).
The enzymology of DNA strand transfer has been of interest since conjugation was first discovered over 50 years ago (2). In the last decade, it has become clear that transmissible plasmids encode a conjugative DNA transfer (CDT) initiator protein that plays a key role in initiating DNA strand transfer. These proteins nick their cognate supercoiled DNA substrate via a site-and strand-specific transesterification, resulting in a covalent protein-DNA intermediate (for reviews, see Refs. 3 and 4). A small minority of the characterized CDT initiator proteins also catalyze a helicase reaction (5)(6)(7)(8)(9)(10)(11)(12)(13). Because only a single strand of the duplex plasmid DNA is transferred to a recipient cell, unwinding of the plasmid is required to produce the transferred DNA strand. This can be accomplished by a DNA helicase or, perhaps, through strand displacement synthesis by a DNA polymerase. Recently, the helicase activity of the Escherichia coli F plasmid CDT initiator protein (TraI protein) has been shown to be essential for DNA transfer (14).
Based on the above description, known conjugative transesterases may be grouped into two classes: (i) those lacking an intrinsic helicase activity (e.g. RP4 plasmid TraI) (15) and (ii) those in which transesterase and helicase activities have been shown to reside within a single protein, as is the case only for the R388 plasmid TrwC protein and the F plasmid TraI protein (the F and R100 plasmid traI genes and deduced amino acid sequences share Ͼ95% identity and will be treated as alleles of the same gene in this report) (8,10,12). The overwhelming majority of described CDT initiator proteins fall into the first class based on sequence homologies (16) 2 and known biochemical properties. However, regardless of class, the CDT transesterases exhibit structural motifs and functional similarities that reflect conservation of the catalytic mechanism (4,16,17). The majority of these do not have helicase motifs. Conversely, the vast majority of available helicase sequences do not exhibit transesterase motifs. Where present in proteins exhibiting both functions, it is tempting to predict that the two activities will reside in independently folding and potentially separable domains.
Support for this idea has been provided by the work of Llosa et al. (10) using the plasmid R388-encoded TrwC protein. Like F plasmid-encoded TraI (F-TraI), TrwC exhibits both 5Ј to 3Ј DNA helicase and R388 oriT-specific transesterase activities in a single polypeptide chain (7,18). Using recombinant DNA techniques, these investigators showed that the transesterase and helicase activities of TrwC could be separated into two overlapping segments of the protein. Coexpression of active overlapping segments of TrwC in a trwC mutant background resulted in poor functional complementation compared with an allele expressing native TrwC (10).
F-TraI is the 1756-amino acid product of the traI gene (19) and is essential for conjugation (20). Also known as E. coli DNA helicase I, TraI was initially purified based on its DNA-stimulated ATPase and DNA helicase activities (21,22). TraI-catalyzed unwinding of duplex DNA was subsequently shown to occur with a 5Ј to 3Ј polarity (6,23). The idea that TraI is the helicase that unwinds the F plasmid during conjugative transfer was suggested when the gene encoding helicase I was mapped to the traI gene on the F plasmid (19). This has now been shown to be the case (14). The transesterase activity of TraI was not discovered and characterized until sometime later (5,8,9,24).
TraI and TrwC exhibit a significant degree of amino acid sequence similarity that includes both the transesterase and helicase motifs (4,18). It is currently thought that the transesterase acts in initiation complex formation, whereas the helicase activity is involved in the subsequent unwinding stage of DNA transfer. Computer-assisted sequence analysis of TraI suggested the possibility of an interdomain segment spanning residues 304 -309. Biochemical characterization of purified proteins encoded by segments of traI terminating at this point revealed the transesterase and helicase activities of F-TraI to reside in non-overlapping, physically separable domains.
Materials
Bacterial Strains-Bacteria were grown in LB medium (25) supplemented with 1.5% agar for plates. The medium was supplemented with antibiotics, as appropriate, at the following concentrations: ampicillin, 100 g/ml; tetracycline, 12 g/ml; and chloramphenicol, 20 g/ml (in methanol). The donor strain for CDT complementation studies was a derivative of DBH10B (Invitrogen). A NaCl-inducible allele of phage T7 gene 1 (T7 RNA polymerase) was moved into DBH10B by P1 transduction. Several transductants were assessed for the presence of appropriate genetic markers and the ability to express T7 RNA polymerase upon the addition of 0.3 M NaCl to the growth medium. A representative isolate was designated DB51. The pOX38T⌬traI plasmid (14) was electroporated into DB51, and a representative isolate was designated DB52. DB52 was transformed with the appropriate complementation plasmids (see below) in single-and double-plasmid transformations. DB52-N contains only the plasmid expressing the N306 allele of traI; DB52-C contains only the plasmid expressing the 309C allele of traI; and DB52-NC contains both complementation plasmids.
DNA, Nucleotides, and Enzymes-DNA oligonucleotides are listed in Table I. Nucleic acids were quantified by spectroscopy at 260 nm. Unlabeled nucleoside 5Ј-triphosphates were from U. S. Biochemical Corp. [ 32 P]ATP and [ 32 P]dCTP were from Amersham Biosciences. Re-striction enzymes, DNA polymerase I (large fragment), and Vent DNA polymerase were from New England Biolabs Inc. and were used as specified by the supplier. Phage T4 DNA ligase was from Roche Molecular Biochemicals.
Plasmid Constructions-Standard cloning techniques were employed essentially as described (25). With the exception of the fragment encoding N365, segments of traI were generated by PCR using Vent polymerase and pMP8 (26) as the template. Constructs were sequenced to ensure the absence of PCR-derived mutations.
The IMPACT protein purification system (New England Biolabs Inc.) was used to express and purify the segments of TraI used in this study. The vector pCYB3 was modified by replacing the lac promoter and sequences upstream of the NcoI site with the T7 RNA polymerase promoter and ribosome-binding site from pET11d (Novagen) by fragment exchange. PCR-generated segments of traI were cloned into the NcoI and SmaI sites of the modified vector. This results in the addition of a glycine (GGG) codon to the extreme 3Ј-end of the traI allele. The proteins were purified from HMS174(DE3) (Novagen) according to the manufacturer's instructions. Protein concentrations were determined using the Bradford protein assay (Bio-Rad) with bovine serum albumin as the standard.
N365 was generated by digestion of pET11d-traI with ClaI and HindIII, fill-in of the 5Ј-overhangs with E. coli DNA polymerase I (large fragment), gel purification, and self-ligation. These manipulations result in a segment of TraI with wild-type sequence up to residue 361, a conservative Asp-to-Glu substitution at position 362, and the non-native sequence LPM at position 363-365, followed by a TGA stop codon. The protein was purified essentially as described for TraI (6).
N200 and N235 were constructed using PCR to amplify the appropriate TraI segment from the N306 construct. The PCR primers used for these amplifications are listed in Table I. The amplified DNA fragments were digested to completion with NdeI and SmaI and cloned into pTYB2 (New England Biolabs Inc.). Both proteins were expressed in E. coli BL21(DE3) (Novagen) and purified according to the manufacturer's instructions (IMPACT system, New England Biolabs Inc.).
TraI⌬252 was constructed using PCR to amplify the traI gene on pET11d-traI (14). The downstream PCR primer contained two stop codons immediately following codon 1504 in the traI sequence to produce this C-terminal truncation of the traI gene. The protein was expressed in E. coli BL21(DE3) cells and purified using the standard TraI purification.
The plasmids used in CDT complementation studies were constructed as follows. The pBR322-derived replication origin present in pET11d-N306 was replaced with the pACYC184 origin by fragment exchange to generate an N306 expression plasmid with a p15A replication origin. The allele of traI encoding 309C was subcloned from the intein fusion expression plasmid into a pUC-derived plasmid encoding resistance to chloramphenicol. The resulting plasmid retained the phage T7 gene 10 transcription/translation signals to drive expression of the gene. Expression of the appropriate functional domain of TraI was verified for each of the constructs in the appropriate donor strain.
Methods
DNA Helicase Assays-A partial duplex unwinding substrate was made essentially as described (27). Briefly, a 91-nucleotide oligonucleotide was annealed to its complementary sequence on purified M13mp6 ssDNA at a molar ratio of 1:1. The 3Ј-end of the annealed oligonucleotide was extended using E. coli DNA polymerase I (large fragment) and [␣-32 P]dCTP. The final length of the oligonucleotide was 93 nucleotides. The preparation was phenol/chloroform-extracted and passed over a Bio-Gel A-5m column. The void volume fractions were pooled, ethanolprecipitated, and suspended in 10 mM Tris-HCl (pH 7.5) and 1 mM EDTA to a final concentration of ϳ5 fmol/l (DNA phosphate).
DNA unwinding reaction mixtures (typically 20 l) contained 25 mM Tris-HCl (pH 7.5), 20 mM NaCl, 3 mM MgCl 2 , 5 mM -mercaptoethanol, 10 fmol of DNA substrate, and 2 mM ATP. Reaction mixtures were assembled at room temperature, and the reaction was initiated by the addition of enzyme. Incubations were carried out at 37°C for 10 min. The reaction mixtures were quenched by the addition of EDTA to 25 mM and SDS to 1%. Reaction products were resolved on an 8% native polyacrylamide gel (20:1 cross-linking) and quantified using a Molecular Dynamics PhosphorImager.
ATPase Assays-Reaction mixtures (30 l) were essentially identical to those used for helicase assays with the following exceptions.
[␥-32 P]ATP (15 pmol) was added to each reaction mixture (final ATP concentration of 2 mM), which contained 0.75 g of M13mp6 ssDNA instead of the partial duplex helicase substrate. Reactions were assembled at room temperature and initiated by the addition of enzyme, and incubation was carried out at 37°C. Aliquots (5 l) were removed at 1-min (TraI) or 2-min (all truncation mutants) intervals and quenched by the addition of 5 l of 50 mM EDTA, 7 mM ADP, and 7 mM ATP. 5 l was spotted onto a polyethyleneimine-cellulose TLC plate (J. T. Baker, Inc., Phillipsburg, NJ) and allowed to dry, and the plates were developed with a mobile phase consisting of 1.0 M formic acid and 0.8 M LiCl. The plates were allowed to dry, and the degree of ATP hydrolysis was quantified using phosphor-storage technology.
Duplex DNA Relaxation Assays-Assays were done in a manner slightly modified from that previously described (8). In addition to the protein (present at the indicated concentrations), a typical reaction mixture (16 l) contained 7 nM supercoiled pBSoriT (or pBS) DNA, 40 mM Tris-HCl (pH, 7.5), 6 mM MgCl 2 , and 15% glycerol. Reactions were assembled at room temperature and incubated at 37°C for 20 min. Reactions were stopped by the addition of proteinase K (Roche Molecular Biochemicals) and SDS to final concentrations of 1 mg/ml and 0.25%, respectively, and allowed to incubate at 37°C for an additional 20 min. The products were resolved on 0.8% agarose gels and visualized by ethidium bromide staining (0.5 g/ml).
DNA Binding Assays-DNA binding assays using 226C, 309C, and 348C utilized the double-filter (nitrocellulose ϩ DE81) technique previously described (38). Protein concentration was varied as indicated, and a 93-bp partial duplex DNA substrate was used as the ligand. Experiments were repeated three or four times, and the data were averaged and fit to a rectangular hyperbola to obtain an apparent K d for DNA binding. The reaction conditions used were the same as described above for the DNA helicase reactions, except that ATP␥S was substituted for ATP at a final concentration of 1 mM.
Gel retardation assays were used to measure the binding of N306 and N235 to a ssDNA oligonucleotide containing the relaxase recognition sequence (see Table I for sequence). The reaction conditions were those used for relaxation assays without the SDS/proteinase K incubation. After a 20-min incubation at room temperature, the binding reaction mixtures were loaded onto a 5% polyacrylamide and 0.125% bisacrylamide gel, and electrophoresis was performed at 200 V for 2 h at 4°C. The running buffer was 2ϫ Tris/glycine (50 mM Tris, 380 mM glycine, and 2 mM EDTA (pH 8.3)). Gels were visualized using a Molecular Dynamics PhosphorImager.
Genetic Assays-The liquid mating assay protocol was carried out as previously described (14). Briefly, DB52-N, DB52-C, and DB52-NC were used as donor strains; DH5␣ was used as the recipient strain. Donor and recipient strains were diluted 1:50 into LB medium from saturated overnight cultures grown under antibiotic selection and allowed to grow to mid-or late-log phase in the absence of selection at 37°C. Donors and recipients were then mixed at a volume ratio of one donor to nine recipients and incubated at 37°C. After 5 min, the mating mixtures were diluted 1:10 into LB medium and incubated at 37°C for an additional 30 min. The mating mixtures were then vigorously vortexed to disrupt mating pairs, and 10-fold serial dilutions were prepared in phosphate-buffered saline. Appropriate dilutions were plated onto LB plates containing streptomycin and tetracycline to counterselect donors and unmated recipients while selecting for transconjugants. Aliquots of the unmated donor and recipient cultures were subjected to 10-fold serial dilution and plated onto LB plates containing the appropriate antibiotics to determine viable donor cell count and viable recipient cell count. Mating frequency was calculated as the number of transconjugants/100 viable donor cells.
Data Base Searching-A degenerate amino acid sequence (YYX 1,2 (D/ E)X 1,2 (D/E)X 1,2 YY) was used to search the Swiss Protein and TREMBL Sequence Databases for proteins encoded by bacterial conjugative plas-mids with the N-terminal two-tyrosine doublet motif shared by TraI and TrwC. 3 Hits were manually scanned for the presence and position of the known transesterase and helicase motifs (16,28,29).
Computer-assisted Sequence Analysis-F-TraI, plasmid R388 TrwC, and plasmid R46 TraH were aligned in a binary fashion using the SIM algorithm (30). The gap opening and extension penalties were 10 and 2, respectively, and the comparison matrix was PAM 200. The amino acid sequence of TraI spanning residues 281-380 was submitted to the PSA server at the BioMolecular Engineering Research Center for secondary structure analysis. 4
RESULTS
To begin an investigation of the functional domains of the F plasmid-encoded TraI protein, the sequence of F-TraI was compared with that of two related proteins, TrwC and TraH. This analysis was aided by a previous study (10) that identified the functional transesterase and helicase domains of TrwC in two separate and overlapping protein segments. The region of overlap (amino acids 192-348) brackets the point at which the N-terminal sequence similarity between TrwC and TraI falls off sharply (Fig. 1). We speculated that an interdomain segment in TraI would fall within this region, if present at all. The 200-amino acid sequence of TraI that spans this region was subjected to computer-assisted secondary structure analysis as described under "Experimental Procedures." The output of this analysis ( Fig. 1) was inspected for regions that had a reasonable probability of being able to form a flexible linker. Constrained structures such as helices and sheets were excluded from consideration in favor of segments more likely to adopt an unconstrained loop/turn conformation. The TraI sequence in this region with the highest predicted probability of a loop/turn structure was LTPGPA (residues 304 -309). These coordinates are nearly coincident with the end of significant sequence identity (as opposed to similarity) between TraI and TrwC. The sequence LTPGPA is not present in TrwC. Two additional regions, on either side of residues 304 -309, with slightly lower probabilities of similar conformation were identified at positions 227-230 and 346 -352.
Using these results as a guide, fragments of the traI gene were cloned, overexpressed, purified, and assessed for biochemical activity. Fig. 2 shows several of the purified proteins used in this study (full-length TraI, two N-terminal segments (N306 and N365), and three C-terminal segments (226C, 309C, and 348C)) resolved on an SDS-polyacrylamide gel. Purified proteins not shown in this figure (N235 and TraI⌬252) were of comparable purity. The names of the protein segments indicate the first native amino acid in the case of 226C, 309C, and 348C and the fact that the protein extends to the native C terminus. N235, N306, and N365 begin at the native N terminus and extend to the indicated native residue. Deviations from native amino acid sequence, where they exist, are described under "Experimental Procedures." TraI⌬252 begins at the native N terminus and extends to residue 1504 of the native protein located ϳ60 residues C-terminal to helicase-associated motif VI. Thus, this protein lacks the C-terminal 252 residues of TraI, but retains both the putative transesterase and helicase domains. The constructions, shown schematically, and the data derived from in vitro biochemical analysis of various segments of TraI are summarized in Fig. 3.
DNA Helicase Domain-The 226C, 309C, and 348C proteins were the logical candidates for an active helicase because the helicase-associated motifs are located within this portion of the protein. Each protein was purified to apparent homogeneity from an expression strain (see Fig. 2), and the purified protein was assayed for its ability to catalyze a helicase reaction using a 93-bp partial duplex substrate. Both 226C and 309C catalyzed unwinding of the 93-bp partial duplex substrate (Fig. 4A). The specific activities of 226C and 309C were 70 and 65%, respectively, that of the native protein based on the slope of the linear portion of the titration curve. On the other hand, the 348C protein was incapable of catalyzing detectable unwinding despite the fact that it is only 39 residues shorter than 309C. Additional studies have shown that 226C and 309C also catalyze unwinding of long (851-bp) partial duplex substrates (Fig. 4B), albeit somewhat less efficiently than native TraI at low protein concentrations. The specific activities of 226C and 309C were 50 and 45%, respectively, that of the native protein determined as described above. However, the extent of the reaction at high protein concentrations was essentially identical (within experimental error) to that of the native protein. As expected, 348C was not able to catalyze unwinding the 851-bp partial duplex substrate.
TraI⌬252, lacking the C-terminal 252 residues, was also purified and analyzed in DNA helicase assays (data not shown). This protein was active as a DNA helicase, exhibiting a specific activity that was Ͼ50% that of the native protein.
Thus, the C-terminal 252 residues, which lie just to the C-terminal side of the helicase-associated motifs, are not essential for the helicase activity of TraI.
Unwinding of a duplex nucleic acid substrate by a helicase is dependent upon nucleoside 5Ј-triphosphate hydrolysis. Therefore, we examined the DNA-stimulated ATP hydrolysis reaction catalyzed by 226C, 309C, 348C, and TraI⌬252 and compared this with the reaction catalyzed by the native protein.
The k cat for the native protein was 108 s Ϫ1 in the presence of ssDNA. Remarkably, the k cat values for 226C, 309C, and TraI⌬252 were reduced to 9, 10, and 14 s Ϫ1 , respectively, although all three proteins exhibited helicase activity similar to that of the native protein (see Fig. 4). The 348C fragment of TraI exhibited a more profound defect in ATPase activity (k cat Ͻ 1 s Ϫ1 ). The significant defect in ATP hydrolysis exhibited by 348C is apparently sufficient to explain the lack of helicase activity and demonstrates that the N terminus of the functional helicase/ATPase domain of TraI lies within the 39
FIG. 1. Schematic similarity comparison of TraI and TrwC and assignment of predicted interdomain segments.
A schematic comparison of fulllength F plasmid TraI and R388 plasmid TrwC is depicted with approximate amino acid coordinates indicated. The active N348 and 192C segments of TrwC identified by Llosa et al. (10) are shown above the full-length schematic of that protein.
The bracket indicates the approximate extent of overlapping amino acid sequence. The black boxes reflect the ϳ40% identity between the TraI and TrwC N-terminal regions and include the transesterase region of each protein. The striped boxes indicate the region of C-terminal similarity containing the helicase motifs (28). TraI and TrwC were aligned using the SIM algorithm (30). For this analysis, the gap opening and extension penalties were 10 and 3, respectively, and the comparison matrix was BLOSUM 100. The secondary structure probability contour plot generated for residues 210 -400 of TraI (see "Experimental Procedures") is also shown. TraI sequences that correspond to high loop/turn probabilities are indicated at the bottom. The numbers correspond to the first and last residues of each string. aa, amino acids. amino acids that distinguish 309C from 348C.
We also measured the binding of 226C, 309C, and 348C to a partial duplex DNA ligand as described under "Experimental Procedures" (Fig. 5). Both 226C and 309C bound the DNA ligand with an apparent K d of ϳ10 nM. The K d measured for the 348C fragment was ϳ90 nM, indicating a defect in DNA binding. Although this binding defect is not likely to be sufficient to explain the lack of helicase activity, it does indicate that the region between residues 309 and 348 is important for DNA binding.
DNA Transesterase Domain-Three N-terminal segments of TraI were expressed and purified as outlined under "Experimental Procedures" (see Fig. 2). The C-terminal end of N365 was chosen based upon available restriction sites and not with regard to potential secondary structure. However, in conjunction with the largest helicase segment, 226C, these two proteins bracket the predicted interdomain region at residues 304 -309. The overlap shared by these two segments of TraI is 139 amino acids, which is roughly comparable to that of the smallest functional segments of TrwC used by Llosa et al. (10).
Purification of N365 yielded both the expected protein and a significant proteolytic breakdown product that copurified with N365 (see Fig. 2, lane 6). Western blot analysis using polyclonal antibodies directed against TraI indicated that this proteolytic fragment was a fragment of TraI (data not shown). Incubation of this protein preparation with a 3Ј-end-labeled oligonucleotide whose sequence encompassed the F plasmid oriT nic site resulted in transfer of the labeled DNA to both protein species (data not shown). Thus, both proteins contain the active tyrosine present in the transesterase domain of TraI. Moreover, because the active-site tyrosine in TraI is within 23 residues (ϳ2.4 kDa) of the N terminus of the full-length protein, 5 the proteolytic cleavage event, estimated at ϳ5 kDa or 40 -50 amino acids, must remove the C-terminal end of N365. If the cleavage event removed the N-terminal end of the protein, it would remove the transesterase active site, and this is not the case. The smaller active product appears to be comparatively stable to proteolysis as judged by the absence of faster migrating species. Thus, folding of the N-terminal region of TraI into a stable transesterase domain is independent of the rest of the protein.
Based upon the fact that the N terminus of the functional helicase (residue 309) coincided with the suspected interdomain region, N306 was constructed and purified (see Figs. 1 and 2). Both N306 and N365 were competent to nick a supercoiled oriT-containing DNA substrate (pBSoriT) (Fig. 6). In this semiquantitative analysis, the smaller transesterase domains exhibited slightly lower specific transesterase activity compared with native TraI. The presence of oriT in the substrate was required to observe transesterase activity; thus, conversion of the DNA from the supercoiled to the open circular form is not due to nonspecific cleavage (Fig. 6). N365 and N306 did not display detectably different activities from each other when present at equivalent concentrations (Fig. 6, compare lanes 3 and 4 with lanes 5 and 6). These results demonstrate the oriT-specific DNA transesterase activity of TraI resides in the N-terminal 306 residues of the 1756-amino acid native protein.
To define the C-terminal end of the transesterase domain, two additional N-terminal fragments of TraI were expressed. N200 encompassed the first 200 amino acids of TraI and is homologous to the first 200 amino acids of TrwC, which has been shown to catalyze sequence-specific transesterification using an oligonucleotide substrate (10). N200 was completely insoluble and could not be analyzed further. The construction of N235 was based on limited proteolysis of N306, which suggested the presence of a stable domain encompassing the first ϳ235 amino acids of TraI. 6 analyzed for transesterase activity. The purified protein failed to catalyze sequence-specific transesterification and failed to bind a ssDNA oligonucleotide that contained the nic sequence (data not shown). On the other hand, N306 bound this oligonucleotide with high affinity as demonstrated using gel retardation assays. To ensure that N235 was properly folded, the secondary structure of the purified protein was examined by circular dichroism spectroscopy. The purified protein exhibited primarily ␣-helical structure, and its circular dichroism spectrum was comparable to that of N306. 6 Therefore, N235 appeared to be properly folded, but unable to bind a ssDNA oligonucleotide that contained nic. Thus, amino acids required for binding of the transesterase domain to its substrate are present within the 70-amino acid segment between residues 235 and 306. It is also clear from this analysis that the Nterminal 306 amino acids represent a minimal functional FIG. 4. Helicase activity assays of TraI, 226C, 309C, and 348C. A, helicase activity assays using either native TraI or the purified segments of TraI and the 93-bp partial duplex substrate were carried out as described under "Experimental Procedures" using the indicated amounts of each protein. G, native TraI protein; f, 226C; OE, 309C; ࡗ, 348C. B, helicase activity assays using either native TraI or the purified segments of TraI and the 851-bp partial duplex substrate were carried out as described under "Experimental Procedures" using the indicated amounts of each protein. G, native TraI protein; f, 226C; OE, 309C; ࡗ, 348C. The data represent the means of three to four determinations. S.D. values were omitted for clarity. In general, the S.D. was Ͻ10% of the mean. transesterase domain, with the C-terminal end of the active transesterase located between residues 235 and 306.
Genetic Characterization of traI Alleles-The functional traI segments generated in this study were tested for their capacity to complement a strain containing a mini-F plasmid lacking the traI gene (DB52, Tra Ϫ ) for CDT as described under "Experimental Procedures." Only the full-length traI gene was able to restore the Tra ϩ phenotype. The segmental traI alleles encoding functional domains of the protein, whether overlapping or abutting, failed to restore transfer in all cases tested (data not shown). This included expression of each functional domain singly and in combination with the other functional domain. This result was expected because previous studies have shown that both the transesterase and helicase activities of TraI are essential for F plasmid-mediated CDT (14). In addition, this result is consistent with the results presented for the analogous TrwC protein from plasmid R388 (10), where coexpression of the two functional domains on overlapping protein segments produced poor complementation.
Data Base Searches for Similar Proteins-The PROSITE and TREMBL Databases were searched with degenerate amino acid sequence patterns, and all hits were subjected to binary alignment with F-TraI as described under "Experimental Procedures." Only three proteins were uncovered (Fig. 7), underscoring the apparent scarcity of known proteins exhibiting the degree of similarity imposed by this approach. It should be noted that an apparent conjugative transesterase-helicase protein (Agrobacterium tumefaciens pTiC58-TraA) has been described (11). pTiC58-TraA was not identified in the data base search because it lacks the two N-terminal tyrosine doublets and the comparatively high amino acid identity exhibited by the other three proteins. DISCUSSION Previous studies have shown that the F plasmid-encoded TraI protein catalyzes two distinct biochemical reactions: a 5Ј to 3Ј DNA helicase reaction and a site-and strand-specific transesterase reaction (5,6,8,9,13). Both of these activities are essential to complete the strand transfer reaction associated with bacterial conjugation (14). The results presented here clearly demonstrate that the transesterase and helicase activities of TraI reside in separable domains of the full-length protein. The N-terminal domain (residues 1-306) harbors the transesterase activity associated with the TraI protein. The remainder of the protein (residues 309 -1756) is an active 5Ј to 3Ј DNA helicase. Thus, the domains of TraI do not overlap. The fact that R388 plasmid TrwC, a protein from the conjugative plasmid R388 that is similar in organization and function to TraI, could be partially separated into these component activities (10) demonstrated a lack of obligatory interdependence of the two activities and raised the possibility that the activities reside in truly distinct domains. This has now been demonstrated for the F plasmid TraI protein, where the two domains can be fully separated without significant loss of biochemical activity.
The transesterase activity associated with purified N306 was FIG. 6. The N306 and N365 segments of TraI exhibit oriT-specific transesterase activity. The ability of N-terminal segments of TraI to specifically nick supercoiled DNA containing oriT was assessed as described under "Experimental Procedures." The DNA substrate (pBSoriT, lanes 1-6; pBS, lanes 7-10) was present at 7 nM and was incubated with the indicated concentrations of each protein for 15 min at 37°C prior to the addition of protein denaturants. Reaction products were resolved on a 0.8% agarose gel that was stained with EtBr to visualize the results. The pBS plasmid was identical to pBSoriT, except that it lacks the oriT sequence from the F plasmid (8). The supercoiled (sc) and open circular (oc) forms of the DNA substrate(s) are indicated on the right. NP, no protein.
FIG. 7. Binary alignments of TraI, TrwC, and TraH. Amino acid sequences were aligned using the SIM algorithm (30) as described under "Experimental Procedures." The shaded boxes indicate well conserved regions among all three proteins. The extent and degree of identity (id) are indicated by the double-headed arrows and the accompanying numeric values. The stippled boxes indicate the region within TraI that is absent from the other two proteins. The white box at the C terminus of each protein represents a segment that is apparently unique to each, as no significant similarities were detected among the three.
qualitatively similar to that of the full-length protein. Although the specific activity of this protein appeared to be somewhat reduced relative to that of the full-length protein, the purified N306 fragment of TraI catalyzed a robust transesterase reaction that was both site-and strand-specific and dependent on negatively supercoiled DNA. A smaller protein fragment (N235) lacked transesterase activity, suggesting that the Cterminal end of the functional transesterase lies within the region between residues 235 and 306. Indeed, the N235 protein failed to bind a ssDNA oligonucleotide containing nic, indicating that the region between amino acids 235 and 306 is important for binding of the transesterase to its DNA substrate. We also note that the prominent proteolytic fragment obtained when N365 was isolated is consistent with the existence of a stable domain. This protein is slightly larger than N306 and represents the N-terminal end of the protein (see "Results"). This suggests that the N-terminal portion of TraI folds into a stable domain that may be slightly larger than the domain defined by N306. The results reported here for the F plasmid relaxase are in contrast with the results reported for the R388 plasmid TrwC relaxase (10). In that case, a smaller protein fragment (residues 1-225) resulted in a protein that catalyzed transesterase activity using an oligonucleotide substrate, but failed to catalyze the same reaction with a supercoiled plasmid. We conclude that the F-TraI transesterase domain occupies the first ϳ310 residues, that it adopts a stable structure with nearly native transesterase activity, and that it is separable from the helicase domain associated with TraI.
The helicase activity associated with 309C was nearly identical to that of the native protein. The 309C fragment catalyzed a processive unwinding reaction with almost the same specific activity as full-length TraI. Remarkably, the 39-amino acid difference between 309C and 348C dictated whether the protein was a functional helicase or completely defective catalytically (i.e. 309C was a fully functional helicase, whereas 348C lacked detectable helicase activity). A similar result was obtained by Llosa et al. (10), in that the segment of TrwC beginning at residue 346 and extending to the native C terminus (346C) lacked ATPase activity, whereas the segment of TrwC beginning at residue 192 was a fully functional helicase. Thus, we have defined the N-terminal end of the minimal functional helicase as beginning between residues 309 and 348. The helicase-associated motifs are contained within a segment of the protein extending from approximately residues 990 to 1450. Thus, there are ϳ300 amino acids at the C-terminal end of TraI that lie outside the helicase-associated domains. We have removed the C-terminal 252 amino acids to construct TraI⌬252, which is also active as a DNA helicase. Thus, the protein fragment extending from residue 309 at the N-terminal end to residue 1504 at the C-terminal end is a functional DNA helicase. The role played by the C-terminal ϳ250 amino acids of TraI is not clear at present. However, preliminary results suggest that this region of the protein is essential for CDT. 7 The size and complexity of the functional TraI helicase were unexpected. The helicase-associated motifs in TraI begin at residue ϳ990, and a putative restart protein (TraI*) whose coding sequence is located within the traI gene beginning at about residue 950 (31) seemed like a good candidate for an active helicase. There is a putative ribosome-binding site located just upstream of a methionine codon, and it has been speculated that TraI* is synthesized as a restart protein (31) much like the small form of the bacteriophage T7 gene 4 protein (32). Our results suggest that if TraI* is synthesized in the cell, it will not harbor helicase activity because it will be miss-ing the region from residues 309 to 950, which we have shown to be essential for helicase activity. In fact, we have directly tested the idea of helicase activity associated with the putative TraI* protein by expressing and purifying a TraI*/maltosebinding protein fusion. This protein was devoid of both ATPase and helicase activities. 5 Thus, the active helicase requires a large region between the N-terminal end of the helicase domain and the helicase-associated motifs.
There is a wealth of data supporting the notion that the evolutionarily conserved amino acids constituting the helicaseassociated motifs in superfamily I DNA helicases serve to couple nucleoside 5Ј-triphosphate hydrolysis with translocation and unwinding of duplex nucleic acids (33)(34)(35)(36)(37). However, there is little information on the role of sequences outside the motifs, as the comparatively low level of sequence conservation makes selection of mutagenic targets difficult. Given the distance between the helicase-associated motifs and the N-terminal end of the functional helicase (ϳ650 amino acids), perhaps this region of the protein is responsible for some activity associated with TraI that has yet to be recognized and defined. Alternatively, this region could play a strictly structural role. It is possible that the absence of the N-terminal 39 amino acids that distinguish 348C from 309C may have negative consequences for the global folding of the C-terminal 80% of TraI. However, this seems unlikely, as the 348C fragment of the protein was soluble and could be purified using the same protocol used to purify the native protein.
In comparing TraI with TrwC and TraH (the two proteins most closely related to TraI in sequence and organization), the most striking difference is the distance from the end of the N-terminal similarity to the beginning of the C-terminal similarity, the latter coinciding with the region containing the helicase-associated motifs (see Fig. 7). In TrwC and TraH, this distance is ϳ200 amino acids, whereas the analogous region of TraI comprises roughly 650 residues. Like TraI, TrwC has been characterized in vitro as a 5Ј to 3Ј DNA helicase (7), but this activity clearly does not require the extensive sequences present in TraI. Thus, there is over three times more "information potential" in TraI than presumably would be required just to enable helicase activity, raising the possibility of the central region having an activity or role distinct from the transesterase or helicase functions. The nature of this function, if any, has not yet been identified. | 9,185.4 | 2002-11-08T00:00:00.000 | [
"Biology"
] |
Resummed predictions for hadronic Higgs boson decays
We present the NNLL′ resummed 2-jettiness distribution for decays of the Standard Model Higgs boson to a bb¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overline{b} $$\end{document}-quark pair and to gluons. The calculation exploits a factorisation formula derived using Soft-Collinear Effective Theory, in which large logarithms of the 2-jettiness are resummed by renormalisation group evolution of the hard, soft and jet contributions to the differential decay rate. We match the resummed predictions to the fixed-order NNLO result using the Geneva framework, extending the validity of the results to all values of the resolution variable and providing a fully exclusive NNLO event generator matched to the Pythia8 parton shower.
Introduction
The lack of any definitive signal of New Physics at the Large Hadron Collider (LHC) suggests that the high-energy physics community must be open to alternative ways to probe Beyond the Standard Model (BSM) effects at collider experiments. In particular, precision measurements of the Standard Model (SM) Higgs sector may be a way to indirectly constrain BSM theories which live at scales beyond our reach, both at the LHC and at future lepton colliders or 'Higgs factories'. It is therefore crucial that theoretical predictions for processes involving the production or decay of the Higgs boson have a precision which matches that of experiment.
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In this work we consider the hadronic decays of a Higgs boson to a bb-quark pair and to gluons. 1 Although these modes are difficult to observe at a hadron collider due to the large QCD background, they may well prove to be useful probes of Higgs physics at a future lepton collider since they contribute significantly to the total width of the Higgs boson.
The dominant decay mode of the Higgs boson is to a bb-quark pair, with a branching ratio of about 58% [2]. An accurate measurement of this channel would allow an extraction of the Yukawa coupling y b , which is an important input to Higgs studies. The hadronic environment at the LHC makes this a challenging prospect -nevertheless, the decay has been observed recently by both ATLAS and CMS in the V H, or Higgsstrahlung, production channel [3,4]. QCD corrections to the partial width are known up to N 4 LO [5][6][7][8][9][10][11][12], and fully differential NNLO calculations have also been available for quite some time [13,14]. Recently, the fully differential N 3 LO calculation has also been completed [15].
The decay channel to gluons, on the other hand, proceeds via a top-quark loop and contributes around 8% to the total width. Since QCD corrections to this channel are indistinguishable from the bb-quark case at higher orders in perturbation theory, one should consider the classes of processes together to obtain a total hadronic width, as performed in ref. [1]. Nevertheless, at NNLO and in the case of kinematically massless b-quarks the processes can be fully separated, since interference terms between the diagrams vanish. Related complications which arise at N 3 LO have been studied in ref. [16]. In the case of massive b-quarks, these interference terms can no longer be neglected -their impact has been studied in ref. [17] and a full NNLO calculation in the massive case has been carried out in refs. [18,19].
In the limit that M H 2m t , the top-quark loop which couples the Higgs boson to gluons can be integrated out to obtain an effective theory with five light active flavours in which the interaction is local. This simplifies the inclusion of QCD corrections and has allowed calculations to be performed at NNLO [20,21] and, for the total width, at N 3 LO [22] and N 4 LO [23]. The effect of including a finite top-quark mass on the total width has also been studied in ref. [24].
In light of the importance of Higgs physics, several other predictions at various accuracies and using different approximations are available beyond those listed here. A complete review of the state of the theoretical calculations for Higgs boson production and decay processes, including the calculation of electroweak corrections, can be found in ref. [25].
In a recent publication [26], the distributions of the thrust variable in these decay processes were considered and fixed-order computations up to approximate NNLO (which contribute at O(α 3 s ) relative to a Born H → bb/gg process) were performed. In that work, the authors noted the poor convergence of the perturbative series for both processes and were able to show that the approximate NNLO corrections obtained from the singular terms of a SCET-derived factorisation formula could ameliorate the scale dependence of the calculations. They also acknowledged several shortcomings of their calculation, one of which related to the size of the logarithms log n τ /τ which are not resummed in a purely fixed-JHEP04(2021)254 order computation and spoil predictivity in the small τ region. Here, we provide resummed predictions at NNLL accuracy which complement the results of ref. [26]. Compared to NNLL, the resummation at NNLL accuracy incorporates the complete O(α 2 s ) singular structure for T 2 → 0, i.e. all 2-loop virtual and corresponding real corrections, allowing us to consistently match to NNLO.
Using the Geneva formalism developed in refs. [27][28][29], we are also able to construct IR-finite events which combine the advantages of the resummed and fixed-order calculations and are matched to a parton shower. 2 Having a Geneva implementation of the H → bb process will also allow us to produce an NNLOPS generator for the signal process pp → V (H → bb). This can be achieved by combining the Higgs boson decay presented here with our previous calculation of the V H production process [31] in the narrow width approximation. Fixed-order calculations for the full pp → V bb process were performed in refs. [32][33][34] in the massless approximation -more recently, a calculation with massive b-quarks also appeared [19]. An NNLOPS generator for W (H → bb) production via the MiNLO method [35][36][37][38] was presented in [39], while a separate NNLOPS H → bb generator was also made available in ref. [40]. Nonetheless, we believe an independent implementation of the combined corrections to both production and decay in the Geneva framework will provide a useful cross-check of previous results. We leave this development to a future publication. This paper is organised as follows. In section 2, we briefly explain how resummed predictions are obtained from a factorisation formula derived in soft-collinear effective theory and provide numerical results for the resummed T 2 distribution in H → bb and H → gg. In section 3, we briefly recap the main features of the Geneva method relevant for the processes at hand. In particular, we discuss various implementation details, as well as how the matching to the parton shower is achieved. We present our Geneva results in section 4. Finally, we report our conclusions and directions for future work in section 5, while we detail the construction of the phase space mappings used and the analytical NNLO decay rates in appendices A and B respectively.
Resummation from Soft-Collinear Effective Theory
In this section we present, for the first time, the NNLL resummation of the 2-jettiness observable, T 2 , for the decay of a Higgs boson into a pair of b-quarks. We also provide results at the same accuracy for the Higgs boson decay into gluons, which were first presented in ref. [30]. We present numerical results for the dimensionless τ ≡ T 2 /(2 M H ) distribution, where M H is the mass of the Higgs boson.
Formulation
Our basic resolution parameter for the hadronic decays of the Higgs boson is the 2-jettiness, defined as
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where k runs over all final state particles with momenta p k = (E k , p k ) and n is the unit 3vector resulting from the minimisation procedure. In the case where all final-state particles are massless, it is related to the more familiar thrust T , which was widely studied for e + e − collisions [41,42] and extended to hadronic collisions in ref. [43], by the relation . For the decays that we consider, we work in the rest frame of the Higgs boson and always have that E cm = M H . Exactly like the thrust variable, the 2-jettiness is constrained kinematically (0 ≤ T 2 ≤ M H ) and its value is related to the spatial distribution of the radiation: in the limit T 2 → 0 the final state consists of two pencil-like jets, while for T 2 ∼ M H there are three or more jets distributed in a more spherical configuration. We consider the decay rate differential in T 2 of a Higgs boson to either a bb-quark pair or to a pair of gluons. We consider massless b-quarks with a finite Yukawa coupling to the Higgs y b . In the gluon case, we work in an effective theory in which the top-quark loop that couples the Higgs boson to gluons has been integrated out, leaving an effective local operator Hgg.
The Born level decay rates for the two processes considered are given by It has been shown, both in QCD and SCET, that the differential decay rate factorises in the small T 2 limit [42,[44][45][46] as where the index i = b, g indicates the process in question.
The decay rate has been factorised into a hard contribution H i (M H , µ), a soft function S i (k, µ) and two jet functions J i n (p 2 n , µ) and J ī n (p 2 n , µ). The hard function is defined as the square of the Wilson coefficients which match the full theory (the SM) onto SCET. In the gluon case, an additional matching is required from the heavy-top limit effective theory we are working in onto the SM -thus, the hard functions can be written as The jet functions describe collinear radiation from the Born-level partons along the jet directions n andn, which can be chosen without loss of generality to be orientated alongẑ, viz. n = (1, 0, 0, 1) andn = (1, 0, 0, −1). The soft function accounts for all soft radiation.
Each component in the factorisation theorem must be evaluated at its own characteristic scale in order to prevent the appearance of large logarithms, viz.
However, since the decay rate must be evaluated at a single scale, we evolve the separate functions to a common scale µ via renormalisation group (RG) evolution and in so doing resum the large logarithms of ratios of scales which appear. The resummed spectrum, differential in the Born kinematics, can then be written as
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where dΓ i B (µ)/dΦ 2 indicates the Born decay rate differential in the two-body phase space and we have used ⊗ to denote the convolutions, dropping the explicit dependence on the convolution variables. The ingredients necessary for NNLL accuracy are all available in the literature and many have been compiled in ref. [26]. For the H → bb case, we take the hard function from ref. [26]. Since we are considering only massless b-quarks, we can use the soft and jet functions as implemented in ref. [27] (and first calculated at NNLO in refs. [47][48][49]) for e + e − → jj, also recycling the evolution kernels from that work. For the H → gg case, the fully expanded hard function, including contributions to the Hgg effective vertex from both SCET and the effective theory where the top-quark is integrated out, appears in ref. [30]. The NNLO jet function [50] and the evolution kernels are also given therein, while we obtain the soft function via a Casimir rescaling of the H → bb case.
Numerical results
We have implemented the resummed calculation, eq.
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Because of the resummation of large logarithms of τ , our results provide a physical description at small τ , as can be seen in figure 1, improving on the resummed-expanded results presented in ref. [26]. However, the range of validity of the resummed calculation is still limited to low τ values, since the factorisation formula we rely on (eq. (2.3)) is only valid there. Comparing the two decay channels, we see that the H → bb process presents a higher peak, located at a lower value of τ , with a narrower width. The peak of the τ distribution in the H → gg case is instead lower and shifted to larger values of τ , with a broader width. This behaviour is in line with expectations based on a naive analysis of the Casimir scaling of the two processes.
In order to extend the validity of the calculation to all values of τ , one needs to match the resummed result to the fixed-order calculation, which provides the physical behaviour at large τ . Indeed, in this region, the nonsingular contribution becomes sizeable and exponentiating the singular contribution is no longer the correct approach. The matching of fixed-order calculations to resummation has long been established at the level of the resummed observable: the most straightforward approach simply adds the results for the resummed and fixed-order distributions in the τ variable and then subtracts the expansion of the resummed result up to the same order included in the fixed-order result. In this way the calculation is free from doubly counted contributions up to the given perturbative order and includes all the higher-order terms properly resummed.
While the approach just outlined works flawlessly for the τ distribution we are resumming, it is not directly applicable to the construction of a fully exclusive event generator. In the next section, section 3, we show how this can be achieved by means of the Geneva method, allowing us to perform the matching at the fully differential level. 3 3 Implementation in the Geneva framework
Geneva in a nutshell
The Geneva framework allows the matching of a resummed to a fixed-order calculation and thence to parton shower programs such as Pythia [51]. In so doing, it provides theoretical predictions which are accurate over the whole phase space and which describe realistic events of high multiplicity. These can then be hadronised and fed into the analysis routines used by the experimental collaborations. The method for separating events into different multiplicity bins and for performing the matching has already been described thoroughly in refs. [27,29] and related references. Therefore, in this context, we limit ourselves to restating the primary outcomes as applicable to the case of Higgs boson hadronic decays up to NNLL T +NNLO 2 accuracy. We remind the reader that in order to achieve a sensible separation between the exclusive 3-jet and the inclusive 4-jet decay rates, we must also perform the resummation of T cut
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Dropping the process label i for ease of notation, the Geneva Monte Carlo expressions for the exclusive 2-jet, 3-jet and the inclusive 4-jet rates are given by 4 where the B j , V j and W j are the 0-, 1-and 2-loop matrix elements for j partons in the final state. In the equations above, we have introduced the shorthand notation to indicate that the integration over a region of the M -body phase space is done keeping the N -body phase space and the value of some specific observable O fixed, with N ≤ M . 4 We make a slight abuse of notation in order to highlight the dependence of the dΓ mc i decay rate on the resolution parameters. When an argument contains a single term, e.g. T cut N , it means that the corresponding quantity has been integrated over up to the value of the argument. An argument TN > T cut N implies instead that the corresponding decay rate remains differential in the relevant resolution variable for values larger than the cutoff.
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The Θ O (Φ N ) term in the previous equation limits the integration to the phase space points included in the singular contribution for the given observable O. For example, when generating 3-body events we use where the map used by the 3 → 4 splitting has been constructed to preserve T 2 , i.e.
and Θ T (Φ 4 ) defines the projectable region of Φ 4 which can be reached starting from a point in Φ 3 with a specific value of T 2 . The usage of a T 2 -preserving mapping is necessary to ensure that the pointwise singular T 2 dependence is alike among all terms in eqs. (3.2) and (3.4) and that the cancellation of said singular terms is guaranteed on an event-by-event basis. The expressions in eqs. (3.3) and (3.5) encode the nonsingular contributions to the 3and 4-jet rates which arise from non-projectable configurations below the corresponding cut. This is highlighted by the appearance of the complementary Θ functions,Θ O , which account for any configuration which is not projectable either because it would result in an invalid underlying-Born flavour structure or because it does not satisfy the T 2 -preserving mapping (see also ref. [31]).
The term V C 3 denotes the soft-virtual contribution of a standard NLO local subtraction (in our implementation, we follow the FKS subtraction as detailed in ref. [52]). We have that with C 4 a singular approximation of B 4 : in practice we use the subtraction counterterms which we integrate over the radiation variables dΦ 4 /dΦ C 3 using the singular limit C of the phase space mapping. U 3 is a LL Sudakov which resums large logarithms of T 3 and U 3 its derivative with respect to T 3 . Its exact form is given by where the Casimir factor C k depends on the flavour content of the 3-jet event, C qqg = 2C F + C A or C ggg = 3C A , and we run the coupling at NNLL order. The term P(Φ N +1 ) represents a normalised splitting probability which serves to extend the differential dependence of the resummed terms from the N -jet to the (N +1)-jet phase space. For example, in eq. (3.2), the term P(Φ 3 ) makes the resummed spectrum in the first term (which is naturally differential in the Φ 2 variables and T 2 ) differential also in the additional two variables needed to cover the full Φ 3 phase space. These splitting probabilities are normalised, i.e. they satisfy The two extra variables are chosen to be an energy ratio z and an azimuthal angle φ. In the soft and collinear limit, z = E sister /(E sister + E daughter ) where the daughter and the sister
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are assigned to be the pair of particles that are closest according to the N -jettiness metric and which therefore set the value of T N , i.e. which minimise the quantity The daughter particle is defined to be the gluon for q → qg splittings, the quark for g → qq and the softer gluon for g → gg. These definitions in hand, the normalised splitting probability is given by where AP sp (z, φ) is the unregularised Altarelli-Parisi splitting function. 5 The implementation of the splitting probability requires us to construct the full Φ N +1 phase space from Φ N and a value of T N . Similarly, we mentioned above that the real integration in the fixed-order part of the calculation requires us to project from Φ N +1 configurations onto Φ N while preserving the value of T 2 . Both of these tasks demand a map that satisfies eq. (3.8) -the construction of such a map is detailed in appendix A.
Implementation details
In this section we discuss the particulars of the implementation of the Higgs boson decay processes in Geneva. Throughout this section we use the same settings and values for SM parameters as in section 2.2. In the H → bb case, we implement the analytic matrix elements found in ref. [14], while in the H → gg case we interface to the OpenLoops package [53][54][55].
Profile scales
The resummation provided by the RGE of the functions in eq. (2.3) correctly accounts for logarithms of the form log(T 2 /2M H ) which become large in size for small values of T 2 . In the fixed-order region, however, where T 2 is larger, such logarithms are more modest in size and continuing to resum them would introduce undesirable higher-order contributions.
We must therefore switch off the resummation before this happens. This can be achieved by setting all scales to a common nonsingular scale in the fixed-order region, µ NS = µ S = µ J = µ H , which stops the evolution ensuring that the resummed contribution is cancelled out exactly by the resummed-expanded. In order to achieve a smooth transition between the resummation and the fixed-order (FO) regimes, we make use of profile scales µ J (T 2 ) and µ S (T 2 ) which interpolate between the characteristic scales and µ NS [56,57]. Specifically, we have that (3.14) JHEP04(2021)254 where the common profile function f run (x) is given by This form has strict canonical scaling below x 1 and switches off the resummation above x 3 ; for a = 1 it matches the form of the profiles used in e.g. ref. [58]. In order to determine the choice of parameters a, x i it is instructive to examine the relative sizes of the singular and nonsingular contributions as a function of T 2 to determine where the resummation should be switched off. This is done for the two decay channels as shown in figure 2. We see that the singular and nonsingular pieces become similar in size at around τ ≡ T 2 /(2M H ) ≈ 0.3, and therefore set for both processes We notice that in the limit τ → 0 the singular contribution becomes an increasingly good approximation to the fixed-order result, reflecting the proper cancellation of the singular terms between the fixed-order and resummed-expanded parts of the calculation. We set the remaining parameters a = 1, ax 0 = 3 GeV/M H for the gg channel following ref. [30], while for the bb channel we set a = 1/2, ax 0 = 2.5 GeV/M H .
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The uncertainties associated with the resummed and fixed-order calculations are estimated by varying the profile scales. For the uncertainty arising from the FO part, we adopt the usual prescription of varying µ FO up and down by a factor of 2 and taking the maximal absolute deviation from the central value as a measure of the uncertainty. This preserves everywhere the ratios between the various scales µ H , µ J and µ S and so the arguments of the logarithms which are resummed by the RGE factors are unaffected. In the resummed case, we vary the profile scales for µ J and µ S about their central profiles while keeping µ H = µ FO fixed. Specifically, defining a variation function (see e.g. ref. [59]) we vary the soft-and jet-function scales such that where η = 1/6. In this way the arguments of the resummed logarithms are varied in order to estimate the size of higher-order corrections in the resummed series while maintaining the scale hierarchy More details on the specifics of this prescription may be found in ref. [59]. In addition, we include two more profiles where we vary all x i transition points by ±0.025 simultaneously. We thus obtain 6 profile variations in total and take the maximal absolute deviation in the result from the central value as the resummation uncertainty. The total uncertainty is then obtained as the quadrature sum of the resummation and fixed-order uncertainties. The profiles and their variations are shown in figure 3 for both the bb and gg cases.
Comparing the spectrum and the derivative of the cumulant
Since the profile scales which we just discussed have themselves a functional dependence on T 2 , the integral of the spectrum that one obtains from eq. (2.5) is not exactly equal to the cumulant in eq. (3.1) evaluated at the highest scale.
Choosing canonical scaling, i.e. µ ∝ T cut 2 , we have where T max 2 is the upper kinematical limit. By integrating the spectrum we therefore obtain not only the cumulant but also unwanted additional terms of higher order. Depending on the convergence properties of the perturbative series, these additional terms can be numerically relevant and cause a sizeable difference between the inclusive decay rate obtained from the resummed calculation and the FO result. To obviate this problem, we supplement the JHEP04(2021)254 spectrum in eqs. (3.2) and (3.4) with an additional higher order term. The contribution of this term is restricted to the region of T 2 where the spurious N 3 LL terms are sizeable, and vanishes in the FO region; crucially, upon integration it ensures that the FO rate is recovered. It takes the form: where κ(T 2 ) and µ h (T 2 ) are smooth functions. It is clear that this vanishes in the FO region where µ h (T 2 ) ∼ M H as required -in order to restrict its contribution further, we also choose κ(T 2 ) to tend to zero in this region to minimise its size before exact cancellation is reached and choose the profile scale µ h (T 2 ) to reach M H at a lower value of T 2 than the rest of the calculation. This prevents the accuracy of the tail of the spectrum from being spoiled, while keeping the resulting changes in the peak region contained within its scale uncertainty band. We tune κ(T 2 ) to recover the correct inclusive rate, both for the central FO scale and also for its variations such that the result of integration is identical to a FO calculation for inclusive quantities.
Power-suppressed corrections to the nonsingular cumulant
The integration of the differential decay rate in eq. (3.1) over the Φ 2 phase space produces an NNLO accurate total width. For differential quantities, however, the O(α 2 s ) terms in eq. (3.1) are guaranteed to be NNLO accurate only up to power corrections in T cut 2 since any projective map one could devise could not preserve all Φ 2 quantities simultaneously. This fundamental limit on the accuracy of event generators actually allows us to sidestep the problem of implementing a full NNLO subtraction -since the total width is the JHEP04(2021)254 only quantity that is certain to be NNLO accurate, we can drop all the O(α 2 s ) terms in the cumulant and achieve the correct NNLO width by reweighting. That is, rather than implementing the full form of eq. (3.1), we instead use which requires only a local NLO subtraction. The remaining nonsingular terms take the form where the functions f i (T cut 2 , Φ 2 ) are at worst logarithmically divergent in the small T cut 2 limit. We include the NLO term proportional to f 1 (T cut 2 , Φ 2 ) in eq. (3.21) via an on-the-fly NLO 2 calculation, but neglect the f 2 (T cut 2 , Φ 2 ) piece. The size of this neglected term as a function of the cut is shown in figure 4 for both processes. We see that at our default value of T cut 2 = 1 GeV the missing O(α 2 s ) terms are of a size ∼ 10 −5 GeV in both cases. This amounts to a relative correction of O(0.4%) for the bb channel and of O(1%) for the gg. Smaller power corrections could naturally also be obtained by modifying the factorisation formula eq. (2.3) to include subleading power contributions [60,61] or by lowering further the value of T cut 2 . In this limit, however, the calculation suffers from numerical problems originating from the stability of the matrix elements and of the NLO subtraction procedure close to extreme soft or collinear configurations, which motivates our default choice.
In order to correct for this discrepancy and obtain the correct NNLO inclusive decay width, we may simply rescale the weights of the Φ 2 events in such a way that we match the known analytic result at NNLO. We are thus able to include the effects of the f 2 term JHEP04(2021)254 in eq. (3.22) on the total cross section that would have been present had we implemented eq. (3.1) literally. Since neither eq. (3.1) nor our approach in eq. (3.21) achieves the exact O(α 2 s ) Φ 2 dependence of all observables, our approximation does not inherently limit the accuracy of our predictions.
Interface to the parton shower
We briefly recap the main features of the parton shower interface in Geneva here and refer the interested reader to section 3 of ref. [29] for a more detailed discussion.
The partonic jet decay rates dΓ mc 2 , dΓ mc 3 and dΓ mc ≥4 each include contributions from higher multiplicity phase space points, but only in those cases where T N (Φ M ) < T cut N . In order to make the calculation fully differential in the higher multiplicities, a parton shower is interfaced which adds radiation to each jet decay rate in a unitary and recursive manner. Ideally, the shower should leave the values of the jet rates and their accuracy unaffected, restoring the emissions in dΓ mc 2 and dΓ mc 3 which were integrated over when the jet rates were constructed and also adding extra final-state partons to the inclusive dΓ mc ≥4 . For illustrative purposes, we consider a shower strongly ordered in T N , such that . . . A shower history of this kind could be constructed by taking the output of a shower ordered in a more conventional variable and reclustering the partons using the N -jettiness metric T N .
In general, the requirement of the preservation of the accuracy of the jet rates after applying the shower on a phase space point Φ N sets constraints on the point Φ M reached after the shower. For the cases in which the showered events originate from Φ 2 events, the main constraint is that the integral of the decay rate below the T cut 2 (which is NNLL +NNLO accurate) must not be modified. The emissions generated by the shower must in this case satisfy T 2 (Φ N ) < T cut 2 , so that they recover the events which were integrated over in the construction of the 2-jet exclusive decay rate and add events with more emissions below the cut. In case of a single shower emission we require also that the resulting Φ 3 point is projectable onto Φ 2 , as these are the only configurations at this order which are included in eq. (3.21). Both of these conditions can be implemented with a careful choice of the starting scale of the shower. The preservation of the decay rate below the cut is then ensured by the unitarity of the shower evolution. In practice, we allow for a tiny spillover up to 5% above T cut 2 in order to smoothen the transition. The showering of Φ 3 and Φ 4 events must be treated more carefully in order to preserve the NNLL +NNLO accuracy of the T 2 spectrum. Crucially, we must ensure that the Φ 4 points produced after the first emission are projectable onto Φ 3 using the T 2 -preserving map discussed in appendix A. Since the shower cannot guarantee this, we instead perform the first emission in Geneva (using the analytic form of the LL Sudakov factor and phase space maps) and only thereafter allow the shower to act as usual, subject to the restriction T 4 (Φ N ) ≤ T 3 (Φ 4 ). We apply this procedure only to the Φ 3 events and find that ) .
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By choosing Λ 3 ∼ Λ QCD , the Sudakov factor U 3 (T cut 3 , Λ 3 ) becomes vanishingly small and we can relax the shower conditions on the 3-jet contributions. The showered events therefore originate almost exclusively from either dΓ mc 2 or dΓ mc ≥4 . We choose starting scales of T cut 2 and T cut 3 for the Φ 2 and Φ 3 events respectively. For the Φ 4 events, the starting scale t needs to be a measure of the hardness of the splitting, for example the 3-jettiness value T 3 . Here we follow the choice made in ref. [40] and set where the energies are defined in the Higgs boson rest frame. After interfacing to the Pythia8 parton shower, we expect the accuracy for observables other than T 2 to be no worse than that of the standalone Pythia8 shower.
Nonperturbative power corrections and hadronisation
The approach described up to now does not take into account nonperturbative power corrections, which can significantly affect the partonic predictions. The framework of SCET allows these nonperturbative effects to be systematically included via the introduction of a shape function f (k, µ) modifying the soft component as [44,62,63] where S pert 2 is the perturbative soft function. At small T 2 ∼ Λ QCD the shape function gives an O(1) contribution to the cross section, while for larger T 2 values one can show that the dominant contribution is of O(Λ QCD /T 2 ) and results in a overall shift of the T 2 spectrum [56]. The same conclusions can be reached using a dispersive model and an effective value for the strong coupling constant in the nonperturbative regime [64][65][66][67].
The resummed predictions obtained by Geneva at the partonic level only include the perturbative soft function, and we delegate the provision of nonperturbative ingredients to the hadronisation models used in Pythia8. Therefore, after the showering stage, the events are interfaced to the phenomenological hadronisation model in Pythia8 without further constraints on the kinematics of the hadronised event. This means that the hadronisation can potentially cause significant shifts of the T 2 spectrum.
It is known that the 2-jettiness and the thrust observables receive different hadronisation corrections, due to the different treatment of the hadron masses in their definitions [68,69]. Since there are currently no experimental data with which we can compare for these decay channels, in this work we consistently use the definition of T 2 in eq. (2.1) even for hadronised events, despite the larger power corrections compared to schemes with a different mass treatment. This is different from the approach taken for the e + e − → jets study in ref. [27], where the definition based on thrust was used to compare to LEP data.
It is important to notice that we do not include uncertainties from these nonperturbative contributions in the results presented in the next section. In our approach, a crude estimate of their size could in principle be obtained by varying the tune parameters of the Table 1. Comparison of Higgs boson partial widths obtained from NNLO analytic expressions and at the partonic level from Geneva. Note that, due to the presence of the power corrections displayed in figure 4, the values do not agree exactly within the statistical error and therefore a reweighting must be performed.
of this work. It is worth noting, however, that in any calculation obtained by matching higher-order calculations with parton shower one has to carefully evaluate which parameters are truly encoding nonperturbative effects and should therefore be tuned.
Results
In this section we present the full Geneva results obtained by matching the resummed calculation to the fixed order. We adopt the same values of SM parameters as in section 2.2 and set T cut 2 = T cut 3 = 1 GeV. We interface to the Pythia8 generator which showers our events 6 and use the e + e − tune 3, turn off QED effects and prevent the decay of b-hadrons. We set the strong coupling used by Pythia8 to α s = 0.118, although ideally, one should perform a dedicated tune to accommodate for this change.
With the setup as described, we verified that we obtain the correct NNLO decay rate up to the power corrections shown in figure 4. The partonic results are presented for each channel in table 1, where the analytic values have been obtained using the formulae appearing in appendix B. In general, the Geneva method also guarantees NNLO accuracy for distributions differential in the Born variables of the process (see for example ref. [31]). In the case of a spin-0 boson decaying into two particles, however, the Born phase space is parameterised by only two angles and is flat in both -there is therefore no non-trivial shape information which can be compared to a fixed-order calculation. We have, however, validated our NLO calculations of H → bbg and H → ggg/H → qqg against aMC@NLO [70] and found perfect agreement. We checked that by increasing the T cut 2 to ∼ 5 GeV we obtain smaller power corrections (see figure 4) -however, since this would limit our higher-order resummed predictions for the shape of the spectrum to T 2 > 5 GeV, in the following we continue to use T cut 2 = 1 GeV and accordingly reweight our events in order to obtain the correct total decay width. 6 The publicly available Pythia8.235 version we used has difficulty parsing events read from an LHEF file in which only one particle appears in the initial state -we therefore add dummy neutrino beams using code provided by S. Prestel to mimic a collider process. A comparison of the NNLO+NNLL results at the partonic and showered levels is presented in figure 5 for the H → bb process and in figure 7 for the H → gg process, while the corresponding comparisons of the showered and hadronised events are shown in figures 6 and 8. The panels in the plots show three different regions of the 2-jettiness spectrum: the peak (leftmost panels), where resummation effects are expected to be dominant; the transition (centre panels), where the resummed and fixed-order calculations compete for importance; and the tail (rightmost panels), where the resummation is switched off and the fixed-order calculation provides the correct physical description. We observe that in the bb channel the T 2 is well preserved by the shower, while hadronisation effects shift the distribution to higher values of T 2 across all regions. This can be compared to the results obtained in ref. [27], keeping in mind the aforementioned difference between the 2-jettiness definitions used at hadron level and the different energy scale which result in competing contributions to the shift.
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In the gg channel, the effect of the shower on the T 2 spectrum is greater, especially at the lowest values of T 2 , but it preserves the shape of the distribution to within the scale variation bands closer to the peak and in the transition region. We also notice that the partonic and showered predictions give a negative cross section for very small values of T 2 , below the JHEP04(2021)254 nonperturbative freeze-out of the profile scales. This behaviour should not be concerning as it happens in a region where the perturbative resummed results are already questionable and, as mentioned before, we do not include any nonperturbative uncertainty. We have verified that the size of the negative value is augmented by the nonsingular corrections which we include via an additive approach. Indeed, when examining the resummed T 2 distribution alone, the behaviour at small T 2 remains negative but is compatible with a value of zero to within the quoted uncertainties.
A peculiar feature is observed in the first bin of figure 7, which contains the cross section below T cut 2 and is positive. This is again a consequence of the missing nonsingular corrections in eq. (3.21), which are included by the reweighting procedure. Since these are particularly large for this process, see figure 4, their effect is to change the sign of the cumulant below T cut 2 . We also observe somewhat larger effects on the spectrum due to hadronisation compared to the bb case, particularly in the peak region. The seemingly unusual behaviour at small T 2 is a consequence of the already discussed shift of the spectrum after hadronisation resulting in a smearing of the first bin. We stress again that the small error bands reported are due to the lack of nonperturbative uncertainties. Figure 9. Jet broadening and the JADE two-to-three differential jet rate at the partonic, showered and hadronised levels for H → bb. Figure 10. Jet broadening and the JADE two-to-three differential jet rate at the partonic, showered and hadronised levels for H → gg.
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Finally, in figures 9 and 10 we show the results for distributions other than the 2-jettiness that we use as input to our Geneva implementation, for the bb and gg cases respectively. We consider the JADE clustering metric y 23 for separating two exclusive jets from three or more [71,72] and the jet broadening (B T ) [73,74] event shape defined as follows where the sum runs over all final state particles andn T is the thrust axis.
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It is important to remark that we do not expect the Geneva method to provide a higher formal accuracy for these observables, but it is nonetheless interesting to observe the effects of our predictions at the various stages. In general the bb decay channel is better behaved after showering, providing results that are compatible with the predictions at the partonic level over the majority of the phase space.
We notice that, at small values of the jet broadening, some unappealing artefacts appear. We have verified that these features are a consequence of the additive matching to the fixed-order calculation, used to include the nonsingular corrections. They are not present, for example, when examining the jet broadening distribution of events obtained from the T 2 resummed calculation alone. We therefore conclude that the secondary peak which appears constitutes an effect beyond the perturbative accuracy of our formulae, despite being numerically large. In the future, one could explore whether by exploiting the freedom in the handling of the recoil by the 3 → 4 mapping one could ameliorate this undesirable effect -however, we do not pursue this further here. We also see deviations for particular values of the observables after hadronisation and hadron decays are included. In particular we notice a significant shift in the JADE y 23 observable for both decay channels, which is not unexpected for this specific jet-clustering measure.
Conclusions
In this work we have resummed the 2-jettiness at NNLL for hadronic Higgs boson decays in the bb and gg channels via a SCET approach. Compared to previous fixed-order results, we observe the expected improved behaviour in the small T 2 region, where the physical Sudakov peak is now described correctly. We have also implemented these processes in the Geneva framework, which has allowed us to match the resummed calculations with NNLO fixed-order predictions and to a parton shower. This has required an examination of the interplay of the singular and nonsingular contributions, in order to determine the region in which resummation effects are dominant and hence design profile scales which provide a smooth transition between the resummed and fixed-order regimes. As a result we have produced NNLO accurate event generators interfaced to the Pythia8 parton shower for the two processes, which provide accurate predictions in all regions of phase space.
We compared predictions at the partonic, showered and hadronised levels, finding the expected good agreement for the total decay rates and for the T 2 distribution up to the showered level. We observed larger differences due to the hadronisation, especially in the gg channel.
The completion of this work will eventually allow us to combine our H → bb result with the Geneva V H production generator in the narrow width approximation, yielding a full NNLOPS generator for the signal channel of the l + l − bb final state. Given the recent observation [3,4] of the Higgsstrahlung process by the ATLAS & CMS experiments at the LHC, this will constitute an important phenomenological result. It will also allow a direct comparison with the only other existing NNLOPS generator for this process [40]. In light of the findings in ref. [26] regarding the convergence of the perturbative series and the N 3 LO results at fixed order which are also available for this decay channel, it might also be JHEP04(2021)254 interesting to consider building an event generator at N 3 LOPS level. Another avenue for development might be the inclusion of a finite b-quark mass in the generator, given recent work on fixed-order calculations [19]. We leave this to future consideration.
A Constructing a 2-jettiness-preserving map
The map used for 3 → 4-body splittings and 4 → 3-body projections presented in this section was first developed and applied to the process e + e − → jj in ref. [27]. Here, we detail the construction of the map as used in that work and in addition provide the translation to the splitting variables T 2 , z and φ needed for the Higgs boson decay case.
We start by considering the case of a splitting, which takes as input N -body phase space points Φ N and generates from them (N+1)-body phase-space points Φ N +1 . Since we wish to calculate the NLO distribution in 2-jettiness, T 2 , while still generating exclusive Φ 3 points, we must use a map that produces Φ 4 points with the same value of T 2 as the Φ 3 points with which we started. Unfortunately, the construction of such a map is challenging since T 2 is a global variable. A more manageable approach is to seek a map which preserves not the exact 2-jettiness, T 2 , but instead a related quantity, the fully recursive 2-jettiness, T FR 2 , defined by the following procedure: 1. Recursively cluster the starting phase space point Φ M down to a Φ 3 point using the N -jettiness metric for final state particles The quantity we obtain through this procedure has the same singular structure as the exact T 2 , with any differences being captured by the nonsingular contributions. Starting from the 3-parton phase space point Φ 3 , which is the input of the splitting map, we label its momenta as
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The thrust axis will lie along the direction of the hardest parton (i.e. along p 1 ), and we have that When we split to a 4-parton event and then cluster back to a massive 3-parton event, the thrust axis is still determined by the most energetic of the three partons and we have that If we are to preserve T FR 2 , clearly eqs. (A.3) and (A.4) must be equal and so the hardest parton in the massive 3-parton event obtained after reclustering must be parton 1. We can then split the massive leg to produce a 4-parton point. The emitter may or may not be the hardest parton -these two cases must be treated separately.
We will now detail how the Φ 4 point is obtained from the Φ 3 point in the two separate cases while preserving T FR 2 . In addition, we will show in each case that taking the singular limits of the Jacobian of the transformation reproduces the limits of the FKS Jacobian and that our fixed-order subtractions in eq. (3.9) therefore survive unaltered.
A.1 Case 1: the emitter as hardest parton
We deal first with the case in which the emitter is the hardest parton, which we call the FR primary (FRp) map. In this case the emitter is p 1 and, denoting the sum of the momenta of the split pair by k, we must have that k p 1 in order to keep the thrust axis in the same direction. We must also have | k| = | p 1 |. These conditions therefore fix the sum of the three-momenta of the split pair.
In order to proceed with the actual construction of the split configuration we use the same choice of variables as in the FKS approach, and therefore adopt a similar notation: we label the momenta in Φ 3 byk 1 ,k 2 ,k 3 , with the emitter chosen ask 3 . For the Φ 4 momenta we use k 1 , . . . , k 4 with the split pair k 3 , k 4 and k = k 3 + k 4 . The recoil momenta are defined as k rec =k 1 +k 2 , k rec = k 1 + k 2 . (A.5) As discussed above, the splitting preserves the three-momentum of the emitter which constrains the momentum of the split pair and the recoil: We must now determine k 0 and define the recoil constituents such that they remain massless and sum to k rec . Since we have that | k| = | k 3 | =k 0 3 , we may obtain an expression for k 0 : Recalling the definitions of the FKS variables Φ FKS rad ≡ {ξ, y, φ}
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we may substitute in and solve the quadratic equation; one obtains Having determined k 0 in terms of ξ and y, we must carefully examine which solutions are kinematically allowed. The specific Φ FKS rad variables determine which (if either) of these roots are permitted. In addition to ensuring that the solutions are real, we must also have that k 0 >k 0 3 and that k 0 3 > 0. The reality constraint gives The effect of the remaining two constraints is determined by the sign of y. For y > 0, only the positive root is a valid solution (since k 0 3 < 0 for the negative root), and we have a stronger constraint on ξ: For y < 0, the positive root is valid over the range in ξ set by the real constraint, and the negative root is valid for ξ > 2k 0 3 /E cm : It remains for us to construct the four momenta of the Φ 4 event. We define 16) and the parameter We assign the recoil by defining a boost B t along k rec with magnitude β t and a constant scaling of momenta α, so that Boosting along the recoil direction and then rescaling momenta allows us to keep the recoil three-momentum fixed. We can solve for the parameters α and β t using
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which gives two constraints: These can be solved in terms of δ andk 0 3 to obtain For the splitting to exist, we must also ensure that 0 < β t < 1. Rewriting β t as , (A. 24) we see that for k 0 , k 0 rec >k 0 3 (i.e. for timelike k, k rec ), the condition on β t is satisfied. Specifically, we requirek The upper bound on k 0 implies the additional constraint where x = k 2 /E 2 cm . This can be translated into a constraint on ξ and y. We may then split k into k 3 and k 4 using the FKS variables in the same way as for the FKS splitting.
We can also invert the procedure and construct the projective map from Φ 4 to Φ 3 . Again we must preserve the three-momentum of the split pair, so that We need only now define the individual partons in the recoil, which we achieve by using the same boost technique as before. Defininḡ where the inverse boost is now along − k rec , as before we can obtain two constraints: Solving, we naturally recover the same α and β t as in eq. (A.22). In this case, however, the constraints 0 < β t < 1 and 0 < α < 1 are automatically satisfied so that the projection from any Φ 4 point onto a Φ 3 point is well-defined.
Substituting eq. (A.10) into eq. (A.34), one can verify that taking the limit α → 1 and expanding about ξ = 0 or y = 1 one obtains the soft or collinear limits of the FKS Jacobian, see e.g. section 5 of [52]. This means that one can use the same counterterms as those of the FKS subtraction to obtain a local cancellation of the infrared divergences.
A.2 Case 2: the emitter as a softer parton
In the case where the emitter is not the most energetic particle, the FRp map is no longer appropriate because we no longer need to keep the thrust-axis aligned with the emitter.
In this case, we can use instead the Catani-Seymour (CS) map [75]. For example, if we assume the emitter is p 2 and perform the splitting considering p 3 as the spectator parton, the hardest parton p 1 is then unchanged by the splitting and the quantity (p 2 + p 3 ) 2 is preserved. 7 This means that the thrust axis remains along p 1 and that the value of T FR 2 is also unchanged. It is left for us to show that the singular limit of the Jacobian when using the CS map with FKS variables is the same as in the FKS case up to an overall rescaling.
To describe the splitting in this case we adopt the CS notation, wherep ij is the emitter andp k is the recoil in the Φ 3 phase space. The daughters of the splitting are labelled p i and p j , while p k is the recoil in the Φ 4 phase space: p ij +p k → p i + p j + p k = p ij + p k .
(A. 35) For the case at hand, we begin by factorising Φ 4 into the 4-parton CS phase space and a radiation part where y ij,k = p i · p j p i · p j + p i · p k + p j · p k = (p i + p j ) 2 (p i + p j + p k ) 2 (A.37) and x, Ω 2 are a set of variables which parameterise the splitting p ij → p i + p j . We now wish to express the {x, cos θ} in terms of the FKS variables {ξ, y} which we do using the 7 When the emitter is instead p3 the rôles of the emitter and spectator are interchanged but the same quantities are preserved.
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defining relations of the CS and FKS variables: Solving, we find that The Jacobian of this transformation is given by which are exactly the soft and collinear limits of the Jacobian in the usual FKS map. Once again, the consequence is that the subtractions are precisely the same as in the FKS case and we are therefore able to use the CS mapping consistently with the FKS subtractions.
A.3 Recasting the mapping for use in the splitting functions
The mapping which we have constructed in this appendix is used not only in the fixed-order pieces of eqs. (3.2) and (3.4) but also to make the resummed spectrum fully differential in Φ 4 via the splitting function defined in eq. (3.13). We must therefore be able to construct JHEP04(2021)254 a Φ 4 phase space point using the mapping given a Φ 3 point and values of three splitting variables. 8 This can be achieved à la FKS, but in order to do so we must express our splitting variables in eq. (3.13) in terms of the FKS variables. We consider four momenta p 12 , p 3 , p 4 before the splitting producing a configuration p 1 , p 2 , p 3 , p 4 afterwards and assume the hierarchy E 1 < E 2 < E 3 < E 4 . Our splitting variables are defined to be the azimuthal angle φ, the 3-jettiness T 3 and an energy ratio z: where | p 12 | = | p 1 + p 2 |. Rewriting, we have that It remains for us to determine the quantity | p 12 | in terms of the Φ 3 momenta. This depends on whether the FRp or CS map is being used. In the FRp case, this is rather straightforward -the FRp map preserves the value of | p 12 | by construction and so we have that | p 12 | = | p 12 |. Thus, the last term in the numerator of eq. (A.56) disappears and the expression simplifies. In the CS case, matters are slightly more complicated. The map preserves the four-momentum of the most energetic particle p 4 while p 3 is the spectator; from the definition of the CS variables, we have that | 13,304.2 | 2020-09-28T00:00:00.000 | [
"Physics"
] |
Parametric amplification of the signals in the electrostatic graviinertial sensor
The challenges of designing simple, reliable, and high sensitivity graviinertial sensors are investigated. The sensor comprises a proof mass (PM) and is fixed with the housing by the elastic torsion suspension. PM makes small rotations under the action of gravitational forces or inertial forces. The distinctive features of the sensor are that the differential electrostatic system provides simultaneous reading of the desired signal and a control the torsional rigidity of suspension. In addition, the PM's rotational angular velocity transforms in the alternating current flowing through the capacitors. The presence of аlternating current (AC) voltage sources allows to get the parametric amplification of AC and significantly to improve the sensitivity of the sensor. In the simplest case, the sensor does not contain any feedback circuits. As an example, calculations of the micromechanical linear accelerations confirm that the periodic modulation of the coefficient of elastic stiffness of the suspension can significantly increase the sensitivity in the low frequency range, even in the absence of parametric resonance. Conditions for suppressions of background current participating in the output signal from a parametric pumping due to the asymmetry of the differential circuits are set. The frequency characteristics calculations of the sensor were carried out. It is expected, that the proposed sensor design ensures minimum noise level, which can be achievable in the graviinertial sensors. This design and the constructed theory can serve as a basis for creating a wide range of graviinertial devices operating on a movable base, for example, linear and angular accelerometer, gravity gradiometer, gravimeters, and inclinometers, which can be realized in the hybrid and in the micromechanical versions.
Introduction
Due to the rapid development of micro-and nano satellites weighing not more than 100 kg and 10 kg, respectively, [3], which are used for the study of celestial bodies and asteroids from outer near space, as well as for studies surface of these objects, there is an urgent need for the development of simple, low-cost and small-size graviinertial devices for placement in these satellites. The results of these studies can are used to examine the internal structure of the heavy bodies, as well as to detect heterogeneities located close to the surface, for example, that may be required during construction anything objects on them [4][5][6][7].
Graviinertial devices include, for example, gravity gradiometers, gravimeters, accelerometers, inclinometers, vibration meters and others. Gravity Gradiometers (GG) used for measurements on moving objects have particular importance among these devices. The development of GG -this is one of the most difficult problems of modern instrumentation design [1,8]. Currently used GG could be divided into two types [1]: the first type is «warm» devices that operate at room temperature, constructed on the basis of rotating linear accelerometers e.g. devices FTG (Full Tensor Gradiometer) or Air-FTG and the AGG (Airborne Gravity Gradiometer), developed by Lockheed Martin Corporation. GG with nonrotating linear accelerometers can be attributed here also, which were designed by ESA (European Space Agency) and existed for 4 years; 2009 to 2013 within the framework of the program GOCE (Gravity field and steady-state Ocean Circulation Explorer) on board Low Earth Orbit satellite [36][37][38].
The second type of GG is «cold» devices operating at the boiling temperature of liquid helium, constructed on the basis of angular accelerometers e.g. the devices HD-AGG (High Definition Airborne Gravity Gradiometry) and VK1, developed by GEDEX (Gedex Systems Inc.), University of Western Australia (UWA) and the University of Maryland (UM). The record of low error in «cold» GG which is under development is focused on the achievement of error 1 Eo (Eo -Eötvös, 1Eo = 10 -9 s -2 ) at the time interval of measurement of one second and noise level of 1 Eo / Hz 1/2 in the frequency band of 0.001 to 1 Hz [ 1, 2,8].
It is recognized that «warm» and «cold» GG have common disadvantages: they are expensive, heavy and bulky, making them difficult to be used in the near space, because they can not be hosted in microand nano satellites. Therefore, the creation of simple and small-sized GG and other graviinertial devices is an actual problem of modern instrumentation. It seems obvious that these devices should be carried in a «warm version» to eliminate the need to create the reserves of liquid helium in satellites.
The development of compact GG is primarily linked with the advent of MEMS (microelectromechanical systems) technology [9,15,19]. However, specific problems exist when fabricating graviinertial devices using MEMS method. First problem is that elastic hangers for the proof mass (PM) must satisfy two conflicting requirements: on the one hand, they must have a high flexibility in the direction associated with the axis of sensitivity of the instrument and, on the other hand, they must have a high strength to resist gravitational action and to withstand shocks and vibrations occurring during start and progress in the space orbit [18].
The second problem is the creation of highly sensitive readout signals generated by the movements of elastically suspended PM having small size and low power consumption. Capacitive displacement sensors can respond these requirements [16]. However, the standard capacitive sensors can only be used with additional radio frequency (RF) generators with a frequency of about (10 5 -10 6 ) Hz to trigger them. The main drawback of these sensors is the presence of parasitic capacitances, and, RF signals that can penetrate in the output circuits of the sensors and generate additional noise limiting the sensitivity of the devices [10,17,23,35].
Third problem is the noise generated inside the instrument [20]. It is known, that with decreasing device size, there is an increase in the zero drift and in the ratio noise/signal [10][11][12][13]. In particular, the growth of the 1/f noise with a decrease in the size of the conductive elements is known [14]. Presumably, for these reasons in the open press there is no information on the use of GG constructed based on integrated technologies.
One of the possible ways to reduce the noise in the small size GG is to develop a hybrid design in which the PM has size as large as it possible [18] with a possible weight of from 100 to 200 g. For measurements in the near-Earth space, the «hybrid» would have a mass of 1 kg, the volume of 1 dm 3 and 0,001 sensitivity Eo / Hz 1/2 . For this design to provide a measurement time of 1 s, the operating frequency should be below 0.04 Hz and the resonance frequency of 1 Hz [8,18]. At the same time, for the purpose of «planetologistik» it is sufficient to have a sensitivity of GG 1 Eo / Hz 1/2 [15,19].
The purpose of this paper is to offer a new concept of building a simple and reliable «warm» electrostatic pendulum sensor, which has high sensitivity and low noise. This concept can be used in the development of graviinertial devices capable of operating both on Earth and in space, and facilitate the solution of the above three problems arising in the development of GG.
Features of the proposed graviinertial sensor
Schematic description of the graviinertial sensor (GIS) is illustrated in Figure 1. The sensor comprises a pendulum elastically suspended in electrical field that is generated by the differential capacitive system and the sources of direct and alternating voltage. It is assumed, that the frequency of the AC voltage is higher than the frequency of the signals being measured, but is low enough to electromechanical sensor circuit considered as a circuit with lumped elements. The electric field sensor performs two functions; it reduces the rigidity of the torsional suspension and provides a readout of the desired signal. The first of these features facilitates the solution to the first problem mentioned previously, since the electric field decreases the known resonant frequency of the sensor. The less the resonant frequency of the sensor, the more sensitivity is allowable [15].
The readout of the useful signal using the inner electrostatic system eliminates the need to use radio frequency generators to simplify circuitry and reduces, in GIS, various internal noise that are generated in the sensor [20], hence facilitating a solution to the second problem mentioned previously.
A distinctive feature of the sensor is that the differential electrostatic system performs direct conversion of PM's angular velocity in current flowing in the electrical circuit. The output current of this device is considered as the desired signal.
Dependency of the PM suspension rigidity on the electrostatic field and the presence of alternating electrostatic fields in the sensor allow periodic modulation of the stiffness of the suspension, and as consequence, allow significant parametric amplification of the output current in this sensor. The current's carrier frequency can be set arbitrarily, that allows shifting it to the frequency range with low noise. This feature can solve the third problem described previously.
Parametric transformation and amplification of signals commonly used in designing tiny sensors NEMS and MEMS, started approximately in 1991 [21]. Practically unlimited number of publications are devoted to the study of the properties of systems with parametric excitation. It has been found that such systems have unique features as compared with the systems of external excitation [24,25]. In particular, in such systems, parametric resonance may occur in several frequency bands (resonance regions), and in the case of linear systems, the maximum value of the oscillation amplitude is not limited in these bands, even if there is energy dissipation. Only the nonlinearity of the parametric system limits the maximum amplitude of the parametric resonance [26]. The dissipation of energy determines the threshold pump amplitude (amplitude modulation), which is a characteristic for each of the resonance zones.
It was proved that the sensors with parametric excitation might have high sensitivity as in a vacuum and in the air [27][28][29][30], and sensors with parametric amplification of signals can be more sustainable, cheap and portable [31] compared to sensors with conventional external excitation.
A simple system was first described in [22], in which the parametric amplification of the signal by modulating the torsion rigidity of the mechanical oscillator, in an electric field was observed. The amplifier of this type is of particular interest because it has been proven that the noise in parametric amplifiers can be reduced to a quantum-mechanical level [21]. These results, in principle, can be produced in any structures size [22].
The above-described properties of the parametrically excited systems are promising for use in GIS to achieve high gain and low noise level. However, the results presented in [21] were obtained near the resonance frequency of the parametric pump that is twice the frequency of the resonator. The GG on a movable base have to have a flat frequency response in the range of operating frequency of the order of 1 Hz or less. Therefore, resonance measurement modes should be avoided in the GIS.
On the other side, parametric amplification of the signals in the non-resonant modes at low-frequency range does not usually investigated. However, as far as it is known, Den Hartog was the first who point out that the work of the parametric pump source can be positive, even in the case of a constant external signal, acting on a parametric system [32]. Hence, it issues from this, that the low frequency signals might be amplified in parametric sensor. We use this feature of parametric system in the sensor is being designed now.
Physical and mathematical models of graviinertial sensor Figure 1 shows the design scheme of the universal sensor, in which the PM has the form of elastically suspended conductive plate 1. Elastic connection sensor's housing with the PM is presented in the form of a torsion 2, whose axis is perpendicular to the plane of the figure. Two conductive electrodes 4 which are attached with fixed non-conductive plate 3. The electrodes 4 form together with PM two capacitors whose capacitance changes when PM tilts. Capacitors, conductive elements and the PM form an electrical circuit, which includes the sources of direct and alternating voltage. Moreover, for completeness, to be able to investigate in the sensor the influence of penetrating noises, noise sources in the form of discrete noise generators are incorporated in the sensor circuit. References [33,34] examined the conditions of static and dynamic stability and modes of free and forced PM vibrations of a similar sensor in the absence of AC sources. It has been shown that the sensor's stability greatly depends on the symmetry of the electrostatic system (ES).
In particular, it was found that significant reduction of stiffness torsion suspension under the action of electrostatic forces, in order to increase the sensitivity of the sensor, it is only possible if the symmetry satisfies stringent requirements of ES. For example, the resonant frequency of the sensor can be reduced tenfold asymmetry if ES does not exceed a few tenths of a percent.
Capacitors, shown in Figure 1, depend on the angle of inclination φ PM. In [33] proposed a method to calculate the capacitors with inclined planes obtained with simple formulas which are convenient for calculating the moments of the forces of the electric field acting on the PM that does not require expansions in powers of the small argument. Using this formula, and assuming that the EC is not symmetrical, introducing electrical asymmetry coefficient γ of this sensor, we have: (1) where: (2) If q 1 and q 2 are charges, respectively, in the capacitors C 1 and C 2 , the moments of the forces acting on the PM from these charges are given by: Given the moment of the elastic forces of the suspension and the directions moments of the mechanical and electrical forces, the resulting moment acting on the PM is: Let, on the PM acts external moment M(t) = M z cos(nΩt), where Ω is the natural frequency of the sensor in the presence only of a source of constant electric field, n is an arbitrary fixed number; M z is the amplitude of this moment. Voltages sources of alternating electric field, represented in Figure 1, can be written in the form (i = 0; 1; 2): where V i -amplitude, Ω p -the resonant frequency of the sensor in the presence of sources of direct and alternating field; n 1 -arbitrary constant number; v -arbitrary number that allows to set the phase of the parametric pumping relative to the phase of the moment of external force; N i (t) и f i (t) -asked random functions to simulate noise on the sensor input. In the calculations we can assume that where rnd(1) -the random number generator, uniformly distributed between zero and one, n 2 -arbitrary number. Let us introduce further notation: Applying the laws of Kirchhoff to the circuit in Figure 1 and using the formula (1)-(5), we obtain a system of equations describing the dynamics of the GIS: (11) where I z -the moment of inertia of the PM with respect to the torsion axis; I 1 and I 2 -currents, as shown in Figure 1. The mathematical model of the sensor, the system described by (9)-(11) is a parametric nonlinear system of differential equations. Exact analytical solutions of the model in general are hardly possible. Therefore, to avoid the «fight against Mathieu equation or Floquet theory» [25], this system will be linearized in order to hold a preliminary analysis and get some interesting relationships between the sensor parameters, and after that the original nonlinear system will be solved numerically. Given that the charges q 1 and q 2 contain constants (q s ) and variable (q v ) components, these charges may be written in the form of: If the notations are introduced and then one can be assumed that all the resistors have fairly small values, so that the parameters τ 1 , τ 2 and τ considered as small. Also it can be assumed that Additionally, one can neglect terms containing q v with degrees higher than the first, as well as members with the time derivative of b 1 (t) and b 2 (t), containing as a multiplier settings τ 1 , τ 2 and τ. Also, a neglect of terms containing the parameters τ 1 , τ 2 and τ to a degree higher than the first, and their products may be done.
Below, it is shown that in the case when in parameters b 1 (t) and b 2 (t) are taken into account only the deterministic voltages sources, in the sensor has to be realized conditions under which the next equality is fulfilled: (13) For simplicity, the symbol «t» in b 1 (t) and b 2 (t) sometimes will be omit. Farther, from (13), in particular, it follows the equalities and given that one can get for charges q 1v and q 2v corresponding linear differential equations. Briefly, we write these equations in matrix form: where, if the notations α 1 = τ 1 +τ 2 γ 1 , α 2 = τ 1 τ 2 -τ 2 , are used: Parameters b 1 (t) and b 2 (t) are defined by formulas (7) and (8). They are independent from moment M z . Therefore, the second term in square brackets in the right-hand side of equation (14) can be regarded as equivalent to external disturbances acting on the PM. These disturbances are due to the presence of direct current (DC) and AC voltage sources in the sensor's electrical system, as well as the presence of noise in the system. Assuming that the amplitude of the direct and alternating voltage sources can be adjusted, easy to see that the effect of the deterministic part of these external forces can be eliminated by ensuring the condition (13). However, in the case of random uncorrelated signals such regulation is hardly possible, and the random component of the disturbances on the sensor input remains.
One equation can be obtained from two equations in (14) for the sum charges q 1v and q 2v . The coefficients (15)−(17) in the equations (14) have identical form for both charges q 1v and q 2v . However, the right-hand sides of equations in (14) differs in view of the factors that are in braces. Taking into account the relation (13), under the total charge will be understood charge q v , defined by the equation: Then, when the conditions (13) and (19) have been satisfied, the desired equation for the total charge q v takes the form: Given that the current is from expressions (19) for the total current one have: (22) Formulas for calculating the currents I 1 and I 2 are given by (10) and (11). If one have an expression for the total current, it can be seen that the total current contains factors b 1 (t) and b 2 (t). As already mentioned, the relevant terms are background signals, because they do not contain measured signal amplitude M z . These background signals can significantly exceed the useful signals. It can be found, that the conditions of suppression of background signals is given by the condition (13).
Let assume, as above, that the voltage sources are deterministic (and can be adjusted). Also, for simplicity, it is assumed that the phases of all sources of noise are correlated with each other, but the values of their amplitudes cannot be adjusted. Then from (10)-(11) it can be found that the deterministic component of the background signal in the total output current (22) will be absent if the following conditions are fulfilled: When the conditions (23)-(25) for suppression of the background signal entering the output signal are satisfied, the issues from the formulas (10) and (11) that the output current I out (t) will have the form: Dependency of I out (t) can be calculated numerically, if to solve a system of (9)-(11) and to find the charges q 1v and q 2v as functions of time.
From the form of the second term in formula (26) that when the sensor ES asymmetry is small, i.e. γ 1 ≈1, the influence of noise generated in the central part of the circuit (Figure 1) that is the proportional amplitude N 0 is significantly attenuated. It also shows that in this case, noises N 1 and N 2 that were generated in the side chain branches also cancel each other if they are in identical phase. The elastic coefficient B 0 (t) in equation (20), contains a constant and a variable parts (Eq. (17)). Permanent part determines the resonant frequency of the sensor. For simplicity, we assume that additional voltage source are absent, i.e. E 1 = 0 V and V 1 = 0 V. Then, if there are conditions (23)-(24), the resonant frequency of the sensor will look like Eq. (27): (27) where -is the resonant frequency of the sensor in the absence of an electric field; and (28) -the square of the resonant frequency of the sensor in the presence of the constant electric field and in the absence of the alternating electric field. From formulas (27) and (28) it follows that the resonant frequency of the sensor depends on the stiffness k and on the voltages E 0 and V 0 . Such presence of electric fields reduces the torsional rigidity of the PM suspension that allows an increase of the sensitivity of the sensor without reducing the hardness of the suspension.
If AC voltage sources are absent and frequency Ω have been set, from (28) it may be found the value of the voltage E 0 a constant electric field, in which this frequency is achieved: The value of the amplitude of the alternating field voltage V 0 at which the frequency setpoint Ω P , it follows from formula (27): (30) From (30) is seen that for a setpoint Ω, the maximum value V 0 = V 0max of an alternating field amplitude at which Ω P = 0 is: As mentioned above, the sensor circuit shown in Figure 1, can be used to measure the various physical quantities. For this purpose, in each case it is necessary to determine the bond M z acting on the PM with the measured signal. In particular, if the gradient of the gravitational field, denoted as Γ, is a measured value, this bond is M z = I z . It should be noted that this formula is too simplified. In reality, the bond of M z and gradient Γ is more complicated [2,39,40]; if the measured value is the angular acceleration «e», of a sensor revolving around the torsion axis, the bond is M z = I z e; if the measured value is a component of the linear acceleration of a sensor revolving perpendicular to the axis of the torsion «a», the bond is: where r -a distance from the center of mass of the PM to the torsion axis; g -is a free fall acceleration.
The new principle in designing the GIS that was stated above including parametric transformation and amplification of the input signal is considered as an example of the micromechanical linear accelerometer. To simplify the numerical analysis, it will be assumed that the sources of constant voltage E 0 , E 1 and E 2 are absent. In addition, it will be assumed that an additional source of AC voltage V P1 (t) and all sources of noise V N0 (t), V N1 (t) and V N2 (t) are also absent. It is assumed Also that the phase setting v = 0 (see Eq. (6)). Under these conditions, a generalized scheme (Figure 1) transforms in the equivalent scheme is shown in Figure 2.
Subject to the above formulas (23)-(25) for compensation of the background current I b , some other formulas are simplified, and they take the next form of: frequency Ω = ω 0 , the value of the resonant frequency of the sensor Ω P is calculated by formula (33). (33) the maximum allowable amplitude of the alternating field is defined as: If to assume that the amplitude V 0 has been set, the condition for suppression of the background current I b (it is the AC voltage source with an amplitude V 2 that is used for this aim) takes the form:
Layout Options of the micromechanical accelerometer and results of calculations
We assume that the PM is made of technical silicon with the density ρ = 2.4 g / cm 3 , and it has a square shape with a side length of L = 12 mm and a thickness of d = 0.36 mm. The horizontal distance from the axis of the torsion to the middle of the electrode r = 6.5 mm; the gap between the electrodes and the PM h = 0.015 mm (see Figure 2). Conductive electrodes have also a square shape with a side length of more than 12 mm. Also, it is assumed that the natural frequency of the PM in the absence of an electric field was set to f 0 = 30 Hz and the resistance values R = R 2 = 5 Ohm. The value of the resistor R 1 is determined by the formula (25), if the value of the coefficient of asymmetry of electrostatic system γ is known.
Calculation of the formulas (3) gives the value of C s = 84.96 pF, the value of angle φ m = 4.024·10 -3 , the mass of PM is given the obvious estimate m = ρL 2 d = 1.244·10 -4 Kg. PM inertia moment about the axis of rotation (torsion axis) is calculated by the well-known formula: (36) that gives I z = 6.75·10 -9 Kg·m 2 .
The calculation of the remaining sensor parameters begin with the calculation of the allowable maximum value of the AC voltage amplitude by formula (34): V 0max = 6.76 V. The value of the viscous damping coefficient D, included in the formulas (9) and (15)-(17), will be calculated from the known relationship D and quality factor Q, as D = I z ω 0 /Q. In the calculations, two values of the quality factor were used: Q = 1000 and Q = 2.
The above formulas (23)- (25) for compensation of the background current I b , were obtained from an analysis of the linearized mathematical model of the sensor. Numerical calculations showed that these conditions are well satisfied in the original non-linear model providing suppression of signals from these sources. However, if at least one of these conditions is fulfilled with an error, the background current (i.e. the component of the current I b in the output of the sensor) will penetrate into the output signal from the AC voltage sources. The said compensation error can be accounted for in the calculations, if for example, formula (35) is rewritten as: According to the calculations, to suppress current I b , the more the parameter of asymmetry γ, the more requirement for permissible error ε. The asymmetry coefficient values that will be used in the calculations is γ = 0.01 and the requirement for error performing conditions compensation is ε = 0.001.
Below are the results of the accelerometer calculations for two values of voltage V 0 satisfying to condition V 0 < V 0max . These values are: V 0 ≡ V 01 = 0.1 V and V 0 ≡ V 02 = 6.7 V. In these cases, as follows from formula (33), the accelerometer design will have the following resonance frequencies f p1 ≈ 29.997 Hz ≈ f 0 and f p2 ≈ 3.988 Hz, respectively. The calculation of the compensating voltage V 2 is held by the formula (37).
Let define the sensitivity parameter of the sensor as a ratio of output amplitude to the amplitude of the measured acceleration: S = I out /a. In Figure 3, the amplitude-frequency characteristics of the accelerometer sensitivity are shown.
The left axis in Figure 3 represents the sensitivity of the sensor as a coefficient that links the output signal as amplitude of the current (22) and output signal as amplitude linear acceleration of a housing: (38) AC power source frequency was chosen from the next conditions: at V 0 = 0.1 V the dimensionless parameter n 1 = 60, so that the pump frequency n 1 ·f p2 ≈ 1800 Hz (see formula (6)). In another embodiment: at V 0 = 6.7 V the parameter n 1 = 451, so that the pump frequency was the same 1800 Hz, i.e. n 1 ·f p1 ≈ 1800 Hz. Another embodiment of the sensor: at the same value V 0 = 6.7 V the parameter n 1 = 60, so that the pump frequency was n 1 ·f p1 ≈ 239.3 Hz. In Figure 3, three solid curves relate to the sensors for which Q = 1000 and the three dotted curves relate to sensors for which Q = 2. In these sensors at M z = 0 and γ = 0, or ε = 0, the background current I b = 0. This proves that in the symmetric sensor, or, in the sensor, which accurately satisfies the conditions of compensation (23)- (25), it is indeed the background signal that does not penetrate into the output signal. The current value I b , generated when ε ≠ 0, restricts the minimum value of acceleration that can be measured by the sensor. This value may be determined by solving the non-linear system (9)-(11) and (22) when adjusting the value of the acceleration a, which define the equality I out = I b .
In these circumstances, the value of I out = 0.048 pA in the sensor with voltage V 0 = 0.1 V and with the pump frequency of 60·f p2 ≈ 1800 Hz meets the acceleration with the value a = a min1 ≈ 1,5·10 -7 g. In sensors with a voltage V 0 = 6.7 V and with the pump frequency of 451·f p1 ≈ 1800 Hz, and with the pump frequency of 60·f p1 ≈ 39.3 Hz, the current values I b , respectively, equal to 358 pA and 43 pA were obtained approximately at the same values minimum acceleration a = a min2 ≈ 3·10 -7 g.
The maximum accelerations amax, measured by the sensor, determines the value of the acceleration a, for which the system of equations (9)-(11) did not have a solution. It was found that in the sensor with a pump frequency of 60·f p2 ≈ 1800 Hz the acceleration a = a max1 ≈ 0.58 g. In the sensor with a pump frequency 451·f p1 ≈ 1800 Hz the acceleration a = a max2 ≈ 5.4·10 -4 g and in the sensor with a pump frequency 451·f p1 ≈ 239 Hz the acceleration a = a max3 ≈ 6.35·10 -4 g. It may to be noted that in the sensors, the nonlinear distortion of the dependence I out on a appears when a ≈ 0.1a max . Figure 4 shows the dependence of the accelerometer output signal at Q = 1000 on the input signal in all ranges of valid input signal values (symbols in this graph correspond to those in Figure 3). From this, it can be clearly seen that the sensor with the maximum resonant frequency has a maximum dynamic range where the sensitivity of the sensor has linear dependence on the input signal, up to a/g = 0.1. The available current I b in the sensor output indicates the presence of asymmetry of electrical circuit. This current can be used to reduce the error ε compensation of asymmetry by manual or automatic control voltage V 2 and the resistance R 2 to eliminate this current (see formulas (25) and (37)). In this case, the dynamic range of the accelerometer measurements can be extended towards small values of the measured signals.
Figures 5a-e shows the dependence of the output signal, expressed in pico Ampere, on time, expressed in seconds, for a sensor having a pump voltage V 0 = 0.1 Volt, the quality factor Q = 1000 and the pumping frequency of 1800 Hz, during measurement of linear acceleration with the amplitude a = 5·10 -3 g that harmonically varying with different frequencies: (a) is the DC signal; (b, d) are the signals with the frequency of 1 Hz and (c) is the signal with the resonance frequency f p2 ≈ 29.9967 Hz. Figure 5e shows the dependence on the action of a constant acceleration having the maximum amplitude a max1 = 0.58 g. Comparing this figure with Figure 5a allows to see the effect of non-linear distortion in the output signal of the accelerometer.
The forms dependencies in Figures 5 are determined by the period of the beat resulting by adding the signal with a frequency equal to the frequency n·f 0 of the measured signal and the signal with the frequency, f p2 is equal to the natural frequency of the sensor.
In the sensor with parametric pumping, it is possible to extend the dynamic range of the sensor to higher values of the measured signal.
This possibility is illustrated in Figure 6, where a presents the output signal of the accelerometer in the case when the sensor has voltage V 0 = 0.1 V and Q = 1 000 leading to a constant acceleration a = 0.60 g, which is greater than the maximum allowable acceleration a max1 = 0.58 g. It can be seen, that the sensor is in an unstable mode, since the output current increases unlimitedly with time. Figure 6 -The method for measuring by the sensor that is in unstable mode. a -proof mass oscillations in unstable mode at a = 0.6 g> a max . b -proof mass oscillation in unstable mode when a ≈ 0.9 g, but the voltage V P0 (t) (dotted curve) is switched on for a short time Figure 6, b shows that, if the sensor with former V 0 and Q is activated only for a certain period of time (in this case, by 0.002 seconds), unlimited current growth is absent, even when the measured acceleration a = 0.9 g > a max1 . The dependence of the output current over the entire range of changes of acceleration a min = 1.5·10 -7 g < a < a max = 0.9 g for this case is represented by the dashed line in Figure 4. It is seen, that Iout has linear relationship that is wider than in previous occasions. It is obvious that such pulsed switching voltage V P0 (t) (see formula (6)) can be repeated any number of times during the one cycle measurements.
The parameters of the micromechanical accelerometer that have been used in the calculations are only to illustrate new possibilities. They are not optimized for a particular measurement task, and can be varied considerably.
Conclusion
In the non-linear sensor with parametric transformation of the measured signal where there are many unique features, the design study requires special consideration. The above calculations in its simplest form have shown that some of these features allow implementing fundamentally new graviinertial sensor scheme and new measurement modes, securing great sensitivity.
This sensor has the new features as follows. The alternating electric field allows fulfilling the direct conversion of the angular speed of the proof mass in the alternating current in the sensor. In addition, the electric field allows to reduce and modulate the elasticity of the hanger and to carry out parametric amplification of the output electric current, even if the constant input signal is measured.
Notable features of parametric amplification of signals found in the literature, gave reasons to assume that the developed design GIS has the lowest achievable level of thermal and excess noise generated in the sensor.
Asymmetry of the electrostatic system in the sensor limits its sensitivity and causes the appearance in the output signal with alternating current generated by an alternating voltage source. The use of an additional source of alternating electric field allows to compensate this asymmetry and to reduce the background current. More compensation can be done by balancing resistance electrical circuits in the sensor. The relations between amplitudes of voltage sources and the values of resistors from one side with values of the asymmetry factor γ and with permissible error of compensation and of balancing ε, from other side, when the background current is absent, have been given. The requirement for error ε compensation and balancing increases with increasing coefficient of asymmetry γ.
As an example, numerical calculations of the micromechanical linear accelerometer were carried out. In particular, it has shown that if the parameters γ and ε do not exceed 0.1 %, a sensor with a resonant frequency of about 30 Hz, using an alternating voltage with an amplitude of 0.1 Volts and pumping frequency at 1800 Hz has a sensitivity that depends almost linearly on the acceleration amplitude in the range of 1.5·10 -7 g < a < 0.1 g. The calculated frequency response of the sensor is a horizontal in frequency range below 10 Hz, where the output signal amplitude is equal to approximately 7.3 nano Ampere. With increasing the voltage of the pump generator, sensor's sensitivity is increased, however, dynamic range and linearity range are reduced.
It should be noted that the calculations of the dynamics of a micromechanical sensor were carried out in the transition mode, moving mass oscillation that does not really matter for a relative small time of measurement. Besides, it was shown the possibility of the existence of the acceleration measurement method in an unstable oscillation mode proof mass, with the proviso that the envelope of the pumping voltage is a pulse with a duration greater than the duration of several periods of the pumping.
Graviinertial sensor design theory is universal; it is applicable to any pendulum sensor with a differential capacitive system. The next challenge will be to build the sensor and test its sensitivity despite possible manufacturing issues. | 8,843.8 | 2017-06-12T00:00:00.000 | [
"Engineering",
"Physics"
] |
Pharmacophore-Based Virtual Screening and In-Silico Explorations of Biomolecules (Curcumin Derivatives) of Curcuma longa as Potential Lead Inhibitors of ERBB and VEGFR-2 for the Treatment of Colorectal Cancer
The newly FDA-approved drug, Axitinib, is an effective therapy against RTKs, but it possesses severe adverse effects like hypertension, stomatitis, and dose-dependent toxicity. In order to ameliorate Axitinib’s downsides, the current study is expedited to search for energetically stable and optimized pharmacophore features of 14 curcumin (1,7-bis(4-hydroxy-3-methoxyphenyl)hepta-1,6-diene-3,5-dione) derivatives. The rationale behind the selection of curcumin derivatives is their reported anti-angiogenic and anti-cancer properties. Furthermore, they possessed a low molecular weight and a low toxicity profile. In the current investigation, the pharmacophore model-based drug design, facilitates the filtering of curcumin derivatives as VEGFR2 interfacial inhibitors. Initially, the Axitinib scaffold was used to build a pharmacophore query model against which curcumin derivatives were screened. Then, top hits from pharmacophore virtual screening were subjected to in-depth computational studies such as molecular docking, density functional theory (DFT) studies, molecular dynamics (MD) simulations, and ADMET property prediction. The findings of the current investigation revealed the substantial chemical reactivity of the compounds. Specifically, compounds S8, S11, and S14 produced potential molecular interactions against all four selected protein kinases. Docking scores of −41.48 and −29.88 kJ/mol for compounds S8 against VEGFR1 and VEGFR3, respectively, were excellent. Whereas compounds S11 and S14 demonstrated the highest inhibitory potential against ERBB and VEGFR2, with docking scores of −37.92 and −38.5 kJ/mol against ERBB and −41.2 and −46.5 kJ/mol against VEGFR-2, respectively. The results of the molecular docking studies were further correlated with the molecular dynamics simulation studies. Moreover, HYDE energy was calculated through SeeSAR analysis, and the safety profile of the compounds was predicted through ADME studies.
Introduction
Curcumin, the biomolecule obtained from turmeric (Curcuma longa, 1.5-3% wt.), has pleiotropic properties, including chemo-sensitizing, anti-oxidant, chemo-protective, antiinflammatory, anti-proliferative, hepato-protective, anti-metastatic, and anti-cancer properties. Curcumin affects most signaling pathways due to its complicated chemistry and molecular structure. Any imbalance in signaling pathways may lead to metastasis [1]. Among the most common types of cancer, colorectal cancer (CRC) is one of the leading cancers, accounting for approximately 10% of cancer incidence and mortality in both males and females [2]. Every year, numerous people are diagnosed with, and die of, colorectal cancer; by 2014, the number of people who died after being diagnosed with cancer had reached 14.5 million, and the number will be expected to increase to nearly 19 million by 2024 [3]. The CRC is either metastatic or locally advanced, and surgical resection is unlikely to be curative. For most patients, chemotherapy can enhance survival and is the only mode of treatment [4][5][6].
There has been much interest in several novel therapeutic approaches for cancer treatment that target the molecular pathways that regulate tumor cell growth or survival. Potential anti-neoplastic treatment targets, such as epidermal growth factor receptor (EGF-R) and vascular endothelial growth factor receptor (VEGF-R), have been investigated [7]. EGF-R and VEGF-R are examples of receptor tyrosine kinases (RTKs), which are trans-membrane proteins with an extracellular ligand-binding domain and an intracellular tyrosine kinase catalytic domain. After binding to their catalytic site, most RTKs form dimers and undergo autophosphorylation of intracellular tyrosine residues [7,8]. Numerous cellular signaling pathways that promote cell growth, survival, and angiogenesis are triggered in response to RTK activation. The emergence of genetic makeup changes is a mediator in the development of colorectal or renal cancer disease. The accumulation of specific growth-inducing factors, such as hypoxia-inducing factors, is caused by mutation or gene silencing (HIF-alpha). These built-up substances function as transcriptional agents that move into the nucleus and trigger the synthesis of growth factors like platelet-derived and epithelial growth factors. These elements begin encouraging metastasis, cell growth, proliferation, and angiogenesis. It is also hypothesized that cancer cells circumvent usual growth constraints by inappropriately activating RTKs by mutation, overexpression, or ectopic ligand production, which is a typical feature of human tumor genesis and progression [9]. In light of this, RTK signal transduction control has emerged as a primary focus of oncology medication development, and several agents have been developed that primarily target the VEGFR signaling pathways.
Potential tyrosine kinase agents such as Axitinib, 5-fluorouracil (5-FU), irinotecan, and oxaliplatin possessed potential inhibition activity against VEGFR 1-3. Other agents that operate by blocking the tyrosine kinase domain of epidermal growth factor receptor (EGFR) utilizing monoclonal antibodies, such as cetuximab or panitumumab, are also available for the treatment of CRC [10,11]. Similarly, drugs that block VEGF receptor activation prevent the induction of metastasis. Several anti-angiogenic agents that target VEGF, including mAbs, TKIs, and decoy compounds (e.g., VEGF Trap), have been entered into clinical practice or are under clinical investigation [12]. Among all these tyrosine agents, only Axitinib is the latest FDA-approved drug integrated into international therapeutic guidelines for treating VEGFR-associated malignancies [13]. Axitinib is an indole derivative that has demonstrated potent and selective activity against multiple cancer cell lines, including renal, colorectal, thyroid, and non-small cell lung cancer disease [14]. Axitinib competitively binds to the ATP binding site of tyrosine kinase and inhibits phosphorylation [15]. In addition, it was reported that Axitinib blocked several growth factors in nano molar ranges, including platelet-derived growth factors, but it remained more selective toward RTKs [15]. However, the use of Axitinib and other kinase inhibitors is associated with certain disadvantages, such as the development of tolerance [16], toxicity, pharmacokinetic instability, and side effects. In particular, Axitinib developed dose-limiting toxicities (stomatitis and hypertension) and severe adverse effects such as myalgia, fatigue, gout, diarrhea, and hypertension [17].
Moreover, cross-tolerance and combination therapy trial data are insufficient to support the treatment therapy's safety in many individuals [17]. Therefore, there is a strong rationale for designing selective inhibitors of both targets to eradicate cancer with the least resistance and side effects. Furthermore, these findings encourage us to develop alternative scaffolds for treating RTKs associated with cancer malignancies [11,12,18]. Among the various types of natural analogues, curcumin derivatives are considered important pharmaceutical agents, possessing anti-angiogenic and anticancer properties [19]. In addition, they are considered promising chemotherapeutic treatment strategies due to their low molecular weight and lack of toxicity against normal cells [20]. Furthermore, they have been reported for their role in growth suppression and apoptosis induction in various cancer cell lines (in vitro), i.e., inhibition of vascular endothelial cell (VEC) proliferation. Moreover, their anti-tumor capabilities have also been identified via in-vivo approaches, i.e., in vivo capillary tube formation and growth [21]. Based on these properties, curcumin analogues remain the lead molecules for the design of analogs with similar safety profiles, increased activity, and better pharmacokinetic profiles [22].
The current study aims to evaluate the curcumin derivatives as the inhibitors of ERBB, VEGFR1, VEGFR3 and VEGFR2 using various in silico approaches. The current study has utilized Axitinib as a parent scaffold for generating a pharmacophore query model against which a library of curcumin derivatives was screened via pharmacophore-based virtual screening, which could generate energetically optimized pharmacophores for lead discovery. The top-ranked hits retrieved via pharmacophore-based virtual screening were further subjected to advanced in-silico approaches. Initially, DFT calculations were performed to understand the electronic properties of all compounds, and optimized structures were obtained for molecular docking studies. Energy-based docking studies were then used to determine the ligand's approximate/plausible positions within the receptor active site and the binding affinities. In addition to the docking studies, molecular dynamic simulation was performed to identify the stability of the docked complex.
Moreover, a similarity search was performed for Axitinib and curcumin derivatives using Tanimoto and Dice similarity coefficients. The results will serve as a new direction for analyzing curcumin derivatives for treating RTKs associated cancer malignancies. Figure 1 depicts the curcumin analogues and Axitinib. Ac S8 S9 S10 S11 S14 S13 S12 S1 S3 Figure 1. Curcumin analogues and FDA-approved Axitinib [19].
Preparation of Chemical Database
The curcumin derivatives were selected on the basis of their broad range of biological activities. The curcumin derivatives were previously reported as potential anticancer agents against various cancer cell lines, including melanoma RPMI 7951, human breast
Preparation of Chemical Database
The curcumin derivatives were selected on the basis of their broad range of biological activities. The curcumin derivatives were previously reported as potential anticancer agents against various cancer cell lines, including melanoma RPMI 7951, human breast cancer, MDA-MB-231, and human umbilical vein endothelial cells, HUVEC [15]. A total of 14 curcumin derivatives were screened against multiple cell lines, and the chemical structures of each derivative were retrieved from the PubChem database. All these derivatives were retrieved in SDF format from the PubChem database and subjected to a preliminary energy minimization process before being converted to the desired format for further insilico investigations. The IUPAC naming of all retrieved curcumin derivatives is provided in Table 1.
Generation of Pharmacophore Model
The single protein-ligand complex can be used to define chemical features based on intermolecular interactions observed with the complex. In the present study, VEGFR-2 in complex with standard Axitinib was retrieved from the Protein Data Bank (PDB ID 4AG8) and subjected to pharmacophore model building. The interactions produced by Axitinib laid the foundation for the generation of pharmacophore features. The database consisting of 14 curcumin derivatives was screened against generated features, and the best-fitted compound was prioritized as a hit molecule. Based on intermolecular interactions, a total of seven features were generated, i.e., two hydrogen bond acceptors (blue sphere), two hydrogen bond donors (purple sphere), and three hydrophobic (orange spheres), as shown in Figure 2. In addition, four hydrogen bond features were observed, i.e., two hydrogen bond donor producing interactions with GLU885 and GLU917 and two hydrogen bond acceptor features involving CYS919 and LEU840 residues in bonding.
Molecules 2023, 28, x FOR PEER REVIEW Figure 2. Generated chemical features of Axitinib based on intermolecular interactions.
Pharmacophore-Based Virtual Screening
After the generation of a pharmacophore query model, the curcumin databa screened against Axitinib's predefined chemical features. It was observed that comp S11 and S14 showed the best-fit chemical features. The compound S11 showed fiv macophore features AADRR (one donor, two acceptors, and two aromatics) w RMSD value of 0.54 angstrom. Similarly, another best-fit compound, S14, show chemical features AAARR (three donors and two aromatics) with RMSD values le 0.9 angstroms. Both these compounds involved important molecular interaction amino acid residues at the active site. Figure 4 illustrates the generation of the pha phore query model on the basis of molecular interactions between Axitinib and VE A total of seven pharmacophoric features were generated, against which compou and S14 were found to be the best matches both with five features. For each com the cut off value was set to a minimum of four. Any compound with less than fou macophoric features was omitted from the hit candidates. The generated and m chemical features are shown in Figure 3.
Pharmacophore-Based Virtual Screening
After the generation of a pharmacophore query model, the curcumin database was screened against Axitinib's predefined chemical features. It was observed that compounds S11 and S14 showed the best-fit chemical features. The compound S11 showed five pharmacophore features AADRR (one donor, two acceptors, and two aromatics) with an RMSD value of 0.54 angstrom. Similarly, another best-fit compound, S14, showed five chemical features AAARR (three donors and two aromatics) with RMSD values less than 0.9 angstroms. Both these compounds involved important molecular interactions with amino acid residues at the active site. Figure 3 illustrates the generation of the pharmacophore query model on the basis of molecular interactions between Axitinib and VEGFR2. A total of seven pharmacophoric features were generated, against which compound S11 and S14 were found to be the best matches both with five features. For each compound the cut off value was set to a minimum of four. Any compound with less than four pharmacophoric features was omitted from the hit candidates. The generated and matched chemical features are shown in Figure 3.
Similarity Index
Implementing the similarity principle is essential for evaluating a query compound's biological and chemical properties and a target dataset. In the present study, Axitinib was utilized as a query molecule, and top hits obtained from pharmacophore-based virtual screening were considered the test dataset. Initially, MACCS and Morgan fingerprints [38] were generated for each molecule in the query and test dataset. Afterward, two similarity coefficients, i.e., Tanimoto and Dice coefficients, were applied using the open-source RDKIT library on both generated fingerprints. The rationale behind generating two different types of fingerprints and implementing similarity coefficients was to enhance the reliability and accuracy of generated outputs. As a result, it was observed that compound S11 showed a slightly higher similarity index with Axitinib, whereas S14 was slightly lower in similarity index. The exact values are given in Table 2.
Density Function Theory (DFTs)
The structural geometries of curcumin derivatives were optimized to steepest decent gradient and frequency calculations were performed using DFT/B3LYP functional correlation and 3-21G as a basis set. In order to perform DFT calculations of curcumin derivatives, all the structure files were converted to the desired format using the Gauss View 6 program after specifying the calculation parameters. All compounds' geometry was optimized in the gas phase.
Similarity Index
Implementing the similarity principle is essential for evaluating a query compound's biological and chemical properties and a target dataset. In the present study, Axitinib was utilized as a query molecule, and top hits obtained from pharmacophore-based virtual screening were considered the test dataset. Initially, MACCS and Morgan fingerprints [23] were generated for each molecule in the query and test dataset. Afterward, two similarity coefficients, i.e., Tanimoto and Dice coefficients, were applied using the open-source RDKIT library on both generated fingerprints. The rationale behind generating two different types of fingerprints and implementing similarity coefficients was to enhance the reliability and accuracy of generated outputs. As a result, it was observed that compound S11 showed a slightly higher similarity index with Axitinib, whereas S14 was slightly lower in similarity index. The exact values are given in Table 2.
Density Function Theory (DFTs)
The structural geometries of curcumin derivatives were optimized to steepest decent gradient and frequency calculations were performed using DFT/B3LYP functional correlation and 3-21G as a basis set. In order to perform DFT calculations of curcumin derivatives, all the structure files were converted to the desired format using the Gauss View 6 program after specifying the calculation parameters. All compounds' geometry was optimized in the gas phase.
The dipole moment and optimization energy of all candidate compounds were determined to understand the extent of reactivity and stability. Additional descriptors such as electronegativity (χ = −1/2(ELUMO + EHOMO), chemical hardness (η = 1/2(ELUMO − EHOMO), softness (S = 1/2η), electron donating power (ω− = (3I + A)2/16(I − A)), electron accepting power (ω+ = (I + 3A)2/16(I − A)), and electrophilicity index (ω = µ/2η) were determined using ionization potential and electron affinity values. The various descriptor values, dipole moment, and optimization energies for all the compounds are given in Table 3. The hardness of any compound is associated with its ability to react with molecules in its vicinity. Therefore, any molecule with a high hardness value is considered the least reactive and more stable. The density functional theory calculations were performed for all the compounds, and according to the results, compound S5 showed the highest hardness value, making it resistant to being attacked by other molecules. In the same way, S2 was found to be the most reactive because of it had the lowest hardness value of S2. As the electronegativity of a compound is its ability to accept an electron from the environment, the DFT results indicated that all compounds showed almost similar electronegativity, but S5 was found to be more prone to ionization from the environment and showed a slightly high electronegativity. The electrophilicity index of all compounds was also calculated, showing derivative S5 to be the most electron-loving among all the compounds. The value of all the compounds for these descriptors is given in Table 4. The results of frontier molecular orbitals energy, i.e., EHOMO and ELUMO, and their energy gap (ELUMO-EHOMO) also indicated that most of the compounds showed equal energy difference and were found to be stable. The values are given in Table 4. The results of other reactivity descriptors, i.e., electron-donating power and electron-accepting power, indicated that the extent of reactivity was also consistent with the results of other global reactivity descriptors. The value for all the compounds is given in Table 5. Ionization energy, along with the electron affinity of compounds, is another approach to understanding the stability and reactivity of a compound. The compounds with higher ionization energy values are least prone to lose electrons and have greater stability. It is also evident from the results that S14 has the highest value of ionization energy which speaks to its inert nature and reliable stability. The same HOMO and LUMO energy, along with energy gap and optimization energy, is given in the tables for all the compounds. For example, from the results of DFT studies, the optimized structure, HOMO, and LUMO, along with their respective energy gap of the highly potent compounds, i.e., S1, S11, and S14, is given in Figure 4. It was notable that HOMO orbitals were localized around the phenyl ring of compound S1, whereas LUMO orbitals were delocalized around the acetate part of the compound. The energy gap between LUMO and HOMO orbitals was 0.142 eV for S1. In terms of compound S11, the HOMO orbitals were localized around the piperidine moiety, representing the electron-donating behavior of the piperidine moiety of the compound. The LUMO orbitals, on the other hand, were delocalized over the majority of the compound. The LUMO/HOMO energy gap for compound S11 was at a minimum of 0.136 eV, representing the high chemical reactivity of the compound. The FMOs analysis of compound S14 revealed that the whole compound was involved in electron-accepting and electron-donating properties, which corresponds to its high chemical reactivity profile.
Molecules 2023, 28, x FOR PEER REVIEW 10 of 28 Figure 4. Optimized structures along with LUMO and HOMO energy transitions for S1, S11, and S14.
Filtration for Drug-Likeness and Virtual Screening
The calculated pharmacokinetics of all the compounds showed that Lipinski's rule of five (RO5); which represents the drug-likeness of the chemical, is not violated by any derivative. Due to appropriate water solubility, lipophilicity and permeability, almost all of the compounds showed excellent absorption. The high bioavailability of the compounds Figure 4. Optimized structures along with LUMO and HOMO energy transitions for S1, S11, and S14.
Filtration for Drug-Likeness and Virtual Screening
The calculated pharmacokinetics of all the compounds showed that Lipinski's rule of five (RO5); which represents the drug-likeness of the chemical, is not violated by any derivative. Due to appropriate water solubility, lipophilicity and permeability, almost all of the compounds showed excellent absorption. The high bioavailability of the compounds was confirmed by the number of rotatable bonds and polar surface area. The compounds' toxicity profiles were also investigated. According to the projected results, all derivatives are non-carcinogenic and have no influence on immunotoxicity, mutagenicity, or cytotoxicity. The ADMET (absorption, distribution, metabolism, excretion, and toxicity) properties of the most powerful derivative were calculated to determine its appropriateness as a therapeutic molecule. The physicochemical properties were molecular weight, density, number of hydrogen bond acceptors (nHA), number of hydrogen bond donors (nHD), topological polar surface area (TPSA), log of aqueous solubility (LogS), log of the octanol-water partition coefficient (LogP), and logP at physiological concentrations (LogD) ( Table 6). Hydrogen bonding is an important chemical parameter in the determination of thermodynamic properties of a compound. Total Polar Surface Area (TPSA) has a significant role in the estimation of polarity which is a major factor contributing toward penetration and permeation. According to the ADMET profile, the compound S1 showed the highest value of TPSA i.e., 93.6. Another parameter i.e., Log S, if a compound is sufficiently lipophilic and it has an ineffective range of aqueous solubility (Log S) then its permeation through membranes will be hindered, as is the case with S6 which was found to be −6.046. The value of all other compounds is given in Table 4. The molecular weights of all derivatives lie within the optimal range (<500), except S12 and in the same way nHA, nHD and TPSA values of all compounds were found to be within the permitted range, whereas derivative S6 has minimum total polar surface area and S2 has maximum polar surface area.
The compounds S2, S9 and S11 have acceptable values (−1 to −5.6) of log S with good aqueous solubility, while remaining derivatives showed deviation from the reference values. The compound S2 exhibited an acceptable log p value while other compounds were found to be borderline with slightly higher values of log P. The log D value of all derivatives is found in-correlation with log p results as given in Table 7. The absorption and distribution profile of all the compounds showed efficient HIA, COCA 2 permeability and MDCK Permeability which represented their potential to penetrate/permeate through cell membranes. Except S11, all the derivatives had efficient potential to cross BBB and showed CNS effects. As far as its interaction with P glycoprotein was concerned, excluding S3, all other derivatives were found to have good PGP substrate properties while S1, S5 and S7 derivatives showed maximum PGP inhibitions whereas derivative S11 also showed moderate PGP inhibition activity, which proved its capability to permeate as shown in Table 8. The metabolism of any drug is an important parameter to understand its behavior in the body. All derivatives showed CYP inhibition activity of varying degrees. All compounds had a moderate rate of renal clearance while S2, S5 and S7 were present with relatively higher rates, and S11 had the highest value of renal clearance shown in Table 9. Any compound with a high level of toxicity cannot be used as a drug and in this regard assessment of mutagenic potential is crucial in the development of drug. The results of toxicity parameters indicated that S9, S10, S11 and S14 have excellent safety profiles in terms of mutagenicity, but S8 was moderately mutagenic and all other derivatives were toxic. The compounds S1, S2, S3, S6 and S10 did not show any carcinogenic potential and were found to be safe. Their safety indicated their appropriateness for drug development as they do not pose a carcinogenic threat in humans. The compounds S4, S5, S7 and S8 were moderately carcinogenic. Only S5 and S7 derivatives were not corrosive to the eye, compounds S4, S5, S6, S7, S8 and S9 showed non-irritant behavior to the cornea, which justified their ocular safety. S6 was found to be moderately eye corrosive, whereas S1, S2 and S3 were found to be moderately irritant. Moreover, S1, S2, S5, S7 and S11 did not have respiratory toxicity the rest were moderately toxic (Table 10). Compounds S1 and S2 did not activate the androgen receptor while S3, S4, S5, S7, and S8 derivatives showed moderate activity while others may activate androgen receptors. Only S1 and S11 possessed activity for the ligand binding domain (LBD), S8 and S9 had moderate potential while the rest of the derivatives had no activity. The compounds S2, S6, S10 and S11 showed moderate activity for estrogen receptors but the rest of the compounds had no activity at all, and none of the compounds under study showed any evidence of antioxidant potential.
Binding Interactions of ERBB
The Molecular Operating Environment (MOE) and AutoDock 4.2 were used to investigate the binding interactions of selected compounds with targeted proteins i.e., ERBB, VEGFR1, VEGFR-2 and VEGFR3. The MOE software predicted poses that were reliable and validated on the basis of RMSD values between native poses and regenerated poses, which motivate us to incorporate binding energies and docking conformations obtained through the MOE software. Multiple protein kinases were selected in order to evaluate the inhibitory potential and selectivity of curcumin derivatives against multiple protein kinases. It was observed that compound S14 had demonstrated the highest selectivity and inhibitory potential against VEGFR2 and ERBB whereas compound S8 was effective against VEGFR1 and VEGFR3. The binding energies of curcumin derivatives against all four targeted proteins are provided in Table 10, whereas the predicted inhibitory constant value (ki) is provided in a Supplementary File (Table S1). In the main manuscript, the binding interactions analysis of top ranked conformations of curcumin derivatives against VEGRF2 and ERBB tyrosine kinase is elaborated, whereas binding interactions analysis of top ranked curcumin derivatives (S8) against VEGFR1 and VEGFR3 is provided in the Supplementary File ( Figures S1-S10).
The docked conformation of curcumin derivatives exhibited potential molecular interactions against all targeted proteins. Briefly, Compound S11 and S14 were top ranked hits identified through molecular docking and MD simulations studies. The binding energies of curcumin derivatives were better than the standard drug irinotecan. Initially, irinotecan was docked with ERBB and the VEGFR2 protein. The following amino acid residues were involved in the formation of the complex with the standard drug (ERBB tyrosine kinase): LYS273, ASP833, VAL704, ARG819, and LEU777. The major binding interactions of the reference compound, i.e., irinotecan, with the targeted protein (ERBB tyrosine kinase), were comprised of strong hydrogen bonds. Hydrogen bond interactions were discovered between the carboxylate group attached to irinotecan's bipiperidine ring and LYS723, ASP833. The pink amino acid residues were hydrophilic groups, while the green hydrophobic amino acid residue (VAL724) formed a Pi-sigma interaction.
The compounds S11 and S14 were involved in different molecular interactions with the following amino acid residues: PHE834, ALA832, ASP833, LEU771, LEU776, VAL753, LEU822, and LEU696, CYS721 for S12, and THR768, LYS723, VAL704, CYS721, ASP833, VAL700, and ARG819 for S14, respectively. The bonding and non-bonding interactions of S11 and S14 within the active pocket of the ERBB protein included the conventional hydrogen bond, the carbon-hydrogen bond, Van der Waals forces, and a weak pi-alkyl bond. The binding interactions revealed that the two strong hydrogen bonds were formed with VAL 753 and LEU 771. In addition, various carbon-hydrogen bonds were formed with ALA832, ASP833. Further non-bonding interactions, included Pi-Pi T-shaped interactions with PHE834. In the same way, the binding interactions of S14 involved two hydrogen bonds between the acyl group and ASP833, VAL700. The pi-sigma, pi-sulfur, and pi-alkyl bonds, along with Van der Waals forces, were formed between S14 and LYS723, VAL704, CYS721 and ARG819. The binding interactions of the reference drug and compounds S11 and S14 are shown in Figure 5. . 3D and 2D interaction of reference compound Irinotecan, S11 and S14 within the active pocket of ERBB tyrosine kinase.
Molecular Interactions with VEGFR2
The docked conformation of standard irinotecan and curcumin derivatives revealed substantial molecular interactions with ERBB and VEGFR2. From the analysis of docking interactions, it was revealed that the two hydroxyl groups of S11 formed two strong hydrogen bonds with GLU 885 and HIS 1026, and all other interactions were weak pi-cations, pi-sulfur, and pi-sigma bonds. The bonding and non-bonding interactions of the most potent derivative, i.e., S14, involved the following amino acids: VAL848; VAL916; ALA866; HIS1026; LEU1019; LEU889; ALA866; PHE1047; LYS868; ILE892. The strongest hydrogen bond among the bonding interactions was established between the oxygen atom of the acyl group and LYS 868, whereas the second hydrogen bond was created between the carbon atom and PHE 1047. In addition to these bonds, various pi-alkyl, pi- Figure 5. 3D and 2D interaction of reference compound Irinotecan, S11 and S14 within the active pocket of ERBB tyrosine kinase.
Molecular Interactions with VEGFR2
The docked conformation of standard irinotecan and curcumin derivatives revealed substantial molecular interactions with ERBB and VEGFR2. From the analysis of docking interactions, it was revealed that the two hydroxyl groups of S11 formed two strong hydrogen bonds with GLU 885 and HIS 1026, and all other interactions were weak pications, pi-sulfur, and pi-sigma bonds. The bonding and non-bonding interactions of the most potent derivative, i.e., S14, involved the following amino acids: VAL848; VAL916; ALA866; HIS1026; LEU1019; LEU889; ALA866; PHE1047; LYS868; ILE892. The strongest hydrogen bond among the bonding interactions was established between the oxygen atom of the acyl group and LYS 868, whereas the second hydrogen bond was created between the carbon atom and PHE 1047. In addition to these bonds, various pi-alkyl, pi-sigma, and Van der Waals forces were also present. The binding interactions of the reference drug and compounds S11 and S14 are shown in Figure 6. sigma, and Van der Waals forces were also present. The binding interactions of the reference drug and compounds S11 and S14 are shown in Figure 6. Figure 6. 3D and 2D interaction of reference compound Irinotecan, S11 and S14 within the active pocket of VEGFR-2 tyrosine kinase.
MD Simulation Studies of VEGFR2 and Compound S14
The molecular dynamics simulations were performed for evaluation of steadfastness of protein-ligand complex under accelerated conditions. The top ranked conformations against each enzyme i.e., VEGFR2 and ERBB were retrieved and subjected to evaluation of stability patterns. The analytical metrics including RMSD, RMSF, contact map analysis, interaction timeline and radius of gyration were utilized for interpretation of protein-ligand complex integrity and stability. . 3D and 2D interaction of reference compound Irinotecan, S11 and S14 within the active pocket of VEGFR-2 tyrosine kinase.
MD Simulation Studies of VEGFR2 and Compound S14
The molecular dynamics simulations were performed for evaluation of steadfastness of protein-ligand complex under accelerated conditions. The top ranked conformations against each enzyme i.e., VEGFR2 and ERBB were retrieved and subjected to evaluation of stability patterns. The analytical metrics including RMSD, RMSF, contact map analysis, interaction timeline and radius of gyration were utilized for interpretation of protein-ligand complex integrity and stability.
The MD simulation studies on the VEGFR2-S14 complex revealed stability patterns for both the apo protein and liganded protein. Concisely, it was notable that the apo protein was extremely stable with an average RMSD of 1.74 angstroms. The RMSD pattern for the apo protein became stable and equilibrated after 10 ns of simulations. In terms of stability pattern of liganded protein, it was observed that liganded protein exhibited modest fluctuations with an average RMSD value of 2.3 angstroms. The slight rearrangement was observed during the initial phase of simulations but after 15 ns, RMSD of liganded protein attained equilibrium and became stable. Moreover, it was notable that ligand remained sufficiently attached to amino acid residues of the active site and produced contacts with shorter bond lengths. The data demonstrate the protein and its associated complex had excellent stability in aqueous media. Figure 7 illustrates the RMSD pattern for the apo and liganded protein. The MD simulation studies on the VEGFR2-S14 complex revealed stability patterns for both the apo protein and liganded protein. Concisely, it was notable that the apo protein was extremely stable with an average RMSD of 1.74 angstroms. The RMSD pattern for the apo protein became stable and equilibrated after 10 ns of simulations. In terms of stability pattern of liganded protein, it was observed that liganded protein exhibited modest fluctuations with an average RMSD value of 2.3 angstroms. The slight rearrangement was observed during the initial phase of simulations but after 15 ns, RMSD of liganded protein attained equilibrium and became stable. Moreover, it was notable that ligand remained sufficiently attached to amino acid residues of the active site and produced contacts with shorter bond lengths. The data demonstrate the protein and its associated complex had excellent stability in aqueous media. Figure 7 illustrates the RMSD pattern for the apo and liganded protein. Figure 7. Root mean square deviation (RMSD) of VEGFR2, and VEGFR2-S14 complex as a function of time. The blue colored trajectory indicates the evolution of RMSD for C alpha atoms, whereas the red trajectory is for the protein-ligand complex.
The RMSF analysis of liganded protein was conducted for the determination of residue wide fluctuations. The amino acid residues of the VEGFR2 protein exhibited minor variations, especially residues belonging to alpha helix and beta strand were significantly stable. This was expected as both these portions of proteins are rigid and exhibit compactness. The most importantly the amino acid residues of active site (140-170) were in contact with S14 and exhibited fewer fluctuations. The average RMSF value of the targeted protein was 0.8 angstroms. In addition, amino acid residues belonging to N and C terminals were slightly less compact with higher fluctuations. Figure 8 shows the RMSF value for each residue of the VEGF2 protein. The RMSF analysis of liganded protein was conducted for the determination of residue wide fluctuations. The amino acid residues of the VEGFR2 protein exhibited minor variations, especially residues belonging to alpha helix and beta strand were significantly stable. This was expected as both these portions of proteins are rigid and exhibit compactness. The most importantly the amino acid residues of active site (140-170) were in contact with S14 and exhibited fewer fluctuations. The average RMSF value of the targeted protein was 0.8 angstroms. In addition, amino acid residues belonging to N and C terminals were slightly less compact with higher fluctuations. Figure 8 shows the RMSF value for each residue of the VEGF2 protein.
Multiple important molecular interactions were produced by S14 with amino acid residues of the active site. Specifically, amino acid residues VAL848, ILE888, Leu889, ILE892, VAL898, Val899, VAL914, VAL916, LEU1019, ILE1044 and PHE1047 were engaged in hydrophobic interactions. Significant interaction times were observed with LYS868, VAL916 and PHE1047 with interaction times of 60%, 90% and 70%, respectively. Furthermore, two hydrogen bonds exist between ASP1046 and CYS1045, respectively. The interaction fraction of ASP1046 was 60% and 10% for CYS1045. Multiple water bridges were also produced during simulation studies. The contact map histograms and contact map timeline are illustrated in Figure 9.
Multiple important molecular interactions were produced by S14 with amino acid residues of the active site. Specifically, amino acid residues VAL848, ILE888, Leu889, ILE892, VAL898, Val899, VAL914, VAL916, LEU1019, ILE1044 and PHE1047 were engaged in hydrophobic interactions. Significant interaction times were observed with LYS868, VAL916 and PHE1047 with interaction times of 60%, 90% and 70%, respectively. Furthermore, two hydrogen bonds exist between ASP1046 and CYS1045, respectively. The interaction fraction of ASP1046 was 60% and 10% for CYS1045. Multiple water bridges were also produced during simulation studies. The contact map histograms and contact map timeline are illustrated in Figure 9. Multiple important molecular interactions were produced by S14 with amino acid residues of the active site. Specifically, amino acid residues VAL848, ILE888, Leu889, ILE892, VAL898, Val899, VAL914, VAL916, LEU1019, ILE1044 and PHE1047 were engaged in hydrophobic interactions. Significant interaction times were observed with LYS868, VAL916 and PHE1047 with interaction times of 60%, 90% and 70%, respectively. Furthermore, two hydrogen bonds exist between ASP1046 and CYS1045, respectively. The interaction fraction of ASP1046 was 60% and 10% for CYS1045. Multiple water bridges were also produced during simulation studies. The contact map histograms and contact map timeline are illustrated in Figure 9.
Molecules 2023, 28, x FOR PEER REVIEW 19 of 28 Figure 9. Illustration of contact map histogram and timeline for 50 ns simulations.
MD Simulations Analysis of the ERBB-S14 Complex
To study the complex's molecular dynamics and stability, the ERBB protein's docked complex with the best pose of S14 was simulated in an aqueous environment for a 50ns trajectory under periodic boundary conditions. The sole protein and its complex were considered an initial point for MD simulation studies. The RMSD value was calculated for the C alpha atoms and protein-ligand complex (ERBB-S14) in order to investigate the stability pattern during simulated trajectory. The RMSD pattern of protein and its com-
MD Simulations Analysis of the ERBB-S14 Complex
To study the complex's molecular dynamics and stability, the ERBB protein's docked complex with the best pose of S14 was simulated in an aqueous environment for a 50ns trajectory under periodic boundary conditions. The sole protein and its complex were considered an initial point for MD simulation studies. The RMSD value was calculated for the C alpha atoms and protein-ligand complex (ERBB-S14) in order to investigate the stability pattern during simulated trajectory. The RMSD pattern of protein and its complex is presented in Figure 10. The RMSD pattern for c alpha atoms of protein became stable and equilibrated after 5 ns of simulation. Initial fluctuations were observed in C and N terminal residues of ERBB which became stable and equilibrated after 5 ns. The average RMSD value for C alpha atoms was 1.8 angstroms. In contrast, the protein-ligand complex was exhibiting slight rearrangement inside the active pocket of the targeted protein. The protein-ligand complex trajectory was stable and equilibrated after 30 ns of simulation but after that the ligand exhibited rearrangements and produced new contacts with active site residues. These rearrangements lasted for 10 ns, and after that the ligand again became stable and the trajectory became equilibrated toward the end of the simulations. On the basis of these findings, it could be deduced that S14 could be an effective inhibitor of VEGFR2, whereas there was modest inhibitory potential observed against ERBB. Figure 10 shows the evolution of the RMSD pattern for protein and protein-S14 complex.
Molecules 2023, 28, x FOR PEER REVIEW 20 of 28 Figure 10. Root mean square deviation (RMSD) of ERBB, and the EGFR-S14 complex as a function of time. The blue colored trajectory indicates the evolution of RMSD for C alpha atoms, whereas the red trajectory represents the protein-ligand complex.
The perturbation of each amino acid residue was evaluated through RMSF analysis over a 50 ns simulated trajectory. Most of the residues were perturbed below 2 angstroms except amino acid residues ranges from 10-30 and 152 to 160. These residues exhibited fluctuations up to 4 angstroms. In addition, it was notable that important residues were in significant contact with S14 indicating the compactness of amino acid residues belonging to the active site. The average RMSF value for liganded ERBB protein was 1.1 angstroms. The root mean square fluctuation of liganded protein is illustrated in Figure 11. The perturbation of each amino acid residue was evaluated through RMSF analysis over a 50 ns simulated trajectory. Most of the residues were perturbed below 2 angstroms except amino acid residues ranges from 10-30 and 152 to 160. These residues exhibited fluctuations up to 4 angstroms. In addition, it was notable that important residues were in significant contact with S14 indicating the compactness of amino acid residues belonging to the active site. The average RMSF value for liganded ERBB protein was 1.1 angstroms. The root mean square fluctuation of liganded protein is illustrated in Figure 11. The contact map analysis and buried surface area was also computed through MD simulations. The important molecular interactions were included hydrophobic and hydrogen bonding interactions. The amino acid residues involved in hydrogen bonding was LYS723 and ARG619 with interaction fraction of 30% and 10% respectively. These residues were buried by S14 for majority of simulated trajectory. In addition, VAL704, LYS723, ARG619 and VAL836 were engaged in hydrophobic interactions. The interaction fraction of following residues was as follows; 20%, 25%, 10% and 10% respectively. Furthermore, water bridges were also contributing toward stability of protein ligand complex. The contact map histogram and contact timeline is illustrated in Figure 12. The contact map analysis and buried surface area was also computed through MD simulations. The important molecular interactions were included hydrophobic and hydrogen bonding interactions. The amino acid residues involved in hydrogen bonding was LYS723 and ARG619 with interaction fraction of 30% and 10% respectively. These residues were buried by S14 for majority of simulated trajectory. In addition, VAL704, LYS723, ARG619 and VAL836 were engaged in hydrophobic interactions. The interaction fraction of following residues was as follows; 20%, 25%, 10% and 10% respectively. Furthermore, water bridges were also contributing toward stability of protein ligand complex. The contact map histogram and contact timeline is illustrated in Figure 12.
The contact map analysis and buried surface area was also computed through MD simulations. The important molecular interactions were included hydrophobic and hydrogen bonding interactions. The amino acid residues involved in hydrogen bonding was LYS723 and ARG619 with interaction fraction of 30% and 10% respectively. These residues were buried by S14 for majority of simulated trajectory. In addition, VAL704, LYS723, ARG619 and VAL836 were engaged in hydrophobic interactions. The interaction fraction of following residues was as follows; 20%, 25%, 10% and 10% respectively. Furthermore, water bridges were also contributing toward stability of protein ligand complex. The contact map histogram and contact timeline is illustrated in Figure 12. The molecular docking provide initial binding energy which provide an estimate of binding affinity between protein and ligand. However, molecular docking is not robust technique in estimating binding free energies. For efficient prediction of binding affinity, MMGBSA analysis were performed which take into account all electrostatic, hydrophilic Figure 12. The contact map analysis and timeline of ERBB-S14 complex.
The MMGBSA Free Energy Calculations
The molecular docking provide initial binding energy which provide an estimate of binding affinity between protein and ligand. However, molecular docking is not robust technique in estimating binding free energies. For efficient prediction of binding affinity, MMGBSA analysis were performed which take into account all electrostatic, hydrophilic and hydrophobic interactions and provide cumulative binding free energy [24]. The both complexes were subjected to MMGBSA analysis and provided in Table 11. The following chemical equation was used to calculate free binding energy calculations [24]; ∆G bind = ∆G SA +∆G SOL + ∆E mm
SeeSAR Analysis
SeeSAR analysis with the most potent derivative was confirmed for ERBB and VEGFR by using SeeSAR by BiosolveIT [25], which visually depicts binding affinity. The HYDE value was calculated, indicating that the green coronas around the atom represent the atoms involved in positively developing the binding affinity; the higher the contribution, the larger the corona size. In the same way, the red-colored coronas around atoms indicated the unfavorable contributions towards binding affinity, and atoms with no significant involvement are not colored. Figure 13 shows the SeeSAR visualization of the most potent inhibitors. Although, as evident from the results, most of the atoms in the molecule contribute favorably to overall binding (indicated by green-colored coronas) in both of the proteins, only two different structural elements are not contributing favorably (indicated by red-colored coronas) because of high desolvation energy.
Molecules 2023, 28, x FOR PEER REVIEW 23 of 28 Figure 13. 3D (A) and 2D (B) interaction of derivative S14 within the active pocket of ERBB and VEGFR2 kinase.
Generation of Pharmacophore Model
The current study developed a pharmacophore model for a protein-ligand complex using the pharmacophore query editor wizard of the Molecular Operating Environment (MOE) [23]. The binding interactions of the protein-ligand complex provide initial points for generating chemical features, which were utilized for developing pharmacophore
Generation of Pharmacophore Model
The current study developed a pharmacophore model for a protein-ligand complex using the pharmacophore query editor wizard of the Molecular Operating Environment (MOE) [26]. The binding interactions of the protein-ligand complex provide initial points for generating chemical features, which were utilized for developing pharmacophore models. MOE makes use of several built-in pharmacophore features, including a hydrogen acceptor (Acc), an anionic atom, a hydrophobic center, an aromatic center (Ar), a cationic atom, and a hydrogen bond donor (Don) [27]. In the current layout, only important chemical features, i.e., hydrogen bond acceptor, hydrogen bond donor, and hydrophobic interactions, were used to develop the pharmacophore model. The PDB ID 4AG8 was used to retrieve the crystal structure of VEGFR-2 in complex with Axitinib (N-methyl-2-[[3-[(E)-2-pyridin-2-ylethenyl]-1H-indazol-6-yl]sulfanyl]benzamide). The crystallographic complex was utilized for the generation of pharmacophore features. Axitinib produced strong interactions with amino acid residues of VEGFR-2. Important amino acid residues and pharmacophore features of Axitinib are shown in Figure 14. It is crucial to validate the created pharmacophore model by screening the decoy molecules and known inhibitors of the targeted protein. The PubChem database retrieved ten known inhibitors of the targeted proteins and tested them against the created pharmacophore model.
Pharmacophore-Based Virtual Screening
Following the generation of a pharmacophore query model, a total of 14 curcumin derivatives were subjected to screening against the developed model. Only those derivatives that satisfied the pharmacophore features criteria were considered hit molecules. These models are essential for discovering novel molecules and are also crucial for antitarget modeling to avoid any adverse effects. In order to validate the generated pharmacophore model, a test dataset comprised of ten reported inhibitors of VEGFR2 (including sorafenib) and ten decoy molecules was constructed and virtually screened against the constructed pharmacophore model. The validated model was then subjected to pharmacophore based screening of curcumin derivatives. The Pharmacophore-based screening is superior to docking when structural information about the target protein or ligand's active conformation is present. Finally, the hit molecules obtained via pharmacophorebased virtual screening were processed further for detailed in-silico investigation. It is crucial to validate the created pharmacophore model by screening the decoy molecules and known inhibitors of the targeted protein. The PubChem database retrieved ten known inhibitors of the targeted proteins and tested them against the created pharmacophore model.
Pharmacophore-Based Virtual Screening
Following the generation of a pharmacophore query model, a total of 14 curcumin derivatives were subjected to screening against the developed model. Only those derivatives that satisfied the pharmacophore features criteria were considered hit molecules. These models are essential for discovering novel molecules and are also crucial for antitarget modeling to avoid any adverse effects. In order to validate the generated pharmacophore model, a test dataset comprised of ten reported inhibitors of VEGFR2 (including sorafenib) and ten decoy molecules was constructed and virtually screened against the constructed pharmacophore model. The validated model was then subjected to pharmacophore based screening of curcumin derivatives. The Pharmacophore-based screening is superior to docking when structural information about the target protein or ligand's active conformation is present. Finally, the hit molecules obtained via pharmacophore-based virtual screening were processed further for detailed in-silico investigation.
Density Functional Theory (DFTs)
The geometric parameters and structural geometries of curcumin derivatives were evaluated/optimized through density functional theory calculations. The density functional theory (DFTs) calculations were performed using the Guassian09W program [28]. The accurate assumptions and structural convergence were achieved through B3LYP functional correlation, and 3-21G as a basis set [29]. The 3-21G was opted as a basis set which offered multiple functions including s and p functions for accurate prediction of electronic properties of compounds. Moreover, 3-21G is commonly employed for fast and accurate assumptions on electron density of compounds. Using the proposed approach, the comprehensive reactivity profile of each compound was evaluated through various matrices including frontier molecular orbitals (FMO) analysis, global and local reactivity descriptor and electrostatic potential map. The resultant output files were analyzed through Guass View 6 [30].
Filtration for Drug-Likeness and Virtual Screening
The safety profile of a drug candidate is paramount in determining the fate of drug discovery and the drug development process. A drug that needs to be administered in the human body must have sufficient absorption, distribution, metabolism, and excretion properties. The in-silico ADMET is a crucial step in the drug discovery process that determines the safety and toxic profile of a drug candidate. The comprehensive pharmacokinetic and safety profiles of selected derivatives were determined via an in-silico approach. The online web server tool, ADMET Lab 2.0, was utilized to predict various physicochemical properties, i.e., ADMET (absorption, distribution, metabolism, excretion, and toxicity) properties [31].
Molecular Docking Studies
The molecular docking studies were performed on the optimized structures of curcumin derivatives obtained from DFT studies. Molecular Operating Environment (MOE) and AutoDock 4.0 were used to perform molecular docking experiments [26,32,33]. The two docking programs were employed in order to enhance the accuracy of the docking protocol. Both software packages were evaluated for their dependability and ability to regenerate docked conformations, and the program that performed best was chosen for additional molecular docking research. The re-docking of all the compounds was carried out using MOE because of its high reliability. For molecular docking studies, two steps are mandatory, i.e., ligand and protein preparations. Each ligand underwent a superficial energy minimization process to begin the docking process using ChemDraw 3D software. Following that, the atomic charges and the potential energy were added. Additionally, various properties of the ligands were measured using the MMFF94x force field [30], and the ligand library was then saved in the required format (MDB). The targeted protein structures were downloaded from the RCSB protein data bank (www.rcsb.com accessed on 1 September 2022) with PDB IDs: 3LMG (ERBB tyrosine kinase), 3HNG (VEGFR1 kinase), 4BSJ (VEGFR3 kinase) and 4AG8 (VEGFR2 kinase) [34]. The first step in protein preparation is adding polar hydrogen atoms to the active sites, followed by potential energy fixation. The protein active pocket is then identified using MOE's built-in site finder, followed by chain type selection. Finally, the two critical components (ligand and protein) are ready to commence the docking process. For each ligand, 30 poses were generated to identify the most stable configuration of the complex. The current study has utilized the London dG scoring function to analyze the interaction efficiency and adjusted it twice using triangular matcher methods. At the end of the process, important docking interaction data, i.e., receptor interactions, associated amino-acid residues, binding energy, and type of interactions, were recorded [25]. The Biovia Discovery Studio Visualizer (2020) and the MOE's inbuilt visualization tool were used to analyze all docking results. The docking results were validated based on the RMSD value, i.e., any pose with low binding energy and an RMSD value of less than 2.0 was considered the best pose.
Molecular Dynamics Simulation Studies
The molecular dynamic study of the best-docked conformation was performed using Desmond software on a CUDA-accelerated GPU system having a 16 core processor and 64 GB Ram memory. A maestro graphical user interface was used to visualize the results of MD simulations [25]. MD simulations were done to determine how binding works and how stable the protein-ligand complex is under fast conditions. Using the OPLS3 forcefield, the best-docked protein-ligand complexes were chosen, and topology files were made for both the protein and the ligand [35]. By adding NaCl charges at a standard concentration of 0.15 M, the system was brought back to a neutral state. The energy gradient was made as steep as possible to eliminate any close contact between atoms. The system was brought into balance in the NVT ensemble for 500,000 steps, then in the NPT ensemble for another 500,000 steps. After that, the simulation was run for 50 ns with periodic boundaries [36]. The PME method [37] was used to figure out the binding energy, Van der Waals forces, and electrostatic interactions. The SeeSAR analysis was also presented in the current study to evaluate the binding affinities of protein-ligand complexes [38].
Compound Similarity Index
The present work also focused on determining the similarity index between FDAapproved Axitinib and top hits obtained via pharmacophore-based virtual screening. Similarity index and structural activity relationship drug design approaches are based on the assumption that molecules with high similarity index compounds have similar properties and similar biological activities. In this context, the current study has investigated the similarity index between Axitinib with known biological activity against a set of curcumin derivatives. The similarity index was quantified using two different similarity coefficients, i.e., the Tanimoto and Dice index [39].
Conclusions
Comprehensive in-silico investigations on previously reported anti-cancer derivatives were performed in the current study to discover potent hits of ERBB and VEGFR-2. Initially, pharmacophore-based virtual screening was conducted. Afterward, the optimization and frequency calculations of selected compounds were carried out using DFT studies, and the optimized structures were further subjected to molecular docking studies. The molecular dynamic simulations were conducted further to support the findings of molecular docking. The compounds S11 and S14 were identified as potent ERBB and VEGFR2 inhibitors whereas compound S8 was predicted as a potential inhibitor of VEGFR1 and VEGFR3. The ADMET properties, MD simulations, and SeeSAR analysis confirmed the study's findings, demonstrating that the selected compounds can be used for further experimental validation. Based on these findings, it is concluded that curcumin derivatives have a strong inhibitory potential against VEGFR1, VEGFR3, VEGFR2 and the ERBB protein, and that they can be used to treat cancer and its associated malignancies. As the current study is based on pure computational investigations, further in-vitro and in-vivo studies are recommended to develop safe and effective inhibitors of cancer proteins. | 12,156.2 | 2023-05-01T00:00:00.000 | [
"Chemistry",
"Biology"
] |
Phage protein Gp11 blocks Staphylococcus aureus cell division by inhibiting peptidoglycan biosynthesis
ABSTRACT Phages and bacteria have a long history of co-evolution. However, these dynamics of phage-host interactions are still largely unknown; identification of phage inhibitors that remodel host metabolism will provide valuable information for target development for antimicrobials. Here, we perform a comprehensive screen for early-gene products of ΦNM1 that inhibit cell growth in Staphylococcus aureus. A small membrane protein, Gp11, with inhibitory effects on S. aureus cell division was identified. A bacterial two-hybrid library containing 345 essential S. aureus genes was constructed to screen for targets of Gp11, and Gp11 was found to interact with MurG and DivIC. Defects in cell growth and division caused by Gp11 were dependent on MurG and DivIC, which was further confirmed using CRISPRi hypersensitivity assay. Gp11 interacts with MurG, the protein essential for cell wall formation, by inhibiting the production of lipid II to regulate peptidoglycan (PG) biosynthesis on the cell membrane. Gp11 also interacts with cell division protein DivIC, an essential part of the division machinery necessary for septal cell wall assembly, to disrupt the recruitment of division protein FtsW. Mutations in Gp11 result in loss of its ability to cause growth defects, whereas infection with phage in which the gp11 gene has been deleted showed a significant increase in lipid II production in S. aureus. Together, our findings reveal that a phage early-gene product interacts with essential host proteins to disrupt PG biosynthesis and block S. aureus cell division, suggesting a potential pathway for the development of therapeutic approaches to treat pathogenic bacterial infections. IMPORTANCE Understanding the interplay between phages and their hosts is important for the development of novel therapies against pathogenic bacteria. Although phages have been used to control methicillin-resistant Staphylococcus aureus infections, our knowledge related to the processes in the early stages of phage infection is still limited. Owing to the fact that most of the phage early proteins have been classified as hypothetical proteins with uncertain functions, we screened phage early-gene products that inhibit cell growth in S. aureus, and one protein, Gp11, selectively targets essential host genes to block the synthesis of the peptidoglycan component lipid II, ultimately leading to cell growth arrest in S. aureus. Our study provides a novel insight into the strategy by which Gp11 blocks essential host cellular metabolism to influence phage-host interaction. Importantly, dissecting the interactions between phages and host cells will contribute to the development of new and effective therapies to treat bacterial infections.
proteins are toxic to or damage the host by immediately inhibiting host biosynthesis in the early stages of infection (3).Investigating the role of these putative phage proteins, particularly those that negatively affect host growth, will not only provide comprehensive insight into phage biology but will also help to better understand how bacteria are reprogrammed during phage infection.Several phage gene products that control host metabolism, e.g., host replication, transcription, and translation machinery, have been documented (4)(5)(6).
Phages have evolved strategies to hijack or manipulate their host's biosynthetic pathways and machinery during infection, and therefore have evolved various mecha nisms to control bacteria in long-term co-evolution and adaptation (7).The majority of known phage-host interactions occur early in the infection process (8), with phage early-gene products interacting with the host proteins to control and functionally shut them down.Studies have shown that phage proteins inhibit bacterial DNA biosynthesis by targeting host DNA polymerase and DNA gyrase (9,10), and affect cell division by inhibiting the essential cell division proteins FtsZ and FtsL or the cytoskeletal protein MreB (11)(12)(13)(14), or modifying or inhibiting bacterial RNA polymerase (15)(16)(17)(18).In addition, other key host processes, such as quorum sensing and glycolysis, are also targeted by phages (19,20).
Understanding the mechanisms by which phage proteins control the host will be valuable for the discovery of new antimicrobial drugs (5).In fact, the discovery of interactions between phage early proteins and essential bacterial proteins has been applied to high-throughput selection of antibacterial compounds (21).Moreover, the characterization of the active sites of the phage-host interaction will be useful for the development of effective approaches to identify small compounds or antibiotic peptides that mimic the antimicrobial activity of phage proteins (22,23).
Although it is critical to understand the interaction between phages and bacteria, our knowledge of the different mechanisms that phages develop to control bacteria is still limited.Due to the lack of sequence similarity to known proteins and the lack of experimental evidence, most of the phage early proteins have been classified as hypothetical proteins with uncertain functions (24).Methicillin-resistant Staphylococcus aureus is one of the most common antibiotic-resistant bacterial pathogens and is considered as a major threat to human health, thus understanding phage-S.aureus interactions will help to develop phage-based antimicrobial strategies to control this notorious pathogen (21,25).
In this study, we first comprehensively screened phage early proteins with growth control effects on S. aureus.One such early protein, Gp11, exacerbated division defects.We further demonstrated that Gp11 interacts with the peptidoglycan (PG) biosynthesis enzyme MurG and ultimately reduces the production of the final precursor molecule, lipid II.Gp11 also interacts with the cell division protein DivIC, which is essential for septal cell wall assembly by disrupting the recruitment of the division protein FtsW.Our results suggest that Gp11 interacts with essential host proteins to disrupt key PG biosynthesis and may provide a strategy to control S. aureus by targeting essential genes.
Gp11 causes growth defects and suppresses S. aureus cell division
Phage early proteins will "shut down" and "take over" the host, leading to host growth defects.To detect bacterial growth inhibition caused by hypothetical phage proteins, we performed a screening for 20 open reading frames (ORFs) of unknown function from S. aureus phage ΦNM1 (26).These genes were cloned into a plasmid driven by the isopropyl-β-D-1-thiogalactopyranoside (IPTG)-inducible promoter.The phage protein Gp104, which has been reported to inhibit the growth of S. aureus (21), was used as a positive control.After dot plating on a solid medium with IPTG induction, expression of gp11 or gp16 caused a reduction in the growth of S. aureus strain RN4220 (Fig. S1).Herein, we focused on characterizing the detailed roles of phage gene gp11 as its overexpression showed the strongest inhibition of the growth of S. aureus (Fig. S1).
To exclude that the inhibitory effect caused by Gp11 was due to the IPTG induction system, a NaAsO 2 induction system was introduced, and the same inhibitory effect was observed (Fig. 1A).Changes in cell morphology were observed after staining with the cell membrane fluorescent dye Nile Red (27).Compared to the control, overexpression of gp11 resulted in a decrease in cell viability (Fig. 1A).Phenotypic defects of larger cell size and abnormal non-spherical morphology of cells were observed compared to the control (Fig. 1B).Strikingly, overexpression of gp11 led to a fraction of cells with misplacement of nascent septa, and multiple parallel septa were frequently seen (Fig. 1B).Altered volume and abnormal cell division were also observed compared to the control.Cell volume increased significantly (Fig. 1C), and overexpression of gp11 also led to the formation of abnormal cells with multiple septa (Fig. 1D).Taken together, these results suggest that Gp11 alters cell morphology and causes growth defects.
Validation of MurG and DivIC as the targets of Gp11
Having obtained the evidence that Gp11 causes growth defects, we hypothesized that it might interact with the essential genes in S. aureus by suppressing their functions.To identify such potential interacting genes, we constructed a bacterial adenylate cyclasebased two-hybrid (BACTH) essential gene library of S. aureus.Essential genes (n = 345) were cloned into plasmids pKT25 or pUT18, and Gp11 interaction targets were exten sively screened (Fig. 2A).To test the feasibility of the screening approach with this library, we applied the known interaction pair Gp104 and DnaI as a positive control (28).As shown in Fig. 2B, Gp104 successfully interacts with DnaI, and Gp11 interacts with both MurG, which encodes a glycosyltransferase involved in PG biosynthesis, and DivIC, which is involved in cell division.A membrane protein called MraY, which is involved in PG synthesis but does not interact with Gp11, was chosen to test the specificity of this assay (Fig. 2B).To further investigate if these interactions with Gp11 play a key role in S. aureus, we used CRISPRi hypersensitivity assay (29).By preventing transcription with a deactivated Cas9, CRISPRi allows sequence-specific knockdown of genes (Fig. S2A).Knockdown of murG, divIC significantly inhibited the growth of S. aureus (Fig. S2B); however, murG knockdown had no effect on bacterial morphology, whereas divIC knockdown showed significantly larger cell volumes (Fig. S2C).The phage-host interaction pair Gp104 and DnaI was used as a positive control, and Gp11 with its non-target DnaI was used as a negative control.The strain overexpressing Gp104 based on dnaI knockdown exhibited enhanced growth sensitivity compared to the control cells expressing Gp104 (Fig. S2D).However, reduction of dnaI levels by CRISPRi after expression of Gp11 showed no difference in growth (Fig. S2E).We conclude that the CRISPRi-based system effectively identifies phage-host interactions.
Next, we identified the targets of Gp11 in S. aureus using this CRISPRi hypersensitiv ity assay.Partial knockdown of the essential gene murG increased the sensitivity of cells overexpressing Gp11 (Fig. 2C).Furthermore, overexpression of Gp11 in the divIC knockdown cells sensitized the cells expressing Gp11 (Fig. 2D), further supporting our result that MurG and DivIC are physiologically important targets of Gp11 in S. aureus.Bacterial growth was impaired after mraY knockdown (Fig. S2B), but no difference was observed in Gp11-expressing cells with or without mraY knockdown (Fig. 2E).
Having confirmed that MurG and DivIC are the targets of Gp11, we hypothesized that growth inhibition by Gp11 could be rescued by overexpression of either MurG or DivIC.Moreover, as shown in Fig. 2F, cell growth could be partially restored when MurG or DivIC was co-expressed with Gp11 in S. aureus.In contrast to DivIC, MurG plays an important role in rescuing cell growth.As a negative control, MraY failed to rescue the growth inhibition caused by Gp11 (Fig. 2F).After staining the cells with the cell membrane fluorescent dye Nile Red, we used fluorescence microscopy to examine the cell morphological changes by evaluating the area of the cells.Cells co-expressing Gp11 with either MurG or DivIC restored the phenotypic defects (Fig. 2G) by showing a significant reversal in cell volume and reducing cell division defects compared to cells expressing Gp11 alone (Fig. 2H and I).Taken together, these results suggest that Gp11 controls cell growth by interacting with MurG and DivIC in vivo.
Gp11 blocks cell division
Gp11 is a 53-amino-acid protein with a predicted double transmembrane helix (Fig. S3A).We examined Gp11 localization using Gp11-green fluorescent protein (GFP) fusion and found that Gp11 was indeed localized on the membrane (Fig. S3B).We performed a screen for Gp11-resistant mutants by generating transformants under conditions of high IPTG to identify key residues in Gp11.By sequencing of potential candidates, three ORF-resistant mutants were screened out as Gp11 S33L , Gp11 G36R , and Gp11 A38E (Fig. 3A; Fig. S3C).Expression of these point mutants revealed that all lost their ability to inhibit S. aureus growth (Fig. S3D and E), but remained localized on the membrane (Fig. S3B).
To further identify the key residues in Gp11 that interact with MurG and DivIC, we performed the BACTH assay.Mutation of G36 and A38 in Gp11 resulted in no interac tion with MurG, whereas mutation of S33 decreased binding affinity to MurG (Fig. 3B).Regarding the interaction of Gp11 with DivIC, the A38E mutant does not make contact with MurG but still interacts with DivIC (Fig. 3C).These data indicate that Gp11 interacts with MurG and DivIC in a different pattern.
The division defects caused by Gp11 suggest that it disrupts the process of cell division.Using a MurG-GFP fusion protein, we observed that localization of MurG was frequently disrupted in cells expressing Gp11 (Fig. 3D).To confirm the role of the key residues of MurG in Gp11 function, the localization of MurG was assessed in the background of Gp11 expression or its point mutants.As shown in Fig. 3D, once the key amino acids were mutated, the localization of MurG was no longer affected.In addition, FtsW, the transglycosylase that is required for the formation of the septal cell wall, is recruited by the trimeric complex of DivIC, DivIB, and FtsL (31).We found that overexpression of Gp11, but not its mutants, disrupted the localization of FtsW, causing the fluorescence to be aggregated (Fig. 3D).We also observed fluorescence aggrega tion of DivIB, but the localization of the early division protein EzrA (32) appear to be unaffected in enlarged Gp11-expressing cells, cells with empty vector, or Gp11 mutants (Fig. 3D).These results suggest that Gp11 binds to MurG, resulting in its mis-localization, and interacts with DivIC to disrupt the recruitment of FtsW, which ultimately result in cell division defects.
Gp11 spatially regulates PG biosynthesis in cell division and promotes phage infection
The interactions of Gp11 with MurG and DivIC led us to hypothesize that Gp11 may affect PG biosynthesis.To evaluate the effect of Gp11 on PG synthesis and the impact on S. aureus cell division, we labeled the cells with the fluorescent D-amino acid 7-hydroxycoumarin carbonyl amino-D-alanine (HADA), a molecule that is incorporated into newly synthesized PGs (33).Compared with the control cells, Gp11-overexpressing cells exhibited a more diffusible HADA signal, which was seen to occur at multiple sites within the cell, including peripheral and multiple partial septa (Fig. 4A), and the newly synthesized PG was depleted at the septum relative to the periphery in Gp11overexpressing cells compared with controls (Fig. 4B), which is consistent with murG knockdown cells (Fig. S4A and B).
MurG is a glycosyltransferase in PG synthesis that transfers N-acetyl glucosamine (GlcNAc) from UDP-GlcNAc to the C4 position of lipid I to form a lipid-linked disaccharide peptide called lipid II (35).We therefore hypothesized that Gp11 targets MurG to inhibit its activity in producing lipid II, and performed an assay to detect cellular lipid II in S. aureus as previously described (34,36).We isolated lipid II from Gp11-overexpressing cells, and the fraction was detected after labeling the stem peptides with biotin-D-lysine (BDL) for immunoblotting (Fig. 4C).As shown in Fig. 4D, a reduction in lipid II was observed in the presence of Gp11, but not its mutants, suggesting that Gp11 inhibits MurG activity, resulting in a reduction in lipid II.Taken together, our results indicate that Gp11 spatially regulates PG synthesis to control cell size.
Because Gp11 has been shown to affect lipid II production, we finally characterized its effect on PG biosynthesis during phage infection in the absence of gp11.We constructed an in-frame gene deletion of gp11 named ΦNM1 Δgp11 and characterized the effect of Gp11 on phage fitness (Fig. 5A).ΦNM1 Δgp11 showed a reduced ability to lyse the host and resulted in smaller phage plaques compared to ΦNM1 (Fig. 5B and C).When Gp11 is expressed in the bacteria, the phage plaque size and phage infection are restored to the levels of wild type (Fig. 5C and D).This implies that Gp11 is an important phage protein involved in the takeover or manipulation of host bacteria.
Consistent with our finding that Gp11 overexpression reduced lipid II production, cells infected with ΦNM1 Δgp11 showed a significant increase in lipid II compared to the ΦNM1-infected strain 2 h after infection (Fig. 4E).Because MurG is a key enzyme in the PG synthesis pathway and directly regulates lipid II production, we therefore conclude that Gp11 inhibits MurG activity and blocks S. aureus cell division by inhibiting PG biosynthesis.
DISCUSSION
With increasing concern about bacterial drug resistance, characterizing new targets has become a strong research focus in infection control.Phages engage in a long evolution ary arms race with their hosts over a period in which early phage proteins "take over" and "shut down" the host (37).Furthermore, bacterial proteins that are preferentially blocked by phage proteins have the potential to serve as novel antibacterial targets, as their disruption could disrupt key processes and slow bacterial growth.In the present study, we performed a comprehensive screening of phage early proteins that inhibit bacterial growth.We have identified a phage protein, Gp11, that inhibits cell division by interfering with PG synthesis.Our results suggest a model in which Gp11 interacts with MurG, leading to reduced production of lipid II, and interacts with DivIC to disrupt recruitment of the divisome complex.We found that expression of gp11 from phage ΦNM1 inhibits bacterial growth and alters cell morphology in S. aureus RN4220 with cell lysis (data not shown), which differs from observations of a lethal but not lytic effect of the phage protein E on Staphylococcus carnosus (38).This lysis effect is also observed in Escherichia coli with empty cell walls (39).The inhibitory effect of Gp11 could be used as a potentially beneficial strategy to combat S. aureus.Our results also suggest that Gp11 alters cell morphology by increasing host cell size.Phage adsorption and replication are closely related to the cell size of bacterial hosts, which affect the fitness and mutual evolution of phages and bacteria (40).The larger size caused by overexpression of Gp11 is consistent with the conclusion that Gp11 promotes phage infection (Fig. 5), supporting the idea that phages inhibit host cell division to propagate their progeny (14).These results suggest that Gp11 is a critical protein for phage ΦNM1 to control its host.
After screening for candidates that interact with phage proteins, we employed a CRISPRi hypersensitivity assay to validate the targets of phage proteins in S. aureus, which allows for the identification of direct phage targets.In this way, we found that Gp11 directly interacts with MurG and DivIC (Fig. 2B).These analyses provide a rapid method for identifying major targets of phages in the host using a dual screening model.As a glycosyltransferase, MurG is essential for bacterial survival by catalyzing the transfer of the GlcNAc motif of UDP-GlcNAc to the C4 hydroxyl MurNAc in lipid I to form lipid II (41) and is also an important target for the development of antimicrobial drugs.Elucidation of the mechanism by which Gp11 impairs cell growth requires a protein-pro tein interaction with MurG.This will provide new information for the development of novel drugs that directly target S. aureus in the future.
Gp11 inhibits cell growth by targeting PG biosynthesis in cell division.It has been reported that the correct localization of the division machinery in the midcell is correlated with PG density, which has been shown to be a marker of cell division (42).Gp11-mediated delocalization of MurG most likely disrupted its function spatiotempor ally.Previous work has also shown that the phage protein DicB inhibits cell division by interacting with and affecting the localization of cell division proteins MinC and FtsZ (43,44).Another phage protein Tip, which interacts with PilB, also antagonizes PilB function by delocalizing PilB from the poles (45).This strategy for phages to affect cell division by disrupting the localization of host division-associated proteins may be a general method for phages to alter host cell shape.
PG synthesis and cell division are inextricably linked, with the cell division septum being the main region of PG synthesis in S. aureus (46).Cell wall attack is one of the major strategies for phage to infect the host, but targeting PG synthesis is uncommon.A small protein like Gp11 targets the essential proteins MurG and DivIC to control its host.This implies the strong evolutionary pressure on phages to develop strategies to control host function by targeting two proteins simultaneously (19,20,47).DivIC is a key component of cell wall dynamics during division, which is essential for proper septum formation (48).The interaction between Gp11 and DivIC prevents the recruitment of FtsW, which interferes with PG biosynthesis at the septum, and overexpression of Gp11 showed a more diffuse HADA signal at the cell periphery (Fig. 4A).These data also support that loss of DivIC causes disruption of cell division as well as increases PG production at the cell periphery, which negatively impacts septum formation and ultimately results in thicker peripheral cell walls (49).During cell division, the late divisome proteins such as FtsW interact with other regulatory proteins to form the mature divisome and initiate septal PG synthesis (50).FtsW is a well-known lipid II-interacting protein (51).In a recent study, FtsW was reported to serve as a peptidoglycan polymerase that polymerizes lipid II at the septum into peptidoglycan (52).The reduction of lipid II in Gp11-expressing cells is consistent with the finding that FtsW was frequently mislocalized (Fig. 3D).We propose that mislocalization of FtsW may contribute to lipid II reduction during phage infection.Since the biosynthesis of the bacterial cell wall is closely coordinated with cell division (48,53), we hypothesized that this could be a viable strategy for phages to influence PG synthesis during cell division and to lyse their host, which has been observed in E. coli (39,54).
The target of Gp11 is relevant to its function as an inhibitor of PG synthesis.Gp11 inhibits the production of the final lipid-linked PG precursor, lipid II, by affecting the activity of MurG (Fig. 4).The altered morphological phenotype of the Gp11 mutant was accompanied by a reduction in lipid II, which is incorporated into the PG layer, helps to maintain cell shape, provides strength to withstand turgor, and is involved in the processes of cell growth and division (55).Notably, we found that infection with ФNM1 Δgp11 significantly increased the production of lipid II (Fig. 4E), which is consistent with previous studies that phage infection inhibits host PG biosynthesis.Previous work has shown that the phage protein Lys M inhibits PG synthesis by targeting MurJ (56).The small RNA phage Qβ encoding the A 2 protein blocked MurA, and the DNA phage ΦX174 encoding E protein inhibited MraY, both of which disrupt PG synthesis (54,57).Although phage proteins have been shown to inhibit PG synthesis, the effect of this inhibition on the phage-infected cell has not been investigated.Here, we elucidated the effect of Gp11 on PG synthesis by comparing the results of wild-type ФNM1 and ФNM1 Δgp11 infections.Our results further explain that Gp11 inhibits S. aureus growth probably by affecting lipid II formation and thus preventing bacteria from maintaining normal morphology.
The exploitation of phage-host interaction has inspired the discovery of antibacterial targets (7).For example, a strategy to search for novel molecular targets of phages used time-resolved fluorescence resonance energy transfer to screen small molecules to disrupt the interaction between Gp104 and DnaI (21) and ultimately identified 11 molecules that were directly active against S. aureus.Recently, Zhang et al. (58) used small molecules to mimic the inhibitory effect of the phage protein Gp46 to develop a super-antibacterial drug that not only shortens the drug development cycle but also broadly inhibits most drug-resistant bacteria.Therefore, studying the Gp11-MurG interaction could provide information for the development of small molecules that mimic the inhibitory effect of Gp11.In summary, the strategy to affect cell division by disrupting the localization of host division-associated proteins may be a general way for phages to reshape the host, and the interaction partners identified here will lay the foundation for future antimicrobial treatment.
Bacterial strains and growth conditions
The strains used in this study are listed in Table S1.Plasmids were cloned in Escherichia coli DH5α.The E. coli BL21(DE3) strain was used for protein overexpression and purification.E. coli strains were grown in Luria-Bertani (LB) broth or on LB agar supplemented with 100 µg mL −1 ampicillin or 50 µg mL −1 kanamycin.S. aureus strains were grown in tryptic soy broth (TSB; Difco) or on tryptic soy agar (TSA; Difco) supplemented with 10 µg mL −1 erythromycin or 10 µg mL −1 chloramphenicol when needed.To induce gene expression, 0.1 or 0.5 mM isopropyl-β-D-1-thiogalactopyranoside (IPTG) was added to the bacterial cultures.
Plasmid construction
The plasmids used in this study are listed in Table S2.All oligonucleotides used in this study are listed in Table S3.Genes were cloned into plasmids using a ClonExpress II One-step Cloning Kit (Vazyme, Nanjing, China).Genomic DNA extracted from S. aureus strain RN4220 using a TIANAmp Bacteria DNA Kit (Tiangen, Beijing, China) was used as the template in the PCR reactions.The plasmid pTLS is for phage early protein overex pression in S. aureus and contains IPTG-inducible constructs with the Cm R marker.All plasmids were constructed via multiple steps of restriction-ligation or Gibson assembly.
Screening of phage genes that inhibit bacterial growth
To identify genes that inhibit bacterial growth, we cloned early genes of unknown function from ΦNM1 according to the previous RNA-seq results (59) into plasmid pTLS under the IPTG-inducible promoter.The plasmids were transformed into S. aureus RN4220 for a spot test.Cultures containing individual plasmids of the phage genes were inoculated onto TSA plates with or without 1 mM IPTG at 37°C for 12 h.
Growth curves and spot dilution assay of S. aureus
For growth curve determination, overnight cultures of the strains were diluted 1:100 in TSB supplemented with 10 µM NaAsO 2 .Cells were grown at 37°C, and the optical density (OD) 600 values were measured hourly using a plate reader (BioTek, Winooski, VT, USA).Cells used for dilutions and subsequent colony-forming unit (CFU) counting were taken from cultures under experimental conditions.Plates with dilutions that resulted in well-separated colonies were used for counting, and total CFUs were calculated.For the spot dilution assay, 10-fold serial dilutions of cultures were prepared in 500 µL phosphate-buffered saline (PBS), and 2 µL of these dilutions was plated on TSA and incubated at 37°C for 12 h.
Construction and screening of the S. aureus essential gene BACTH library
A plasmid library containing 345 essential genes of S. aureus was constructed.The genes were amplified by PCR and ligated to the bacterial two-hybrid vector pUT18 and pKT25 provided in a BACTH System Kit (Euromedex, France).Plasmids were purified from the assembled clones to generate plasmid libraries.To screen the targets of phage proteins, 1 µL of the mixed essential gene plasmids was transformed into competent BTH101 cells harboring bait plasmids expressing phage proteins, and the transformants were plated on a MacConkey agar plate according to the manufacturer's instructions.The red colonies were selected for assaying β-galactosidase activity (60).
Bacterial two-hybrid assay
The BACTH system was used to detect protein-protein interactions (61).Briefly, the "bait" and "prey" proteins were fused to pKT25 and pUT18, respectively, and heat-shocktransformed into BTH101 competent cells lacking a functional cyaA gene.Transformants were grown on LB agar for 2 days at 30°C.Three clones were selected and grown for 16 h at 30°C with shaking in LB containing 50 µg mL −1 kanamycin, 100 µg mL −1 ampi cillin, and 0.5 mM IPTG.The Miller assay was used to spectrophotometrically quantify β-galactosidase activity and to identify the protein-protein interactions (60).Results are representative of at least three independent replicates.
CRISPRi hypersensitivity assay
CRISPRi-mediated inhibition of essential gene expression was performed as described (62).Using pISA-IPTG, the base-pairing region was designed to target the essential gene on the coding strand adjacent to the protospacer motif NGG.dCas9 protein expres sion was induced with IPTG.Results are representative of at least three independent replicates.To test the efficacy of the essential gene knockdown strain, relative growth in liquid TSB containing 1 mM IPTG was measured and compared to the growth of the no-sgRNA control at mid-log phase using a plate reader (BioTek).To verify the targets of Gp11 in S. aureus, a low inducible concentration was selected to knock down essential genes without affecting bacterial growth, and the plasmid pTR-gp11 was transformed into a strain containing the CRISPRi system.The growth of CRISPRi S. aureus knockdown mutants relative to no-sgRNA control was measured after overexpression of Gp11 using a flat-bottomed 96-well plate.
Labeling of S. aureus strains
The S. aureus strains were labeled with cell membrane fluorescent dye 9-diethyla mino-5H-benzo [α] phenoxazine-5-one (Nile Red) as previously described for fluorescence microscopy (27).To label S. aureus membranes, cells were stained with Nile Red (MedChemExpress, New Jersey, USA) at a final concentration of 5 µg mL −1 for 5 min at room temperature, washed twice with PBS, and then 2 µL cultures was plated onto slides for imaging.To label the nascent PG of S. aureus, cells were incubated with fluorescent d-amino acid HADA (MedChemExpress) at a final concentration of 250 µM for 30 min at 37°C with shaking, washed with PBS to remove the unbound dye, and then plated on a slide for imaging (63,64).The labeled cells were observed using phase contrast and the 4′,6-diamidino-2-phenylindole channel on an Olympus microscope.
Microscopy and image analysis
To detect Gp11 overexpression in S. aureus growth, cells were stained with the cell membrane fluorescent dye Nile Red for 5 min at room temperature and washed twice with PBS before microscopy.To study the localization of Gp11 and its mutants, Gp11 or its mutants fused with GFP were cloned into expression vector pCI and then elec trotransferred into S. aureus.Transformants were grown at 37°C in TSB medium, induced with 1 mM IPTG, and harvested by centrifugation at 5,000 × g for 3 min at OD 600 = 0.4.Supernatants were decanted, and pellets were resuspended in PBS for imaging.To further evaluate the effect of Gp11 on MurG localization, Gp11 was co-transformed with MurG-GFP in S. aureus.Cells were harvested at OD 600 between 0.4 and 0.6 with the addition of 10 µM NaAsO 2 and 100 µM IPTG and then centrifuged at 5,000 × g for 3 min, the supernatant was discarded and washed twice with PBS and resuspended.Bacterial solution (2 µL) was placed on a slide for sampling and microscopic observation.The localization of the corresponding proteins was monitored by fluorescence visualization using an Olympus fluorescence microscope at 488 nm excitation.All images were taken on an Olympus inverted microscope at 10× and 100× magnification using a 100× oil immersion phase contrast objective.Microscope control and image acquisition were performed in NIS Elements (Nikon, Melville, NY, USA).Cell area was analyzed using the MicrobeJ (65) and ImageJ (66).
Gp11 point mutant isolation
Point mutations of Gp11 were isolated as previously described (5,13).Briefly, S. aureus RN4220 cells were transformed with pTLS-gp11 and cultured overnight on TSB agar with 1 mM IPTG.The resistant colonies were harvested, and plasmids were extracted using a FastPure Plasmid Mini Kit (Vazyme).The plasmids were then retransformed into competent S. aureus RN4220 cells, and the resultant colonies were picked for spot dilution assay as described above to check growth inhibi tion.Plasmids contained in clones that no longer inhibited bacterial growth were subjected to sequencing analysis.
Mutant construction of gp11 in ΦNM1
The ΦNM1 gp11 knockout strain was constructed using a CRISPR system.The plasmid pCas9 expressing Cas9 containing guide RNA spanning nucleotides 74-93 of gp11 with the upstream and downstream fragments of gp11 was transformed into S. aureus RN4220.A plaque assay was performed as previously described to select for the Gp11 knockout strain (26).Briefly, 100 µL S. aureus and 10 µL phage were mixed with 5 mL soft TSA and 5 mM CaCl 2 and poured on TSA containing 1 mM IPTG and 10 µg mL −1 erythromycin.Plaques were selected for validation using the primers listed in Table S2.
Phage infection assay
Overnight cultures of S. aureus RN4220 were diluted 1:100 in fresh TSB containing a final concentration of 5 mM CaCl 2 to OD 600 = 0.2, and 200 µL of cells was added to each well of a 96-well plate.ΦNM1 WT or ΦNM1 Δgp11 phages were immediately added to each well at the indicated multiplicity of infection of 1 and 0.01, respectively.After phage infection, growth was measured every 15 min at 37°C using a shaking plate reader (Biotek).The growth curve experiment was replicated at least three times independently.
Lipid II purification
Lipid II extraction from S. aureus cells was performed as described (34).Briefly, overnight cultures of S. aureus WT or overexpressing Gp11 were diluted to OD 600 = 0.01 and grown in TSB at 37°C to OD 600 of 0.5-0.6.Cells were harvested after centrifugation at 4,000 × g for 10 min, and the pellets were resuspended in PBS and added to 8.75 mL CHCl 3 :MeOH (1:2).The mixture was vortexed at 25°C for 10 min and then centrifuged at 4,000 × g for 10 min to remove cell debris.The supernatant was transferred into a new centrifuge tube containing 5 mL CHCl 3 and 3.75 mL PBS (pH 7.4).The mixture was vortexed for 10 min and centrifuged at 4,000 × g for 10 min to achieve phase separation.The material between the top aqueous and bottom organic layer was collected, dried in a vacuum desiccator, and resuspended in 20 µL of dimethyl sulfoxide (DMSO).
Western blot analysis of biotinylated lipid II
Biotinylation and detection of lipid II were performed as described (67).Briefly, 2 µL of lipid extraction solubilized in DMSO was added to a solution containing 4 µM PBP4, 3 mM BDL in reaction buffer (12.5 mM HEPES, 2 mM MnCl 2 , 250 µM Tween-80, pH 7.5) to a total volume of 10 µL.After incubation for 1.5 h at room temperature, the reaction was quenched with 10 µL of 2× SDS loading buffer.The final mixture (3 µL) was loaded onto a 4%-20% gradient polyacrylamide gel and run at 100 V for 1 h.The final mixture was transferred to an immunoblot polyvinylidene fluoride membrane (Bio-Rad, Hercules, CA, USA).BDL-lipid II was detected by blotting with streptavidin-horseradish peroxidase (1:10,000 dilution) (Beyotime, Shanghai, China).
Statistical analysis
Statistical significance between two groups was analyzed by unpaired Student's t-test (two-tailed) using GraphPad Prism 8 (GraphPad Software, Boston, MA, USA).
FIG 1
FIG 1 Overexpression of Gp11 in S. aureus alters cell morphology.(A) Effect of Gp11 overexpression on S. aureus cell growth.(B) Effect of Gp11 overexpression on S. aureus cell shape as visualized by phase-con trast and fluorescence microscopy.Arrows indicate septal defects as multiple.Cells were stained with membrane dye Nile Red.Scale bar, 2.5 µm.(C) Cell volume was measured using MicrobeJ.Cells were harvested after 2 h incubation with 10 µm NaAsO 2 .(D) Quantitation of cells with septal defects as multiple septa (abnormal), and nascent or complete septum (normal) after treatment with 10 µm NaAsO 2 for 2 h.In this plot, n = 198 (Vec) and 91 (Gp11) cells; P values were determined by unpaired Student's t-test.**P < 0.01 and *P < 0.05.
FIG 2
FIG 2 Validation of the targets of Gp11 in S. aureus.(A) Flowchart for screening Gp11-interacting proteins from S. aureus essential-gene BACTH libraries.With libraries being collected in an essential-gene plasmid pool and equimolar mix, the plasmid library was then transformed into Escherichia coli BTH101 reporter cells, which contain the phage gene, and plated on MacConkey agar plates.(B) In a bacterial two-hybrid assay of Gp11 interaction with MurG and DivIC, the known interaction pair Gp104 and DnaI was used as a positive control, while Gp11 and MraY as a negative control.(C) CRISPRi-based assay revealed MurG as the target of Gp11.The growth of S. aureus by knockdown of murG after expression of Gp11 (Gp11 + sgRNA murG ) relative to no sgRNA control (Vec 1 + Vec 2 ).(D) The growth of S. aureus by knockdown of divIC after expression of Gp11 (Gp11 + sgRNA divIC ) relative to no sgRNA control (Vec 1 + Vec 2 ).Each data point represents three independent replicates.P values were determined by unpaired Student's t-test.**P < 0.01, *P < 0.05, and n.s.: no significant difference.(E) The growth of S. aureus by knockdown of mraY after expression of Gp11 (Gp11 + sgRNA mraY ) relative to no sgRNA control (Vec 1 + Vec 2 ).(F) Growth assay of cells expressing Gp11, MurG, DivIC, or MraY on solid medium.(G) Microscopic images of S. aureus expressing Gp11, MurG, and DivIC.Cells were stained with membrane dye Nile Red.Scale bars, 2.5 µm.(H) Cell volume was measured using MicrobeJ.Cells were collected after 2 h incubation with 10 µM NaAsO 2 and 100 µM IPTG.From left to right, n = 467, 418, 118, and 510 cells.P values were determined by unpaired Student's t-test.**P < 0.01.(I) Quantitation of cells with septal defects (abnormal), and nascent or complete septum (normal) after cells were treated with 10 µM NaAsO 2 and 100 µM IPTG for 2 h.
FIG 3
FIG 3 Gp11 acts to block cell division.(A) Summary of the identified mutants, all of which map to a hypothetical protein encoded by the gene gp11 in S. aureus ΦNM1.The structural model of Gp11 predicted by AlphaFold (30), and the fraction of each mutant of Gp11 is indicated.(B) Analysis of the interactions between MurG and the mutants of Gp11 through the bacterial adenylate cyclase-based two-hybrid (BACTH) system.(C) Analysis of the interactions between DivIC and the mutants of Gp11 through BACTH.(D) The localization of MurG, DivIB, FtsW, and EzrA were monitored in the presence of Gp11 or its mutants.The cells were collected after 2 h incubation with 10 µM NaAsO 2 and 100 µM IPTG.Scale bars, 2.5 µm.
FIG 4
FIG 4 Gp11 targets peptidoglycan biosynthesis by inhibiting the activity of MurG.(A) S. aureus cells expressing Gp11 or its mutants were stained with the fluorescent cell wall marker D-amino acid 7-hydroxycoumarin carbonyl amino-D-alanine (HADA) and analyzed by phase-contrast and fluorescence microscopy.Scale bars, 2.5 µm.(B) Images of individual cells expressing Gp11 or its mutants were used to calculate the fluorescence ratio of the septal versus cell peripheral fluorescence signal.n ≥ 30.P values were determined by unpaired Student's t-test.**P < 0.01 and n.s.: no significant difference.(C) The terminal D-Ala residue of the lipid II stem peptide was labeled with the biotin-D-lysine probe BDL using S. aureus PBP4 (34).(D) Western blot of lipid II after overexpression of Gp11 and its point mutants in S. aureus strain RN4220.(E) Western blot of lipid II after cells were infected with ΦNM1 and ΦNM1 Δgp11 . | 8,626.8 | 2024-05-16T00:00:00.000 | [
"Biology"
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Integration of Liver Glycogen and Triglyceride NMR Isotopomer Analyses Provides a Comprehensive Coverage of Hepatic Glucose and Fructose Metabolism
Dietary glucose and fructose are both efficiently assimilated by the liver but a comprehensive measurement of this process starting from their conversion to sugar phosphates, involvement of the pentose phosphate pathway (PPP), and conversion to glycogen and lipid storage products, remains incomplete. Mice were fed a chow diet supplemented with 35 g/100 mL drinking water of a 55/45 fructose/glucose mixture for 18 weeks. On the final night, the sugar mixture was enriched with either [U-13C]glucose or [U-13C]fructose, and deuterated water (2H2O) was also administered. 13C-isotopomers representing newly synthesized hepatic glucose-6-phosphate (glucose-6-P), glycerol-3-phosphate, and lipogenic acetyl-CoA were quantified by 2H and 13C NMR analysis of post-mortem liver glycogen and triglyceride. These data were applied to a metabolic model covering glucose-6-P, PPP, triose-P, and de novo lipogenesis (DNL) fluxes. The glucose supplement was converted to glucose-6-P via the direct pathway, while the fructose supplement was metabolized by the liver to gluconeogenic triose-P via fructokinase–aldolase–triokinase. Glucose-6-P from all carbohydrate sources accounted for 40–60% of lipogenic acetyl-CoA and 10–12% was oxidized by the pentose phosphate pathway (PPP). The yield of NADPH from PPP flux accounted for a minority (~30%) of the total DNL requirement. In conclusion, this approach integrates measurements of glucose-6-P, PPP, and DNL fluxes to provide a holistic and informative assessment of hepatic glucose and fructose metabolism.
The liver is a key site for the metabolism of dietary sugar, with glucose and fructose being the principal species absorbed into the portal vein blood outside of milk products. In mammals and many other organisms, the fate of dietary sugar is heavily influenced in real time by systemic glucose homeostasis, with the main priorities being maintenance of a threshold level of blood glucose for the central nervous system and erythrocyte function, while also minimizing large excursions of blood glucose levels. At the same time, sugar is sensed as a precious and desirable nutrient to be sequestered as rapidly and efficiently as possible [1]. This balance is achieved via a highly flexible and well-regulated hepatic metabolic network. Not only can it rapidly switch between net hepatic glucose production and uptake, but it can also direct temporary sugar surplus into short-term storage as Metabolic model for the synthesis of glycogen and triglyceride from glucose or fructose in the liver. The model includes glucose-6-phosphate oxidation by the pentose phosphate pathway (PPP) to provide NADPH for conversion of acetyl-CoA to fatty acyl-CoA via de novo lipogenesis. The 13 C-enriched glucose and fructose precursors are highlighted in red and the sampled metabolites, glycogen and triglyceride, are highlighted in blue. The metabolite pools whose 13 C and 2 H enrichments are reported by the sampled metabolites, namely, glucose-6-P, triose-P (dihydroxyacetone phosphate and glyceraldehyde 3-phosphate) and lipogenic acetyl-CoA, are highlighted in boxes. Glycogen synthesis from glucose via glucose-6-P from gluconeogenic precursors, including pyruvate and triose-P sources, is also indicated (direct and indirect pathways, respectively). For simplicity, some metabolic intermediates, as well as ATP/ADP and NAD/NADH interconversions, are not shown. Abbreviations are as follows: DHAP-dihydroxyacetone phosphate; F-1-P-fructose-1-phosphate; F-6-P-fructose 6-phosphate; F-1,6-P2-fructose-1,6-bisphosphate; G-6-P-glucose 6-phosphate; Gly-glyceraldehyde; Gly-3-P-glyceraldehyde 3-phosphate; OA-oxaloacetate; PEP-phophoenolpyruvate; Ru-5-P: ribulose-5-P. Metabolic model for the synthesis of glycogen and triglyceride from glucose or fructose in the liver. The model includes glucose-6-phosphate oxidation by the pentose phosphate pathway (PPP) to provide NADPH for conversion of acetyl-CoA to fatty acyl-CoA via de novo lipogenesis. The 13 C-enriched glucose and fructose precursors are highlighted in red and the sampled metabolites, glycogen and triglyceride, are highlighted in blue. The metabolite pools whose 13 C and 2 H enrichments are reported by the sampled metabolites, namely, glucose-6-P, triose-P (dihydroxyacetone phosphate and glyceraldehyde 3-phosphate) and lipogenic acetyl-CoA, are highlighted in boxes. Glycogen synthesis from glucose via glucose-6-P from gluconeogenic precursors, including pyruvate and triose-P sources, is also indicated (direct and indirect pathways, respectively). For simplicity, some metabolic intermediates, as well as ATP/ADP and NAD/NADH interconversions, are not shown. Abbreviations are as follows: DHAP-dihydroxyacetone phosphate; F-1-P-fructose-1-phosphate; F-6-P-fructose 6-phosphate; F-1,6-P 2 -fructose-1,6-bisphosphate; G-6-P-glucose 6-phosphate; Gly-glyceraldehyde; Gly-3-P-glyceraldehyde 3-phosphate; OA-oxaloacetate; PEPphophoenolpyruvate; Ru-5-P: ribulose-5-P.
Glycogen
The conversion of glucose-6-P to lipids requires the generation of NADPH. The PPP couples the oxidation of glucose-6-P to NADPH generation; hence, in principle, a portion of sugar carbons can be sacrificially oxidized such that the remainder can be converted to lipids. In the liver, NADPH can be derived from other sources [2] and, to the extent that these contribute to de novo lipogenesis (DNL) reducing equivalents, then sugar carbons are spared from PPP oxidation. The PPP is also a conduit for converting hexose sugars to pentose phosphate precursors for nucleotide biosynthesis, which is a continual requirement for hepatocyte growth and turnover. 13 C-Isotopomers of newly synthesized glycogen derived from [U-13 C]glucose and [U-13 C]fructose inform direct and indirect pathway fluxes [3], as well as the fraction of glucose-6-P that underwent PPP oxidation [4]. 13 C-isotopomers of newly synthesized triglyceride fatty acids and glycerol moieties inform the contributions of these sugars to DNL and glyceroneogenesis [5]. The main objective of this study was to integrate these measurements into a comprehensive description of hepatic glucose and fructose metabolism, starting with their initial phosphorylation to sugar phosphate intermediates and culminating with their conversion to triglycerides. Given the role of excessive sugar consumption and elevated DNL activity in the pathogenesis of non-alcoholic fatty liver disease (NAFLD) [6][7][8], such knowledge will improve our understanding of the role of hepatic glucose and fructose metabolic fluxes in promoting this condition. Figure 1 shows the metabolic model for lipogenesis from glucose and fructose. Fructose is assumed to be converted to triose phosphates via the canonical fructokinase-aldolasetriokinase pathway, while glucose is converted to glucose-6-P via glucokinase. Glucose-6-P can also be synthesized from triose phosphates by gluconeogenesis (GNG). Glucose-6-P is disposed of by conversion to glycogen, by PPP oxidation, and by glycolysis. Glycerol-3-P destined for triglyceride synthesis is mostly derived from the glycolytic triose phosphate pool. The pyruvate product of glycolysis is oxidized to acetyl-CoA, which can be recruited for fatty acid synthesis via DNL. One critical aspect in interpreting the formation of glycogen and triglyceride 13 C-isotopomers from the 13 C-glucose or fructose precursors is that turnover of the product pools may not be complete over the duration of the experiment, resulting in artefactual dilutions of glycogen and lipid 13 C-isotopomer enrichments.
Metabolic Model
To determine the fractions of glycogen and triglyceride that were synthesized while the 13 C-sugar precursors were present, deuterated water ( 2 H 2 O) was administered over the same period. The 2 H enrichment of glycogen and triglycerides relative to body water informs these fractions [3,5,9] and, by sequential 2 H and 13 C NMR analysis, this information can be determined without interfering with the quantification of the 13 C-isotopomer distributions [3,5,10]. Figure 2 shows the principal 13 C-isotopomers of selected metabolite pools following the metabolism of [U- 13 C]glucose. Under the experimental conditions, the 13 C-isotopomer distribution of newly synthesized glycogen is assumed to reflect that of glucose-6-P. The direct pathway metabolism of [U-13 C]glucose generates [U-13 C]glucose-6-P and the [U-13 C]glycogen isotopomer. [U-13 C]Glucose-6-P that undergoes PPP oxidation and recycling generates [1,2-13 C 2 ]glucose-6-P and other partially labeled glucose-6-P isotopomers [4]. In addition, [U-13 C]glucose that undergoes glycolytic-gluconeogenic recycling (either intrahepatic or via the Cori cycle) generates triose-P isotopomers, principally [1,2,3-13 C 3 ]and [2,3-13 C 2 ]triose-P [11]. These are incorporated into glucose-6-P and glycogen via GNG, which is also historically referred to as the indirect pathway [12]. The fraction of newly synthesized glycogen derived from the indirect pathway can be estimated from the analysis of its 2 H enrichment from 2 H 2 O [3]. Hence, the 13 C-isotopomer distribution of the GNG precursor pool (GNG-triose-P) can be inferred from that of glycogen after correction for the indirect pathway fraction. Glycerol-3-P for fatty acid esterification is derived from the reduction of dihydroxyacetone phosphate; hence, its 13 C-isotopomer distribution, read from the analysis of newly synthesized triglyceride glycerol, provides a readout of triose-P 13 C-isotopomers. Acetyl-CoA isotopomers that are generated from triose-P can be diluted by unlabeled non-triose substrates such as acetate before their incorporation into fatty acids. When the 13 C-label is provided as [U-13 C]fructose (Supplementary Figure S1), it generates the same set of hexose and triose-P 13 C-isotopomers. Note that the formation of [U-13 C]glucose-6-P from [U-13 C]fructose can occur via the condensation of [U-13 C]glyceraldehyde-3-P and [U-13 C]dihydroxyacetone-P. The probability for [U-13 C]glucose-6-P formation is related to the fractional enrichments of these triose-P precursors.
are generated from triose-P can be diluted by unlabeled non-triose substrates such as acetate before their incorporation into fatty acids. When the 13 C-label is provided as [U-13 C]fructose (Supplementary Figure S1), it generates the same set of hexose and triose-P 13 C-isotopomers. Note that the formation of [U-13 C]glucose-6-P from [U-13 C]fructose can occur via the condensation of [U-13 C]glyceraldehyde-3-P and [U-13 C]dihydroxyacetone-P. The probability for [U-13 C]glucose-6-P formation is related to the fractional enrichments of these triose-P precursors. Figure 2. 13 C-Isotopomers of selected metabolic intermediates generated from [U-13 C]glucose metabolism into lipogenic and glycogenic pathways. These include hepatic glucose-6-P-inferred from the analysis of newly synthesized glycogen; triose-P recruited for gluconeogenesis (GNG-triose-P)-inferred from the analysis of indirect pathway glycogen 13 C-isotopomers; triose-P supplying glycerol-3-P for fatty acid esterification and acetyl-CoA units for de novo lipogenesis-inferred from the 13 C-isotopomer analysis of newly synthesized triglyceride glycerol; and the acetyl-CoA pool supplying lipogenesis-inferred from the 13 C-isotopomer analysis of newly synthesized fatty acids. For the metabolite carbon skeletons, the filled and unfilled circles represent 13 C and 12 C, respectively. The shading highlights those 13 C-isotopomers that inform the enrichment of the lipogenic acetyl-CoA pool by [U-13 C]acetyl CoA from both glycolytic precursor and fatty acid product perspectives, and the colors indicate isotopic enrichment equivalence (same color) or non-equivalence (different colors). For simplicity, in depicting the fatty acid labeling, only the 13 C-isotopomers of the last two fatty acid carbons (representing the first acetyl-CoA moiety to be incorporated into de novo lipogenesis) are shown. 13 C-Isotopomers of selected metabolic intermediates generated from [U-13C]glucose metabolism into lipogenic and glycogenic pathways. These include hepatic glucose-6-P-inferred from the analysis of newly synthesized glycogen; triose-P recruited for gluconeogenesis (GNG-triose-P)-inferred from the analysis of indirect pathway glycogen 13C-isotopomers; triose-P supplying glycerol-3-P for fatty acid esterification and acetyl-CoA units for de novo lipogenesis-inferred from the 13C-isotopomer analysis of newly synthesized triglyceride glycerol; and the acetyl-CoA pool supplying lipogenesis-inferred from the 13C-isotopomer analysis of newly synthesized fatty acids. For the metabolite carbon skeletons, the filled and unfilled circles represent 13C and 12C, respectively. The shading highlights those 13C-isotopomers that inform the enrichment of the lipogenic acetyl-CoA pool by [U-13C]acetyl CoA from both glycolytic precursor and fatty acid product perspectives, and the colors indicate isotopic enrichment equivalence (same color) or non-equivalence (different colors). For simplicity, in depicting the fatty acid labeling, only the 13C-isotopomers of the last two fatty acid carbons (representing the first acetyl-CoA moiety to be incorporated into de novo lipogenesis) are shown.
Animal Studies
Animal studies were approved by the University of Coimbra Ethics Committee on Animal Studies (ORBEA) and the Portuguese National Authority for Animal Health (DGAV), approval code 0421/000/000/2013. A total of nine adult male C57BL/6J mice obtained from Charles River Labs, Barcelona, Spain, were housed at the University of Coimbra UC-Biotech Bioterium. They were maintained in a well-ventilated environment and a 12 h light/12 h dark cycle. Upon delivery to the Bioterium, mice were provided a two-week interval for acclimation, with free access to water and standard chow, comprising of 60% mixed carbohydrates, 16% protein, and 3% lipids. Following this period, the chow was supplemented with a 55/45 mixture of fructose and glucose present at a concentration of 30% w/v in the drinking water for a period of 12 weeks. At the beginning of the final evening, mice were administered with an intraperitoneal loading dose of 99% 2 H 2 O containing 0.9 mg/mL NaCl (4 mL/100 g body weight), and the drinking water was enriched to 5% with 2 H 2 O. The fructose/glucose mixture in their drinking water was replaced with mixtures of identical composition, but with 20% enriched [U-13 C]fructose for five mice and 20% enriched [U-13 C]glucose for the remaining four mice. At the end of this dark cycle, mice were deeply anesthetized with ketamine/xylazine and sacrificed by cardiac puncture. Arterial blood was immediately centrifuged, and plasma was isolated and stored at −80 • C. Livers were freeze-clamped and stored at −80 • C until further analysis.
Analysis of Glycogen and Triglyceride Isotopic Enrichments by NMR
Liver portions of~500 mg were powdered under liquid nitrogen and extracted with methyl tert-butyl ether, as previously described [5]. Glycogen from the insoluble pellet was extracted, purified, and derivatized to monoacetone glucose (MAG), as previously described [3]. Triglycerides from the organic fraction were separated from other lipids, as previously described [13].
NMR Analysis of Glycogen 2 H and 13 C-Enrichments
Proton-decoupled 2 H-NMR spectra of MAG samples at 50 • C were obtained with a Bruker Avance III HD 500 spectrometer using a 2 H-selective 5 mm probe incorporating a 19 Flock channel. Samples were resuspended in 0.5 mL 90% acetonitrile/10% 2 H-depleted water, to which 50 µL of hexafluorobenzene were added. 2 H-NMR spectra were obtained with a 90 • pulse, 1.6 s of acquisition time, and a 0.1 s interpulse delay. The number of free-induction decays (f.i.d.) collected ranged from 2000 to 10,000. Positional 2 H enrichments were determined using the MAG methyl signals as an intramolecular standard [14]. To quantify plasma body water 2 H enrichments, triplicate 10 µL samples of plasma were analyzed at 25 • C by 2 H NMR, as previously described [15], but with 50 µL of hexafluorobenzene added to the NMR sample. Proton-decoupled 13 C NMR spectra at 25 • C were obtained with a Varian VNMRS 600 MHz NMR spectrometer equipped with a 3 mm broadband probe. 13 C NMR spectra were acquired at 25 • C using a 60 • pulse, 30.5 kHz spectral width, and 4.1 s of recycling time (4.0 s of acquisition time and 0.1 s pulse delay). The number of acquisitions ranged from 2000 to 18,000. The summed f.i.d. was processed with 0.2 Hz line-broadening and zero-filled to 512 K before Fourier transform.
NMR Analysis of Triglyceride 2 H and 13 C Enrichments
Purified triglycerides were dissolved in~0.5 mL CHCl 3 . To these, 25 µL of a pyrazine standard enriched to 1% with pyrazine-d 4 and dissolved in CHCl 3 (0.07 g pyrazine/g CHCl 3 ), and 50 µL C 6 F 6 were added. 1 H and 2 H NMR spectra were acquired with an 11.7 T Bruker Avance III HD system using a dedicated 5 mm 2 H probe with 19 F lock and 1 H-decoupling coil, as previously described. 1 H spectra at 500.1 MHz were acquired with a 90 • pulse, 10 kHz spectral width, 3 s acquisition time, and 5 s pulse delay. Overall, 16 f.i.d. were collected for each spectrum. 2 H NMR spectra at 76.7 MHz were obtained with a 90 • pulse, a 1230 Hz sweep width, an acquisition time of 0.67 s, and interpulse delay of 8 s. For 13 C isotopomer analysis by 13 C NMR, dried triglyceride samples were dissolved in 0.2 mL 99.96% enriched CDCl 3 (Sigma-Aldrich) and acquired using the same parameters as for the MAG samples. For each 13 C spectrum, 2000-4000 f.i.d. were collected. 13 C and 2 H NMR spectra were analyzed with ACD/NMR Processor Academic Edition software (ACD/Labs, Advanced Chemistry Development, Inc.).
Estimation of Substrate Contributions to Lipogenesis from Analysis of Newly Synthesized Glycogen and Triglyceride 13 C Isotopomers
As indicated in Figure 2, the 13 C-isotopomer distributions of newly synthesized glycogen informs that of glucose-6-P, while the 13 C-isotopomer distributions of newly synthesized triglyceride glyceryl and fatty acid moieties inform the precursor enrichments of triose-P and lipogenic acetyl-CoA pools, respectively. For each of these reporter metabolites, all 13 C-isotopomers that are either metabolized to form lipogenic [U-13 C]acetyl-CoA (i.e., glucose-6-P and triose-P) or are an immediate product (TG-fatty acid) were defined as 13 C IUA . These 13 C IUA correspond to the shaded 13 C-isotopomers of glucose-6-P, triose-P, and fatty acids shown in Figure 2 and provide the basis for quantifying the isotopic dilution of the 13 C-enriched carbons of glucose and fructose as they are metabolized to lipids.
Glucose-6-P 13 C IUA = Σ glycogen isotopomers × 1/f glycogen (1) Glucose-6-P is derived from the phosphorylation of dietary glucose and from GNG. For the [U-13 C]glucose tracer, enrichment of [U-13 C]glucose-6-P is assumed to be entirely from the direct pathway metabolism of [U-13 C]glucose. The direct pathway fraction (f direct ), which also includes sources of unlabeled glucose present in the diet, -can be estimated from the positional 2 H enrichment distribution of glycogen [3] (Supplementary Table S2). On this basis, 13 C IUA enrichment of the dietary glucose precursor pool can be estimated as follows: Dietary glucose 13 C IUA = [U-13 C]Glucose-6-P 13 Since the fraction of glucose-6-P synthesized by GNG is represented by the indirect pathway fraction of newly synthesized glycogen (f indirect ), which can be estimated from the glycogen 2 H enrichment distributions (see Supplementary Table S2), then 13 C IUA of the GNG precursor pool can be calculated. For the [U-13 C]glucose tracer, [U-13 C]glucose-6-P needs to be excluded from Σ glycogen isotopomers since it is generated via the direct pathway. The glucose-6-P isotopomers formed via gluconeogenesis that can generate [1,2-13 C 2 ]acetyl-CoA are [1,2-13 C 2 ]-, [1,2,3-13 C 3 ]-, [5,6-13 C 2 ]-, and [4,5,6-13 C 3 ]glucose-6-P ( 13 C IUA-GNG ): For [U-13 C]fructose, all glycogen isotopomers are included since they are by definition all derived via the indirect pathway: The 13 C IUA of triose-P and lipogenic acetyl-CoA are estimated by adjustment with the newly synthesized triglyceride glyceryl fraction (f glyceryl ) and fatty acid fractions (f fatty acid ) Metabolites 2022, 12, 1142 7 of 14 estimated from the triglyceride 2 H enrichment distribution [5] (Supplemental Table S2), as follows: Triose-P 13 C IUA = Triglyceride glyceryl 13 Acetyl-CoA 13 C IUA = Triglyceride fatty acid 13 C IUA × 1/(f fatty acid ) (5) where the measured glyceryl 13 C IUA is the sum of triglyceride glyceryl isotopomers with 13 C in both positions 2 and 3, and the fatty acid 13 C IUA is the sum of fatty acid isotopomers with 13 C in both ultimate (ω) and penultimate positions. The fraction of lipogenic acetyl-CoA derived from triose-P was estimated from the ratio of acetyl-CoA and triose-P 13 C IUA as follows: Triose-P → Acetyl-CoA = 100 × Acetyl-CoA 13 C IUA /Triose-P 13 C IUA The fraction of acetyl-CoA derived from non-triose-P metabolites, such as acetate, was estimated as the difference: Non-triose-P → Acetyl-CoA = 100 − Triose-P fraction (7) For the mice provided with [U-13 C]glucose and unlabeled fructose, the fractional contribution of dietary glucose to triose-P was estimated from the ratio of triose-P to dietary glucose 13 C IUA . This fraction was adjusted for total lipogenic acetyl-CoA flux by multiplication with the fraction of Acetyl-CoA derived from triose-P (Equation (6)) and for the loss of glucose-6-P carbon 1 as CO 2 via the PPP.
Estimation of the Fraction of Glucose-6-P Metabolized by the PPP
The fraction of glucose-6-P oxidized by the PPP was estimated from the 13 C-isotopomer distributions of glycogen, as previously described [4]. The PPP fraction was normalized to total lipogenic acetyl-CoA flux by multiplication with the product of Equation (6).
Statistical Analyses
All results are presented as means ± standard deviations. All datasets were submitted to a Shapiro-Wilk normality test and homoscedasticity test (F test of equality of variances). If both groups presented a normal distribution, then an unpaired Student's t-test was applied (Welch-corrected if variances were unequal). Otherwise, the Mann-Whitney U-test was employed.
Enrichment of Hepatic Metabolic Pools from [U-13 C]Glucose and [U-13 C]Fructose
The 13 C-isotopomer distributions in the glucose-6-P and triose-P pools were almost all accounted for by 13 C IUA species (Supplementary Table S1). For the mice provided with [U-13 C]glucose, the glucose-6-P pool had the highest 13 C IUA abundance, with the principal isotopomer being [U-13 C]glucose-6-P. From glucose-6-P to glycerol-3-P and acetyl-CoA, there was a stepwise dilution in 13 C IUA consistent with an inflow of unlabeled triose-P and acetyl-CoA carbons, respectively ( Table 1). The enrichment of the gluconeogenic triose-P pool via indirect pathway metabolism or Cori cycling was relatively low, with the principal contribution coming from PPP activity, as seen by the dominance of [1,2-13 C 2 ]glucose-6-P over that of [5,6-13 C 2 ]glucose-6-P (Supplementary Table S1) [16]. Following its ingestion and subsequent absorption, the [U-13 C]glucose supplement was diluted almost four-fold by other unlabeled glucose sources by the time it reached the liver (Table 1). Table 1. Fractional enrichments (%) of 13
Acetyl-CoA (Equation (5))
[U- 13 For mice provided with [U-13 C]fructose, the highest 13 C IUA abundances were found in the GNG precursor and triose phosphate pools with dilution at both glucose-6-P and acetyl-CoA pools (Table 1). This enrichment distribution indicates that, under our experimental conditions, fructose was mostly metabolized to triose-P by the liver, followed by carbon flows into both glycogenic and lipogenic pathways. Had the fructose been fully metabolized to glucose in the intestine prior to reaching the liver [17], this would have resulted in a 13 C IUA distribution resembling that observed with [U-13 C]glucose, i.e., highest for glucose-6-P, then progressive dilution at triose-P and acetyl-CoA pools. Finally, in contrast to [U-13 C]glucose, the dietary [U-13 C]fructose supplement underwent relatively minor dilution (~1.3-fold) from competing gluconeogenic precursors at its point of entry into the GNG pool.
Sourcing of Lipogenic Acetyl-CoA Carbons Reported by [U-13 C]Glucose and [U-13 C]Fructose and PPP Activity
A comparison of the contributions of different sources to lipogenic acetyl-CoA estimated from [U- 13 Table 2. Both tracers report a substantial contribution (40-50%) of non-sugar substrates such as acetate to the lipogenic acetyl-CoA pool, even with chronic high-sugar feeding. Under our study conditions, the bulk of triose-P destined for lipogenesis was derived from either dietary glucose or fructose, with only minor contributions from other gluconeogenic precursors. For the four common component fluxes reported by both tracers, the biggest divergence was found for the triose-P and non-triose-P acetyl-CoA sources, while estimates for the contributions of dietary glucose and GNG precursors to the lipogenic triose-P were in better agreement. Figure 3 shows the values of these fluxes obtained by combining and averaging the data derived from the [U-13 C]glucose and [U-13 C]fructose measurements. This includes the overall PPP flux, which represents the sum of PPP fluxes attributed to glucose-6-P derived from dietary glucose (i.e., direct pathway) and glucose-6-P derived from GNG sources (indirect pathway) reported by [U-13 C]glucose and [U-13 C]fructose, respectively. Our data indicate that about 11% of glucose-6-P had undergone PPP oxidation. While our previous measurement of fractional PPP utilization of glucose-6-P in these livers showed modest but significant differences between [U-13 C]glucose and [U-13 C]fructose tracers [4], the significance was lost after the values were normalized to that of lipogenic acetyl-CoA flux ( Table 2). Table 2. Estimates of substrate fluxes contributing to lipogenic acetyl-CoA expressed as a fraction of total lipogenic acetyl-CoA flux into fatty acid synthase from 2 H enrichment and 13 C-isotopomer analysis of a group of mice provided with 2 H 2 O and [U-13 C]glucose tracers (n = 4), and a group provided with 2 H 2 O and [U-13 C]fructose (n = 5). The estimated pentose phosphate pathway (PPP) fluxes involved in glucose-6-P oxidation and carbon recycling to regenerate glucose-6-P (Glucose-6-P → PPP → Glucose-6-P) are also shown.
General Overview
Triose-P Acetyl-CoA
General Overview
We developed a method for quantifying the major fluxes associated with hepatic sugar metabolism that can be easily applied to mice and other small animal models. We demonstrated that this approach can utilize 13 C-isotopomer information from either [U-13 C]glucose or [U-13 C]fructose. In principle, it could also function with other 13 Csugar tracers that have been used as probes of hepatic carbohydrate metabolism such as galactose [18,19] or glycerol [16,20,21]. Alongside the 2 H 2 O tracer, these can be formulated into the animal's food or drinking water, allowing hepatic metabolic activity to be measured in unperturbed ad libitum feeding conditions. Although dietary glucose is metabolized by most, if not all, tissues, we can nevertheless identify that which is metabolized first-pass by the liver as intact [U-13 C]glucose. Paradoxically, although fructose metabolism is more strongly associated with the liver compared to glucose, our metabolic analysis does not provide direct information on hepatic [U-13 C]fructose prior to it being metabolized to sugar phosphates. This means that, unlike the first-pass hepatic metabolism of [U-13 C]glucose, we cannot be certain that the observed labeling of hepatic glucose-6-P and triose-P from [U-13 C]fructose was entirely the result of hepatic [U-13 C]fructose metabolism.
Hepatic Versus Extrahepatic Fructose Metabolism
The liver was long believed to be the principal site for fructose metabolism, but this has been recently challenged with evidence of other tissues, notably the intestine, with the capacity of enterocytes for fructose phosphorylation and incorporation into glycolytic and gluconeogenic fluxes [17]. Moreover, and perhaps not surprisingly, any fructose that is not immediately absorbed can also be avidly metabolized by the intestinal microbiome [22,23], with products such as acetate being subsequently absorbed and recruited as lipogenic substrates by the liver [23]. As proposed by Jang et al., [17], the extent of intestinal versus hepatic fructose metabolism may be related to the total amount of sugar ingested, with low intakes being accommodated entirely by the intestine, and the liver metabolizing any surplus above and beyond the intestinal capacity for fructose disposal. Our mice were kept for 18 weeks on standard chow that was accompanied by drinking water containing 30 g/100 mL of a 55/45 fructose/glucose mixture. There was no other source of drinking water provided. Assuming a daily water intake of~7 mL water per mouse [24], this would require ingestion of~10 mL of the mixture, resulting in about 2.5 g of ingested sugar (1.38 g fructose and 1.12 g glucose). Given the average mouse mass of 35 grams, this translates to 39 g of fructose and 32 g of glucose per kg body mass over 24 h, or an average of~1.6 g kg −1 fructose and~1.3 g kg −1 of glucose per hour. If we compare these quantities to the criteria of low and high-dose sugar intake established by Jang et al. based on single gavages of 0.5 g kg −1 and 2 g kg −1 of a 1:1 fructose/glucose mixture, respectively [17], then our mice had a sugar intake that was well beyond the high dose defined by Jang et al. Under our study conditions, much, if not most, of the fructose would be expected to be metabolized by the liver, which is consistent with our observed hepatic metabolite 13 C enrichment patterns from [U-13 C]fructose.
PPP Flux in Relation to De Novo Lipogenesis
The fraction of glucose-6-P that was oxidized by the PPP was estimated to be 11%. The incorporation of n equivalents of acetyl-CoA into the fatty acid polymer requires 2n-2 equivalents of NADPH; hence, the synthesis of palmitate from 8 acetyl-CoA consumes a total of 14 NADPH. Since two NADPH are generated for each glucose-6-P carbon oxidized to CO 2 via the PPP, a total of 1.17 glucose-6-P equivalents are required to generate the necessary number of NADPH for the synthesis of each palmitate as follows: 4 Glucose-6-P → 8 Acetyl-CoA → 1 Palmitate 1.17 Glucose-6-P → 14 NADPH → 1 Palmitate Therefore, if glucose-6-P is the sole contributor of lipogenic acetyl-CoA and if the PPP is the sole source of NADPH, then the fraction of glucose-6-P that is utilized by the PPP relative to the total used for lipogenesis (i.e., PPP oxidation plus acetyl-CoA generation) is 1.17/(4 + 1.17) = 23% (this relationship also approximates for C18 fatty acids: 22.9% versus 22.6% for C16). In adipose tissues, glucose-6-P is considered to be the main precursor of acetyl-CoA [25], with the PPP considered to be the principal source of NADPH [26]. An in situ measurement of PPP flux in human adipose tissue via a microdialysis method yielded a PPP fraction of 17-22%, approaching the theoretical value for quantitative glucose-6-P conversion to fatty acids [27]. In the liver, lipogenic acetyl-CoA is derived from sources other than glucose-6-P, notably acetate. Therefore, under these conditions, if the PPP was the sole source of NADPH, then a higher fractional PPP flux per equivalent of glucose-6-P converted to acetyl-CoA would be required. For example, if acetate and glucose-6-P each contribute 50% of acetyl-CoA for palmitate synthesis as follows: 4 Acetate → 4 Acetyl-CoA 2 Glucose-6-P → 4 Acetyl-CoA 1.17 Glucose-6-P → 14 NADPH then, to provide the theoretical amount of NADPH, the fraction of glucose-6-P that undergoes PPP oxidation would need to increase to 1.17/(2 + 1.17) = 37%. Our data indicate that glucose-6-P accounted at most for about half of lipogenic acetyl-CoA, but only 11% was oxidized by the PPP. This suggests that the PPP accounted, at the most, for only about 11/37, or about 30%, of the total NADPH demand for DNL under these conditions (If NADPH derived from PPP oxidation was also consumed by other processes, such as the reduction of oxidized glutathione, then its fractional contribution to DNL would be even less than 30%). Other possible sources of cytosolic NADPH include cytosolic NADP-malic enzyme 1 and NADP-isocitrate dehydrogenase 1 [2] and folate-mediated serine catabolism [28].
Limitations of the Approach
There are several important limitations of our approach that must be taken into account when interpreting the results. As previously discussed, our mouse model involved a very high intake of sugar that ensured that the fructose component was predominantly metabolized by the liver. If the amount of sugar was reduced, then it is likely that a much higher proportion of the [U-13 C]fructose would be metabolized by the intestine to form 13 Cisotopomers of glucose, lactate, and other metabolites [17], and these would be the principal products seen by the liver rather than [U-13 C]fructose. Nevertheless, aside from the uncertainty in determining the contribution of fructose to the hepatic gluconeogenic triose-P pool, the 13 C-isotopomer distributions of glycogen and triglycerides would still provide valid information on PPP fluxes, glyceroneogenesis, and the contribution of glucose-6-P and non-glucose-6-P sources to DNL. Under high sugar intake conditions, Jang et al. reported a substantial amount of fructose metabolism by the intestinal microbiota [17], with acetate being a principal product [23]. The microbial fermentation of [U-13 C]fructose results in the formation of [U-13 C]acetate, whose incorporation into DNL is indistinguishable from that of [U-13 C]acetyl-CoA derived from hepatic [U-13 C]fructose metabolism. To the extent that the fermentative metabolism of [U-13 C]fructose contributes to the fatty acid 13 C-isotopomer enrichment, then the fraction of acetyl-CoA derived from non-glucose-6-P sources would be expected to be underestimated, and, accordingly, the contribution of glucose-6-P to DNL overestimated. However, when these parameters obtained from [U-13 C]fructose are compared with those derived from [U-13 C]glucose (Table 2), they show a strong tendency to report higher non-glucose-6-P and lower glucose-6-P fractions. One possibility is that, given the very high sugar intake, there may have also been extensive microbial metabolism of [U-13 C]glucose. Glucose is normally efficiently absorbed in the small intestine, but small intestinal bacterial overgrowth [29,30], possibly induced by high sugar diets [31], can result in a portion of the glucose being fermented instead. Finally, the PPP flux is based on the sugar phosphates that are recycled back to fructose-6-P and glucose-6-P and does not take into account those pentose-P equivalents that were recruited for nucleotide biosynthesis. Thus, the PPP estimate represents a lower limit of the real oxidative glucose-6-P flux.
Conclusions
Hepatic metabolism and assimilation of dietary sugar involves the co-ordination of gluconeogenic, glycogenic, PPP, glycolytic, and lipogenic fluxes. While there are longstanding methodologies for measuring these fluxes individually, until now there has been no approach for quantifying fluxes through the entire ensemble. We demonstrate that, with a combination of 2 H 2 O and a [U-13 C]hexose sugar that can be either glucose or fructose, these fluxes can be quantified in mice under natural feeding conditions by analysis of liver glycogen and triglyceride 13 C-isotopomers. In addition to confirming a previous study that a substantial fraction of lipogenic acetyl-CoA is derived from sources other than glucose-6-P, even during high sugar feeding [5], our analysis also reveals that the PPP was not the main supplier of NADPH for DNL, at least under our study conditions. Such information could be valuable in improving our understanding of hepatic sugar metabolism under different physiological and pathophysiological states.
Supplementary Materials: The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/metabo12111142/s1, Figure S1: 13 C-Isotopomers of selected metabolic intermediates generated from [U-13 C]fructose metabolism into lipogenic and glycogenic pathways. These include hepatic glucose-6-P-inferred from the analysis of newly-synthesized glycogen; triose-P recruited for gluconeogenesis (GNG-triose-P)-inferred from the analysis of indirect pathway glycogen 13 C-isotopomers; triose-P supplying glycerol-3-P for fatty acid esterification and acetyl-CoA units for de novo lipogenesis-inferred from the 13 C-isotopomer analysis of newlysynthesized triglyceride glycerol, and the acetyl-CoA pool supplying lipogenesis-inferred from the 13 C-isotopomer analysis of newly-synthesized fatty acids. For the metabolite carbon skeletons, the red filled and unfilled circles represent 13 C and 12 C, respectively. The shading highlights those isotopomers that form [U-13 C]acetyl CoA and the colors indicate isotopic equivalence (same color) or non-equivalence (different colors). For simplicity, in depicting the fatty acid labeling, only the 13 C-isotopomers of the last two fatty acid carbons (representing the first acetyl-CoA moiety to be incorporated into DNL) are shown.; Table S1: Liver glycogen 13 C-isotopomer enrichments from mice provided with [U-13 C]glucose (n = 4) and [U-13 C]fructose (n = 5). The glycogen 13 C-isotopomers shown in bold text are metabolized to [U-13 C]acetyl-CoA. Table S2: Newly synthesized glycogen fraction (f glycogen ) with direct and indirect pathway contributions to the newly synthesized glycogen (f direct and f indirect ), and newly synthesized triglyceride glyceryl and fatty acid fractions (f glyceryl and f fatty acid ) from 2 H-enrichment data of liver glycogen and triglyceride, respectively.
Institutional Review Board Statement:
The study was conducted in accordance with the University of Coimbra Ethics Committee on Animal Studies (ORBEA) and the Portuguese National Authority for Animal Health (DGAV), approval code 0421/000/000/2013.
Informed Consent Statement: Not applicable.
Data Availability Statement: The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request. The data are not publicly available due to privacy.
Conflicts of Interest:
The authors declare no competing interest. | 8,120 | 2022-11-01T00:00:00.000 | [
"Medicine",
"Biology"
] |
Effect of flame retardants on mechanical and thermal properties of bio-based polyurethane rigid foams
A soy oil-based polyol (HSBP) was synthesized from epoxidized soy oil through a ring-opening reaction with distilled water. A phosphorus-containing flame retardant (DOPO–HSBP) was synthesized through the reaction of 9,10-dihydro-9-oxa-10-phosphaphenanthrene-10-oxide (DOPO) and HSBP. A nitrogen-containing flame retardant (T–D) was prepared by the reaction of diethanolamine with glycol diglycidyl ether. The structures of HSBP, DOPO–HSBP, and T–D were characterized by Fourier transform infrared spectroscopy (FT-IR) and nuclear magnetic resonance (1H NMR). The flame-retardant rigid polyurethane foam (PPUFs and NPUFs) was prepared successfully by mixing HSBP, DOPO–HSBP, and T–D. The effects of DOPO–HSBP content on the mechanical, thermal, and flame-retardant properties of PPUFs and NPUFs were investigated by tensile tests, thermogravimetric analyses (TGA), limiting oxygen index (LOI), and UL-94 vertical burning level. The morphology of PPUFs and NPUFs was studied via scanning electron microscopy (SEM). With the increase in the percentage of DOPO–HSBP added, the flame retardant property of rigid polyurethane foam (RPUF) was greatly improved. When the phosphorus-containing flame retardant DOPO–HSBP was added to 50% of the RPUF with the nitrogen-containing flame retardant T–D, the LOI value of the foam increased from 18.3 to 25.5, and the UL-94 result was classified as “V-0” with almost no effect on the mechanical properties of the RPUF. The results showed that the phosphorus and nitrogen synergistic flame retardants of DOPO–HSBP and T–D can endow excellent flame retardant properties to RPUF without affecting its mechanical properties.
Introduction
Rigid polyurethane foam (RPUF) is an economical and efficient energy-saving material that is widely used in elds of furniture, transportation, construction materials, refrigerator insulation because of its light weight, high strength, and excellent mechanical and thermal insulation properties. [1][2][3][4] However, its porous structure makes it easy to be ignited and burn rapidly aer being exposed to re, releasing large amounts of heat and smoke, leading to serious re accidents. 5,6 This limits the application of rigid polyurethane foam in many elds. Therefore, the study of ame retardant rigid polyurethane foams is of great importance.
In order to improve the ame retardancy of RPUF, adding ame retardants to RPUF would be effective. 6 There are two main approaches to add ame retardants to RPUF: additive-type ame retardants and reactive-type ame retardants. 7,8 Examples of additive ame retardants include expandable graphite (EG), 9,10 ammonium polyphosphate (APP), 11 melamine and its derivatives, 12,13 inorganic phosphorus-containing compounds, 14 etc. However, they are gradually replaced by another way due to their poor compatibility, the large negative impact on the mechanical properties, and the easy leaching of the RPUF. 15 Reactive ame retardants are more stable in RPUF, and the ame retardant element P/N is introduced into the main chain of RPUF by participating in the foaming reaction to achieve the ame retardant effect. [16][17][18][19] DOPO and its derivatives are some of the reactive ame retardants that have attracted much attention in recent years. Compared with other straight-chain small molecule ame retardants, DOPO and its derivatives have better stability due to their aromatic structure. 20,21 For instance, in the work of Wang et al., a bifunctional ame retardant (PDEP) based on DOPO and phosphate was synthesized, and the LOI of RPUF was increased from 18.5 to 22.9 by the addition of this ame retardant. 22 However, a single ame retardant system can only improve the ame retardancy of the foam to a very limited extent. Some studies indicate that the synergistic effect of phosphorus and nitrogen can greatly improve its ame retardant efficiency. 23 In addition to the ame retardancy of rigid polyurethane foams, biodegradability has also been a major concern for environmental protection and sustainable development in recent years. The adoption of bio-based polyols to prepare RPUF would be a good answer for those concerns. 24 Vegetable oil can be used to produce bio-based RPUF due to the presence of many reactive sites on its aliphatic chain. For example, Veronese et al. synthesized RPUFs by using soybean oil or castor oil. 25 Guo et al.
prepared soy-based polyol from epoxidized soy oil ring-opened by methanol and the resulting RPUF exhibited comparable mechanical and insulating properties to other foams from petrochemical feedstocks. 26 Ji et al. synthesized different soybased polyols by reacting epoxidized soy oil with methanol, phenol, and cyclohexanol. At 25 wt% of soy-based polyol, the introduction of phenol can improve the mechanical and thermal properties of the foam. 27 The purpose of this work is to synthesize soybean oil-based polyol as a raw material for RPUF, a polyol DOPO-HSBP as a P-containing ame retardant, and polyol T-D as an Ncontaining ame retardant. The effects of the content of DOPO-HSBP and the phosphorus-nitrogen synergistic effect of T-D addition on the mechanical properties and ame retardant properties of RPUF were analyzed using the mechanical test, scanning electron microscopy (SEM), thermogravimetric analysis (TGA), LOI, and UL-94. Finally, the RPUFs with greatly improved ame retardancy and almost no effect on mechanical properties were successfully synthesized.
Preparation of DOPO-HSBP
The DOPO-HSBP was prepared by reacting DOPO with HSBP. During a process, 40 g HSBP, 25.8 g DOPO, 12.5 g TEA, and 40 g dichloromethane were added to a round-bottomed threenecked ask equipped with a mechanical stick. Carbon tetrachloride was added dropwise to the reaction mixture at ice bath over 30 minutes. The temperature of the reaction was maintained at 25 C for 24 h. Aer the reaction completion, the reaction mixture was extracted with ethyl acetate and washed with deionized water. Ethyl acetate and deionized water were removed by rotary evaporator. The preparation route of DOPO- HSBP was shown in Scheme 1. The properties of the HSBP and DOPO-HSBP were listed in Table 1.
Preparation of T-D
Diethanolamine (54 g) and glycol diglycidyl ether (62 g) were charged into a round-bottomed three-necked ask equipped with a mechanical stick and a thermometer. The temperature of the reaction was maintained at 85 C for 6 h. Aer the reaction completion, the resulting product can be used for the next step without any treatment. The preparation route of T-D was shown in Scheme 2.
Preparation of rigid polyurethane foams (RPUFs)
The RPUFs were prepared using a free-rise method according to the formulation as shown in Table 2. The -NCO/-OH ratio of the systems was set as 1.1. The polyol blends were mixed with surfactant (AK8805), catalyst (dibutyltin dilaurate), and blowing agent (distilled water), in the required proportions under ambient conditions for approximately 120 s. The pMDI was added quickly into the mixture and mixed for another 15 s. Finally, the mixture was immediately poured into an open mold to produce free-rise foam. The obtained RPUFs were completely cured at room temperature for 7 days before analysis. The preparation route and structure of RPUFs are shown in Scheme 3.
Characterization
FT-IR spectra were measured by Spectrum One PerkinElmer Fourier transform infrared spectrometer (PerkinElmer Co., American). The FT-IR spectra were collected using 64 scans in the wavenumber range of 4000-400 cm À1 with a resolution of 4 cm À1 .
1 H NMR spectra were tested by Varian Inova 600 nuclear magnetic resonance spectrometer (American Varian Co., American) at room temperature, using tetramethylsilane (TMS) as a reference, CDCl 3 as solvent for sample. The density of RPUF samples was measured according to the American Society of Testing Materials (ASTM) designation: D162208 (2008). The average values of ve samples were recorded.
The compressive strength of foams was recorded on a CMT4000 universal testing machine according to (Shengzhen, China) according to ASTM designation: D1621-10. Each sample used for the test was 50  50  50 mm 3 (length  width  height). At least ve samples were tested to obtain average values in mechanical tests.
A NETZSCH 209F1 TA Instruments was employed for thermogravimetric analysis (TGA), and the RPUF samples were heated to 750 C at a heating rate of 10 C min À1 under a dynamic nitrogen ow of 50 mL min À1 .
The morphologies of the foams were analyzed with a JSM-6510LV scanning electron microscope (SEM) operating at 20 kV, and the samples were sputter-coated with a thin layer of gold. The scanning electron microscopy was measured along parallel foam rise direction.
Results and discussion
FT-IR spectra of HSBP, DOPO-HSBP, DEA, TMA, and T-D The FTIR spectra of HSBP and DOPO-HSBP are shown in Fig. 1. The aromatic C-H absorption around 3066 cm À1 . 32 The absorption around 755 cm À1 and 1596 cm À1 corresponds to vibration with Ph-P and C]C stretching in aromatic functional groups respectively. 33,34 The absent peak at 2385 cm À1 (P-H) indicated that the reaction of HSBP and DOPO has done. 35 Fig. 2 shows the FTIR of TMA, DEA, and T-D. It can be observed from the spectrum of TMA that the peak at 912 cm À1 , 852 cm À1 , 1254 cm À1 , and 757 cm À1 corresponds to epoxy bond characterized absorbing. In the FTIR spectra of T-D, the disappearance of the epoxy absorption peak. The stretching vibration peak at 1100 cm À1 and the deformation vibration peak at 1455 cm À1 in TMA corresponds to C-O-C and -CH 2 respectively still exist. The characterized absorbing peak at 1125 cm À1 and Fig. 4 compares the 1 H NMR spectrum of T-D with that of TMA. We can see that a new peak is observed at 4.89 ppm (peak g). Furthermore, the peak related to CH-O-C of TMA at 3.17 ppm (peak b) disappears in the spectra of T-D. All the aforementioned results suggested the successful synthesis of T-D.
Apparent density
The apparent density of PPUFs and NPUFs prepared from blends with different ratios of DOPO-HSBP is shown in Fig. 5. The relevant literature shows that the apparent density of rigid polyurethane foam is closely related to the compressive strength. 38 It can be observed from Fig. 5 that the apparent density of both PPUFs and NPUFs tends to decrease with the increase of DOPO-HSBP content. When the content of DOPO-HSBP increased from 0 to 50%, the apparent densities of PPUFs and NPUFs decreased by 18% and 30%, respectively. These changes could be attributed to the decrease in crosslink density of the foam due to the addition of DOPO-HSBP. However, it is not difficult to nd that the apparent density of NPUF-50 is still higher than that of neat RPUF. This indicates that the moderate addition of T-D and DOPO-HSBP has almost no effect on the physical properties of the foams.
Microphotographs
The morphology changes of PPUFs and NPUFs are shown in Fig. 6. A typical RPUF structure was observed in Fig. 6, with open and closed pores of the sphere or polygonal shape. By adding phosphorus-containing ame retardant DOPO-HSBP, it can be seen that there is a signicant increase in the cell size compared with the PPUF-0, but with the further increase of DOPO-HSBP content from 10% to 50%, the cell size of the foam is reduced by 14%. This may be due to the decrease in the hydroxyl value of DOPO-HSBP compared to HSBP, which leads to a decrease in the cross-link density of the foam, a decrease in the number of pores, and an increase in the cell sizes. When the content of DOPO-HSBP increases further, the cell growth in the foaming process is weakened due to its higher viscosity, which eventually leads to smaller pores. On the other hand, it can be clearly observed that when the N-containing ame retardant T-D is added, there is a slight increase in the foam pore size compared to the foam without the ame retardant added. Comparing PPUF and NPUF, we can see that when T-D is added, the pore size still increases and then decreases with the increase of DOPO-HSBP content, but the cell size of NPUF-50 has been reduced to a size close to RPUF-0. This may be due to the high hydroxyl value and low viscosity of T-D. This means that NPUF-50 has little effect on the foam cell size compared with the RPUF-0, and the foam can still retain its original excellent properties such as thermal insulation. Table 3. At low strains, the foam exhibited linear-elastic deformation, followed by a continuous deformation platform, which may be the result of brittle fracture of the pore structure of the polyurethane foam, and at high strains, the densication of the foam caused the polymer to harden, making stress continues to increase. 39 It was reported in the literature that the mechanical properties of RPUFs are closely related to the hydroxyl value of the polyol, the size of the foam pores, and the density of the foam. 40 As shown in Table 3 , which leads to a lower cross-link density of the foams, thus resulting in larger foam pores and ultimately a reduction in the compressive strength of the foams. The addition of T-D greatly compensates for this shortcoming, as its higher hydroxyl value greatly increases the crosslink density of the foams and acts as a hard segment during synthesis, increasing the composition of the hard segment of the foams. This leads to an overall increase in the compressive strength of the foams. According to GB T 21558-2008, it can be observed that the compressive strength of all the foams meets the standard of compressive strength ($180 kPa) in rigid polyurethane foams for building insulation. Therefore, the potential application of soy oil-based rigid polyurethane foams in the eld of building insulation can be illustrated.
Dimensional stability
In addition to mechanical strength, dimensional stability is another important characteristic of rigid polyurethane foam used in roong, insulating, or any other constructing materials. Standard specications for dimensional stability had been reported to be less than 3% of linear change at 70 C for 24 h. 41 From Table 3, we can see that the dimensional changes of all the foams are less than 3% and the dimensional changes of the foams aer T-D addition are less than 1%, so the dimensional changes of all the foams meet the standard specications for dimensional stability.
Thermogravimetric analysis
To evaluate the thermal stability of the prepared PPUFs and NPUFs, TGA is conducted under the ow of nitrogen. The TG and DTG curves of PPUF and NPUF samples are illustrated in Fig. 8, and the representative parameters are summarized in Table 4. The degradation of foams can be divided into two stages: the degradation in the rst stage of weight loss at 300 C to 350 C is due to the decomposition of carbamate bonds in the hard segment, and the degradation in the second stage of weight loss at 450 C to 500 C is attributed to the thermal degradation in the so segment. 42 Conventionally, the thermal stability of RPUFs is described by the temperatures of 5% weight loss (T 5% ) considered as the temperature for the onset of degradation. 43 It can be seen that as the content of ame retardant DOPO-HSBP increased to 50%, the T 5% of the foam decreased from 277 C to 269 C, and the T 5% of the foam further decreased to 243 C aer the addition of ame retardant T-D. The results showed that the initial decomposition temperature of RPUF showed a decrease aer the addition of DOPO-HSBP and T-D. This may be caused by the lower decomposition temperature of DOPO-HSBP and T-D. In addition, it can be seen from T max1 and T max2 that the temperature of all PPUFs and NPUFs was increased at T max , which indicates that the ame retardant will improve the heat endurance of RPUF.
According to the TGA results of the prepared foams, the char residues of the foams prepared with different ame retardants were enhanced compared to the pure RPUF. Noticeably, the char residue of NPUF-40 has the largest increase, reaching 13.93%, which indicates that the addition of DOPO-HSBP and T-D can signicantly increase the char residue of RPUF. 44
Flame retardancy and combustion behaviors
To evaluate the ammability of PPUFs and NPUFs, the results of LOI and UL-94 tests for PPUFs and NPUFs with different mass ratios of DOPO-HSBP are presented in Table 5, and digital photos of the vertical burn test (UL-94) are shown in Fig. 9. With the addition of ame retardant DOPO-HSBP, the LOI value of the foam increased from 18.3 to 25.2, and the UL-94 result was classied as "V-0 rating", which signicantly improved the ame retardancy. When ame retardant T-D was added, the possible synergistic effect of phosphorus (DOPO-HSBP) and nitrogen (T-D) could improve the ame retardant activity in the gas-phase and condensed-phase, which increased the LOI value to 25.5 and further improved the ame retardant effect. 45 Combined with the UL-94 data in the table and the digital photo gure, it can be seen that the NPUF-50 foam can be selfextinguished and no dripping appears in a short time aer burning, which effectively prevents the spread of re. The formation of a char can be observed on the surface aer combustion, which can effectively prevent heat and oxygen from diffusing into the internal matrix of the polymer and improve the ame retardancy of the foam. 46 All of the above revealed the addition of DOPO-HSBP and T-D is benecial to improve the ame retardant properties of the foam.
Conclusions
In this study, a phosphorus-containing bio-based polyol DOPO-HSBP and a nitrogen-containing polyol T-D were synthesized and added as ame retardants to an environmentally friendly soy oil-based rigid polyurethane foam prepared from soybean oil. It was observed that the synergistic effect of phosphorus and nitrogen of ame retardants DOPO-HSBP and T-D greatly improved the ame retardancy of RPUF by LOI and UL-94, and the LOI value increased from 18.3 to 25.5, and the UL-94 grade was improved to "V0", this may be because DOPO-HSBP and T-D are decomposed from the foam at a lower temperature, thus preventing further burning of the foam earlier and more efficiently. The compressive strength and SEM of the foam showed that both the compressive strength and the size of the pores of the NPUF-50 sample were almost unchanged compared to the polyurethane rigid foam without ame retardant. Therefore, with the addition of ame retardants DOPO-HSBP and T-D in appropriate amounts, it can not only greatly improve the ame retardant properties of the foam but also has little effect on the mechanical properties of the foam. Moreover, the compressive strength and dimensional stability of rigid polyurethane foam prepared from bio-based polyols meet the standards of construction and other elds. From the TG and DTG data of the foams, it can be observed that the addition of DOPO-HSBP and T-D greatly improved the T max and carbon residue of the foams, which also conrms the improvement of the ame retardant properties of the foams by DOPO-HSBP and T-D. Therefore, it can be seen that the phosphorus and nitrogen synergistic ame retardant system for foam ame retardant performance is much higher than the phosphorus ame retardant system alone. This research would help us to further research and develop novel bio-based RPUF materials with excellent ame-retardant effects.
Conflicts of interest
There are no conicts to declare. | 4,440.8 | 2021-09-14T00:00:00.000 | [
"Materials Science",
"Engineering"
] |
User-centered design in AAL
This paper presents the results of an online survey conducted in Austria that aimed at investigating the application of user-centered design (UCD) methods in projects developing technologies that support older adults in their everyday lives. We explored which methods are known to teams, which methods have been applied in projects developing active and assisted living (AAL) technologies and the perceived suitability of these methods. The questionnaire considered methods for three different phases within the development process: gathering information about needs, communicating these needs to the developers and evaluating systems. Furthermore, we explored which stakeholders are included in gathering information about needs and in evaluating systems. The results show that more general methods that are not specific to UCD, such as interviews and questionnaires, are widely used. Older users were included in most projects, particularly for the evaluation. There was, however, an indication that the information about the needs collected may not be successfully communicated to the developers. Overall, the results support the need to spread information about the breadth of methods available and their suitability to people involved in developing these types of technologies.
Introduction
The age pyramid is shifting in many European countries as a result of a decreased birthrate and higher life expectancy. While there is concern about how to finance care for the growing number of older people, as a smaller proportion of the population will be working [10], this can also be viewed as an economic opportunity: "creating new markets for goods and services which respond to the needs of an older clientele" [10, p. 10], sometimes also termed the silver economy. During the past few years, the development of products and services for an ageing society has gained substantial attention and has also been promoted via various national and European funding programmes. As an example, the European Union (EU) co-financed the development of information and communication technologies (ICTs) within the Active and Assisted Living Programme with a total budget of around 600 million Euros between 2008 and 2013 [7].
These types of technologies also support human needs, as they may allow older people to stay in their own homes, something many express a desire to do [27]. There is a variety of possibilities [see [32]]: safety systems, e.g., to check if someone fell; security systems to support peace of mind, e.g., checking whether windows were closed; behavior monitoring systems, like those that detect changes in sleep patterns, something associated with the onset of dementia; systems to facilitate communication, e.g., video 1 3 conferences with family members; entertainment systems, e.g., to remind people their favorite show is about to start; and home automation systems, e.g., to facilitate opening windows or shades.
Despite the investments, wide market penetration of active and assisted living (AAL) solutions has not been achieved yet. According to Peek et al. [27] there are a number of barriers to adoption, e.g., concerns about costs, privacy, usefulness and ease of use. The ease of use can effect both the effort required to learn the system, but also the effectiveness in case of emergency. It is also a primary factor in acceptance by older people [8]. Moreover, there is consensus that user involvement and the integration of various stakeholders during the design and development process is important to success. However, an evaluation of the AAL Programme of the EU concluded that although end users are included in many projects, users are not integrated sufficiently and projects are not fully user-centered [7, p. 10]. Thus, the roots of the problem may lie in the development, as the needs may not be fully understood, or because these barriers may not be considered sufficiently.
In order to gather information about the use of user-centered methods in projects developing AAL technology, we conducted an online survey in Austria. The results show that there is a need to spread knowledge about the different methodological approaches that are available, which in turn could support the development of future AAL products and services.
This paper is structured as follows: In the next section, we describe the theoretical background, providing information about challenges when working with older adults and the importance of participatory and user-centered design approaches. Afterwards, we describe our methodological approach in section three, and present the results in section four. The paper finishes with a discussion (Sect. 5), as well as conclusions and suggestions for future work, which are presented in section six.
Background
User-centered design (UCD) and participatory design (PD) are generally thought to support success of projects developing software systems [2]. There are many methods to choose from, the best choice depending on various factors [5]. Thus, the choice of methods may depend also on the user group.
Differences when working with older users
Older users are a very diverse group, which can make it challenging to design systems that are usable for them [16]. Older people include a wide age range from 60 to 120 and have gained different experience during their lives. Hence, when developing systems for this particular user group the challenge is to adequately address the breadth of needs that exist. Many older people have physiological limitations. Some of these limitations differ from those experienced by younger populations. For example, there are age-specific vision problems, e.g., age-related farsightedness (presbyopia), cataracts and age-related macular degeneration (AMD). There is also an age-related form of hearing loss (presbycusis) that effects higher tones in particular. Older people are more likely to have arthritis, making it difficult or even painful to grasp things such as pens, knobs and buttons, and thus also potentially make it more difficult to operate technical devices. Statistics show that older people are more likely to have multiple disabilities [22]. Thus, although older people are not characterized primarily by their limitations, these need to be considered if systems are to be usable for the broader user group. Another difference with older people is that some have little experience with ICTs. At the same time, older people do not want to use technology specific to older adults that may brand them as frail [27].
Moreover, in telehealth, there are often many different stakeholders involved, each with different goals [28]. For example, there may be informal carers (e.g., family members) and professional carers who receive notifications or alarms. There may also be medical professionals that interpret the data. Furthermore, managers of care organizations and policy makers may also be involved. It can be challenging to satisfy the different needs of these groups, as care givers and older people often have different priorities, for example, carers putting a higher priority on security, whereas older people also consider other aspects, such as the aesthetics [9].
Importance of methods
In projects developing AAL technologies, the choice of methods applied may need to be adapted based on the aspects described above. To this end, after the aforementioned evaluation report, the EU-funded AAL Programme provided a toolbox of methods for this domain [36].
There may be special considerations when older users are involved. The UCD paradigm does not really account for the fact that the needs of user groups may change over time, for example, due to ageing [16]. Some projects have also found that even small aspects about the environment that at first do not seem to be relevant can be important when designing for older people [35]. Perhaps due to this, special methods have been developed for co-designing with older users (e.g., [30]). Furthermore, researchers have reported on different ways to work successfully with older users [24,33,34].
Many projects developing AAL technologies include users, as indicated by the evaluation of projects funded by the the AAL Programme of the EU [7]. However, a closer analysis indicates that, at least in funded projects, users and stakeholders are still not involved sufficiently, especially in the early phases [14].
In other areas, researchers have carried out studies to gain understanding of the UCD methods applied by practitioners. This has been done both through surveys [25] and interviews [15,23]. There have also been investigations about specific contexts [3,21]. In the area of AAL, previous research has studied the application of UCD in specific projects developing AAL technologies [12,17]. However, the choice of methods may be based on attributes specific to projects, such as how restricted the budget is, access to users, how complex the task is, or how customizable the product is [4,5]. Thus, it is of interest to investigate the application of methods more generally and also their suitability from the perspective of the people working in this area. Furthermore, decisions made early in the development process [11] can be hard to change later, so the point at which information is gained from stakeholders is also relevant.
Based on this, we set out to look at what methods are being used in projects developing AAL technology, which of these are thought to be useful, in which phases users are involved and which user groups are included. Since projects may split the development between different teams, we also looked at the communication in projects, e.g., between the people who research user needs and those who design and develop the systems.
Research methods applied
In order to investigate the usage and suitability of methods in the AAL context we carried out an online questionnaire. Rather than looking at a single project, in this paper, we focus on the methods applied and their perceived suitability in projects developing AAL technologies.
The questions about methods based on the phases of UCD of ISO 9421-210 [1], i.e. understanding the context of use, specifying the requirements, design and evaluation. Since we were focusing on the involvement of users, the phases specifying the requirements and the design were not considered. However, many decisions are made during the design and development. Furthermore, the development itself may be done by a different team or partner. Thus, we also asked about methods used to communicate the requirements, e.g., between those who investigate user needs and those who design and develop the solutions.
The choice of methods in the questionnaire included wellknown methods. In an effort to determine whether people were applying the chosen methods because they did not know other methods, we also asked about their familiarity with these methods. The methods were not defined explicitly to the participants and so based on each participant's interpretation of the named method. An effort was made to select specific methods in order to allow less room for interpretation. An overview on the methods that were included in the questionnaire is provided in Sect. 3.1.
Finally, we asked about the user inclusion. So that people did not just list all stakeholders, for this question we asked respondents to consider one specific project.
The analysis evaluated each question and calculated the percentage of people with each answer. For the questions relating to knowledge of the methods, usage of them and stakeholder inclusion, the absolute counts were used, so that the total number, or n, is constant. Thus, the percentages shown in the figures can be compared. The results were then evaluated to determine which methods were the most and the least known. To simplify comparisons for the readers, the methods are presented in the same order in every figure and table.
For the perceived suitability of the methods, only those who know the method can judge its suitability. Thus, the percentages presented are based only on those participants who knew each method. In order to be able to compare the results despite the different number of people who know each method, it is necessary to consider the standard error of the sample compared to the whole group. The standard error can be calculated as follows [18, p. 160 where n is the total number and p is the proportion of the people who know the method. The proportion can be calculated using p = n1 / n, where n1 is the value shown (i.e., those who know the method) and n is the total number of participants (i.e., 28). If the intervals defined by the result plus/minus the standard error overlap, the methods can be considered to be equally suitable (although, the inverse is not necessarily the case) [18, p. 64]. The 'best' methods are shown in bold in the tables, i.e., those for which the intervals overlap with the method rated by participants to be most suitable. Those described in the text as 'least' suited are those where the interval overlaps with the method rated least suitable.
With regard to the suitability, suitability for functionality and interaction aspects were considered separately. According to the definition of usability from ISO 9241 both the effectiveness and efficiency of the system are a factor. These are impacted by both functionality or requirements, i.e., if the system does what the users need, and interaction or design, i.e., how they do it. It was expected that some methods, both for the gathering needs and evaluation phases, would be more suited to one of these. Thus, we asked for which of these, or both, each of the methods was suited.
To gain access to a wide group of participants, the questionnaire was advertised through AAL Austria, which has approximately 60 members from Austria, including companies, care organizations, universities and research organizations. The questionnaire was available for two months.
In all, 47 participants took part in the survey. Of these, 28 questionnaires were complete enough that they could be considered in the analysis. Since the questions build on previous questions, for a questionnaire to be considered it was necessary that people answer all questions, i.e., if they knew the method, if they had used it and if they thought it was suitable, because if the final question was not answered, it would be unclear if the method was not used due to lack of knowledge about the method or due to the perceived suitability.
Including only one country, ensured a more comparable set of results, since in the wider European context, other things might effect the methods chosen, e.g., cultural aspects, social norms or educational system. It is important to stress that although small, Austria is one of the countries with the greatest involvement in those projects funded by the AAL Programme [14].
Items included in the questionnaire
In the following, the methods included in the questionnaire are listed and briefly characterized. The phases considered included gathering information about the needs, communicating the needs to developers and evaluation. Whereas gathering information about the needs relates to the first phases of UCD, i.e., understanding and specifying the context of use and specifying the user requirements, the methods for communicating the needs to developers serve to transmit this information to those who do the actual design and development. Methods specifically for design were not included, as these do not have a direct link to the users.
Observation can provide valuable insights [29]. Shadowing also involves observations, but also allows for questions to help understand behavior. The cultural probes [13] and mock-ups methods allow feedback based on artifacts. Contextual inquiry is a more extensive UCD method, including observations and discussions in the normal context. Focus groups, questionnaires, workshops and interviews can be used in a user-centered approach [29], though are more general methods that are not specific to UCD. Both focus groups and workshops involve multiple people at the same time.
The use case method is used to describe the interaction with the system to achieve a goal, and may be limited to the interaction with users, or may also consider other actors, such as external systems. The other methods are specifically from the user-centered tradition: personas describe fictitious users, scenarios describe some situations in which the system may be used and storyboards show the interaction including the system graphically.
Heuristic evaluation is based on expert input and does not involve users, while co-discovery always includes users and cognitive walkthrough can be done with or without users. The diaries and experience sampling methods allow users to record their usage and impressions over a longer time. The Wizard of Oz and paper prototyping methods allow for earlier feedback using prototypes, before a system version is working. Non-verbal feedback, physiological measurements and eye-tracking allow for a more objective feedback, and can also be used with people with cognitive impairments who are less able to express their impressions. Again, questionnaires, workshops and interviews can be used in a usercentered approach, though are more general methods. We did not explicitly ask about usability testing, since it is not interpreted in the same way by all people, i.e., whether it must be done in lab or not, though some methods included, such as eye-tracking or physiological measurements imply usability testing was done.
Information about stakeholder inclusion was only gathered about the phases gathering information and evaluation, since the methods for communicating the needs do not require users.
Types of stakeholders include: -primary end users; -family and friends; -care experts; -end user organizations; -public bodies; -insurance companies.
For most AAL systems, the primary end users are the older users. Family and friends, and care experts are people who know about the target group, but also may use the system, for example, to communicate with older people or respond to alarms. End user organizations potentially provide access to a larger number of older users and represent their interests. Public bodies are particularly important in countries with nationalized health care and social services, like the one studied, as the costs of these systems may amortize for them in a few months [6]. Insurance companies were included, because just as they give a discount for people having burglar alarms, they may in the future support systems that, for example, reduce the incidence of falls.
Of the methods included in the questionnaire, the toolbox of methods for AAL [36] also includes the methods shadowing (for gathering information), personas and storyboards (both for communicating needs), as well as co-discovery, cognitive walkthrough, Wizard of Oz and paper prototyping (all for evaluation). With the exception of storyboards, all of these methods are recommended for use with users; shadowing, personas, co-discovery and Wizard of Oz can also be applied with users who have impairments [36].
Furthermore, basic demographic data was collected about the participants, including their sex, level of education, professional background, type of organization they work for, e.g., research or company, size of the organization they work for and experience in AAL, i.e., number of projects they have been involved in.
Information about the participants
Of the 28 participants who completed the questions being evaluated, more than half of the participants were female (57%), 43% were male. Moreover, the majority of participants had higher education, i.e., university or a college degree (93%). The rest (7%) of the participants had at least a high-school equivalent.
Regarding the professional background, people from a wide variety of fields were included. One fourth (25%) studied computer science or mathematics. Almost one fifth indicated that they have a background in sociology or communication science. A small percentage of participants had a background in health care or therapy (14%) or economics, including health economics (11%). A small amount of participants indicated social sciences (7%). Other areas that were mentioned were political science and law (4%), export and administration (4%), telecommunications (4%), management (4%) and psychology (4%). One person (4%) did not specify their professional background.
More than two thirds were working in the field of research (68%); more specifically 36% were working at a university and 32% in other types of research institutions. A small percentage of the participants were working in companies (14%) or provided services (11%); 7% of the participants chose the category 'other', one with a comment that they worked as a lobbyist.
Finally, there was a good distribution of organization sizes. One fourth of our sample was working in a microenterprise (i.e., fewer than 9 employees). Almost one-fifth (18%) indicated that they were working in a small-sized enterprise (i.e., fewer than 50 employees). A small amount of participants (11%) indicated they were working in mediumsized enterprise (i.e., fewer than 250 employees) and almost half of the participants (46%) chose the category large-sized enterprise. By looking at the types of organization and size, it is possible to conclude that at least 12 different organizations were included.
Regarding their experience in AAL, participants reported being involved in between 1 (18%) and 15 projects (7%), with an average of 4.5.
Methods used in AAL projects
The results about the methods used in projects developing AAL technologies are presented by the phases described previously: first gathering information about needs, then recording and communicating the results and finally evaluation. At the end, the results relating to the stakeholders included are presented.
The results are structured as follows: -first, we present how frequently each of the methods were used in projects developing AAL technologies; -since familiarity with methods affects the methods applied, we then present which methods were known to the participants; -next we present the perceived suitability of the methods.
For this, only those methods known to the respondents were considered in the results; -finally, after presenting all of the results about the methods, we present which stakeholders were included and in which phase(s).
Methods for gathering information about needs
The methods people used in projects are shown in Fig. 1. The methods used most often were interviews, questionnaires, focus groups and workshops. All of these methods have been used by more than two-thirds of participants. The methods used least were shadowing, contextual inquiry and cultural probes. All of these were used by less than one-third of the participants. This may be in part, because these methods were also known by fewer participants (see Fig. 2). The UCD specific method contextual inquiry was known by only 43%, although it has existed since 1990 [20]. As expected, the general methods, i.e., workshops, questionnaire and interviews were known by all.
This leads us to the question of whether the usage relates to the perceived suitability or the knowledge about the method. In Table 1 we see the perceived suitability, both for gathering information about functionality and the interaction between the users and the system. The percentages in this table are based on those participants that indicated that they knew the method (shown in the column labeled n1). Note that the functionality needed is related to the task and environment, and the interaction is more closely related to the users and the technology. Results show that focus groups, workshops, questionnaires and interviews were thought to be most suitable for gathering information about functionality (over 85% of those who knew). The mock-ups and observation methods were thought to be most suited for understanding the interaction. Overall, both cultural probes and shadowing were thought to be among the least suitable methods for gathering information in projects developing AAL technologies, either about the functionality or interaction.
Methods for communicating needs to developers
In Fig. 3, we see that all methods have been used by more than two-thirds of participants, with use cases and personas being the most common (both 86%). Figure 4 shows that scenarios, use cases and personas are known to all, and even Fig. 2 Knowledge of methods for gathering information (n=28) storyboards were known to all but one of the participants (96%). Table 2 shows the perceived suitability, again based only on those who knew the method. For visualizing needs, all methods can be considered as equally suitable. Use cases and scenarios, which include information about the tasks, were thought to be most suited for evaluation (57 and 68%, respectively).
The methods rated best for communication were the same, regardless of whether communication was with project partners or external stakeholders. The personas, scenarios and use cases methods were known to all participants, and were thought to be suited for communication by at least 68%.
Methods for evaluating systems
The methods used for evaluation are shown in Fig. 5. Of these, only co-discovery was used by less than one-third of participants. A wide variety of methods are used widely (over four-fifths of participants), including diaries, physiological measurements and eye-tracking. As with gathering information, we see the general methods, i.e., questionnaires, workshops and interviews, were most widely used by participants.
Methods such as Wizard of Oz were not widely used, which may relate to the fact that they were also known by fewer participants (see Fig. 6). Figure 6 shows that the least used methods were also less well known. Co-discovery was least known (only 32%), even though it is in the toolbox of AAL methods [36].
The perceived suitability of the methods is shown in Table 3. We asked about suitability with regard to both functionality and interaction, as was done for the methods for gathering information about needs. Again this is based only on those respondents who knew the methods. This shows a different picture. The Wizard of Oz method was thought to be the most effective for evaluating the interaction by participants who know the method. For evaluating functionality, the general methods questionnaire and interviews were among those thought to be most effective, along with diaries and Wizard of Oz (all at least 80% of participants who knew it). The co-discovery method, although unknown to most and not widely used, was still thought to be suitable for evaluating functionality by 67%, and was not among those rated least suitable.
Types of stakeholders included
To get a more accurate view about the inclusion of stakeholders, we asked participants to answer the questions 48% ± 10 37% ± 9 37% ± 9 30% ± 9 Scenarios 28 57% ± 9 68% ± 9 71% ± 9 57% ± 9 Use cases 28 50% ± 9 82% ± 7 71% ± 9 68% ± 9 Personas 28 57% ± 9 68% ± 9 71% ± 9 43% ± 9 with one particular project in mind. Please note that one person did not answer this question, so the total number here is 27. Figure 7 shows the stakeholders that have been included in gathering information about the needs. Older people were generally consulted most, while insurance companies were not consulted. Regarding functionality, end users and end user organization are included most often (both 74%), followed by care experts (67%). With regard to aspects related to interaction, end-user organization and care-experts were included most often (63 and 59% respectively).
With regard to the evaluation, end-users were included by almost all (93%) respondents (see Fig. 8). Both enduser organizations and care experts were included by more than half of the participants.
Discussion
In the following we discuss aspects related to the choice of methods, user inclusion and communication in teams.
Choice of methods
In terms of methods used, we see that the expert review methods, heuristic evaluation and cognitive walkthrough, are less commonly used. Since 96% of participants had used eye-tracking in a project and eye-tracking is done in combination with usability tests, the results indicate usability tests were widely done. The prevalence of usability tests is in accord with what has been reported more generally in projects by Lindgaard [23]. The usage of diaries for evaluation (by 96%) indicates that in many cases the evaluation were done for an extended period of time. The extent of eye-tracking is surprisingly high. This, however, may relate to the fact that in Austria eye-tracking is widely used in the usability community, for example at CURE (Center for Usability Research & Engineering in Vienna), the usability labs at some universities (including the University of Salzburg and the University of Applied Sciences Technikum Wien) and also some of the more established usability consulting groups.
Both during gathering information and evaluation, general methods such as interviews, questionnaires and workshops were widely used. Although these methods are not specifically included in the usability planner [5], they are considered to be part of UCD [29]. These findings match the research of Gray [15] that many developers think being user-centered is more of a mindset than a method, and apply "remarkably few explicit user research methods" (p. 4049). Also other studies in Europe have found that more general methods that are not specific to UCD are applied in UCD (e.g., [3,21]). Bednarik and Krohns [3] found that this was due in part to perceived costs and lack of UCD know-how. For some methods, the results on perceived suitability support that it may indeed be due to know-how, e.g., Wizard of Oz and co-discovery were not widely known, though were thought to be appropriate by those who knew these methods. The choice may also be related to the fact that people from other disciplines were included. In the area of health services, methods such as interviews and observations are often applied rather than UCD specific methods, such as mock-ups for gathering information or co-discovery for evaluation [26]. Generally, a high level of knowledge of methods was present, even though participants included people from other professions, such as health care and sociology. This may, however, also relate to the fact that most had been involved in more than one project (72%). The fact that people gained knowledge about UCD through previous projects could help to explain why the contextual inquiry method was not widely known, even though it has been in existence for many years [20] and has been considered by other recent studies of UCD (e.g., [15]). However, Bednarik and Krohns [3] reported that this is a more advanced method and was also not used by any participants in their study.
Other researchers have reported the difficulty of dealing with intangible issues with older people [24]. At the same time, AAL systems may include intangible concepts, such as the sensors that are needed for monitoring activity. With regard to this, it is interesting to note that methods that could support making the functioning of the system more tangible before the system is completed, such as mock-ups and Wizard of Oz, were widespread and also among those rated most suitable.
It is also interesting to compare the results to methods described in the toolbox for AAL [36]. Some methods recommended there were not widely known, such as co-discovery. With regard to suitability, most of the methods from the toolbox included in the questionnaire were also thought to be suitable by those participants who knew them: personas, codiscovery, Wizard of Oz, cognitive walkthrough and paper prototyping (all considered to be suitable for some aspect by more than 60% of people who knew them). Wizard of Oz was considered to be one of the best methods, and also paper prototyping was thought to be suited for evaluation (both thought to be suitable by at least 86% of those who knew it). This is of particular interest as these methods support getting early feedback. The situation with shadowing and storyboards is less clear, for although some rated these methods as suitable, they were among those rated to be least suitable. This is particularly striking with storyboards, where all but one of the participants knew the method, though less than 50% found it to be suitable, even for communication between project partners for which the toolbox specifically recommends it.
Stakeholder inclusion
The results indicate that primary end users were included in many projects, both for gathering information about the needs and during the evaluation. This is interesting, since another study also done in Austria concluded that users were included too little [14]. It is also remarkable, since it may be difficult to test with older people due to a variety of factors, e.g., cognitive or physical limitations, but also the effort to learn a new system due to limited knowledge about ICTs, so that some even suggest using more indirect methods with older users [31].
This perceived lack of involvement may be because actual end users, i.e., the older adults, were only included during the evaluation, whereas end-user organizations and care experts were included earlier in many projects, i.e., for gathering information about user needs. The focus on input from care experts early on is concerning, as Dahl et al. [9] found that with emergency response systems, care experts were more concerned with security (i.e., functionality), whereas older people put focus on aspects such as aesthetics and usability. In practice, it was precisely about aspects related more to the interaction rather than the functionality about which end-users were included less frequently. However, since users were included in evaluation, these aspects may still be able to be corrected. This underlines the importance of methods that enable earlier feedback, like Wizard of Oz and paper prototyping-which were also thought to be suitable by a high percentage of those who knew them.
The lack of inclusion of older adults in the early phases does not have to relate to a bias against older people. In a certain sense, the care experts represent the customer. In their study of UCD practice in small companies, Bednarik and Krohns [3] found that also in other areas developers did not distinguish between 'users' and 'customers'.
Communication in teams
Another interesting aspect is the communication of the needs. Most methods studied were known to the participants and had also been used in a project. However, unlike the other phases considered, here only one method was considered to be suitable by more than 80%-use cases, a method which is also used more generally in software engineering and which is not specific to UCD. It was considered to be suited specifically for communicating between project partners, at least some of which will be developers. This is interesting in view of results from a previous study looking at specific projects [12], in which it was found that there are problems with the communication in teams, specifically between those carrying out the needs analysis and the developers. It is essential that developers understand the needs, as during the development they may make decisions both about the functionality and design. These decisions can have a decisive impact on whether products can be a commercial success, even when comparing systems from the same company [19]. Furthermore, it has been demonstrated that even technical design decisions made during the early phases development, e.g., regarding the system architecture, affect qualities of systems that are crucial to success and can be difficult to change in a later stage [11]. This indicates that additional methods for communicating the needs to the developers could support having more successful AAL products in the future.
Conclusion
This paper presented a survey of UCD practice in projects developing technology to support older people. Due to the shifting age pyramid, there is great potential in these technologies, however, there are also many barriers to adoption. This study aimed to support future teams in choosing appropriate methods by investigating the perceived suitability of different methods.
Results show that many projects rely on general methods that are not specific to UCD, such as interviews, questionnaires and workshops. Despite this, if known, more advanced methods are perceived as suitable for gathering information about stakeholder needs and for evaluating systems, e.g., mock-ups and Wizard of Oz. Based on this, it can be concluded that the use of more advanced UCD approaches can support projects developing AAL technologies in gathering the actual needs of all relevant stakeholder groups and evaluating systems. Furthermore, results indicate that the primary end users are often included only later, i.e., for evaluating systems, indicating promise also in methods supporting earlier inclusion of older people.
With regard to methods for communicating needs to developers, results indicate use cases were thought to be best suited. However, generally, the methods studied for communicating needs between project partners were rated with a low level of suitability, so further methods seem to be needed. Furthermore, since use cases is a method from traditional software development, it may be advantageous to investigate more versatile methods, that can be used both with project partners and external stakeholders without software development knowledge, and that are also suited to communicate the different types of information developers need to ensure the systems are effective, efficient and satisfactory.
In conclusion, future work should focus on raising awareness of more advanced methodological approaches among stakeholders involved in innovative projects in the field of AAL. To achieve this, also toolkits that support the selection of appropriate methods and their application could be useful.
In addition, the development of new methods for communicating stakeholder needs within projects could support more success in the future. | 8,474.2 | 2018-07-23T00:00:00.000 | [
"Computer Science"
] |
Corrections: Kim, T.; et al. Some Identities for Euler and Bernoulli Polynomials and Their Zeros. Axioms 2018, 7 , 56
The authors, Kim and Ryoo in [1], studied Euler polynomials and Bernoulli polynomials withan extended variable to a complex variable, replacing real variable x by complex variable x + iy,and achieved several useful identities and properties [...]
Corrigendum
The authors, Kim and Ryoo in [1], studied Euler polynomials and Bernoulli polynomials with an extended variable to a complex variable, replacing real variable x by complex variable x + iy, and achieved several useful identities and properties.
The authors would like to note that these results can also be derived from a different approach by considering Euler polynomials and Bernoulli polynomials with a pair of two variables, as shown in [2], instead of a complex variable.
For example, Masjed-Jamei, Beyki and Koepf in [2] introduced the new type Euler polynomials given by 2e pt e t + 1 which are considered without a complex variable. On the other hand, the authors in [1] considered the Euler polynomials and Bernoulli polynomials with a complex variable instead of x variable as follows: and which imply the equivalence definitions to Equation (1) as and Here, the authors considered the Euler polynomials and Bernoulli polynomials of a complex variable, by treating the real and imaginary parts separately, which are able to introduce the cosine Euler polynomials, the sine Euler polynomials, the cosine Bernoulli polynomials, and the sine Bernoulli polynomials such as Equations (2) and (3).
After the paper "Some Identities for Euler and Bernoulli Polynomials and Their Zeros in Axioms 2018, 7, 56." by T. Kim and C.S. Ryoo was published, we realized that some results of the paper "A New Type of Euler Polynomials and Numbers in Mediterr. J. Math. (2018) 15: 138." by M. Masjed-Jamei, M.R. Beyki, and W. Koepf were published ahead with some identical results, which are consistent with the ones in the paper [1].
The authors in [1], after the publication, were aware of that Hacéne Belbachir, the reviewer of the paper [2], left the question related to the extension of a variable in Mathematical Reviews (MR3808565) of the American Mathematical Society: "Is it possible to obtain their results by considering the classical Euler polynomials of complex variable x + iy, and treating the real part and the imaginary part separately?" The approach in Equation (2) can be an affirmative answer to the question.
Thus, we want to inform our readers that some results of Reference [2] have been published before the paper [1]. In addition, their related works are presented in [3], in which some similar results are shown as their consistent works in [2].
The authors conclusively note that some of the results in both [1,2] are derived from these two different approaches mentioned above.
In addition, the identical results in both [1,2] are listed as follows.
Corrections
In addition, while reviewing our paper, we found some typing errors: Equation (11) should be revised by E n (x + iy) − E n (x − iy) 2i , and Equation (31) should be also replaced by | 725.2 | 2019-10-01T00:00:00.000 | [
"Mathematics"
] |
COVID-19 lockdown implementation in Ghana: lessons learned and hurdles to overcome
COVID-19 exacts huge health and economic burdens on the global economy. To minimize spread of the virus, most governments of the wealthiest countries implemented lockdowns—a tough preventive measure. Ghana implemented a partial lockdown of two major cities, then lifted it in few weeks despite rising numbers of cases. This Viewpoint presents perspectives of key stakeholders in the public about lockdown implementation in Ghana. Respondents characterize the lifting of the lockdown as hasty, poorly communicated, and lacking transparency. Most would have preferred a longer lockdown despite the pressures it imposed especially on the urban poor. Participants expressed uncertainty about the health systems' ability to respond to increases in disease transmission and to provide education, engagement, and empowerment needed in communities, but even so would have preferred a longer lockdown. We offer lessons for more effective policy and implementation of lockdowns.
Introduction
The novel SARS-CoV-2 (COVID-19) is a global public health burden, having caused over 259 million confirmed cases and about 5 million confirmed deaths worldwide as of November 2021. It is the worst pandemic in the century [1]. Experts' predictions and lay persons' speculations painted a gloomy picture, claiming the burden would be higher in Africa and might exacerbate conditions of weak health systems on the continent. But the burden across Africa has been lower and less severe than predicted [2]. Some scholars have speculated causes to include the largely young population of Africa, some hidden or cross immunity from other diseases, and warm temperatures [3]. All these factors may have benefitted Ghanaians, and contributed to a relatively lower burden of the disease in the region.
Many countries have instituted restrictive measures on free movement of persons and goods to help limit the spread of the virus. These restrictions created chaos early in the pandemic, forcing people to adjust to a 'new normal' and to adhere to the WHO. The Government of Ghana implemented a partial lockdown on March 30, 2020 in its two most populous cities, Accra and Kumasi. The President of the country, His Excellency Nana Addo Dankwa Akufo-Addo, announced the policy and security agencies enforced it. A stay-at-home order applied to almost all people in the two cities and most activities. Exceptions included individuals providing or accessing food, water, beverages, public toilets and baths, health services, electricity, banking, and those in key institutions, such as the media, Members of the Executive, the Legislature, and the Judiciary. The Government lifted the lockdown during the third week of its implementation as numbers of new cases of COVID-19 continued to rise [4]. The abrupt change of policy prompted debates among the public and policy-makers as to whether the lockdown had achieved its intended purpose.
Although researchers have conducted several studies on lockdown globally, none explored the perception of the general public on lockdown implementation in Ghana. This Viewpoint presents perspectives of the public on the lifting of the lockdown and its policy implications in Ghana. We also provide policy recommendations for effective lockdown implementation and preparedness for future outbreaks.
Key informant interviews
We gathered data from April 23, 2020 to July 1, 2020, immediately after the government lifted the lockdown. We selected a total of 101 key informants through a purposive and snowball sampling approach. We sought interviewees knowledgeable about the policy, the social context, and technical information about the COVID-19 pandemic. Participants included educated community opinion leaders, community members, media personalities, health professionals, academics, and students. Restrictions, such as social or physical distancing, made it infeasible for researchers to conduct face-to-face interviews. We designed interview guides using google forms and administered the survey online, using WhatsApp. We conducted the study in accord with the ethical principles of the Declaration of Helsinki, World Medical Association [5] because the COVID-19 restrictions made it difficult to obtain ethical clearance from the local ethics committee. Participation of this study was entirely voluntary-we informed participants of their right to participate, decline, or withdraw from the study at any time without consequence. Because the study aimed to explore only opinions of participants without exciting strong feelings or emotions, there was no risk for participants. Researchers guaranteed privacy, confidentiality, and anonymity of the information shared by interviewees. Researchers explained the objective of the study and encouraged all participants to read and understand the purpose of the study before consenting to participate. We used a conventional content analysis approach to interpret responses [6], through the lens of the WHO criteria for lifting lockdown. According to the WHO [7], any country considering a lift of lockdown should ensure that: • Disease transmission is under control. • Health system is able to "detect, test, isolate, and treat every case and trace every contact." • Hotspot risks are minimized in vulnerable places. • Schools, workplaces, and other essential places have established preventative measures. • The risk of importing new cases can be managed. • Communities are fully educated, engaged, and empowered to live under a new normal.
We also explored and analyzed perspectives of stakeholders on factors relevant to the Ghanaian context. We included issues to develop and expand our understanding about the phenomenon within the local context. These pertain to whether: • The lockdown implementation was appropriate and achieved its objective (contributed to a reduction in the spread of the disease) before it was lifted, or it was lifted prematurely. • The decision to lift the lockdown was transparent and evidence-driven. • The decision to lift the lockdown was to achieve political gains or not. • The health system of Ghana would be able to detect, test, isolate, and treat every case and trace every contact should cases and mortality increase.
Characteristics of participants and participants' views
About 57.5% of the respondents were between 33 and 67 years with the mean age of 31.4 ± 8.9, about 58.6% of informants were males, and 57.3% lived in cities that experienced the lockdown. Approximately 10.8% of participants were COVID-19 frontline workers, 49.5% had university degree, 29% had postgraduate education, and 39.1% were senior-level professionals (Table 1).
Most participants (58.2%) agreed with the statement that the government's decision to lift the lockdown was premature. Most respondents (54.1%) reported agreed that lifting the lockdown was inappropriate because it had not yet achieved its objective of slowing the rate of transmission of the virus. An overwhelming number of respondents (80.6%) asserted that the lifting of lockdown was dangerous and could lead to an escalation in COVID-19 spread. Many interviewees (43.3%) opined that the decision-making processes used in lifting the lockdown lacked transparency. Many (36.7%) believed the decision to lift lockdown was not evidence-driven, about (35.7%) of study participants believed that the decision was evidence-based (Table 2). Respondents did not believe a desire to achieve political gain motivated the swift decision by government to lift the lockdown. Instead, they reported key reasons to be exacerbation of socioeconomic inequalities of the urban poor and the economic impact of lockdown on the informal sector, the largest source of employment in the country.
The populations of Accra and Kumasi constitute about 17% of the Ghanaian population [8]. In both cities, low-income residents of urban slums comprise a substantial population of artisan workers paid daily wages. Given the important economic and social role residents of Accra and Kumasi play in the civic life of Ghana, participants stressed that the lockdown indirectly had an impact on the entire Ghanaian economy.
Some interviewees (40.8%) emphasized the ability of the health system of Ghana to respond to the present threat of COVID-19, particularly detecting, testing, isolating, and treating and tracing every case and contact. Others disagreed (38.6%) or expressed uncertainty (38.6%) about the ability of the health system to respond to any escalation in the disease burden. Participants highlighted the inadequacy of resources both financial, material, and human resources to contain a rise in cases and mortality. One health worker noted that "the health system can be able (to respond to rise in the cases of COVID-19) when resourced" (Frontline worker, interviewer 22). Those challenging the health system included inadequacy of personal protective equipment (PPE) for health professionals, limited numbers of health professionals, and limited capacity of hospitals to manage increases in cases. A majority (60.8%), however, agreed that the risk of importing new cases could be managed. Although several participants disagreed with the statement that hotspot risks had been minimized in vulnerable places, the majority believed that schools, workplaces, and other essential sites had established preventative measures.
Many respondents (47.4%) noted uncertainty as to whether communities had been fully educated, engaged, or well empowered to live under a 'new normal' set of conditions. Participants shared their worries that community members would not adhere to COVID-19 preventive measures without government-regulated lockdown due to low levels of knowledge about COVID-19; sociocultural barriers to observing physical distancing like handshaking, hugging, and eating with family and friends, and poor attitudes for adhering to practices including wearing masks and practicing hand hygiene. Overall, respondents' opinions favored government mandated lockdown as an indirect reminder of the existence and extent of COVID-19, and to take precautionary measures against transmission. Most respondents (46.9%) were unsure as to whether the transmission was under control or not, and agreed that "Ghanaians in other regions were expecting their lockdown only for them to be surprised" when the government instead
Context-specific related questions
The lifting of the lockdown is appropriate because it has achieved its objective lifted it in the two cities. Table 3 presents the summary of the barriers and facilitators of lockdown implementation.
Policy implications to Ghana and the wider African context
Recent global health crises include Hantavirus Pulmonary Syndrome, Severe Acute Respiratory Syndrome (SARS), H5N1 Influenza, H1N1 Influenza, Middle East Respiratory Syndrome (MERS), and the Ebola virus outbreak [9,10]. Preparedness, targeting disease prevention, is critical as hospitals may struggle to care for an increased magnitude of patients, especially given resource constraints. This reasoning contributed to decisions in most countries to impose restrictions due to COVID-19, including lockdowns. Even so, adequate preparation and response to outbreaks requires resources for the public health infrastructure. Hospitals and clinics have detected and treated most of those infected during COVID-19 outbreaks [11]. Based on the current WHO data, Ghana's government expenditure on health as a percentage of total government expenditure is low, around 6.82% in 2014 [12]. COVID-19 has highlighted the often-ignored need for a massive boost in governments' health spending, especially investment in the public health infrastructure to meet growing health needs and expectation of citizens. An early study in Lebanon showed nationwide lockdown in 2020 had a significant impact on minimizing the spread of the pandemic and containing the virus [13]. What is an appropriate policy response or a disproportionate one? What works well in one country may not be as effective elsewhere. Lockdown implementation in some lower-middle-income countries (LMICs) proved to be effective [13], but not so in Ghana where government halted implementation due to intra-urban socioeconomic inequalities and the economic impact of lockdown on informal sector workers. Thus, we encourage policy makers to consider all contextual factors in their countries when planning a lockdown.
What might be unintended consequences on people, particularly on vulnerable groups? In many LMICs, including Ghana, lockdown led to several unplanned consequences. In two Ghanaian cities lockdown distressed those with few resources, particularly residents of the urban slums; halted activities of the informal sector, the largest sector and source of employment, and the major contributor to the national income; and slowed socioeconomic activities in major cities. Restrictions of all forms, including lockdown, bans on public gathering, religious services, schools, workplaces, and public places of entertainment, and bans on travel and sporting activities all produced socioeconomic and health adversity for people and the economy. In Ghana, these provoked swift action by the Government of Ghana to lift the lockdown.
To navigate such complexities more effectively, decision makers should move to a problem-solving strategy that addresses specific problems as part of a wider, dynamic system [14] and focuses on appropriate and sustainable solutions--an approach known as systems thinking. Systems thinking for COVID-19 will necessitate health system leaders to manage district health systems more effectively. The role of district managers is crucial: they are strategically positioned to work directly with local actors, particularly community members, to engage them in systems thinking, and strengthen health system performance and response to COVID-19.
Use of local data to generate knowledge helps policy-makers identify and effectively respond to specific challenges [15]. Information should be clearly and timely communicated to all stakeholders to foster effective, coordinated efforts against outbreaks. Communication about the core components and capabilities of public health can provide guidance needed to promote commitment for sustainable public health services, especially among the general public, academics, private sector policymakers, regulators, public health professionals, and professional organizations [11]. Disease outbreaks, whether from an influenza epidemic or an act of bioterrorism [16], may pose unique challenges for disease detection, treatment, and prevention [17]. Often feeble decision-making capacities at the district level have contributed to poor management and coordination of health service delivery, and hindered scale-up of proven health interventions [18]. Thus, there is an urgent need to build district manager capacities for systems thinking and practice for sustainable solutions during public health emergencies. Pandemics start with and end in the community. Community engagement is crucial for health systems preparedness and response to diseases and outbreaks. Governance in Ghana relies on both traditional and civil leaders with distinct, yet sometimes overlapping, powers and interests in managing societal problems. Although the president communicated the lockdown strategy and security agencies chiefly enforced it, traditional and civil leaders played key roles in managing transmission mitigation strategies for the COVID-19 lockdown. Communities trained and engaged in outbreak preparedness and response become vital contributors to effective detection and resilient response to disease outbreaks [16]. This includes improved adherence to prevention measures such as wearing masks, regular washing of hands, and practice of social or physical distancing-even without government-regulated restrictions.
Conclusions
Disease outbreaks will continue to disrupt health systems and economies. Because COVID-19 lockdown in Ghana distressed the urban poor and halted activities of the informal sector, government prematurely lifted lockdown despite the increase in numbers of new cases. Even so, there is good news. Policy-makers can pursue initiatives to improve adherence to preventive measures-not just to reduce further transmission of the virus, but to sustain progress. Restrictive measures are sometimes warranted to ensure effective prevention of further spread of viruses, and to facilitate a successful detection and treatment for public safety and preservation of life. We recommend evidence-informed decision-making, effective communication and transparency, and improving preparation of country's health systems to "detect, test, isolate, and treat every case and trace every contact." These actions will determine how rapidly nations can succeed in the fight against COVID-19, especially in bringing economies to normality by lifting lockdowns or other restrictions.
Informed consent Researchers explained the objective of the study and encouraged all participants to read and understand, before they consent to participate in the research.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/. | 3,679.2 | 2022-01-04T00:00:00.000 | [
"Political Science",
"Medicine",
"Economics"
] |
Joint estimation of preferential attachment and node fitness in growing complex networks
Complex network growth across diverse fields of science is hypothesized to be driven in the main by a combination of preferential attachment and node fitness processes. For measuring the respective influences of these processes, previous approaches make strong and untested assumptions on the functional forms of either the preferential attachment function or fitness function or both. We introduce a Bayesian statistical method called PAFit to estimate preferential attachment and node fitness without imposing such functional constraints that works by maximizing a log-likelihood function with suitably added regularization terms. We use PAFit to investigate the interplay between preferential attachment and node fitness processes in a Facebook wall-post network. While we uncover evidence for both preferential attachment and node fitness, thus validating the hypothesis that these processes together drive complex network evolution, we also find that node fitness plays the bigger role in determining the degree of a node. This is the first validation of its kind on real-world network data. But surprisingly the rate of preferential attachment is found to deviate from the conventional log-linear form when node fitness is taken into account. The proposed method is implemented in the R package PAFit.
Supplementary Figure S1. Some examples of choosing the optimum regularization parameters. In all these networks, the true distribution of node fitnesses is a gamma distribution with mean 1 and variance 1/s * . For each combination of r and s, A k and η i are estimated using the learning data, and then the log-likelihood of the unseen testing data is calculated. The optimal combination of r and s is the one that gives the highest log-likelihood of the unseen testing data. The lightblue band at estimated points represents the estimated two-sigma confidence intervals of the associated point estimates.
Next we specify the regularization parameters of A k (the parameter r) and η i (the parameter s). For the regularization of A k , we set r = 0.1, as Pham et al. 2 have shown through simulations that a small amount of regularization helps reducing the error in estimating A k . To investigate the effect of mis-specification of the true distribution of node fitnesses, we consider three different values for the regularization parameter s: 0.1, 1 and 10.
To summarize, the simulation settings are as follows. For each of the 48 combinations of true functions of A k and true distributions of η i , we generate 100 networks according to the GT model. Starting from a seed network with 20 nodes, at each time-step, m(t) = 5 new edges and n(t) = 1 new node were added, until a total of 5000 nodes is reached. We then apply PAFit to each generated network. Regarding η i , we consider three cases: s = 0.1, 1 and 10. Regarding A k , the parameter r is fixed at 0.1. The A k are also grouped into logarithmic bins and the number of bins B is 20. Supplementary Fig. S5 shows average relative errors e η and e A averaged over 100 repetitions.
First consider e η in estimating η i , we see that PAFit outperforms the growth method, even when the regularization parameter s is mis-specified. The effect of mis-specifying s is clear, when the case s is equal to the true parameter s * almost always gave the lowest error.
Next, let us consider the performance of PAFit through e A . Since there are no existing methods that estimate A k with considerations for node fitness, we have to introduce the following two variants of PAFit to be served as reasonable baselines. The first variant, called baseline1, estimates A k while fixing the fitness of node v i at the number of new edges it has acquired in the growth process, i.e. letting η i = ∑ i z i (t). Since we can see PAFit markedly outperforms baseline1 in all situations, the seemingly reasonable heuristic of using the number of acquired new edges as fitness results in surprisingly poor estimation. In the second variant called baseline2, we essentially ignored the effect of fitness by fixing η i = 1 for each node v i . Note that this is equivalent to the method proposed in our previous work 2 . PAFit outperforms baseline2 in almost all cases except when A k = k α when α is near 1.5.
With such a large value of the attachment exponent, the winner-take-all effect becomes prominent even in finite data. As explained in the Introduction Section of the main text, the winner-take-all situation indicates a situation where only a handful of nodes, perhaps even only one node, actually acquire new edges, while the vast majority of nodes do not acquire any new edges at all. This winner-take-all effect drastically skews the amount of data for each node. Also note that, e A generally increases with α in this model. This phenomenon, which has also been confirmed in the case of estimating A k in isolation 2 , indicates that the estimation problem gets "harder" as the degree of the winner-take-all effect increases. The simulated results suggest that fixing η i = 1 for all i in such cases, which serves as a regularization that helps to reduce the dimension of the problem, actually 1 ) when the true node fitnesses are sampled from a log-normal distribution. First row: A k = max(k, 1). Second row: A k = 3 (log max(k, 1)) 2 + 1. The plots are on a log-log scale. The lightblue band at estimated points represents the estimated two-sigma confidence intervals of the associated point estimates. For the first row, the growth method gave the correleration coefficient between estimated and true fitness r η = 0.74 (the higher the correleration coefficient, the better the estimation) and the relative error e η = 0.27 (the lower the relative error, the better the estimation). With the chosen (r, s) being results in better estimation of A k . The effects of mis-specifying s on estimating A k is surprising: the value s = 0.1 gives better estimation of A k than other values of s, even when the true parameter s * is not 0.1. Note that in the log-linear model with α ≥ 1, the specification of s seems to be unimportant, since all values of s gave almost the same error.
Overall, we can conclude that PAFit can indeed estimate both A k and η i successfully. PAFit also performs better than the growth method in estimating η i . The specification of s seems to be important, but when the mis-specification is not so great (as in this example, about 10 times), the estimated results of both η i and A k do not worsen much.
S1.4 Estimation results when varying the ratio between learning data and full data
While we have used p = 0.75 in the main text, here we present estimation results for two additional cases when the ratio p between the learning data and the full data is 0.5 and 0.9. When p = 0.5, the optimal combination of the regularization parameters is (r, s) = (0.28, 32.47), while this combination is (r, s) = (0.03, 2.66) when p = 0.9. When the ratio between the 4/16 5e−02 5e−01 5e+00 5e+01 5e−02 5e−01 5e+00 5e+01 True fitness Degree k + 1 Estimated PA function Proposed method Constant η a: Growth method 5e−02 5e−01 5e+00 5e+01 5e−02 5e−01 5e+00 5e+01 True fitness Estimated fitness learning data and the full data is p, recall that full,p andη full,p are the estimated PA function and the estimated fitness using the full data with the optimal (r, s), respectively (see Fig. 2). Similarly, here we let learn,p be the estimated PA function using the learning data with the same optimal (r, s). Supplementary Fig. S6a shows learn,p and Supplementary Fig. S6b shows full,p for three different values of p. Supplementary Fig. S7 showsη full,0.75 in comparison withη full,0.5 andη full,0.9 for nodes whose number of acquired edges is at least 50.
Overall, the results concerning the PA function do not change significantly if we use p = 0.9 or p = 0.5. In Supplementary Fig. S6, we notice that learn,0.75 and full,0.75 are reasonably similar, and they are both strikingly close to both learn,0.9 and A full,0.9 . Since we use full,p for subsequent analyses, the closeness of full,0.75 and full,0.9 indicates there is almost no change if we choose p = 0.9. While learn,0.5 is substantially different from full,0.5 , full,0.5 are reassuringly close to A full,0.75 . This closeness again implies that the results concerning the PA function does not change significantly even if p = 0.5.
The results concerning node fitness also do not change significantly if we use p = 0.9 or p = 0.5. In Supplementary Fig. S7, the point (η full,0.75 ,η full,0.9 ) are strikingly close to the y = x line. The R 2 coefficient, whose values close to 1 often indicate Supplementary Table S1. Summary of true PA functions used in Monte Carlo simulations. There is a total of 16 different functions.
a linear relationship, is 0.99 in this case. Although the points (η full,0.75 ,η full,0.5 ) deviate a bit from the y = x line , the R 2 coefficient is 0.91, which can still be considered high.
S1.5 Additional data analyses in the Facebook wall-post dataset
We show in Supplementary Fig. S8 the same degree growth curves as in Fig. 6, but this time with the horizontal axis being time. The same trend in which nodes with high fitness have steep growth curves is still visible here, but is difficult to see due to the differences in birth times of the curves. Nevertheless this figure reveals some additional information that cannot be seen in Fig. 6. One might notice a sudden increase in the number of new nodes at each time-step from around time-step 600. This increase can be seen more clearly from the change in the slope of the number of new nodes n(t) in Supplementary Fig. S9a. The increase of new nodes leads to an increase of the number of node fitnesses we have to estimate. One might worry that there might be not enough data to do this adequately.
Fortunately, since this increase in n(t) is accompanied by an increase in the number of new edges m(t) ( Supplementary Fig. S9b), the normalized number of new edges is stable ( Supplementary Fig. S9c), and thus the whole system is in fact stable. The normalized number of new edges, which is defined as µ(t) = m(t)/ ∑ j:v j exists at t A k j (t) η j , can be intuitively viewed as the amount of new data available at time-step t, after taking into consideration the differences in network sizes or degree distributions, etc. at different time-steps. µ(t) is calculated using the observed k i (t), while in Supplementary Methods Section S1.6 it was calculated using the expected k i (t).
We note that the oscillations observed in µ(t) are caused by the oscillations in m(t). The normalized number of new edges µ(t), by definition, can be affected by m(t) and ∑ j:v j exists at t A k j (t) η j , and the latter in turn can be affected by n(t). But while there is no periodicity in n(t) (Supplementary Fig. S9d), a weekly period can be seen clearly in both the autocorrelation function of m(t) (Supplementary Fig. S9e) and µ(t) (Supplementary Fig. S9f). We found that the cause of this periodicity is that m(t), the number of new wall-posts, tends to increase toward the middle of the week and decrease on weekends ( Supplementary Fig. S10).
Although Eq. (S1) implies that we can only compare the growth rate of two curves in Supplementary Fig. S8 at the same time-step, it is possible to use µ(t) to compare the growth rate of two degree growth curves of some nodes v 1 and v 2 (v 1 and v 2 can be the same) at two different time-steps t 1 and t 2 . Assuming η 1 and η 2 are the fitness of v 1 and v 2 respectively, the corresponding growth rates of the two curves are A k 1 (t 1 ) × µ(t 1 ) × η 1 and A k 2 (t 2 ) × µ(t 2 ) × η 2 . Furthermore, if k 1 (t 1 ) = k 2 (t 2 ), i.e. the curve of v 1 at time t 1 is on the same horizontal level with the curve of v 2 at time t 2 in Supplementary Fig. S8, then we can ignore the PA factor when comparing them, and the two (relative) growth rates reduce to µ(t 1 ) × η 1 and µ(t 2 ) × η 2 .
S1.6 Calculating expected degree growth curves
In short, the theoretical degree growth curves in Fig. 6 are expected degree growth curves calculated by evolving the whole network from the initial time-step using the estimated PA function (Fig. 5b) and estimated fitness of all real nodes (Fig. 5c), with the number of new edges and new nodes are kept exactly the same as in the observed evolution process. Specifically, for each η = 8, 4, 2, 1, 0.5 and 0.25, we repeat the following procedure: • Step 0: We include a generic "ghost" node v ghost with fitness η into the network at the initial time with initial degree k ghost (0) = 10. Set t = 0.
• Step 1: If t = T − 1, go to Step 3. Otherwise, for every node v i that appears in the network at time t we calculate Figure S6. Estimated PA functions in the Facebook wall-post dataset using the learning data ( learn,p ) and the full data ( learn,p ) for three cases when p, the ratio between learning data and full data, is 0.5, 0.75 and 0.9. The closeness of full,0.75 , full,0.9 and full,0.5 implies that the results concerning the PA function in the main text does not change significantly if p = 0.9 or p = 0.5.
S2 Supplementary Methods
In Section S2.1, we discuss related work on estimating PA and node fitness. We provide the definition of the undirected GT model in Section S2.2. The derivation of the log likelihood function is shown in Section S2.3. Finally, Section S2.4 provides the MM algorithm for estimation.
S2.1 Related work
Here we discuss existing work that is related to our proposed method. First consider the case when either A k or η i does not change with time, which is the situation we assume in this paper. In this case, the problem of estimating the PA function A k while fixing η i equal to 1 for all i has attracted the attention of many researchers, and there are a number of estimation methods [2][3][4][5][6][7][8][9] . While most of these methods assume the log-linear form A k = k α , Pham et al. 2 recently provided a statistical method that does not assume any functional form for A k . Assuming linear PA (A k = k) upfront, Zhang et al. 10 proposed a method to find the optimal weight to combine the PA and clustering mechanisms. Middendorf et al. 11 used discriminative classification techniques to classify an evolving network according to one of the many network evolving mechanisms, including the linear PA mechanism. For the problem of estimating fitness in the time-invariant case, Kong et al.'s growth method 1 is the only existing method we know of that estimates η i , albeit under the assumption that A k = k. Their method estimates η i by using the following asymptotic formula related to the degree of a node with its fitness: The slope of the least-squares fit of logt to log k i (t) gives us the fitness η i . The fact that the growth method is an asymptotic method imposes several limits on the resulting estimation. Firstly, we have no assurances of how the method will behave on finite data. For example, the slope of the least-squares line of best-fit in Eq. (S2) might very well be negative, and thus lead to a nonsensical estimated value for η i . Secondly, the assumptions needed to derive the asymptotic formula can be wrong in real-world networks. Most strikingly, the linear A k assumption might not be supported by the observed data, as shown in the main text. From another different view point, Blasio et al. 12 considers the problem of distinguishing the effects of PA and fitness through statistical tests. They assumed that the PA effect only works in the linear form A k = k, and did not consider the problem of estimating fitness. Supplementary Figure S7. Estimated fitness in the Facebook wall-post dataset using the full data, for three cases when p, the ratio between learning data and full data, is 0.5, 0.75 and 0.9.η full,p is the estimated fitness using the full data when the ratio between the learning data and the full data is p. p = 0.75 is the value used for the results in the main text. The three cases give similar fitness values.
If we allow time-variation in either the PA function or node fitness, there is a growing body of methods for estimating A k or η i . But comparing with the focus of our paper, the main focus of most of these estimation methods has been on a narrower class of complex networks, namely citation networks, where the effects of time on the probability that a paper or a patent will be cited are substantially studied and modeled. The time effect in these methods is also aptly called aging to describe the widely-used model in which A k (t) or η i (t) gradually decrease as the time t increases [13][14][15] . For the estimation of A k with aging, various methods have been proposed [16][17][18] . All of them assume that η i = 1 for all i. For estimating η i with aging, some notable methods 19,20 are provided in the context of citation networks. Note again that the PA effect in these methods is assumed to be linear.
Lastly, generalizations of the ER random network model have long been proposed to model static networks. Since static networks are without growth, PA does not enter the picture, and the mechanism driving the birth of new edges is node fitness. For example, in the β -model 21 , or p 1 -model as it was originally called 22 , the probability of an edge is proportional to the product of the fitness of its two end nodes. This model is closely related to the well-known Bradley-Terry model 23 , which is often used to model pair comparisons. Statistical aspects of these models, including estimation methods and asymptotic properties, have been studied extensively 21,[24][25][26][27] . From another related direction, asymptotic properties of some important statistics, such as the maximum degree K, of the BA model have also been researched rigorously 28,29 . All these works might be important references when we want to investigate asymptotic properties of the PAFit method. Figure S8. Degree growth curves in Fig. 6 with time as horizontal axis. The dashed lines are theoretical growth curves of a generic node with true fitness η = 8, 4, 2, 1, 0.5 and 0.25, based on the GT model. These curves are added as visual guides, and are calculated using the procedure described in Supplementary Information Section S1.6. Nodes with high fitness can still be seen to have dominating growth curves. Using this figure, we can compare the growth rate of curves at the same time-step. Growth rates of curves at two different time-steps can also be compared if we use the information from µ(t), the normalized number of new edges. a: same curves as in Fig. 6a (200 randomly chosen curves from nodes whoseη < 1). b: same curves as in Fig. 6b (200 randomly chosen curves from nodes whose 1 ≤η < 2). c: same curves as in Fig. 6c (200 randomly chosen curves from nodes whoseη ≥ 2).
S2.2 The undirected GT model
For an undirected network, the GT model defines the probability π i, j (t) of a new edge e i, j as follows.
for i = j, and with k i (t) and k j (t) are degrees of nodes v i and v j at time-step t.
S2.3 Derivation of the log-likelihood function
Suppose that we observe the sequence {G t } T t=0 of networks. Let K and N be the maximum degree and the final number of nodes in a GT model network, respectively. Let A = [A 0 A 1 · · · A K−1 ] and η = [η 1 η 2 · · · η N ] be the parameter vectors we want to estimate.
The likelihood of the whole dataset can be built up sequentially from the likelihood of data at each time-step. For the initial graph G 0 , we assume that its distribution is governed by some parameter vector θ * that does not involve A and η. For example, if G 0 is an Erdös-Rényi random graph in which the numbers of nodes and edges both follow a Poisson distribution with mean 1, then θ * is the vector [1 1]. Conditioning on G t−1 (t ≥ 1), the probability P(G t |G t−1 ) is the product of two terms: P (m(t), n(t)|G t−1 , θ (t)) and P (G t |G t−1 , m(t), n(t), A, η). The first term is the probability of the numbers of new edges and new nodes given G t−1 , which is assumed to be governed by a parameter vector θ (t) that does not involve A and η. The vector θ (t) can be the mean parameters of Poisson distributions, for example. The second term is the probability of how the new edges and new nodes form G t given G t−1 , m(t) and n(t).
Since θ * and θ (t) do not involve A and η by assumption, we can ignore all but the first term on the right hand side of Eq. (S5) in deriving the MLE of A and η. We denote this term by l (A, η), which means the log-likelihood of the data with respect to A and η. . This µ(t), which can be intuitively viewed as the amount of new data available at each time-step, is actually quite stable in the region around time-step 600. d: Autocorrelation function of n(t). There is no periodicity here. e: Autocorrelation function of m(t). There is a clear weekly period. f: Autocorrelation function of µ(t). There is also a clear weekly period. Thus the periodicity of µ(t) is caused by the periodicity of m(t), which in turn is caused by the tendency of m(t) to increase toward the middle of the week and to decrease on weekends.
At the onset of time-step t, denote z i (t) be the number of new edges that connect to node v i . First consider the directed GT model. Although the directed GT model defined by Eq. (2) does not completely determine G t , it completely determines the in-degree statistics, which are enough for the estimation of A k and η i . So we abuse the notation a bit and write P (G t |G t−1 , m(t), n(t), A, η) for the probability of the in-degree statistics in G t given the conditional. Now having defined the notation, the term P (G t |G t−1 , m(t), n(t), A, η) is then a multinomial distribution probability. This comes from the observation that given m(t), the quantities z 1 (t), z 2 (t), . . ., z N (t) follow a multinomial distribution with parameters π 1 (t), π 2 (t), . . ., π N (t), where π i (t), the probability that a newly added edge at time t connects to node v i , is Here we use two conventions: if node v j does not exist in the network at time t, then k j (t) = −1 and A −1 = 0. Note that both A k and η i are only identifiable up to a multiplicative constant, as can be seen from Eq. (S6). For the formal treatment in this section, we assume that A 0 = 1 and η 1 = 1. In practice, one can normalize A k and η i separately as one deems fit. We can write down the log-likelihood function: with C being a constant that depends neither on A or η. We note about the concavity of the log-likelihood function. In general, l (A, η) is not jointly concave in A and η. But using the same calculation as in Pham et al. 2 , we can show that for any fixed value A * of A, l(A * , η) is concave in η. Similarly, for any fixed value η * of η, we can show the concavity of l(A, η * ).
In the undirected GT model, the probability of an edge e i, j given by Eqs. (S3) and (S4) can be transformed as follows.
where I is the indicator function and π i (t) is defined in Eq. (S6).
For the case i = j, by viewing an undirected edge e i, j as two directed edges connect to v i and v j , we can see that the log-likelihood function in Eq. (S7) correctly captures the log-likelihood of e i, j , up to an additive constant of log 2. For the case i = j, since we interpret a loop as one directed edge, we miss an additional term of log π i (t) in the log-likelihood function. Denote l undirect (A, η) as the log-likelihood of the undirected GT model, and ζ i (t) as the number of self-loops of node v i at time t. Recall that l (A, η) is the log-likelihood of the converted directed network under the directed GT model. Then we have l (A, η) is exactly the log-likelihood of the undirected network, and so the algorithms described in the next section can be applied without any modifications.
S2.4 Algorithms for maximizing the objective function
Here we describe an MM algorithm for maximizing the objective function h(A, η) in Eq. (3). The strategy here is the same as what can be found in Pham et al. 2 for the case of estimating A k in isolation. First we find an MM algorithm for maximizing the log-likelihood function (Eq. (4)). The algorithm for maximizing h(A, η) is then based on this algorithm. Solving the likelihood equation ∂ l/∂ A = 0 and ∂ l/∂ η = 0, we obtain for i from 2 to N. (S10) Since A k and η i appear in both sides of Eqs. (S9) and (S10), an explicit solution for A and η is difficult to obtain. In order to maximize Eq. (S7), we start from some initial value for A and η at step q = 0 and then iteratively update: and for i from 2 to N, (S12) until some convergence condition is met. The running time of each iteration depends on the number of η i and A k we have to estimate. Recall that we often perform binning, in which we set A k = ω i for all k in the i-th bin. All algorithms described in this section remain valid with A k 's replaced by ω i 's. Assuming that the number of bins is B, the running time of each iteration is O(T N + T B). The number of iterations needed depends on the convergence condition and the particular dataset.
In order to show that the algorithm consisting of Eqs. (S11) and (S12) can indeed increase the log-likelihood function l(A, η) at each iteration, we first find a minorize function Q (A, η) of l at the point (A (q) , η (q) ). Such a function Q, by definition 30 , satisfies Q ≤ l at all points and Q(A (q) , η (q) ) = l(A (q) , η (q) ). Consider the function One can check that Q defined by Eq. (S13) is a minorize function of l. Next, it can be easily verified that Eq. (S11) is in fact the solution of ∂ Q/∂ A = 0, thus Q (A, η) ≤ Q A (q+1) , η . Finally, we have l(A (q) , η (q) ) = Q(A (q) , η (q) ) ≤ Q A (q+1) , η (q) ≤ l A (q+1) , η (q) , which shows that Eq. (S11) indeed increases the log-likelihood. In the same way we can show that Eq. (S12) further increases l from l A (q+1) , η (q) .
13/16
Note that, the current algorithm (Eqs. (S11) and (S12)) first calculates A (q+1) , and then use A (q+1) to calculate η (q+1) . It is possible to calculate A (q+1) and η (q+1) in parallel by modifying the current algorithm. Define then Q is a minorize function of l at point (A (q) , η (q) ). The key point here is that the two sets of equations ∂ Q /∂ A = 0 and ∂ Q /∂ η = 0 are separable, so we can calculate A (q+1) and η (q+1) in parallel by using Q instead of Q. Nevertheless, we prefer the current algorithm in Eqs. (S11) and (S12), since cyclic updating of A and η is potentially faster than updating in parallel 30 . Furthermore, the update formulas in Eqs. (S11) and (S12) are also conceptually simpler. Next we derive the update equation for η i for the objective function in Eq. (3). The new formula for η (q+1) i is similar to Eq. (S12), but with the discount from s added: , except when s < 1, the estimated fitness of a node whose ∑ T t=1 z j (t) = 0 is simply 0. Finally, we derive the update for A k when the regularization term in Eq. (5) is added. Although the same derivation can be found in Ref. 2, we also record it here for completeness. A (q+1) k is the solution of a univariate equation which can be derived as follows. First we need to find a minorize function of Eq. (5). The strategy is the same as what can be found in Ref. 30. For a concave function g(x), we have the following inequality that comes directly from the definition of a concave function. (S14) We can easily verify that the right hand side of Eq. (S14) is a minorize function of Eq. (5). Combining this function with the minorize function of the log-likelihood (see Eq. (S13)), we get a minorize function Q A of h(A, η) at iteration q. The main point of deriving Eq. (S14) is that by using Eq. (S14), at each iteration we can turn the K + 1-variable maximization problem ∂ Q A /∂ A = 0 into K + 1 problems ∂ Q A /∂ A k = 0 in which each is univariate and can be easily solved in parallel. | 7,358.4 | 2016-09-07T00:00:00.000 | [
"Computer Science"
] |
Mycobacterium tuberculosis Complex in Remains of 18th–19th Century Slaves, Brazil
To the Editor: Nineteenth century Rio de Janeiro, Brazil, was marked by increased illness and deaths from tuberculosis (TB). By the twentieth century, it was still believed that most TB cases in the Americas originated from Europe; the “virgin soil” hypothesis for African (1) and Amerindian populations was accepted. However, modern and archeological DNA evidence confirms the wide distribution of Mycobacterium tuberculosis complex (MTC) and TB in the Old and New Worlds.
Rio de Janeiro was a main entry port for millions of Africans captured for the slave trade. Pretos Novos (New Blacks) Cemetery (PNC; 1769–1830) was created in Rio de Janeiro as a burial ground for the many slaves who died at market. Comingled bone fragments (≈5,000) from ≈30 persons were recovered at PNC; most bones were broken and had been exposed to fire (2,3). Bioanthropological analysis determined most of the bones were from men 18–25 years of age (2); none had lesion consistent with TB.
Femurs from 16 persons were surveyed for M. tuberculosis ancient DNA (aDNA). The thick shafts of femur offered a preserved condition for molecular analysis, and the bones could be individualized, avoiding duplication of samples. Paleogenetic investigation guidelines were followed. Sample preparation, aDNA extraction, and PCR were performed at the Paleogenetics Unit (Oswaldo Cruz Foundation, Rio de Janeiro) an isolated environment exclusively dedicated to aDNA research.
Before removal of the bone surface, samples were decontaminated by ultraviolet light (15 min/all sides), frozen in liquid nitrogen, and subjected to manual trituration. Bone powder (≈200 mg) was then incubated with digestion buffer (56°C, 48–72 h) as described (4). aDNA hybridizations with MTC probes were conducted as described (4). By using 2 segments of mitochondrial DNA (mtDNA) hypervariable segment I (HVS-I) target, we determined the ancestry of the humans from whom the bones were derived (4). To control for recent contamination, we compared the HVS-I sequences with those in GenBank and also in a database for the laboratory staff.
Using the hybridization assay with insertion sequence (IS) 6110 target, we detected MTC aDNA in bones from 4/16 persons (samples PN1, PN8, PN13, PN15); 3 of these samples (PN1, PN8, PN13) were also positive for IS1081 target, confirming MTC infection (Table). HVS-I target was retrieved from 3 samples (PN6, PN14, PN15), which enabled determination of the human mtDNA haplotypes (L3e2, L3d1, L1c2, respectively) (Table). The haplotypes showed that the 3 persons were of African descent (GenBank accession nos. {"type":"entrez-nucleotide","attrs":{"text":"JQ639893","term_id":"408667348"}}JQ639893–Q639895). Our findings are consistent with those from studies based on current African populations, which show that haplotype L1c is restricted to central Africa (5) and L3d and L3e are most frequently found in western and central Africa, respectively (6).
Table
Results of genetic analyses of Mycobacterium tuberculosis complex hybridization and human mtDNA haplotypes from human bone samples collected from Pretos Novos Cemetery, Rio de Janeiro, Brazil*
Historic data (3) showed that 95% of persons buried in PNC were New Blacks, meaning they were born in Africa and died just after arriving in America. Our mtDNA results confirm historic and genetic records that indicate a large percentage of persons brought to Brazil as slaves originated from western–central and western Africa. This makes the PNC samples unique for the paleogenetic purpose of this investigation.
The endemicity of TB in Rio de Janeiro during the colonial period was confirmed by Jaeger and colleagues, who demonstrated MTC infection in 56.6% of persons with European ancestry buried at Nossa Senhora do Carmo Church (4). The difference in the frequency of MTC found in the remains of slaves buried in PNC and of Europeans buried at Nossa Senhora do Carmo Church may be explained by the types of samples analyzed and the epidemiologic conditions of both groups. The cremation of corpses at PNC may also partly explain the difference. The finding of MTC aDNA in the remains of 25% of persons buried at PNC could be an underestimation of infection.
Our finding that some of the slaves buried in PNC had TB infection when they arrived in Brazil is in agreement with previous findings of the differential distribution of TB and with a tuberculin survey on the African continent, supporting the hypothesis of native African TB (7,8). Therefore, the hypothesis of Africa as virgin soil for TB (1,9) cannot be easily supported. The incidence of TB among the slaves/Blacks in Rio de Janeiro was less than expected given their social and sanitary conditions (10), especially in a TB-endemic situation (4). Previous exposure to MTC might explain their apparent relative resistance.
Other evidence showing African contact with Europeans before the sixteenth century, supports the existence of TB in Africa (8), and TB was prevalent in urbanized centers along coastal areas of western Africa (7,8). Although some of those cases were probably the result of European contact, it is not possible to exclude that some were caused by TB native to Africa. We can affirm that persons buried in PNC, who were transported to Brazil as slaves from Africa, brought TB infection with them; whether the infection was caused by European TB endemic to Africa or by TB native to Africa is not known.
To the Editor: Nineteenth century Rio de Janeiro, Brazil, was marked by increased illness and deaths from tuberculosis (TB). By the twentieth century, it was still believed that most TB cases in the Americas originated from Europe; the "virgin soil" hypothesis for African (1) and Amerindian populations was accepted. However, modern and archeological DNA evidence confirms the wide distribution of Mycobacterium tuberculosis complex (MTC) and TB in the Old and New Worlds.
Rio de Janeiro was a main entry port for millions of Africans captured for the slave trade. Pretos Novos (New Blacks) Cemetery (PNC; 1769-1830) was created in Rio de Janeiro as a burial ground for the many slaves who died at market. Comingled bone LETTERS fragments (≈5,000) from ≈30 persons were recovered at PNC; most bones were broken and had been exposed to fire (2,3). Bioanthropological analysis determined most of the bones were from men 18-25 years of age (2); none had lesions consistent with TB.
Femurs from 16 persons were surveyed for M. tuberculosis ancient DNA (aDNA). The thick shafts of femur offered a preserved condition for molecular analysis, and the bones could be individualized, avoiding duplication of samples. Paleogenetic investigation guidelines were followed. Sample preparation, aDNA extraction, and PCR were performed at the Paleogenetics Unit (Oswaldo Cruz Foundation, Rio de Janeiro) an isolated environment exclusively dedicated to aDNA research.
Before removal of the bone surface, samples were decontaminated by ultraviolet light (15 min/all sides), frozen in liquid nitrogen, and subjected to manual trituration. Bone powder (≈200 mg) was then incubated with digestion buffer (56°C, 48-72 h) as described (4). aDNA hybridizations with MTC probes were conducted as described (4). By using 2 segments of mitochondrial DNA (mtDNA) hypervariable segment I (HVS-I) target, we determined the ancestry of the humans from whom the bones were derived (4). To control for recent contamination, we compared the HVS-I sequences with those in GenBank and also in a database for the laboratory staff.
Using the hybridization assay with insertion sequence (IS) 6110 target, we detected MTC aDNA in bones from 4/16 persons (samples PN1, PN8, PN13, PN15); 3 of these samples (PN1, PN8, PN13) were also positive for IS1081 target, confirming MTC infection (Table). HVS-I target was retrieved from 3 samples (PN6, PN14, PN15), which enabled determination of the human mtDNA haplotypes (L3e2, L3d1, L1c2, respectively) (Table). The haplotypes showed that the 3 persons were of African descent (GenBank accession nos. JQ639893-Q639895). Our findings are consistent with those from studies based on current African populations, which show that haplotype L1c is restricted to central Africa (5) and L3d and L3e are most frequently found in western and central Africa, respectively (6).
Historic data (3) showed that 95% of persons buried in PNC were New Blacks, meaning they were born in Africa and died just after arriving in America. Our mtDNA results confirm historic and genetic records that indicate a large percentage of persons brought to Brazil as slaves originated from western-central and western Africa. This makes the PNC samples unique for the paleogenetic purpose of this investigation.
The endemicity of TB in Rio de Janeiro during the colonial period was confirmed by Jaeger and colleagues, who demonstrated MTC infection in 56.6% of persons with European ancestry buried at Nossa Senhora do Carmo Church (4). The difference in the frequency of MTC found in the remains of slaves buried in PNC and of Europeans buried at Nossa Senhora do Carmo Church may be explained by the types of samples analyzed and the epidemiologic conditions of both groups. The cremation of corpses at PNC may also partly explain the difference. The finding of MTC aDNA in the remains of 25% of persons buried at PNC could be an underestimation of infection.
Our finding that some of the slaves buried in PNC had TB infection when they arrived in Brazil is in agreement with previous findings of the differential distribution of TB and with a tuberculin survey on the African continent, supporting the hypothesis of native African TB (7,8). Therefore, the hypothesis of Africa as virgin soil for TB (1,9) cannot be easily supported. The incidence of TB among the slaves/ Blacks in Rio de Janeiro was less than expected given their social and sanitary conditions (10), especially in a TB-endemic situation (4). Previous exposure to MTC might explain their apparent relative resistance. Other evidence showing African contact with Europeans before the sixteenth century, supports the existence of TB in Africa (8), and TB was prevalent in urbanized centers along coastal areas of western Africa (7,8). Although some of those cases were probably the result of European contact, it is not possible to exclude that some were caused by TB native to Africa. We can affirm that persons buried in PNC, who were transported to Brazil as slaves from Africa, brought TB infection with them; whether the infection was caused by European TB endemic to Africa or by TB native to Africa is not known. | 2,350.6 | 2013-05-01T00:00:00.000 | [
"Biology"
] |
3D Numerical Modeling of the Summit Lake Lava Flow, Yellowstone, USA
Volcanic eruptions belong to the extreme events that change the Earth’s landscape and affect global climate and environment. Although special attention is given to super-eruptions, the non-explosive rhyolitic (highly viscous) eruptions and large lava f lows are no less important. In this paper, we study an ancient lava f low with a volume of ~50 km3 in the Summit Lake region, Yellowstone, which is one of the best studied large intraplate igneous provinces. We develop three-dimensional (3D) numerical models of isothermal lava f low to analyze the influence of the underlying surface and lava flow viscosity on the advancement and duration of the flow. The modeled dynamics of flow propagation fairly well agrees with the measured values provided that the average angle of inclination of the underlying surface slightly differs from the present-day value (by ~1.3) presumably due to the pressure change in the magma chamber during the eruption. With the increase in lava viscosity, the f low slows down and its thickness increases leading to a change in the f low morphology.
INTRODUCTION
Highly viscous rhyolitic lavas form flows varying in thickness from tens to hundreds of meters and typically having rather short, a few km, length. Rhyolitic flows are frequently associated with the continental hotspots, that is, the rising jets of the hot mantle rocks (or plumes). The Yellowstone hotspot in the U.S., which is currently located beneath the state of Wyoming, is the most widely known example. Seismic tomography reveals a low velocity channel beneath the Yellowstone National Park, which is interpreted as a mantle plume (Sigloch et al., 2008). This hotspot is most likely to be responsible for the formation of melt feeding the super-eruptions and large lava flows, and, thus, for the development of a volcanic province stretching over several states west of Wyoming as a result of the motion of the North American plate above the hotspot during the last 17 million years e.g., (Morgan, 1971;Smith et al., 2009;Camp et al., 2017).
The Yellowstone's large rhyolite flows in the geological past are poorly known objects. Using the analytical solution of the problem of the viscous incompressible fluid flow on a flat surface (Huppert, 1982), Loewen et al. (2017) have shown that the emplacement of rhyolite flow in the Summit Lake region (Fig. 1a) as a resulted of lava eruption 124 ka ago occurred over ~2-5 years at temperatures of 800C and high magma discharge rates above 100 m 3 s -1 . These high discharge rates are, however, concomitant with low magma ascent rates (below 1 cm s -1 ) because lava erupted through a fissure with a length of about 6 km long and a wide cross-section area which allowed the eruption to remain effusive (non-explosive).
Although the analytical solution allowed for estimating several important physical parameters of lava flows in the Summit Lake region of Yellowstone (Loewen et al., 2017), it is of particular interest to determine the influence of the viscosity of lava flows on the morphology and duration of lava emplacement. Despite the fact that high viscosity of the rhyolite lava flows typically prevents them from spreading far away from the vent, in some cases lava can propagate a distance up to a few km if the volume of the erupting magma and the thickness of the lava flow are sufficiently large or if the magma has higher temperature which reduces its viscosity. In this case, lava flow is IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 57 No. 2 2021 TSEPELEV et al. cooling slowly, its viscosity does not increase and, therefore, the flow can advance a great distance from the vent. The numerical assessments of the rate of the heat loss from conductive cooling of the large rhyolite lavas have shown that the cooling of the lava flow with a thickness of 100-300 m is very slow and is further retarded by the formation of a carapace (a crust) and the release of latent crystallization heat (Manley, 1992). The models show that thick lava flows can remain active for several decades. At the same time, as the lava flow cools, the yield stress of its cooled crust will affect its dynamics (Balmforth and Craster, 2000) and lead to more complex lava flow morphologies (Fink andGriffiths, 1998). However, Loewen et al. (2017) have shown that a large-volume rhyolitic lava flow at the Summit Lake does not feature complex morphological structures, and hence, the lava flow can be modeled by a gravity-driven isothermal viscous fluid flow.
The lava flow in the Summit Lake region of Yellowstone has been selected as a case study because of its significant volume (about 50 km 3 ) and thickness (100-250 m). At a relatively short duration of the lava extrusion, the lava flow cools insignificantly forming a thin crust on the upper surface of the flow. Although in the case of nonlinear heat exchange (convective and radiative heat transfer) the crust becomes thicker than in the case of pure convective heat transfer at the interface with air (Tsepelev et al., 2019), this thickening of the crust does not substantially affect the advancement of the thick lava flow. Therefore, as the first approximation, the flow can be assumed isothermal. In this paper, we consider a three-dimensional (3D) model of isothermal lava flow in the Summit Lake region of Yellowstone to analyze the influence of the surface topography and the lava viscosity on lava flow advancement and the duration of its emplacement.
STATEMENT OF THE PROBLEM
We consider a 3D numerical model of the f low of a two-phase incompressible immiscible viscous f luid which approximates lava extrusion (one phase) from a volcanic vent into the air (another phase) and the subsequent lava f low. The model domain is limited from below by the topography of the studied terrane, where l 1 and l 2 are horizontal dimensions and l 3 is the height of the model area. In this domain, we study the flow of a viscous Newtonian inhomogeneous incompressible fluid in the field of gravity. In Cartesian coordinates, this flow is described by the non-stationary Navier-Stokes equation (Ismail-Zadeh and Tackley, 2010;Tsepelev et al., 2019) with the initial condition : (1) and continuity equation (2) where is the velocity vector, is the vector of external mass forces, g is the gravitational acceleration, p is the pressure, is the density, is the viscosity, is the spatial variable, and t is the time. The advection of a two-phase fluid with an initial condition is described by the equation: ( 3) where determines the volume fraction of the fluid at point at time t. At the initial time, the model domain is filled with air and therefore The density and viscosity are then described by the following equations: (4) where: and are the density and viscosity of air, are the lava density and viscosity. Although thermal effects have an impact on the formation of lava crusts and on lava flow, it was shown that at high magma discharge rate, the crust is fairly thin compared to the lava flow thickness (~3-5%) (Tsepelev et al., 2019). The lava crust cracks, drifts with lava flow driven by gravity until its thickness is small, and does not significantly affect the advance of the flow (Tsepelev et al., 2016). This model considers lava flow due to gravity without thermal effects.
No slip condition is prescribed at the lower and side boundaries of the model domain. At the part of the lower boundary that contains the vent, it is prescribed that , where is the rate of magma extrusion. At the upper boundary of the model domain, we specify the conditions . The Yellowstone Summit Lake lava flows contribute to the present-day terrain topography of the region. To model the lava flows in the geological past, the present terrain topography should be transformed to account for the thickness of the erupted lavas. Namely, let be the present topography of the studied region; the lava , D = 20 km. Figure 1b illustrates the model topography calculated in this way.
Thus, the lava flow modeling problem is reduced to solving Eqs. (1)-(4) with the above initial and boundary conditions in the model domain . In the numerical modeling, all variables are reduced to the dimensionless form with the time scale , length scale h, and velocity scale .
NUMERICAL METHOD
In the numerical analysis of the model problem, we use the Ansys Fluent software (https://www. ansys.com/products/fluids/ansys-fluent) based on the finite volume method. The model domain is subdivided into hexahedrons that make up finite volumes. Numerical codes use a multiphase unsteady VOF model, and the solver uses a timeimplicit integration scheme for equations (1)-(3) to jointly determine the velocity and pressure fields and the volume fraction of fluid. The pressure and the Laplacian are approximated by second-order numerical schemes; for the discretization of the convective terms we use monotonic schemes (e.g, Ismail-Zadeh and Tackley, 2010). The pressure-velocity coupling in Eq. (1) is implemented using PRESTO! approximation and the SIMPLE numerical method (Patankar and Spalding, 1972) with relaxation parameters 0.01 and 0.3 for the velocity and pressure, respectively. Due to the nonlinearity of the problem, the time step is selected in the range from 1 to 10 s depending on stability and so that to optimize the rate of convergence of the solution of the system of linear algebraic equations (SLAE) obtained after the discretization of the problem. The SLAE is solved by the multi-grid method (e.g., (Ismail-Zadeh and Tackley, 2010)).
The main difficulty in the numerical modeling of the problem at hand is that the ratio of the lava viscosity to the air viscosity is about 14 orders of magnitude. To perform a stable numerical experiment, we introduced a nonadaptive numerical grid such that in the region of the lava-air boundary, the grid was refined in the vertical direction. This allowed us to reduce the numerical diffusion in the vicinity of this boundary. Also, we selected an implicit scheme for joint integration of the systems of differential equations which allows for stable calculations with a relatively large time step. Although implicit integration schemes do not need the Courant number to be strictly constrained ( where is the velocity magnitude, is the time step, and is the spatial step (Courant et al., 1928)), the large time steps lead to the increase in numerical diffusion at the lava-air boundary and to the physically implausible results; therefore, the time step was chosen sufficiently small. The explicit integration schemes which are much less burdensome for their numerical implementation failed to provide stable calculations even at low Courant numbers. The time step and the relaxation parameter for the velocity were chosen empirically so that to ensure stable computation process.
Highly viscous lava flows are laminar because the Reynolds number is fairly small (<10 -6 ) for the viscosity and density parameters of the lava, characteristic length and flow velocities in the models under study (see Table 1). The air does not affect the dynamics of lava flows because its viscosity and density are substantially lower than those in lava, and the lava-air interface is considered as a free-surface boundary. And, although the Reynolds number in the air is quite large, the Fluent software allows avoiding turbulent currents in the air layer.
RESULTS
It is assumed that magma in the Yellowstone Summit Lake region erupted from the volcanic vent along a 4-km long elliptical fissure (Fig. 1a) located in the model topography along the С-С' profile. Here, we consider three numerical experiments: (1) lava flow along the surface topography reconstructed above, (2) lava flow along an inclined underlying surface, and (3) lava flow with an order of magnitude higher viscosity than in experiment 1. The values of model parameters are presented in Table 1. The lava density ( k g m -3 ) corresponds to the density of rhyolitic rocks with a high silica content (Loewen et al., 2017). Lava viscosity is calculated by the for-2350 l mula (Huppert, 1982) where V is the lava f low volume (~50-55 km 3 ), Q is the lava discharge rate (~2000-6000 m 3 s -1 ), and r is the radius of the front of the lava flow (~10-12 km). In this work, we use two viscosity values ( Pa s and Pa s) which lie within the viscosity range determined for lavas with temperatures between 750 and 850C and water content of about 0.1 wt % (Farquharson et al., 2015;Romine and Whittington, 2015;Loewen et al., 2017). Experiment 1. The evolution of the lava flow during the first 8 months after the beginning of the eruption is illustrated in Fig. 2. Lava moves almost axisymmetrically during up to two months after which the terrain impedes its propagation in the northern and southeastern directions and makes the flow moving southwest and northeast. Eight months later, the region that is presently covered by rhyolitic lava is filled with model lava except for its southernmost and westernmost edges; however, the southeasterly propagation of model lava visible in Fig. 2 starting from the fourth month is not supported by the observations. The lava flow along section B-B' is asymmetric: lava spreads 2 km northeast and more than 22 km southwest from the presumed vent. In the northeast, there is no present topographic high that could restrain lava flow in this direction. Lava viscosity, 5.6 × 10 9 Pa s 5.6 × 10 9 Pa s 5.6 × 10 9 Pa s Air density, 1 kg m -3 Air viscosity, 10 -4 Pa s Considering that the lava flow extent accounts for possible weathering and erosion (Christiansen, 2001), we may assume that either in the past there was an elevation obstructing the northeasterly flow, or the average slope of the underlying surface in the past was slightly different (by ~1.3) from the present. This can be explained by the overall deformation of the Yellowstone caldera due to the change in pressure in the magma chamber during lava outflow, although there is no evidence in support of this assumption in the literature.
Experiment 2.
For testing the hypothesis about the change in the angle of inclination of the underlying surface, we carried out a numerical experiment with gravitational acceleration modified in such a way as to generate a southwesterly flow condition without changing the terrain ( Table 2). The numerical results of experiments 1 and 2 are compared in Fig. 3. In experiment 2, the model lava flow is directed towards the southwest and the present area covered by lava in the south becomes almost completely filled with the model lava over six months (Fig. 3b). However, the model lava extends beyond the present boundary of the lava flow in the west and east which can probably be associated with the inaccurate construction of the model surface topography or with the chosen discharge rate or the duration of the flow. At the same time, lava fairly densely fills the present lava area in the northeast although the lava flow slowly moves in the northwest direction.
Experiment 3. Viscosity influences the lava flow morphology and its advancement. We performed the numerical experiment simulating the lava flow in the case when lava viscosity is an order of magnitude higher than in the previous experiments (Table 1). Figure 4 shows the 3D image of the model lava flow in the cases of experiment 1 (left column, Pa s) and experiment 3 (middle column, Pa s). The spreading patterns of these lava flows are compared in the right column. Figure 5 illustrates the comparison of the model results along three profiles А-А', B-B' and C-C' for experiments 1 and 3. Due to the high viscosity assumed in experiment 3, the flow in 6 months 4 months 2 months the horizontal direction slows down, hence, the thickness of the lava flow increases changing its morphology (Fig. 5).
DISCUSSION AND CONCLUSIONS
The numerical results have shown a good agreement between the measured and modeled surface configuration and thickness of the model lava provided that the average sloping angle of the underlying surface slightly (by ~1.3) differs from the present value. The viscosity in the numerical experiments is within the limits estimated by Loewen et al. (2017) for the lava flows in the Summit Lake of Yellowstone, although the estimates for lava viscosities have uncertainties associated with the uncertainty in the estimates of the volume of the erupted lava.
We note that with a volume of the erupted lava of 50 km 3 and with a model lava discharge rate of 3500 m 3 s -1 (magma extrusion rate ~2.7 m s -1 ) it would take about 5.5 months of continuous eruption through the model fissure. However, the maximum width of the model fissure is fairly large (400 m) and unrealistic. Therefore, the numerical results need to be corrected in terms of time through changing the fissure's width. With the maximum fissure's width decreased to 40 m and the same extrusion rate, it will take ~4.6 years for the eruption of the same amount of lava. This is consistent with the estimates of lava flow duration in the Summit Lake region. Overall, the 3D lava flow modeling has confirmed the estimates that were obtained using the analytical solution for the thin layer approximation model (Loewen et al., 2017) and allowed a more detailed study of the dynamics and morphology of the Summit Lake lava flows depending on flow direction and viscosity.
ACKNOWLEDGMENTS
We are grateful to I.N. Bindeman (University of Oregon, USA) for providing digital elevation data for Summit Lake and for discussing the results. We are also grateful to V.O. Mikhailov, V.B. Smirnov, and the anonymous reviewer for their constructive comments.
FUNDING
The work was supported by the Russian Science Foundation (project no. 19-17-00027 to OM), Russian Foundation for Basic Research (project no. 20-51-12002 to IT), and the Deutsche Forschungsgemeinschaft, project DFG IS203/14-1 to AIZ). Numerical experiments were carried out on the Uran computing cluster (Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg).
OPEN ACCESS
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"Geology"
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High temperature singlet-based magnetism from Hund’s rule correlations
Uranium compounds can manifest a wide range of fascinating many-body phenomena, and are often thought to be poised at a crossover between localized and itinerant regimes for 5f electrons. The antiferromagnetic dipnictide USb2 has been of recent interest due to the discovery of rich proximate phase diagrams and unusual quantum coherence phenomena. Here, linear-dichroic X-ray absorption and elastic neutron scattering are used to characterize electronic symmetries on uranium in USb2 and isostructural UBi2. Of these two materials, only USb2 is found to enable strong Hund’s rule alignment of local magnetic degrees of freedom, and to undergo distinctive changes in local atomic multiplet symmetry across the magnetic phase transition. Theoretical analysis reveals that these and other anomalous properties of the material may be understood by attributing it as the first known high temperature realization of a singlet ground state magnet, in which magnetism occurs through a process that resembles exciton condensation.
U ranium compounds can feature a fascinating interplay of strongly correlated and itinerant electronic physics, setting the stage for emergent phenomena such as quantum criticality, heavy fermion superconductivity, and elusive hidden order states [1][2][3][4][5][6][7][8][9][10][11][12][13] . The isostructural uranium dipnictides UX 2 (X = As, Sb, Bi) present a compositional series in which high near-neighbor uranium-uranium coordination supports robust planar antiferromagnetism (T N~2 00K, see Fig. 1a, b) 7,8 . Of these, the USb 2 variant has received close attention due to the discovery of several unexplained low temperature quantum coherence phenomena at T < 100K 7,[9][10][11] , and a remarkably rich phase diagram incorporating quantum critical and tricritical points as a function of pressure and magnetic field 12,13 . However, the effective valence state of uranium and the resulting crystal field state basis defining the f-electron component of local moment and Kondo physics have not been identified.
Here, X-ray absorption (XAS) at the uranium O-edge and numerical modeling are used to evaluate the low energy atomic multiplet physics of USb 2 and UBi 2 , revealing only USb 2 to have significant Hund's rule correlations. These investigations yield the prediction that USb 2 must be a uniquely robust realization of a singlet-ground-state magnet, in which magnetic moments appear via the occupation of low-energy excited states on a non-magnetic background (Fig. 1c). The evolution of crystal field symmetries and magnetic ordered moment across the antiferromagnetic phase transition is measured with linear dichroism (XLD) and elastic neutron scattering, confirming that the magnetic transition in USb 2 occurs through an exotic process that resembles exciton condensation.
Results
Electron configuration of uranium in UBi 2 and USb 2 . Unlike the case with stronger ligands such as oxygen and chlorine, there is no unambiguously favored effective valence picture for uranium pnictides. Density functional theory suggests that the charge and spin density on uranium are significantly modified by itinerancy effects 14,15 (see also Supplementary Note 1), as we will discuss in the analysis below, making it difficult to address this question from secondary characteristics such as the local or ordered moment. However, analyses in 2014-2016 have shown that resonant fine structure at the O-edge (5d→5 f transition) provides a distinctive fingerprint for identifying the nominal valence state and electronic multiplet symmetry on uranium [16][17][18][19] . X-ray absorption spectra (XAS) of UBi 2 and USb 2 were measured by the total electron yield (TEY) method, revealing curves that are superficially similar but quantitatively quite different (Fig. 2a). Both curves have prominent resonance features at hυ~100 and 113 eV that are easily recognized as the 'R1' and 'R2' resonances split by the G-series Slater integrals 16 . Within models, these resonances are narrowest and most distinct for 5 f 0 systems, and merge as 5f electron number increases, becoming difficult to distinguish beyond 5f 2 (see Fig. 2a (bottom) simulations). The USb 2 sample shows absorption features that closely match the absorption curve of URu 2 Si 2 16 , and are associated with the J = 4 ground states of a 5f 2 multiplet. This correspondence can be drawn with little ambiguity by noting a one-to-one feature correspondence with the fine structure present in a second derivative analysis (SDI, see Fig. 2b).
The R1 and R2 resonances of UBi 2 are more broadly separated than in USb 2 , and the lower energy R1 feature of UBi 2 is missing the prominent leading edge peak at hυ~98.2 eV (peak-B), which is a characteristic feature of 5f 2 uranium 16,17 . The UBi 2 spectrum shows relatively little intensity between R1 and R2, and the higher energy R2 resonance has a much sharper intensity onset. All of these features are closely consistent with expectations for a 5f 1 multiplet, and the SDI curve in Fig. 2b reveals that the R1 fine structure of UBi 2 is a one-to-one match for the 5f 1 multiplet. We note that a close analysis is not performed for R2 as it is influenced by strong Fano interference (see Supplementary The U(Sb/Bi) 2 crystal structure is shown with spins indicating the antiferromagnetic structure in UBi 2 (T N~1 80 K) and USb 2 (T N~2 03 K). The uranium atoms have 9-fold ligand coordination with base (S1), middle (S2), and pinnacle (S3) ligand layers as labeled in a with respect to the central uranium atom. c, d In-plane ferromagnetic nucleation regions are circled in c doublet and d singlet ground state magnetic systems. The singlet crystal field ground state has no local moment, causing much of the lattice to have little or no magnetic polarization Note 2). The lack of prominent 5f 2 multiplet features suggests that the 5f 1 multiplet state is quite pure, and the measurement penetration depth of several nanometers (see Methods) makes it unlikely that this distinction between UHV-cleaved UBi 2 and USb 2 originates from surface effects. However, the picture for UBi 2 is complicated by a very rough cleaved surface, which our STM measurements (see Supplementary Note 3) find to incorporate at least two non-parallel cleavage planes. Surface oxidation in similar compounds is generally associated with the formation of UO 2 (5f 2 ) and does not directly explain the observation of a 5f 1 state. We note that even with a clean attribution of multiplet symmetries, it is not at all clear how different the f-orbital occupancy will be for these materials, or what magnetic moment should be expected when the single-site multiplet picture is modified by band-structure-like itinerancy 10,11 (see also Supplementary Note 1). The effective multiplet states identified by shallow-core-level spectroscopy represent the coherent multiplet (or angular moment) state on the scattering site and its surrounding ligands, but are relatively insensitive to the degree of charge transfer from the ligands 20 .
Nonetheless, the 5f 1 and 5f 2 nominal valence scenarios have very different physical implications. A 5f 1 nominal valence state does not incorporate multi-electron Hund's rule physics 21,22 (same-site multi-electron spin alignment), and must be magnetically polarizable with non-zero pseudospin in the paramagnetic state due to Kramer's degeneracy (pseudospin ½ for the UBi 2 crystal structure). By contrast in the 5f 2 case one expects to have a Hund's metal with strong alignment of the 2-electron moment (see dynamical mean field theory (DFT + DMFT) simulation below), and the relatively low symmetry of the 9-fold ligand coordination around uranium strongly favors a non-magnetic singlet crystal electric field (CEF) ground state with Γ 1 symmetry, gapped from other CEF states by roughly 1/3 the total spread of state energies in the CEF basis (see Table 1). The Γ 1 state contains equal components of diametrically opposed largemoment |m J = + 4 > and |m J = -4 > states, and is poised with no net moment by the combination of spin-orbit and CEF The energies in millielectron volts of low-lying 5f 2 multiplet symmetries are shown for four crystal field parameter sets. Parameters in the first column (CEF(1)) follow the relative energy ordering suggested in ref. 8 . (S1 < S2~S3, as the S1 bond is relatively short), and are used for all simulations. The state symmetries are summarized in Supplementary Note 5, which includes an energy level diagram. ΔCEF is defined as the gap between the highest energy J = 4 CEF state and the ground state. CEF parameters listed as (S1/S2/S3) for the sites defined in Fig. 1a. These values have units of millielectron volts, and define delta function potentials for Sb atoms in the (S1) base, (S2) middle, and (S3) c-axis pinnacle of the Sb 9 cage around each uranium atom. Specifically, the energy parameters indicate the energy added by a single Sb atom to an m j = 0 f-orbital oriented along the U-Sb axis. Source data are provided as a Source Data file interactions. This unusual scenario in which magnetic phenomena emerge in spite of a non-magnetic singlet ground state has been considered in the context of mean-field models [23][24][25][26] , and appears to be realized at quite low temperatures (typically T <~10 K) in a handful of rare earth compounds. The resulting magnetic phases are achieved by partially occupying low-lying magnetic excited states, and have been characterized as spin exciton condensates 23 .
Multiplet symmetry from XLD versus temperature. To address the role of low-lying spin excitations, it is useful to investigate the interplay between magnetism and the occupied multiplet symmetries by measuring the polarization-resolved XAS spectrum as a function of temperature beneath the magnetic transition. Measurements were performed with linear polarization set to horizontal (LH, near z-axis) and vertical (LV, a-b plane) configurations. In the case of UBi 2 , the XAS spectrum shows little change as a function of temperature from 15 to 210K (Fig. 3a, b), and temperature dependence in the dichroic difference (XLD, Fig. 3b) between these linear polarizations is inconclusive, being dominated by noise from the data normalization process (see Methods and Supplementary Note 4). This lack of temperature dependent XLD is consistent with conventional magnetism from a doublet ground state. The XLD matrix elements do not distinguish between the up-and down-moment states of a Kramers doublet, and so strong XLD is only expected if the magnetic phase incorporates higher energy multiplet symmetries associated with excitations in the paramagnetic state. By contrast, the temperature dependence of USb 2 shows a large monotonic progression (Fig. 3c, d), suggesting that the atomic symmetry changes significantly in the magnetic phase. The primary absorption peak (hυ~98.2 eV, peak-B) is more pronounced under the LH-polarization at low-temperature, and gradually flattens as temperature increases. The LV polarized spectrum shows the opposite trend, with a sharper peak-B feature visible at high temperature, and a less leading edge intensity at low temperature. This contrasting trend is visible in the temperature dependent XLD in Fig. 3d, as is a monotonic progression with the opposite sign at peak-C (hυ~100.8 eV).
Augmenting the atomic multiplet model for 5f 2 uranium with mean-field magnetic exchange (AM + MF) aligned to match the T N~2 03K phase transition (see Methods) results in the temperature dependent XAS trends shown in Fig. 3e. The temperature dependent changes in peak-B and peak-C in each linear dichroic curve match the sign of the trends seen in the experimental data, but occur with roughly twice the amplitude, as can be seen in The dichroic difference (LH-LV) is shown with temperature distinguished by a rainbow color order (15K (purple), 40K (blue), 80K (green), 120K (yellow), and 210K (red)). c, d Analogous spectra are shown for USb 2 . Arrows in d show the monotonic trend direction on the peak-B and peak-C resonances as temperature increases. e, f Simulations for 5f 2 with mean-field magnetic interactions. g A summary of the linear dichroic difference on the primary XAS resonances of USb 2 , as a percentage of total XAS intensity at the indicated resonance energy (hυ = 98.2 eV for peak-B, and hυ = 100.8 eV for peak-C). Error bars represent a rough upper bound on the error introduced by curve normalization. h The linear dichroic difference trends from the mean field model. Source data are provided as a Source Data file. Shading in g, h indicates the onset of a magnetic ordered moment avoidedsee Methods). However, it is difficult to compensate for a factor of two, and the discrepancy is likely to represent a fundamental limitation of the non-itinerant mean field atomic multiplet model. Indeed, when the competition between local moment physics and electronic itinerancy is evaluated for USb 2 with dynamical mean field theory (DFT + DMFT), we find that the uranium site shows a non-negligible~25% admixture of 5f 1 and 5f 3 configurations (Fig. 4a).
Magnetic ordered moment and the nature of fluctuations. Compared with conventional magnetism, the singlet ground state provides a far richer environment for low temperature physics within the magnetic phase. In a conventional magnetic system, the energy gap between the ground state and next excited state grows monotonically as temperature is decreased beneath the transition, giving an increasingly inert many-body environment. However, in the case of singlet ground state magnetism, the ground state is difficult to magnetically polarize, causing the energy gap between the ground state and easily polarized excited states to shrink as temperature is lowered and the magnetic order parameter becomes stronger. Consequently, within the AM + MF model, many states keep significant partial occupancy down to T < 100K, and the first excited state (derived from the Γ 5 doublet) actually grows in partial occupancy beneath the phase transition (see Fig. 4b). Of the low energy CEF symmetries (tracked in Fig. 4b), Γ 5 and Γ 2 are of particular importance, as Γ 5 is a magnetically polarizable Ising doublet, and Γ 2 is a singlet state that can partner coherently with the Γ 1 ground state to yield a z-axis magnetic moment (see Supplementary Note 5). These nonground-state crystal field symmetries retain a roughly 1/3 rd of the total occupancy at T = 100K, suggesting that a heat capacity peak similar to a Schottky anomaly should appear at low temperature, as has been observed at T <~50K in experiments (see the supplementary material of ref. 10 ). Alternatively, when intersite exchange effects are factored in, the shrinking energy gap between the Γ 1 and Γ 5 CEF states at low temperature will enable Kondolike resonance physics and coherent exchange effects that are forbidden in conventional magnets.
Critical behavior at the Néel transition should also differ, as the phase transition in a singlet-ground-state magnet is only possible on a background of strong fluctuations. Measuring the ordered moment as a function of temperature with elastic neutron scattering (Fig. 4c) reveals that the UBi 2 moment follows a trend that appears consistent with the β = 0.327 critical exponent for a 3D Ising system 27 . The order parameter in USb 2 has a sharper onset that cannot be fitted sufficiently close to the transition point due to disorder, but can be overlaid with an exponent of β~0. 19, and may resemble high-fluctuation scenarios such as tricriticality (β = 0.25 28,29 ). This sharp onset cannot be explained from the AM + MF model (blue curve in Fig. 4c), as mean field models that replace fluctuations with a static field give large critical Another approach to evaluate the importance of fluctuations is to lower the Néel temperature by alloying with non-magnetic thorium (Th), as U 1-x Th x Sb 2 (see Fig. 4d), thus quenching thermal fluctuations at the phase transition. Performing such a growth series reveals that the magnetic transition can be suppressed to T N~1 00 K, but is then abruptly lost at x~0.7, consistent with the need for fluctuations across a CEF gap of k B T N~1 0 meV, which matches expectations from theory for the energy separation between Γ 1 and Γ 5 (see Table 1 and Methods).
Discussion
In summary, we have shown that the USb 2 and UBi 2 O-edge XAS spectra represent different nominal valence symmetries, with USb 2 manifesting 5f 2 moments that are expected to create a Hund's metal physical scenario, and UBi 2 showing strong 5f 1 -like symmetry character. The CEF ground state of a paramagnetic USb 2 Hund's metal is theoretically predicted to be a robust non-magnetic singlet, creating an exotic setting for magnetism that resembles an exciton condensate, and is previously only known from fragile and low temperature realizations. The temperature dependence of XLD measurements is found to reveal a symmetry evolution consistent with singlet-based magnetism. Neutron diffraction measurements show a relatively sharp local moment onset at the transition, consistent with the importance of fluctuations to nucleate the singlet-based magnetic transition, and suppressing thermal fluctuations in a doping series is found to quench magnetism beneath T N <~100K. Taken together, these measurements are consistent with a singlet-based magnetic energy hierarchy that yields an anomalously large number of thermally accessible degrees of freedom at low temperature (T < 100K), and provides a foundation for explaining the otherwise mysterious coherence effects found in previous transport, heat capacity, and ARPES measurements at T < 100K 7,[9][10][11] . The interchangeability of elements on both the uranium (demonstrated as U 1-x Th x Sb 2 ) and pnictogen site suggests UX 2 as a model system for exploring the crossover into both Hund's metal and singlet-ground-state magnetic regimes.
Methods
Experiment. The samples of UBi 2 and USb 2 were top-posted in a nitrogen glovebox and then transferred within minutes to the ultra high vacuum (UHV) environment. The samples were cleaved in UHV and measured in-situ, with initial U Oedge spectra roughly 30 minutes after cleavage. The UV-XAS measurements were performed in the MERIXS (BL4.0.3) in the Advanced Light Source with base pressure better than 4 × 10 −10 Torr. The switch between linear horizontal polarization (LH-pol) and linear vertical polarization (LV-pol) is controlled by an elliptically polarizing undulator (EPU) and keep precisely the same beam spot before and after the switch. The incident angle of the photon beam was 30°, which gives a 75% out-of-plane E-vector spectral component under the LH-pol condition and 100% in-plane E-vector under the LV-pol condition. The XAS signal was collected by the total electron yield (TEY) method. The penetration depth of VUV and soft X-ray XAS measured with the TEY method is generally in the 2-4 nm range set by the mean free path of low energy (E <~10 eV) secondary electrons created in the scattering process 30 , making it a much more bulk sensitive technique than single-particle techniques such as angle resolved photoemission. Air-exposed UBi 2 can degrade rapidly due to oxidization. No evidence of a large volume fraction of oxide or other phases was found from neutron scattering data for USb 2 and UBi 2 . Possible sample oxidation was surveyed by measuring oxygen L 1 -edge XAS via TEY for both USb 2 and UBi 2 during the uranium O-edge XAS experiments. An oxygen L 1 -edge signal was visible at the cleaved surface of both samples, and found to have similar intensity for both USb 2 and UBi 2 samples (Supplementary Note 6).
The O-edge XAS curves observed under LH-pol and LV-pol polarization are normalized by assigning constant intensity to the integrated area of the R1 region. Spectral intensity was integrated between featureless start (95 eV) and end points (102 eV) for both UBi 2 and USb 2 . The linear dichroism of the XAS in the main text is defined as: where I LH(max) is the XAS intensity maximum under LH-pol condition within R1 region. The monotonic temperature linear dichroism of USb 2 in the main text is a solid result under different data normalization process but linear dichroic rate can be influenced by some factors, for example the irreducible background in I LH(max) . In the simulation, tuning the broadening factor is also easy to change simulated linear dichroic rate which make seriously quantitative comparison of the linear dichroism between experiment and the simulation meaningless. Neutron diffraction measurements were performed on single crystals at the BT-7 thermal triple axis spectrometer at the NIST Center for Neutron Research 31 using a 14.7 meV energy and collimation: open -25′ -sample -25′ -120′. For USb 2 , the magnetic intensity at the (1, 0, 0.5) peak was compared to the nuclear intensity at the (1, 0, 1) peak, while the temperature dependence of the (1 1, 0.5) peak was used to calculate an order parameter. For UBi 2 , the temperature-dependent magnetic intensity at the (1, 1, 1) peak was compared to nuclear intensity at (1, 1, 1) peak at 200K, above the Néel temperature. In both cases, an f 2 magnetic form factor was assumed 32 .
Atomic multiplet + mean field model (AM + MF). Atomic multiplet calculations were performed as in ref. 16 , describing 5d 10 5 f n → 5d 9 5 f n+1 X-ray absorption in the dipole approximation. Hartree-Fock parameters were obtained from the Cowan code 33 , and full diagonalization of the multiplet Hamiltonian was performed using LAPACK drivers 34 . Hartree-Fock parameters for 5f multipole interactions renormalized by a factor of β = 0.7 for UBi 2 , and a more significant renormalization of β = 0.55 was found to improve correspondence for USb 2 . This difference matches the expected trend across a transition between 5f 2 and 5f 1 local multiplet states. Core-valence multipole interactions renormalized by β C = 0.55, consistent with other shallow core hole actinide studies 35 . The 5f spin orbit is not renormalized in USb 2 but renormalized by a factor of 1.15 in UBi 2 due to the much larger spin orbit coupling on bismuth. A detailed comparison of simulation results generated from two sets of Hartree-Fock parameters is included in Supplementary Note 7.
Total electron yield is dominated by secondary electrons following Auger decay of the primary scattering site. We have assigned core hole lifetime parameters to describe this decay, and adopted the common approximation that the number of secondary electrons escaping from the material following each core hole decay event is independent of the incident photon energy. For the 5f 1 simulation, the core hole inverse lifetime is Γ = 1.4 eV at hυ < 100 eV, Γ = 1.8 eV at 100 eV < hυ < 108.5 eV, and 6.5 eV at hυ > 108.5 eV. For 5f 2 and 5f 3 simulations, feature widths were obtained from a core hole inverse lifetime set to Γ = 1.3 eV (hυ < 99 eV), Γ = 1.5 eV (99 eV < hυ < 103.5 eV), and 6.5 eV (hυ > 103.5 eV). In the 5f 3 simulation, assigning the 103 eV XAS feature to R1 (longer lifetime) as in the Fig. 2 makes it more prominent than if it is assigned to R2 (shorter lifetime). It is also worth noting that scenarios intermediate to 5f 2 and 5f 3 do not necessarily closely resemble the 5f 3 endpoint, and spectral weight in the 103 eV 5f 3 XAS peak may depend significantly on local hybridization. However, in real materials, 5f 3 character is associated with a downward shift in the R1 resonance onset energy that is opposite to what is observed in our data 36 . The mean field model was implemented by considering the USb 2 uranium sublattice with Ising exchange coupling between nearest neighbors: where A ,i is the 5f 2 single-atom multiplet Hamiltonian, J i,k is an exchange coupling parameter with distinct values for in-plane versus out-of-plane nearest neighbors, and S z,i is the z-moment spin operator acting on site i. Mean field theory allows us to replace one of the spin interaction terms (S z,k ) with a temperature-dependent expectation value, and describe the properties of the system in terms of a thermally weighted single-atom multiplet state ensemble. The specific values of individual J i,k terms are unimportant in this approximation, however their signs must match the antiferromagnetic structure in Fig. 1, and the sum of the absolute value of nearneighbor terms must equal J eff = ∑ <k> |J n,k | = 43 meV to yield a magnetic transition at T N = 203 K. When considering the doped case of U 1-x Th x Sb 2 , the expectation value < S z,k > is effectively reduced by weighting in the appropriate density of 0moment 5f 0 Th sites. The CEF energy hierarchy has not been fine tuned. Perturbation strengths are scaled to set the lowest energy excitation to 10 meV, a round number that roughly matches the lowest k B T N value at which a magnetic transition is observed in U 1-x Th x Sb 2 . This assignment gives a total energy scale for crystal field physics that is approximately comparable to room temperature (ΔCEF~k B T N ), as expected for this class of materials, and the associated orbital energies were found to correspond reasonably (within <~30%) with coarse estimates from density functional theory. The crystal field parameters are listed in the first column of Table 1.
The low temperature ordered moment of M = 1.90 μ B seen by neutron scattering is matched by downward-renormalizing the moment calculated in the mean field model to 62% (see Fig. 4d shading). Within density functional theory (DFT) models, the consideration of itinerant electronic states provides a mechanism to explain most of this discrepancy. In DFT simulations, the spin component of the magnetic moment is enhanced to M S~2 μ B 14,15 , larger than the maximal value of M S~1 .4 μ B that we find in the 5 f 2 (J = 4) atomic multiplet picture. This larger DFT spin moment is directly opposed to the orbital magnetic moment, resulting in a smaller overall ordered moment. The ordered moment in the multiplet simulation could alternatively be reduced by strengthening the crystal field, but this is challenging to physically motivate, and has the opposite effect of reducing the spin moment to M S < 1 μ B .
Density functional theory + dynamical mean field theory (DFT + DMFT). The combination of density functional theory (DFT) and dynamical mean-field theory (DMFT) 37 , as implemented in the full-potential linearized augmented plane-wave method 38,39 , was used to describe the competition between the localized and itinerant nature of 5f-electron systems. The correlated uranium 5f electrons were treated dynamically by the DMFT local self-energy, while all other delocalized spd electrons were treated on the DFT level. The vertex corrected one-crossing approximation 38 was adopted as the impurity solver, in which full atomic interaction matrix was taken into account. The Coulomb interaction U = 4.0 eV and the Hund's coupling J = 0.57 eV were used for the DFT + DMFT calculations.
Code availability. Though the source code used for these multiplet calculations is not publicly available, there are excellent options with equivalent capabilities such as CTM4XAS (http://www.anorg.chem.uu.nl/CTM4XAS/) and Quanty (http:// www.quanty.org).
Data availability
All relevant data of this study are available from the corresponding author upon reasonable request. | 6,283.2 | 2019-02-07T00:00:00.000 | [
"Physics"
] |
RNA Panel Sequencing Is an Effective Tool to Help Classify Splice Variants for Clinical Oncogenetic Diagnosis
,
Introduction
Oncogenetics is aimed at stratifying the risk of cancer in the population, in order to offer appropriate monitoring.For this, pathogenic variants in cancer predisposition genes are sought by sequencing and comparison to the reference sequence of these genes.With the deployment of NGS methods, the number of genes analyzed for each patient has increased considerably in clinical routine.Thus, very many variants in these genes are identified, for which it is essential to determine whether they are pathogenic or neutral for the function of the protein.A classification system has been proposed by Plon et al. [1].The American College of Medical Genetics and Genomics then published recommendations for variant classification that are widely used in oncogenetic laboratories [2].This makes it possible to effectively classify all variants identified by NGS analysis, according to the current knowledge, but the majority unfortunately remain variants of unknown significance (VUSs).Indeed, 15-25% of patients who underwent cancer multigene panel testing are found to carry at least one VUS, depending on the genes tested [3,4].
Among these VUSs, an important proportion are predicted to have an impact on splice mechanisms by various splice prediction software programs [5,6].For example, Karam et al. studied 307,812 patients that underwent multigene cancer panel testing [4].They found 52,831 patients (17%) with 15,859 unique VUSs, including 1,672 variants with predicted splicing impact (10.5%).Moreover, some hereditary cancer genes may be enriched in splicing mutations [7].Prediction of splicing impact on every variant is thus crucial when analyzing diagnostic DNA panel sequencing.These algorithms make it possible, when the prediction is negative, to exclude an impact on the splicing of variants of unknown significance.False negatives are relatively rare (negative predictive value > 95% for SpliceAI, for example, [8]), which often makes it possible to classify these variants as likely benign.However, a relatively high rate of false positives is reported: for example, in silico models yielded a 25% false-positive rate in Karam et al.'s study on 64 variants [4].Wai et al. also reported positive predictive values between 46 and 83% depending on the software used, in a study of 257 experimentally validated variants [8].A positive prediction therefore does not make it possible to classify VUSs, but it encourages further investigations on RNA.Thus, different methods for studying RNA have been reported, but they all can be difficult to apply in routine diagnostics [9].Here, we present a multigene capture approach to study transcripts of targeted genes.This technique is very close to the multigene panel techniques traditionally performed in constitutional genetics laboratories.It is therefore easily applicable in diagnostic laboratories, and it can still be supplemented by other techniques if necessary, such as RT-PCR or minigenes.
Since 2016, 5,113 patients with hereditary predisposition to cancer were analyzed by multigene panel sequencing in the oncogenetics department of Centre Jean Perrin.3,766 variants of unknown significance were identified, including 450 VUSs (12%) with positive splice prediction.This study presents our RNA panel analyses on 53 different VUSs in order to evaluate the efficiency of the method to classify splice variants.
Material and Methods
2.1.Ethical Approval.All patients signed an informed consent for the use of their samples for research purposes.The study was approved by an ethics committee (CPP Sud-Est VI: 2023/CE18).
Selection of Splice Variants
. Between 2016 and 2022, 5,113 patients consulting the oncogenetics department of the Centre Jean Perrin underwent hereditary cancer predisposition panel analysis, according to national or international recommendations where available, or according to data from literature (Table 1).All variants identified on this DNA panel were subjected to the SpIP and SpliceAI prediction algorithms.Fifty-three VUSs were selected for an RNA panel, during multidisciplinary meetings based on the clinical presentation of the families and the role of the gene: In addition, four samples were included to search for deep intronic variants (patients presenting a severe clinical phenotype (Lynch syndrome, for example) but no constitutional pathogenic variant identified by the DNA panel).Finally, four other samples with exon duplication identified by the DNA panel were also included for duplication characterization.
2.3.Targeted Panel on Peripheral Blood RNA.Peripheral blood was collected in PAXgene blood RNA tubes, after informed consent was obtained from each patient.Total RNA was isolated using the PAXgene Blood RNA kit (Qiagen, Courtaboeuf, France).Screening for transcript abnormalities was performed by sequencing a panel of 48 genes associated with hereditary cancer syndromes (Table 1).Libraries were prepared using the KAPA RNA Hyper Prep kit (Roche, Mannheim, Germany).Sequences of interest were then captured with a custom design of Nimblegen SeqCap EZ Choice or Hypercap (Roche, Mannheim, Germany) and sequenced on a MiSeq or Nextseq 550 instrument (Illumina, San Diego, USA).
Reads were aligned to the human reference genome (genome assembly GRCh37) using STAR aligner v2.7.10a (Spliced Transcript Alignment to a Reference) [10].Splice-Launcher was used to compute a junction read count matrix.A list of transcripts to use as reference is given to Splice-Launcher to compute the relative expression over natural junctions and detect abnormally expressed junctions [11].
2.4.RT-PCR Analysis of Peripheral Blood RNA.RNA was reverse-transcribed using oligo(dT) primers with the Superscript III First-Strand Synthesis System for RT-PCR (Life Technologies, Saint Aubin, France), and cDNA was amplified using two different pairs of primers located around the predicted splice effect.RT-PCR products were separated by electrophoresis both on an Agilent Bioanalyzer DNA1000 chip (Agilent, Les Ulis, France) and on an agarose gel.After purification using Agencourt Ampure XP (Beckman Coulter, Villepinte, France) or the MinElute PCR Purification kit (Qiagen, Courtaboeuf, France), RT-PCR products were sequenced by using the BigDye Terminator kit (Fisher Scientific, Illkirch, France).
Minigene Splicing Assay.
A splicing reporter minigene assay of some variants was performed using the pCAS2 vector, as described [12].Exons or introns in which the variants are located were PCR amplified from patients' genomic DNA using the FastStart High Fidelity PCR System dNTP Pack v7 (Roche, Mannheim, Germany) and forward and reverse primers carrying restriction sites for BamH1 and MluI, respectively.PCR products were cloned into the pCAS2 vector.All constructs were verified by Sanger sequencing using the BigDye Terminator kit (Fisher Scientific, Illkirch, France).Wild-type and mutant constructs were transfected into HeLa cells.Cells were harvested after 24 h, and total RNA was extracted using the RNeasy mini kit (Qiagen, Courtaboeuf, France).Reverse transcription was performed using the Superscript III First-Strand Synthesis System for RT-PCR (Life Technologies, Saint Aubin, France) following the manufacturer's instructions.cDNA was amplified with AmpliTaq DNA polymerase (Fisher Scientific, Illkirch, France) using pCAS-KO1-F (5 ′ -TGACGT CGCCGCCCATCAC-3 ′ ) and pCAS-2R (5 ′ -ATT GGTTGT TGAGTTGGTTGTC-3 ′ ) as forward and reverse primers, respectively.PCR products were separated on an Agilent Bioanalyzer DNA1000 chip (Agilent, Les Ulis, France).Each PCR product was purified using Agencourt Ampure XP (Beckman Coulter, Villepinte, France) and sequenced using the BigDye Terminator kit (Fisher Scientific, Illkirch, France).
2.6.Immunohistochemistry. PTEN expression was determined by IHC on 3 μm paraffin sections with the PTEN (D4.3)XP rabbit monoclonal antibody (Cell Signaling Technology, Beverly, MA, United States).Antigen retrieval was carried out for 90 min in CC1 buffer on a Benchmark-ULTRA immunostainer (Roche, Mannheim, Germany).The antibody was incubated for 1 hour at 1/125 dilution at room temperature, and the revelation was done with the Ultraview DAB kit (Roche, Mannheim, Germany).The sig-nalSlide PTEN IHC control slide is used to validate the technique.
Results
We performed targeted blood RNA sequencing to help classify 53 different VUSs with potential splicing impact (Table 2).Several biological or technical replicates were carried out to test the intra-and intersample reproducibility of the technique.Two variants were analyzed for several patients: BRCA2 c.6842-8_6842-7del was analyzed for three different patients and NF2 c.1122+6T>C for two patients.The results observed were very similar regardless of the patient.For eight other variants, technical replicates of RNA libraries and targeted sequencing were performed, showing good reproducibility of the method (data not shown).For all variants for which an effect on splicing was demonstrated by the RNA panel, this effect was verified by RT-PCR and Sanger sequencing, except for CDH1 c.1901C>T because the splice effect observed was already published [13].For eight variants without splice effect on the RNA panel, we also carried out RT-PCR and Sanger sequencing to confirm the absence of any impact on splicing.Finally, for three variants of particular clinical importance, monoallelic minigene analysis was also performed in order to check the partial effect or NMD implication.
For the 53 VUSs analyzed, 20 (37.7%) induced partial or total modification of the transcript and 10 variants could be classified as pathogenic or likely pathogenic (Figure 1).For the other 10 variants, either a partial effect on splicing or in-frame exon skipping was observed, which did not make it possible to conclude on pathogenicity.Among the 33 VUSs that did not show an impact on splicing, 21 could be classified as likely neutral.For six variants, no abnormal transcripts were observed, but in the absence of any heterozygous exonic variant to verify the presence of the two alleles and exclude allele dropout by nonsense-mediated decay, 3 Human Mutation 7 Human Mutation these remained VUSs.For the last six variants, we were able to conclude that there was no effect on splicing, but these were missense variants for which the functional impact of the amino acid modification was not known.
We compared the performance of two popular splicing prediction software programs: SpliceAI [14] and SpIP [6] (Table 3).SpIP is a random forest model running a cascade of bioinformatics tools.Briefly, SPiP uses a SPiCE tool for the consensus splice sites (donor and acceptor sites), MES for the polypyrimidine tract between -13 and -20, BPP for the branch point area between -18 and -44, a homemade score to reveal cryptic/de novo activation, and ΔtESRseq for exonic splicing regulatory elements up to 120 nt from the exon boundaries.SpliceAI is a deep neural network that accurately predicts splice junctions from an arbitrary pre-mRNA transcript sequence.Considering all positive predictions regardless of score, we found better sensitivity for Spli-ceAI than SpIP (81% vs. 47%) but a slightly lower specificity (94% vs. 100%) (Table 3).Focusing on variants with splicing altering predictions greater than 50%, the sensitivity rises to 79% for SpIP and 92% for SpliceAI.Most of the positive predictions with SpIP but negative with SpliceAI were for predictions below 50%, for which no impact on splicing was demonstrated by the RNA panel.Only two variants (NF2 c.1122+6T>C and MLH1 c.882C>G) were negative with SpliceAI and highly positive (>90%) with SpIP.Our RNA panel showed no splice impact for the NF2 variant but a partial exon 10 skipping of MLH1 for c.882C>G.Finally, one variant (PALB2 c.2379C>T) was negative for SpIP but highly positive for SpliceAI (66%) but gave no abnormal transcripts in our RNA panel.The 13 variants with negative predictions for both algorithms showed no impact on transcripts in our RNA panel.
In addition to the 53 VUSs studied for their impact on splicing, we analyzed the RNA panel in two other situations: the search for deep intronic variants and the characterization of large tandem duplications.For samples with a severe clinical phenotype (Lynch-like syndrome, for example) but no constitutional pathogenic variant identified using DNA, we tested if RNA could show abnormal transcripts, suggesting a pathogenic deep intronic variant.Four patients with a suggestive clinical phenotype but without mutations found on the DNA panel were tested: one patient showed a severe breast cancer family and three patients developed Lynch syndrome spectrum tumors with protein expression profiles suggestive of a mutation in an MMR gene.For one of them, a deep intronic variant could be demonstrated (MLH1 c.791-489_791-20del, see the specific paragraph on this variant).Finally, we used targeted RNA sequencing to characterize large duplications.We tested four samples with duplications of at least one exon to assess whether the duplication was in tandem (Table 4).For three cases, chimeric reads proved the duplication in tandem, allowing reclassification of these duplications as pathogenic.
PTEN c.206+6T>G.
A 39-year-old woman presenting clear cell papillary adenocarcinoma of the endometrium was seen in an oncogenetics consultation at the Jean Perrin Center.She was thyroidectomized at the age of 26 for a multihetero nodular thyroid with elevated calcitonin; examination of this thyroidectomy did not find C-cell hyperplasia or medullary carcinoma, but several adenomas were found on both lobes, and there was a small oncocytic adenoma in the left lobe.Panel sequencing of blood DNA revealed the intronic variant c.209+6T>G in the PTEN gene.This variant is predicted by both SpIP and SpliceAI to impact the consensus splice site of exon 3 (Table 2).The skipping of exon 3 of the PTEN gene results in the loss of 16 amino acids within the phosphatase domain and is recognized as pathogenic [15].Analysis of RNA extracted from peripheral blood by panel sequencing showed equal depths of full-length and exon 3-omitted transcripts, revealing that the skipping of exon 3 is total in the altered allele.The same result was observed by RT-PCR of the same RNA sample (Figure 2(a)), using primers specifically amplifying the PTEN cDNA and not its pseudogene.There was no exonic variant present to verify the absence of a normally spliced product for the variant allele.A monoallelic splicing test by minigene resulted in major but partial exon 3 skipping (Figure 2(b)).These contradictory results do not allow us to conclude on a complete or partial effect.This may be due to a differential impact of the variant on splicing depending on the tissue.Nevertheless, the mother of this patient, who carries the PTEN variant, developed breast cancer at 65 years old and underwent partial thyroid surgery at ages 27 and 39 for multiheteronodular goiter.Moreover, immunohistochemistry on the endometrial tumor of this patient showed a complete loss of PTEN protein expression (Figure 2(c)).Overall, we classified this variant as likely pathogenic.New analysis of our DNA panel with the DELLY tool [16] identified a large deletion in intron 10 of MLH1 c.791-489_ 791-20del.This deletion is predicted by SpIP to impact splice mechanisms (alter BP + alter by creating cryptic 36.17%(26.46%-45.88%)).No heterozygous exonic variant was present in MLH1 in the constitutional DNA to confirm transcription of the 2 alleles.Thus, it is possible that a part of the aberrant transcript was degraded by NMD, explaining the partial exon skipping observed.To check this hypothesis, we performed a monoallelic test by minigene treated or not with puromycin, an NMD inhibitor.The results show total exon 10 skipping with the MLH1 c.791-489_791-20del plasmid and very partial exon 10 skipping with the wild-type MLH1, regardless of puromycin treatment (Figure 3(c)).In addition, a cosegregation study showed that two carriers of the variant have developed colorectal polyps and two obligate carriers developed colon and/or uterine cancer (Figure 3(a)).Altogether, we consider this variant to be likely pathogenic.
3.3.BRCA2 c.68-8_68-7delinsAA.A woman with breast cancer at age 49 and pancreatic cancer at age 71 was seen in our oncogenetics consultation.Her brother had prostate cancer at age 76.DNA panel sequencing identified the BRCA2 c.68-8_68-7delinsAA variant, which weakens the acceptor splice site according to SpIP prediction algorithms (alter by Spice 69.57% (61.89%-77.25%)).Analysis of the patient's blood RNA by panel sequencing showed partial skipping of BRCA2 exon 3 (r.68_316del,42% of the variant-carrying allele).Because of the partial effect observed and the low reading depth of BRCA2 (due to the low expression of this gene in lymphocytes), we analyzed the RNA panel for this sample in triplicate (different libraries and different sequencing runs).We confirmed exon 3 skipping for 42 to 82% of the variant-carrying allele.Exon 3 is in-frame, but complete exon 3 skipping has been proven to be pathogenic [17].The partial effect of c.68-8_68-7delinsAA has been described by other techniques (fragment analysis and competitive Q-PCR) [18,19].In our RNA panel, we also observed another minor transcript with skipping of exon 3 + 4 bases of exon 4 (r.68_320del, between 0 and 25% of the variantcarrying allele, depending on the replicate).This transcript is not predicted by the algorithms and has therefore not been studied by published targeted methods.RT-PCR and Sanger sequencing with primers in exons 2 and 6 confirmed the major exon 3 skipping, but we could not detect the minor r.68_320del transcript (if present), potentially due to insufficient sensitivity of this technique.These data are not sufficient to conclude on the pathogenicity of the BRCA2 c.68-8_68-7delinsAA variant and will have to be supplemented by minigene analysis including exons 3 and 4 of BRCA2.Long-read sequencing could also help to understand the impact on several exons.Finally, this variant is included in the French cosegregation study COVAR [20], in order to progress on its clinical significance.9 Human Mutation 3.4.MSH2 c.(1076+1_1077-1)_(1276+1_1277-1)dup.A 43year-old woman presented with endometrioid adenocarcinoma.Her siblings were affected with cancer of the uterus (at 41 and 54 years old) and rectal cancer at 38 years old.Her grandfather had colon cancer at age 56, and a paternal great-aunt presented with cancer of the uterus at age 40 (Figure 4(a)).One of the uterine cancers presented microsatellite instability and loss of MSH2 and MSH6 protein expression.The analysis of MMR genes by Sanger sequencing did not reveal any pathogenic variant, but this family is still suspected of Lynch syndrome.Thus, a constitutional mutation in hereditary colon cancer genes was investigated by DNA panel sequencing.Duplication of MSH2 exon 7, c.(1076+1_1077-1)_(1276+1_1277-1)dup, was identified.Short-read DNA sequencing cannot distinguish whether this duplication is in tandem (and is therefore pathogenic because it alters the reading frame) or whether the extra copy of exon 7 is inserted elsewhere in the genome (and therefore does not alter the transcription of the MSH2 gene).Our panel of blood-extracted RNA offered a quick and easy response to this question as we could directly observe the MSH2 transcripts that contained the exon 7 repeat (Figure 4(b)).We concluded that the duplication of MSH2 exon 7 is pathogenic in this family.
Discussion
Multigene panel sequencing of total RNA extracted from peripheral blood was performed to study the splice impact of variants on transcripts.This technique is easy to implement in a routine oncogenetics laboratory and allows direct observation of aberrant transcripts.Unlike RT-PCR, it is a technique without a priori, so there is no need to start with a fixed hypothesis about how the modified transcript is structured.Of the 53 VUSs studied, 10 could be classified as pathogenic or likely pathogenic, due to their impact on splicing as highlighted by the RNA panel.Twenty-one intronic or synonymous variants could be classified as probably neutral, as the RNA panel showed no impact on splicing, and it is therefore very unlikely that these silent variants modify protein function.For six missense variants, an effect on splicing could be excluded, although this did not change their class, since an impact of the amino acid modification could not be excluded.Our RNA panel enabled us to modify the classification of 58% of the variants studied (31/53).Karam 11 Human Mutation results on the reclassifying rate facilitated by RNA analysis vary greatly depending on the choice of variants tested.Although SpliceAI showed a better sensitivity than SpIP in our results, one variant (MLH1 c.882C>G) caused a partial exon 10 skipping that was predicted by SpIP but not by SpliceAI.Moreover, SpIP was already shown to have better performance than SpliceAI in the branch point area and in exonic regions [6].All variants with negative predictions with both algorithms were confirmed to have no impact on the transcripts.In the future, we have therefore chosen to classify synonymous or intronic variants with no prediction of splicing as probably neutral, without RNA studies.Variants with moderate predictions (between 20 and 50% with SpIP and/or SpliceAI) can be studied by RNA panels with a good chance of classifying when a heterozygous exonic variant is present to allow observation of both alleles.However, few of these variants showed an impact on splicing (2/17, 11%).For our subsequent RNA panel analyses, we therefore decided to systematically study only variants with strong splicing predictions (SpIP and/or SpliceAI).
The variants that remained VUSs illustrate the different limits of the technique.The first limit is the difficulty evaluating nonsense-mediated mRNA decay (NMD) if no heterozygous exonic variant is present.This problem could be solved by working with lymphoblastoid lines, which can be treated with puromycin to inhibit NMD.Otherwise, monoallelic tests with a minigene system can be used with puromycin, but these techniques require cell culture equipment.RNA panel and minigene analyses are not mutually exclusive and could therefore be used successively: an RNA panel could be performed as part of routine diagnostics, while minigene analyses could be performed only when the RNA panel is unable to determine the pathogenicity of certain clinically important variants.
Concluding on the pathogenicity of a variant may also be complicated by the observation of partial effects on splicing and aberrant splicing that preserves the reading frame.Recent recommendations have been published by the ClinGen Splicing Subgroup to help classify splice variants according to the ACMG framework [21].Physiological alternative splicing events have been described for many predisposition genes, 12 Human Mutation and they can help the interpretation of VUS splicing impact [22][23][24][25][26][27].Nevertheless, functional studies remain necessary to advance on the classification of variants with partial or inframe splicing effects.Another limitation of this blood RNA panel is its dependence on the expression of genes of interest in lymphocytes.BRCA2, for example, is poorly expressed in blood, although we did obtain sufficient depth of coverage.Moreover, variant classification based on blood RNA panel results should be performed with caution, especially if the observed splicing is normal.Indeed, the effects on splicing could be different on the target tissues [28].To our knowledge, alternative splicing of breast predisposition genes seems to be similar in blood and breast tissues [26,27], suggesting that the observed results are pertinent for evaluating the associated risks.
For most variants, the RNA panel alone made it possible to answer the question of the effect on splicing.RT-PCR can be used to confirm the quantification of the different transcripts by another technique (in the event of a partial effect, for example).It can also be useful for low-expressed genes.Minigene is a monoallelic test with the possibility of treatment with puromycin.It can be used when degradation by NMD cannot be excluded in the RNA panel.Both techniques are therefore still necessary for the partial or complex splicing effects observed in the RNA panel.
This RNA sequencing panel may also be of interest for characterizing large duplications.Four RNA analyses were performed for patients with one or two exon duplications detected on gDNA panel analyses.For two of them, it was possible to observe a tandem duplication of the exons and to conclude that the variants were pathogenic.For the duplication of exons 11 and 12 of PMS2, we could not conclude because of the very homologous pseudogene in this region.For the last patient with exon duplication, we did not find any reads showing tandem duplication, probably because the exon duplication was elsewhere in the genome.
Finally, RNA panel sequencing could likely be used to identify the production of aberrant transcripts due to deep intronic variants not detected by classical DNA panel analyses.Only four analyses of this type were carried out in our study, one of which identified the MLH1 c.791-489_791-20del variant in a typical Lynch syndrome family.We believe that these RNA analyses could be offered for patients with a strong family history suggesting a genetic predisposition to cancer but without a pathogenic variant found on the DNA panel.
As a conclusion, blood RNA panel sequencing is an easy technique to implement in an oncogenetics laboratory, and it was revealed to be an efficient tool to help classify VUSs with predicted splice effect.It could also be useful for characterizing large duplications and for researching deep intronic variants' impact on expressed transcripts.Nevertheless, it provides only an argument in favor or not of the pathogenicity of the variants, which must be interpreted with caution, especially for partial effects or for low-expressed genes.
Data Availability
Most of the data analyzed during this study can be found within the published article and its tables.Any additional raw data are available from the corresponding author on reasonable request.
Figure 2 :Figure 3 :
Figure 2: Study of the PTEN c.206+6T>G variant.(a) RT-PCR analysis on blood sample RNA: peripheral blood of the patient with the PTEN c.206+6T>G variant was collected in PAXgene blood RNA tubes.RT-PCR analysis was performed with primers mapping to exons 2 and 5, and PCR products were separated by bioanalyzer electrophoresis.The 370 bp peak corresponds to the reference PTEN transcript, and the 325 bp peak corresponds to a PTEN transcript lacking exon 3. RT-PCR products were then analyzed by Sanger sequencing.(b) Minigene analysis: HeLa cells were transfected with pCAS2 vectors including wild-type or mutant PTEN sequences.Total RNA was isolated, RT-PCR analysis was performed using pCAS primers, and PCR products were separated by bioanalyzer electrophoresis.The 280 bp band corresponds to the reference PTEN transcript, and the 235 bp band corresponds to a PTEN transcript lacking exon 3. (c) PTEN immunohistochemistry: PTEN expression of the endometrium tumor was determined by immunohistochemistry on 3 μm paraffin sections with a PTEN rabbit antibody (Cell Signaling Technology).The PTEN IHC control slide was used to validate the technique.
Figure 4 :
Figure 4: Study of the MSH2 c.(1076+1_1077-1)_(1276+1_1277-1)dup variant.(a) Pedigree: filled symbols indicate patients affected with cancer.Open symbols indicated relatives unaffected with cancer.The type of cancer and age at presentation are given under the symbol.MSI: tumoral microsatellite instability; M2/M6-: tumoral extinction of MSH2 and MSH6 protein expression (seen by immunohistochemistry).(b)Panel sequencing on blood sample RNA: peripheral blood of the patient with the MSH2 exon 7 duplication was collected in PAXgene blood RNA tubes.Targeted panel sequencing was performed using KAPA kits and probes on the Illumina device.Sequences were visualized and manually analyzed using Integrated Genomics Viewer (Broad Institute) software.
Table 1 :
List of the 48 genes sequenced in the CJP familial cancer panel.
Table 2 :
Summary of the 53 variants studied by our targeted RNA panel.
Table 3 :
Performance comparison of SpIP and SpliceAI tools in predicting abnormal splicing.
Table 4 :
Classification of large duplications by the targeted RNA panel. | 5,938.8 | 2024-04-02T00:00:00.000 | [
"Medicine",
"Biology"
] |
PARSIMONIOUS MACHINE LEARNING MODELS IN REQUIREMENTS ELICITATION TECHNIQUES
elicitation
Introduction.Business analysis as an extension of requirements engineering is crucial to software development.The main business analysis deliverables are requirements and designs used as a basis for solution implementation, testing, and deployment.In turn, the critical input for the tasks of analysis, specification, and modeling of requirements and design for software is the information collected during the elicitation.Standard approaches to the requirements-gathering process have been systematized and described in the form of dozens of standard elicitation techniques.Industrial guidelines and empirical studies contain detailed descriptions of the techniques' elements and usage considerations but do not provide an elicitation selection process [1].
Consequently, one of the challenges for business analysts/requirement engineers, especially novice ones, is the selection of the appropriate requirements elicitation techniques that best fit their project.As a result, some of them are misused, others are never used, and only a few are constantly applied.To solve the problem, a machine learning model to predict/recommend using the following elicitation techniques as Interviews, Document Analysis, Process Analysis, and Interface Analysis depending on the project's context was proposed [1].
In the study [2], the model's prediction accuracy was increased by transforming the dataset from imbalanced to balanced, thus making a Random Forest Classifier learner unbiased to the majority class.Feature importance score was identified by mutual information criteria, i.e., independent from the machine learner classifier.It served as an assurance that the feature's score doesn't depend on the learning algorithm's bias.Ten features with the most significant importance score were reported in tables 4-5 as predictors for choosing the elicitation technique.
However, in both [1] and [2], selecting the best model from the candidates remained based on the performance metrics such as Accuracy and AUC.
A model selected that way is also called a "best-fit" model.The "best fit" model is complexit includes many parameters in order to better approximate training data.The more variables included in a model, the more dependent the model becomes on the observed data so that it can fail on the test data due to noisy, uninformative, and unrepresentative data being included in the model.i.e., a "best-fit" model is prone to overfit data [3].
Although the "best-fit" models included twenty features, we took ten features with the most significant importance score, which potentially may be incorrect if the model due to include less than ten features.
To eliminate the mentioned problems for the model proposed in works [1][2] in the current study, we will develop a parsimonious model that still accurately predicts/recommends using the techniques: Interviews, Document Analysis, Process Analysis, and Interface Analysis.
Analysis of last achievements and publications.The principle of parsimony suggests a model should be as simple as possible concerning the included variables, model structure, and several parameters.It is a desired characteristic of a model defined by a suitable trade-off between squared bias and variance of parameter estimators [4].The construction of the parsimonious model happens in the following steps: A stepwise selection is based on a statistical algorithm that checks for the "importance" of variables and either includes or excludes them based on a fixed decision rule.The "importance" of a variable is defined in terms of a measure of the statistical significance of the coefficient(s) for the variable.The statistic used for linear regression is an F-test; for logistic regressionlikelihood ratio, score, and Wald test.
A "best subsets" are the number of models containing one, two, three variables, and so on, which are fitted to determine the "best" according to specified criteria.
Due to meeting the current research's goals, only the "best subsets" approach from the listed able can be applied.The statistical measure that is commonly used to compare models with different numbers of parameters based on the parsimonious principle is the Akaike Information Criterion (AIC).It measures the distance between a candidate model and the accurate modelthe closer the distance, the more similar the candidate is to the truth model.AIC calculates the distance between models as expected relative to Kullback -Leibler (K-L) divergence.Although AIC is a consistent estimator of K-L divergence, there is no statistical test to compare values of AIC [8][9].
Another criterion to compare candidate models is Bayesian Information Criterion (BIC), derived from Bayesian statistical analysis and estimates.BIC approximates a Bayes factor with desirable properties for hypothesis testing and model selection [10][11][12][13].BIC is calculated for each candidate model by equation ( 1) which takes values in the set {0, 1} and which is built with learner algorithms: logistic regression, support vector machine (SVC), or decision tree classifiers (RandomForestClassifier), a maximized loglikelihood from ( 1) is calculated as a logistic loss function: ) log( 1)), where i p is a probability with which a fit model predicts a positive class The model with the smallest BIC is preferable because the complex models are almost always likely to fit the data better, so the first term in definition (4) will have a low value; however, the second provides a way to penalize these extra parameters, therefore causes BIC is increasing.To assess the goodness of fit of the selected candidate models compared to etalon (or best-fit) models in works [14] is proposed to apply testing of the hypothesis based on a difference between sample means of the model's performance metric.When the mean accuracy of the selected parsimonious models is 1 A and the mean accuracy of best-fit models is 2 A then the parsimonious models fit if the null hypothesis is not rejected by the computed twotailed p-value of the t-statistic (eq.6).
Вісник Національного технічного університету «ХПІ».Серія: Системний 84 аналіз, управління та інформаційні технології, № 1 ( 9)'2023 where n is the number of the parsimonious models included in the test; ddof is the delta degree of freedom with a value equal to 1.Other classification metrics, such as AUC, f1 score, precision, recall, and Jaccard score, can be used to measure the goodness of the parsimonious model in the same manner as specified in equation 6 for the accuracy metric.
The problem statement.We aim to build parsimonious models for four datasets considered in works [1][2] to avoid overfitting problems associated with the best-fit models.To design an algorithm for assessing a parsimonious model's performance compared to the best-fit model and selecting the best candidate.To execute tests to prove that the proposed algorithms can be used with other datasets.
Experiment Methodology.Our experiment methodology for constructing and assessing the parsimonious model is specified per each phase of the supervised learner model's creation lifecycle [15].
Data preparation and acquisition.Original data was formed based on a survey conducted among business analysts and requirement engineers in Ukraine regarding their use of requirement elicitation techniques and their context.Three hundred twenty-eight practitioners completed the survey.Four respondents were disqualified due to incorrect data: non-filled industrial sector and non-filled team types.The features included in the dataset used in this study are two types: features to describe the project's context; features to list all elicitation techniques used in the project.The following features belong to the first type: country; project size: smalltill 15 The dataset contains information about the features, along with the names of target classes such as "Elicitation", "Document Analysis", "Interface Analysis", and "Process Analysis".However, a feature with the same name as a target class is not included in the list of features.Databases' characteristics and imbalanced ratios calculated as majority-to-minority samples are specified in table 1.
Data preprocessing.The imbalance predictors matrix X and a target vector y were transformed into balanced X*, y* by applying SMOTE method.This method allows us to In lines 2-5, candidate models are fitted with increasing by one number of included features.The first candidate model includes one feature, and the last candidate includes F features, where F is the maximum number of features in our datasets.In line 2, i-features are sorted according to their mutual information (MI) score in descending order; the i-features are selected from the start of the sorted list with MI scores.In lines 3-4, the predictors' matrix is truncated to include only selected features, and a target variable and train and test subsets are formed from it.In lines 5-6, a model fits with the training subset, and performance metrics accuracy (Acc) and area under the ROC curve (AUC) are calculated on the test subset.In lines 7-8, if the model object's calculated performance satisfies the minimum performed level of accuracy (Acc_min) and AUC (AUC_min), then the model object is saved in the result vector S .
A general guideline is used in supervised machine learning with the following intervals for accuracy and AUC metrics: if Accuracy/AUC = 0.5, then this is a guessing equal to flipping a coin; if 0.5 < Accuracy/AUC < 0.7, then this is poor classification; if 0.7 < Accuracy/AUC < 0.8, then this is an acceptable classification; if 0.8 < Accuracy/AUC < 0.9, then this is an excellent classification; if Accuracy/AUC >= 0.9, then this is outstanding discrimination.The above rules are to be used to set minimum values of Accuracy and AUC for the algorithm (fig.1).If in the result of the execution of the algorithm vector S is empty, then we propose to lower the minimum values of the performance metrics.If vector S is not empty, then we can move on to grade candidate models by Bayes factor and grades the steps undertaken are described as per pseudocode (fig. For each model object from S in line 2 is identified a BIC weight, denoted as m w .Then in lines 3-6, each model is graded according to the Bays factor's rules."Positive" models are saved to vector 1 M ."Strong"to vector 2 , M "Very Strong"to vector 3 M .In current work, we ignored "weak" candidates.,, M M M compared to best-fit models B was done through the steps as per pseudocode (fig.3).
Input: In lines [1][2][3][4], mean values, the t-statistic, and the two-tailed p-value of the normal distribution for "very strong" models are computed.In lines 5-7, if the null hypothesis is not rejected, then a parsimonious model is added to the result vector R .Lines 8-9 are executed if the goodness of fit test is failed for models from 3 M .In this case, steps 2-7 are repeated with "strong" and "positive" models.Lines 11-14 are executed only if all models from ,, M M M failed goodness of fit test.In that scenario, the model M with the best performance is selected from Study results and their discussion.Multiple candidate models are created according to designed algorithm (fig.1).Applied Bayes factor grades as specified in fig. 2 allowed to select: a "very strong" parsimonious model to recommend Interviews as an elicitation technique that included eight features and evaluated with performance Accuracy = 90 %; AUC = 98 % (fig.4, a) which are 4 % and 1 % lower than Accuracy and AUC of best-fit model (table 2 -"Interviews"); a "very strong" parsimonious model to recommend Document analysis as an elicitation technique that included five features and evaluated with performance Accuracy = 90 %; AUC = 95 % (fig.4, b) which are 1 % and 2 % lower than Accuracy and AUC of best-fit model (table 2 -"Document Analysis").
A "strong" parsimonious model to recommend Interface analysis as an elicitation technique that included nine features and evaluated with performance Accuracy = 81 %; AUC = 88 % (fig.5, a) which are 3 % and 2 % lower than Accuracy and AUC of best-fit model (table 2 -"Interface Analysis"); a "strong" parsimonious model to recommend Process analysis as an elicitation technique that included fifteen features and evaluated with performance Accuracy = 81 %; AUC = 86 % (fig.5 As specified in fig.3, the hypothesis test is applied with the models' performance metrics from table 2. A null hypothesis H0: the mean difference between the parsimonious and best-fit models' accuracies is 0.An H1 hypothesis: the difference between the accuracies is different.T-statistic per equation 7 gives t = -2.8.The pvalue with the degree of freedom equal to 3 is 0.066, which is greater than 0.05, so our H0 is accepted, i.e., the parsimonious models are accepted, and best-fit can be ignored.Similarly, the hypothesis test with a null hypothesis H0: the mean difference between the values of AUC of the parsimonious model and the values of AUC of best-fit models is 0. H1 hypothesis: the mean difference between AUC values is different.T-statistic per equation 7 gives t = -7.The p-value of t = -7 with the degree of freedom equal to 3 is 0.006, which is less than 0.05, so our H0 is rejected, and the best-fit model is preferable due to the reduced parsimonious model's performance based on the mean value of AUC.
Thus, it can be concluded that applying the algorithm as per fig. 3 with each performance metric in sequence helps to identify when a parsimonious model's performance is degraded and decide on the suitable model's selection.We accepted the built parsimonious models in the current test experiment because the model's accuracy didn't deteriorate based on the goodness of fit test.
Conclusions and perspectives of further development.In the current study, the algorithms to build parsimonious candidate machine learning models and select the best candidate were designed and tested with four datasets collected for requirement elicitation technique selection.The results showed that the best candidate models graded as "very strong" and "strong" reduced the number of features: three times for Interviews and Interface analysis, five times for Document analysis, and 1.7 times for Process analysis.It helped to avoid the overfitting data problem.
The designed algorithm to assess the goodness of fit of the parsimonious models was applied with two performance metrics: accuracy and AUC in sequence.Based on the received results is concluded that by applying the proposed procedure, the gaps in the performance of the parsimonious model compared to the best-fit model can be detected, and a decision on the suitable model's selection can be made.
In summary, the obtained results allow us to recommend using a parsimonious model instead of the best-fit model to predict the using the particular elicitation technique in IT projects and form recommendations based on that model.
Several directions for future research can be considered, such as creating machine learning models for other business analysis techniques, e.g., specification and modeling, prioritization, and structure of business analysis architecture.
Fig. 2 .
Fig. 2. Steps to grade the candidate models Model validation.The assessment of the goodness of fit of models from 1 2 3
Fig. 3 .
Fig. 3. Steps to assess goodness of fit of parsimonious models algorithm (fig.3.)leaves experts to finally judge which model to use if all parsimonious candidate models failed the assessment.It could be either best-fit models from B or the parsimonious model with the best performance metrics because their minimum values are set as an input parameter of the algorithm (fig.2).
Fig. 5 .Fig. 4 .
Fig. 5. Candidate model(s) BIC weight, Accuracy, AUC: a -Interface analysis; b -Process analysis candidate models from the same dataset but include a different number of features; compare and select the best candidate as a final parsimonious model; assess the fit of the selected candidate. | 3,493 | 2023-07-15T00:00:00.000 | [
"Computer Science"
] |
PAbFold: Linear Antibody Epitope Prediction using AlphaFold2
Defining the binding epitopes of antibodies is essential for understanding how they bind to their antigens and perform their molecular functions. However, while determining linear epitopes of monoclonal antibodies can be accomplished utilizing well-established empirical procedures, these approaches are generally labor- and time-intensive and costly. To take advantage of the recent advances in protein structure prediction algorithms available to the scientific community, we developed a calculation pipeline based on the localColabFold implementation of AlphaFold2 that can predict linear antibody epitopes by predicting the structure of the complex between antibody heavy and light chains and target peptide sequences derived from antigens. We found that this AlphaFold2 pipeline, which we call PAbFold, was able to accurately flag known epitope sequences for several well-known antibody targets (HA / Myc) when the target sequence was broken into small overlapping linear peptides and antibody complementarity determining regions (CDRs) were grafted onto several different antibody framework regions in the single-chain antibody fragment (scFv) format. To determine if this pipeline was able to identify the epitope of a novel antibody with no structural information publicly available, we determined the epitope of a novel anti-SARS-CoV-2 nucleocapsid targeted antibody using our method and then experimentally validated our computational results using peptide competition ELISA assays. These results indicate that the AlphaFold2-based PAbFold pipeline we developed is capable of accurately identifying linear antibody epitopes in a short time using just antibody and target protein sequences. This emergent capability of the method is sensitive to methodological details such as peptide length, AlphaFold2 neural network versions, and multiple-sequence alignment database. PAbFold is available at https://github.com/jbderoo/PAbFold.
Supporting Information Contents:
Table 1A: Full sequence information for all scFv and antigen proteins Table 1B: MSA for the scFv chimera variants, with loop and linker region annotation Figure 1: Comparison of AlphaFold2 Myc scFv predictions to Fab crystal structure Figure 2: AlphaFold2 predictions for scFv interacting with full length antigen proteins Figure 3: Illustration of AlphaFold2 peptide predicted placements and confidence thereof Figure 4: Structure superposition analysis for Myc and HA scFv variants relative to reference crystal structures Figure 5: In the context of Myc, testing prediction performance versus sliding peptide window parameters Figure 6: Testing detection of Myc epitope inserted into three locations in an unrelated 3 rd -party protein Figure 7: HA epitope prediction for three anti-HA scFvs Figure 8: Comparing prediction performance for mBG17 using multimer-v2 and multimer-v3 Figure 9: Comparing prediction performance for Myc using multimer-v2 and multimer-v3 and the new MSA Figure 10: Comparing prediction performance for HA using multimer-v2 and multimer-v3 and the new MSA Figure 11: Comparison of 9 major systems after recreating MSAs locally with downloaded databases Figure 12: Comparison of 9 major systems after recreating MSAs with colabfold after MMSEQS rebuilt the old databases for our use Figure 13: Comparison of the 9 major systems without using any MSA, using only the single sequence Figure 14: Comparison of the contents of the MSA for Myc-2E2 after being generated by the 4 major methods: old generation, new generation, local generation, and MMSEQS rebuilt specialty server.Figure 15: Overview table of whether or not each MSA generation type could accurately detect the experimentally determined epitope in each of the 9 major systems.1B Supplemental AlphaFold2 frequently placed peptides on the opposite side of the CDRH3 from the Myc epitope (grey), it was not confident in these peptide placements (low, small, blue pLDDT spheres).In contrast, some of the peptides placed around the CDRH3, and in positions similar to the native epitope (grey) were placed with higher pLDDT confidence (increasingly large spheres trending from green to yellow to orange and red).D) The top ranked peptide as predicted by PAbFold with sequence QKLISEEDLL (red) and the crystal structure solution of the Myc epitope (grey).Supplemental Figure 4: RMSD comparison (all numbers have units of Å) for AlphaFold2 predicted scFv structures compared to reference crystal structures, A) 2or9 (Myc) and B) 1frg (HA), respectively.The loops of the scFv more closely mimic the crystal structure when the epitope peptide is present.The backbone also undergoes subtle changes during docking that make it slightly more similar to the crystal structure.These structures were aligned by identifying the framework residues in all structures, then aligning the framework region Cα with the Kabsch algorithm (49, 50).Specifically excluded from this process were the heavy and light CDR loops of the structures, as well as the flexible linker structure that connects the heavy and light chains due to the inherent floppy, unstructured nature of this region.After aligning the framework regions of the AlphaFold2 predicted structures and the crystal structures (2or9 and 1frg respectively), an RMSD of these Cα was calculated and is reported as the first column 'BB Cα RMSD'.
Supplemental
Without further alignment, loop placement was analyzed with an all backbone RMSD by calculating the RMSD between the C, Cα, N, and O along the backbone of all residues in the scFv that were not used for the framework superimposition.This RMSD is reported in the second column as 'Loop all backbone RMSD'.Finally, to investigate peptide predicted placement and potential scFv:epitope interactions, an all-atom RMSD was calculated between the crystal structure and the AF2 predicted peptide structure (no additional alignment).Because the apo structure lacks a peptide position, this is only reported in the 'Docked' category and is in the 3 rd column labeled 'Epitope all atom RMSD'.One script was written for each scFv (Myc and HA), and can be found in the Zenodo deposition of our data (https://zenodo.org/records/10884181)because this analysis is not a key part of PAbFold.Briefly this analysis reveals that all three HA scFv variants have predicted framework regions and loop regions in the apo structures that closely match the reference structure (0.56-0.58 Å and 1.21-1.39Å).Accordingly, when the cognate epitope peptide is present, it can be placed with relatively high accuracy for all three scFvs (3.1-3.2Å), with only small changes in the loops (1.39 Å to 1.25 Å, 1.32 Å to 1.26 Å, and 1.21 Å to 1.27 Å).In contrast, the apo structures for the three Myc scFvs have a much higher deviation in the loop regions (2.87 to 3.06 Å).
When the epitope peptide is added, there is significant motion in the loops consistent with an "induced fit" description.In the two chimeric Myc scFvs (Myc-15F11 and Myc-2E2) the final loop RMSD is reduced to 1.51-1.61Å, and the epitope peptide is successfully predicted (2.45-2.68Å).However, despite a lower apo-state loop RMSD (2.87 Å), the loop RMSD for the wild-type Myc scFv only drops to 1.75 Å, and the epitope peptide placement does not match the experimental structure (6.69 Å).This is consistent with the failure of the wild-type Myc scFv AlphaFold2 predictions in main text Figure 2. Similarly, with a fixed peptide length of 10 and a sliding window step size of 1 (F), 2 (G), and 5 (H), we can see the practical epitope detection outcome was similar for a sliding window of 1 and 2, but resolution and accuracy were reduced for a sliding window step size of 5. To more fully illustrate the strong learned bias that AlphaFold2 has for placing any peptides among the CDR loops, we predicted the structure of Myc-2E2 in complex with several control peptides.These negative control peptides bind to the generally expected antibody binding site, but with poor pLDDT.I) GSx5 in magenta (GSGSGSGSGS) had a score (mean peptide from Simple Max method pLDDT) of 29.5.(GGGGS) 2 in orange (GGGGSGGGGS) had a score of 31.9.G 10 in red (GGGGGGGGGG) had a score of 33.
Supplemental
Lastly, J) A 10 in cyan (AAAAAAAAAA) had a score of 41 and is the only negative control peptide to have an alpha-helical secondary structure (presumably due to the increased alpha helical propensity of alanine).and PDB70 ( 220313)) (blue).
Figure 1 .
Alignment of AlphaFold2 predicted scFv structures to an anti-c-Myc Fab crystal structure.A) Alignments of AlphaFold2-derived wild-type Myc scFv, Myc-2E2 scFv, and Myc-15F11 scFv structures with a Myc Fab crystal structure (PDB: 2orb).Predicted scFv structures are shown in dark blue, 2orb Myc Fab structures are shown in light blue.B) RMSD values comparing structural similarities between the wild-type Myc scFv, Myc-2E2 scFv, and Myc-15F11 scFv structures with a Myc Fab crystal structure (PDB: 2orb) were computed by the PyMOL align command.Supplemental Figure 2: Alphafold2's best attempt to dock whole sequences with the respective sequence's scFv.A) The whole HA protein structure and scFv complex as predicted by AF2, with the correct epitope sequence highlighted in magenta.B) Shows the same structure by highlighted by confidence (pLDDT) of the structure with AF2.Similarly, the entire Myc protein-scFv complex are shown with C) the correct epitope highlighted in magenta and D) the confidence of the structure shown, and again for the mBG17 Nprotein-scFv complex in E) and F).Supplemental Figure3: AlphaFold2 places all peptides near the CDR loops.The predicted Cα coordinates for all scFv (excluding the flexible linker) were extracted, and all were aligned together using the Kabsch algorithm (49, 50).With the scFvs structurally aligned, an all-against-all RMSD was calculated for the epitope peptides.To visually represent each peptide as a single point, the coordinates for all epitope atoms were averaged.The "central" exemplar epitope (cyan) is the peptide with the smallest sum of RMSD to all other peptides.A) The average and quartile for peptide placement relative to the central peptide via Box-and-Whisker plot reveals that AlphaFold2 largely places all epitopes in the same area.The Myc CDRH3 runs through the middle of a traditional paratope pocket, it isn't a "cradle" for the epitope to sit on.AlphaFold2 places peptides on both sides of the CDRH3, causing significant spread in the peptide placement.B) An example of an exemplar, most-central predicted peptide structure (cyan) for the peptide PKSCASQDSS (cyan) bound to the Myc-2E2 scFv (green) that is distant from an example outlier peptide (magenta, peptide PHSPLVLKRC, center-tocenter distance 14.8 Å).All peptide placements are still in contact with CDRH3, consistent with a strong AlphaFold2 bias to place peptides in a typical antibody binding site.C) The Myc-2E2 scFv (pale-green) and the average epitope placement (cyan) peptide alongside the crystal structure solution of the Myc epitope (grey).Remaining peptide placements are represented as a cloud of spheres at the mean peptide position.Each peptide sphere is colored and sized by epitope pLDDT (ranging from 20 to 90).Although
Figure 5 .
Assessment of peptide size and sliding window sizes on epitope prediction efficacy.Myc-2E2 scFv:peptide structures were predicted with peptides of 8 (A), 9 (B), 10 (C), 11 (D), and 12 (E) amino acid lengths derived from the Myc protein with a sliding window of 2 amino acids, and pLDDT scores from each predicted structure were plotted against the Myc amino acid position and sliding window length target.F) Negative control peptides bind to antibody binding sites, but with poor pLDDT scores.
Figure 6 :
PAbFold epitope detection is independent of position within target sequence.The Myc epitope (EQKLISEEDL) was added into the beginning, middle, or end of the 99-a.a.HIV protease sequence (Genbank Accession: NP_705926.1)prior to epitope scanning structure prediction.Positions of the Myc epitope sequence added to in the A) N-terminus B) middle and C) C-terminus of the HIV protease sequence.D) Highlights the ranked sequences recovered from each experiment in A, B, and C. Supplemental Figure 7: Alphafold2 can accurately predict the HA linear epitope in different scFv backbones.The anti-HA VH and VL antibody sequences were used to generate either A) wild-type scFv or CDR loop grafted onto the B) 15F11 or C) 2E2 antibody backbones.The Influenza A virus hemagglutinin protein sequence (Genbank AUT17530.1)was used as the target antigen and processed into 10 amino acid overlapping peptides with a 1 amino acid sliding window.The structures for each scFv:peptide pair were predicted with Alphafold2, and pLDDT values for each scFv:peptide pair are shown.D) The top-ranking epitope sequences via pLDDT scores are reported via the consensus method.Sequence underlining represents overlap with the known HA epitope (HA a.a.114-125: YDVPDYASL).E) The top-ranking epitope sequences via pLDDT scores are reported via the simple max method.Supplemental Figure 8: A comparison of Alphafold2 multimer version 3 and multimer version 2 applied to the mBG17 system.The experimental epitope, DDFSKQLQQS, is still easily identified with all three scFv backbones (wildtype, 15F11, and 2E2).Supplemental Figure 9: Myc comparison of epitope identification accuracy, comparing model types.Performance variation with AlphaFold2 model (multiple versions 2 and 3) and MSA versions (most up to date version of the ColabFold MSA server uses UniRef30 (2302) and PDB100 (220517)) vs the old MSA server (when this data was initially generated, ColabFold MSA server used UniRef30 (2202) and PDB70 (220313)).The left column is the WT scFv, the middle column is the CDR loops spliced onto the 15F11 backbone, and the right column is the CDR loops spliced onto the 2E2 backbone.Performance was ablated when using MM3 and the new MSA, and significantly degraded when using MM2 with the new MSA.For AF2-MM2 Old MSA, see Figure 2. Supplemental Figure 10: HA comparison of epitope identification accuracy, comparing model types.A comparison of the differing AlphaFold2 models with the Myc system (multimer version 3 and 2) along with a comparison of the new MSA (most up to date version of the ColabFold MSA server uses UniRef30 (2302) amd PDB100 (220517)) vs the old MSA server (when this data was initially generated, ColabFold MSA server used UniRef30 (2202) and PDB70 (220313)).The left column is the WT scFv, the middle column is the CDR loops spliced onto the 15F11 backbone, and the right column is the CDR loops spliced onto the 2E2 backbone.For AF2-MM2 Old MSA, see Supplemental Figure 7. Supplemental Figure 11: Local remake of the databases used by the MMSEQS server.Databases were downloaded (UniRef30 (2202) and PDB70 (220313)) and were queried locally to produced MSA's for testing.These runs all were done with the multimer version 2 model of Alphafold 2. The left column is the WT scFv, the middle column is the CDR loops spliced onto the 15F11 backbone, and the right column is the CDR loops spliced onto the 2E2 backbone.The first row is the HA system, the second row is the Myc system, and the final row is the mBG17 system.Supplemental Figure 12: Server remake of the MMSEQS databases.The databases were rebuilt by the MMSEQS team UniRef30 (2202) and PDB70 (220313)) on the Colabfold MSA server and were queried produced MSA's for testing.These runs all were done with the multimer version 2 model of Alphafold 2. The left column is the WT scFv, the middle column is the CDR loops spliced onto the 15F11 backbone, and the right column is the CDR loops spliced onto the 2E2 backbone.The first row is the HA system, the second row is the Myc system, and the final row is the mBG17 system.Supplemental Figure 13: Single Sequence mode (no MSA's) of epitope prediction with AF2.These runs all were done with the multimer version 2 model of Alphafold 2 in single sequence mode (i.e.no MSA was used) as a negative control, to highlight the importance of a quality MSA.The left column is the WT scFv, the middle column is the CDR loops spliced onto the 15F11 backbone, and the right column is the CDR loops spliced onto the 2E2 backbone.The first row is the HA system, the second row is the Myc system, and the final row is the mBG17 system.Supplemental Figure 14: MSA overlap between the 4 generation methods.Here we highlight the number of unique entries that are shared amongst all of the MSA methods, those being: 1) using the databases right now via colabfold (PDB30 2302 and PDB100 230517) (green) 2) the databases after they had been accessed via colabfold and cached for repeated use (UniRef30 (2202) and PDB70 (220313)) (yellow), 3) downloading the databases locally (UniRef30 (2202) and PDB70 (220313)) and attempting to create the MSAs ourselves (red), and 4) querying the databases after the MMSEQS team rebuilt them for our use via colabfold (UniRef30 (2202)
Table 1A
EQKLISEEDLSupplemental Table BB Ca RMSD Loop all backbone RMSD Epitope all atom RMSD BB Ca RMSD Loop all backbone RMSD Epitope all atom RMSD | 3,703 | 2024-04-19T00:00:00.000 | [
"Computer Science",
"Biology"
] |
Effects of Contents of Multiwall Carbon Nanotubes in Polyaniline Films on Optical and Electrical Properties of Polyaniline
We investigate the effects of different contents of multiwall carbon nanotubes (MWCNTs) on optical and electrical properties of polyaniline (PANI). The MWCNTs/PANI composites are deposited on glass substrates coated with indium tin oxide (ITO) by the spin-coating technique. The scanning electron microscopy shows that nanotubes are coated with the PANI layer and x-ray diffraction patterns show that all deposited composite films have an amorphous character. The analysis of a UV-vis spectrophotometer indicates the blue shift of the absorbance peak and a decrease in optical band gap value by the enhancement of the CNT content in the PANI matrix while the Urbach energy increases. The Raman spectrum shows the blue shift 1404→1417 cm−1 and photoluminescence spectra show an increase in the intensity of characteristic PANI peak at 436 nm with the increasing CNT content.
( Received 30 June 2016) We investigate the effects of different contents of multiwall carbon nanotubes (MWCNTs) on optical and electrical properties of polyaniline (PANI). The MWCNTs/PANI composites are deposited on glass substrates coated with indium tin oxide (ITO) by the spin-coating technique. The scanning electron microscopy shows that nanotubes are coated with the PANI layer and x-ray diffraction patterns show that all deposited composite films have an amorphous character. The analysis of a UV-vis spectrophotometer indicates the blue shift of the absorbance peak and a decrease in optical band gap value by the enhancement of the CNT content in the PANI matrix while the Urbach energy increases. The Raman spectrum shows the blue shift 1404→1417 cm −1 and photoluminescence spectra show an increase in the intensity of characteristic PANI peak at 436 nm with the increasing CNT content. PACS Polyaniline is one of the most attractive conductive polymers due to its high chemical, environmental and thermal stability up to 420 ∘ C, low cost, ease of synthesis, high electrical conductivity and simple doping/dedoping chemistry. [1−4] Recently, nanomaterials have been studied by many researchers due to their industrial applications. [5−8] On the other hand, carbon nanotubes (CNTs) have extraordinary electrical and mechanical properties due to their unique atomic structure. The large surface area provided by the hollow cores and outside walls of nanotubes makes them applicable as a gas sensor. [9] The formation of PANI/CNT composites can improve the electrical, optical and gas sensing properties of polyaniline. CNTs can increase the number of interacting sites for sensing different gases. The charge transfer between PANI and CNT can enhance their electronic interaction. [9] PANI/CNT composites have wide applications in fuel cells, [10,11] solar cells, [12] photovoltaic devices, sensors and biosensors, [13,14] thermoelectric devices, [15] functional membranes, [16] capacitors, [17] and artificial muscles. [18] In this Letter, composites based on multiwall carbon nanotubes (MWCNTs) and doped PANI are prepared with the solution mixing method and spin coated on indium tin oxide (ITO) coated glass. We aim to study the effect of different CNT contents on PANI's optical, structural and morphological properties.
Synthesis of polyaniline was performed by chemical oxidative polymerization of 0.3 M aniline in 1 M HCl solution and dropwise addition of (NH 3 ) 2 S 2 O 8 in the same molar ratio to aniline for 2 h with stirring continuously at 0-5. The solution was refined and the product was washed with 1 M HCl and dried under vacuum for 24 h. The resulting product was emeraldine salt (ES) form of polyaniline. PANI HCl powder remained in 0.1 M ammonia solution and was stirred for 6 h at room temperature. The chemical sediment was refined and washed, respectively, then was dried in vacuum for 24 h to attain emeraldine base (EB) PANI.
PANI was mixed with acid sulfonic camphor (CSA) as a strong acid for protonation of EB PANI, while ES form is not directly soluble in any organic solvent. [19] The mixture was dissolved in 12 mL chloroform and stirred continuously by magnetic stirrer for 6-7 days. MWCNTs (1, 2, 4 wt%) were separately dispersed in 5 ml chloroform by ultrasonication for 2 h. This solution was dispersed in prepared doped PANI solution by using ultrasonication for 30 min. Pre-production solution was deposited on ITO-coated glass (1 × 1 cm 2 ) as a substrate by the spin coating technique at a speed of 2500 rpm. Before use, the substrate was ultrasonically cleaned in heated acetone and ethanol solutions. The spin coated film was dried at 60 ∘ C in the vacuum for 1 h. The obtained composite thin films with 1, 2 and 4 wt% of MWCNTs were denoted as PC1, PC2 and PC3, respectively.
The UV-vis spectra were obtained by using a Varian Cary-500 spectrophotometer. Photoluminescence properties of the samples were studied by a Cary Eclipse spectrometer equipped with a xenon lamp at room temperature. The morphology was characterized by scanning electron microscopy (SEM) (KYKY-EM3200). Raman spectra were recorded by using a Thermo Nicolet (960, USA). An atomic force microscope (AFM) was used to study the surface topography of the CNT/PANI composite films.
The typical SEM image of the PC2 sample containing 2 wt% MWCNTs in PANI is shown in Fig. 1. The MWCNTs are obviously seen in the SEM image as large bundles of tangled carbon nanotubes covered by polymer. A large number of porosity defects are present on the composite surface, which suggests its application as gas sensors based on porous semiconductors. To investigate the surface topography, atomic force microscopy (AFM) studies have been carried out for PANI and MWCNT/PANI composite films. Figures 2(a)-2(c) show the three-dimensional AFM images of PANI, PC1 and PC3 films, respectively, for a surface of 5 µm × 5 µm. The abundance of topography for different samples is shown in Fig. 2(d). Distribution of particle sizes on the surface of PANI and PC1 films is presented by a perfect Gaussian line indicating nearly uniform surface topography. However, the particle size distribution in the PC4 film is not quite a perfect Gaussian line. Figure 2(e) shows the rms roughnesses of PANI, PC1 and PC3. An increase of surface roughness is observed by increasing the amount of CNTs in the composite film. Figure 3 shows the XRD pattern of the PC3 sample (4 wt% of CNTs) on ITO-coated glass. The peaks at 2O-30, 35, 50 and 60 are related to the ITO film coated glass. [20] There is no clear peak corresponding to PANI and CNTs in XRD patterns. Similar results are observed for all the samples prepared in this investigation confirming the amorphous nature of the prepared composite. UV-vis absorption spectra of all the samples are shown in Fig. 4. The characteristic absorption peaks of PANI appear in 347, 404 and 731 nm, which are due to -* , polaron-* and -polaron transitions, respectively. [18,21] Figure 4 shows a blue shift from PANI to PCs at 731 nm. This shift could be due to redistribution of polaron density in the band gap of PANI due to the impact of CNTs [19] and also because of the increase of the interaction energy caused by interaction of polyaniline with MWCNTs. [22] Moreover, the increase of CNTs in PANI causes a continuous absorption of incident light from 404 to 731 nm, which means an increase of localized state density within the band gap.
Bandgaps of pure PANI and PCs are calculated by using the Tauc equation [19] given by 117801-2 where g , , and ℎ are the bandgap energy, the absorption coefficient, the proportionality constant and the photon energy, respectively, and is the index having the values of 1 2 , 3 2 , 2 and 3 depending on the mode of transition. Band gaps of PANI and PCs are shown in Fig. 5 considering a direct transition for = 1 2 . Figure 5 indicates a decrease in the band gap by increasing the CNT content in composites from 3.44 eV for PANI to 3.40, 3.37 and 3.29 eV for PC1, PC2 and PC3, respectively, which can be assigned to the interaction of MWCNTS with PANI, [22] which creates sub-band states in the PANI band gap accompanied by a narrowing of the band gap. [24] In amorphous materials a dense localized state can exist between valence and conduction bands called the Urbach energy (or the Urbach tail) due to the structural disorder. The Urbach energy is related to the width of the tails of localized state and indicates the grade of disorder in the amorphous semiconductors. [25] At lower photon energy the Urbach rule is dominant on absorption as follows: where 0 and u are a constant and the Urbach energy, respectively. The inverse of the slope of ln as a function of (ℎ ) (as shown in Fig. 6) gives u . The calculated u are 0.8, 1.16, 1.5 and 2 eV for PANI, PC1, PC2 and PC3, respectively.
The obtained values of the Urbach energies and bandgap energies are compared as shown in Fig. 7, which indicates the antithetic behavior of these energies by increasing the CNT content. This figure shows that the Urbach energy increases with the CNTs, which results in the rise of localized state formation in PANI chain. [24] Figure 8 shows the Raman spectra of PANI and PC composites. Characteristic Raman shifts of PANI are located at 1300, 1417 and 1588 cm −1 , which are assigned to C-N + , [26] C-C stretching and C=C stretching vibration, [27] respectively. Figure 8 shows a 13 cm −1 blue shift of 1404→1417 cm −1 from PANI to PC3, which is due to -* electron interaction between PANI and MWCNTS. [26] The intensity and width of Raman peak are also increased by increasing the CNT content.
PL spectroscopy of PANI and PC composites in the range of 400-500 cm −1 is depicted in Fig. 9. The excitation wavelength is taken as 350 nm for all the samples at room temperature, due to the benzenoid -* transitionary. [28,29] As shown in Fig. 9, the emission peak is observed at 436 nm, which is assigned to the transition from the polaron band to the band 117801-3 structure of PANI. [30] The intensity of the Pl spectrum is obviously increased by increasing the CNT content due to the higher extent of -conjugation in nanocomposites. [22] The variation of PL peaks' area as a function of the CNT content in Fig. 10 clearly indicates that the increase in the CNT content leads to an increase in the PL peak area, which is correlated to the amount of density of trap states. [31] In summary, effects of different CNT contents on optical, structural and morphological properties of CSA-doped PANI have been studied. The SEM image clearly indicates the presence of CNTs in the composite. The AFM results show that the increasing amount of CNT ends in the increase of the rms roughness. The UV-vis spectroscopy presents two absorbance peaks related to PANI in all the samples and the blue shifts appear in the composites due to the impact of added CNTs. The band gap value decreases and the Urbach energy increases with the increasing CNT content, which are assigned to the rise of localized states in PANI chains. The Raman spectroscopy shows the characteristic peaks of PANI for all the samples. The blue shift is depicted in the Raman spectrum, which is due to the -* electron interaction between PANI and MWCNTs. The photoluminescence spectroscopy exhibits that the emission wavelengths of all the sam-ples are centered at 436 nm, and the intensities of the emission peaks are increased with the rise of the CNT content due to the higher extent of conjugation in nanocomposites. | 2,706.2 | 2016-11-28T00:00:00.000 | [
"Physics"
] |
Robustness of topologically protected edge states in quantum walk experiments with neutral atoms
Discrete-time quantum walks allow Floquet topological insulator materials to be explored using controllable systems such as ultracold atoms in optical lattices. By numerical simulations, we study the robustness of topologically protected edge states in the presence of decoherence in one- and two-dimensional discrete-time quantum walks. We also develop a simple analytical model quantifying the robustness of these edge states against either spin or spatial dephasing, predicting an exponential decay of the population of topologically protected edge states. Moreover, we present an experimental proposal based on neutral atoms in spin-dependent optical lattices to realize spatial boundaries between distinct topological phases. Our proposal relies on a new scheme to implement spin-dependent discrete shift operations in a two-dimensional optical lattice. We analyze under realistic decoherence conditions the experimental feasibility of observing unidirectional, dissipationless transport of matter waves along boundaries separating distinct topological domains.
I. INTRODUCTION
Topological insulators are quantum materials behaving like an ordinary insulator in the bulk and yet allowing, in two dimensions and above, matter waves to propagate along their boundaries through a discrete number of edge modes [1,2]. The distinguishing property of these materials is the existence of so-called topologically protected (TP) edge modes, which are robust against continuous deformations of the material's parameters, including spatial disorder, provided the bulk remains insulating (i.e., no gap closing). In one dimension (1D), a discrete number of TP edge states can exist in the presence of special symmetries (e.g., particle-hole symmetry in superconducting quantum wires), with their energy being exactly pinned to the midpoint of the energy gap. In two dimensions (2D), the most notable example of a topological insulator is a two-dimensional electron gas in a high magnetic field, where the transverse conductance is found to be quantized in multiples of e 2 /h (integer quantum Hall effect, IQHE) [3]. Over the years, this effect has been verified by experiments to one part in 10 9 despite impurities and other imperfections, which unavoidably occur in actual physical samples [4]. Its robustness is today well understood in terms of the topological structure of the Landau levels, which form well-separated energy bands [5].
In general, the robustness of edge states in these insulating materials results from energy bands with nontrivial topological character. Topologically nontrivial bands are often related to an obstruction to define the Bloch wave functions over the whole Brillouin zone using a single phase convention [6]. This obstruction to a global choice of the gauge can be understood as resulting from a twist of the Bloch wave functions, much as the twist in the Möbius strip represents an obstruction to define an oriented surface. The twists of the energy bands are quantified by topological invariants, which are integer quantum numbers assigned to each isolated band of *<EMAIL_ADDRESS>the bulk. These can be, for instance, winding numbers Z (e.g., for the Su-Schrieffer-Heeger model) or just Z 2 numbers with two possible values denoting trivial and nontrivial topological phases (e.g., for particle-hole-symmetric quantum wires). The characteristic of such invariants is that they are unchanged under a continuous modification of the system parameters, provided that the energy gap and the relevant symmetries are preserved. In particular, two insulators are said to belong to different topological phases if the sums of the topological invariants of the occupied bands are different [7,8].
A topological argument with far-reaching physical implications, known as the bulk-boundary correspondence principle, establishes a relation between the topological invariants and the number of TP edge modes at the boundary between two topological phases [9]. Simply stated, it predicts that any spatial crossover region separating two bulks hosts a minimum number of edge modes given by the difference of the bulk invariants. These modes are topologically protected as they cannot disappear by a continuous deformation of the system parameters, including a deformation of the boundary's shape. In the IQHE, for instance, the number of current-carrying TP edge modes is equal to the sum of the Chern numbers of the Landau levels below the Fermi energy [10].
TP edge modes at the boundary of a 2D topological insulator are immune to Anderson localization. Even if we allow for local disorder (of any amount in the region adjacent to the boundary), including shape irregularities, topological arguments predict that TP edge states maintain their metalliclike character notwithstanding the disorder, their wave functions being fully delocalized around the whole length of the insulator [9]. As a consequence, any wave packet formed by a superposition of TP edge states propagates coherently along the boundary, instead of being confined within some region by the disorder. Moreover, transport along the boundary is virtually immune to backscattering too [11], for the wave packet would need to tunnel to the opposite edge of the insulator material in order to couple to a counterpropagating edge mode, a process that is exponentially suppressed with the size of the sample.
Besides being interesting per se, topological insulators have stimulated great interest in the possibility to exploit TP edge states for engineering ballistic electronic transport in dissipationless solid-state devices and for enabling topological protection of quantum information [12]. In recent years, IQHE devices have attained an exquisite level of control, which enabled the demonstration of quantum devices such as an electronic Mach-Zehnder interferometer [13] and a twoelectron Hong-Ou-Mandel-like interferometer [14]. However, these systems still require high magnetic fields on the order of 10 T in order to make the energy gap between Landau levels (i.e., the cyclotron frequency) larger than cryogenic temperatures below 4 K. Larger gaps are obtained with high-mobility graphene IQHE devices, which hold promise to operate at room temperature, although still requiring high magnetic fields [15]. In a different approach, the quantum anomalous Hall effect avoids external magnetic fields by exploiting a ferromagnetic topological-insulator state induced by spontaneous magnetization, although demanding, in return, cryogenic temperatures well below both the Curie point and the magnetically induced energy gap [16,17]. The discovery of the quantum spin Hall effect in HgTe/CdTe quantum wells started the quest for topological insulators with a large gap that do not rely on magnetic fields [18]. However, the gap size of these novel materials still requires, at least so far, cryogenic temperatures < 10 K to function [19].
Topological insulator materials are challenging to synthesize, and only a few topological phases have hitherto been accessible with solid-state materials [20]. This has motivated the search for topological phases in nonelectronic systems, which also allow implementing the same wave-mechanical principles underlying topological insulators. Because of their high degree of control and flexibility, ultracold atoms trapped in an optical lattice are ideal systems to shed new light on the origin and dynamics of topological insulators. In particular, these systems have enabled the direct measurement of the Berry-Zak phase [21] and Wilson lines [22], the realization of the Haldane model [23], the observation of the anomalous transverse velocity [24], demonstration of the Thouless pump mechanism [25,26], the realization of compacted artificial dimensions [27,28], and the measurement of the Berry flux [29] as well as Berry curvature [30]. Besides ultracold-atom systems, TP edge modes have also been observed in microwave photonic crystals [31], photonic quasicrystals [32,33], and even mechanical spring systems [34,35].
Discrete-time quantum walks (DTQWs) with trapped ultracold atoms [36] offer a versatile and highly controlled platform for the experimental investigation of topological insulators. We note that even a single atom coherently delocalized on a periodic potential is sufficient to simulate topology-induced transport phenomena, provided that the energy bands have a nontrivial topological structure. In DTQW experiments, an ultracold atom trapped in an optical lattice undergoes a periodic sequence of internal rotations and spin-dependent translations. This approach can be understood to fall under the more general class of Floquet topological insulators, systems that are periodically driven in time with a period T . After an integer number of periods (i.e., steps), their quantum evolution is reproduced by an effective (Floquet) Hamiltonian that is topologically nontrivial [37]. Varying the protocol for the DTQW is a way to engineer the effective Hamiltonian. In this way, effective Hamiltonians from all universality classes of topological insulators [7,8] can be realized by quantum walks [38].
Floquet topological insulators are especially attractive because of the possibility to control their topological properties via an external periodic drive [39,40] while avoiding any external magnetic field. An optical analog of Floquet topological insulators was demonstrated using an array of evanescently coupled waveguides on a honeycomb lattice [41], with the external periodic drive being effectively implemented by a helicoidal deformation of the waveguides. DTQWs are well suited for creating TP edge modes on the fly by locally controlling the parameters of the external drive. Furthermore, beyond simulating static topological insulators, DTQWs allow us to explore the richer topological structure inherent to Floquet systems, which is not entirely represented in the effective Hamiltonian but instead rooted in the details of the quantum walk sequence. For example, a 1D quantum walk can host TP edge states between domains with the same effective Hamiltonian [42]. Experimental evidence of this phenomenon was shown in a photonic DTQW setup, although only with a small number of steps [43]. In 2D, experimental proposals based on periodically driven cold-atom systems have recently put forward the idea to create boundaries between distinct topological phases, for instance, in the quantum spin Hall model using an atom-chip implementation [44] and in the Haldane model using a brick-wall optical lattice [45]. These proposals, as well as the optical experimental demonstration in Ref. [41], rely on topological invariants derived from the effective Hamiltonian, without studying in detail the whole topological structure predicted by Rudner et al. [46] for 2D Floquet topological insulators. Floquet topological invariants play instead a central role in the cold-atom proposal in Ref. [47] to implement the Rudner model, as well as in the present work.
In our laboratory we choose a single massive Cs atom with two long-lived hyperfine states as the quantum walker, which we coherently delocalized in optical lattices over ten or more lattice sites [48]. However, quantum superposition states in such a large Hilbert space are always highly fragile because they are subject to decoherence and dephasing mechanisms arising from the openness of the quantum system. In DTQWs decoherence leads to a quantum-to-classical transition of the walk evolution dominated by the dephasing process affecting the coherences in the coin degree of freedom, as we have shown previously [48]. It is generally accepted that disturbances with frequencies beyond the energy gap lead to the destruction of the TP edge states. However, in most condensed-matter systems, these effects are often suppressed by operating at cryogenic temperatures [49]. In DTQWs, disturbances on the coin operation, as well as spin dephasing, effectively act with infinitely wide spectrum and therefore extend over the whole band gap, so that we expect the loss of protection in the long-time limit. In the 1D split-step walk, Obuse and Kawakami [50] showed that while topological protection is preserved under weak spatial disorder, temporal fluctuations of the coin angles destroy it. However, a quantitative modeling of decoherence effects, which is essential for future experiments, is still missing.
In this paper, we study how environment-induced dephasing affects TP edge states in one-and two-dimensional quantum walk setups and how diffusive spreading has an impact on the existence and form of TP edge states in general. Moreover, we formulate an experimental proposal under realistic conditions on how to observe ballistic transport of quantum walks using ultracold atoms in optical lattices.
This paper is structured as follows: In Sec. II, we introduce DTQW protocols in one and two dimensions and provide a short overview of their topological structure and corresponding TP edge states. We discuss the arising edge phenomena and analyze their robustness under spatial deformations of the topological phase boundary. In Sec. III, we investigate how the shape and evolution of the edge states are affected under decoherence. Furthermore, we give insight into the limits concerning the model of stroboscopic decoherence, which was employed in Ref. [48]. The numerical simulations in this analysis are carried out using realistic experimental parameters, which are chosen based on the experimental proposal discussed in Sec. IV. In Sec. IV, we present an experimental scheme to realize a two-dimensional spin-dependent optical lattice and discuss the experimental requirements to create spatial boundaries between Floquet topological phases as well as to observe TP edge states under realistic decoherence conditions.
A. The system
We consider a particle with two internal spin states, labeled s ∈ {↑ , ↓}, that is positioned on a cubic lattice with lattice constant a. We will specifically address the cases of N = 1 and N = 2 dimensions, which can be implemented in current experimental apparatuses, as explained in detail in Sec. IV. We label the nodes of the N -dimensional cubic lattice with x = (x,y, . . .) ∈ Z N . Thus, in the absence of decoherence, the quantum state of the walker after n steps is a pure state |ψ n , which comprises a superposition of the basis states |x,s .
The dynamics of the DTQW is defined by a sequence of unitary operations (protocol), which can be of two types: the coin-toss operation and spin-dependent-shift operations. The coin toss is realized by a unitary rotation of the spin state into superpositions of |↑ and |↓ , where σ i is the ith Pauli matrix. The coin angle θ determines the amount of rotation of the spin state and is a function of the lattice position x, θ = θ (x). The rotation axis is chosen to be along the y direction of the Bloch sphere. Note that different choices of the rotation axis in the x-y plane are equivalent up to a unitary transformation of the spin basis vectors {|↑ , |↓ }. The evolution of a pure state |ψ n in time is described by a unitary walk operator W applied periodically at discrete time steps t = n T , n ∈ N: Note that the quantum evolution of the walker is periodically driven in time with a Floquet period T , which is the duration of a single step.
In this work we focus on two DTQW protocols, which allow us to study the most relevant physical properties of topological phases of discrete-time quantum walks in one and two dimensions. In a 1D lattice, we consider the so-called split-step-walk protocol defined in Ref. [38] as which consists of two spin rotations separated by spindependent shifts in the x direction. In a 2D lattice, we study the quantum walk defined by where after each coin operation both spin states are shifted in opposite directions [51]. Note that the shift operators commute,
B. Topological phases and symmetries
In the context of Floquet theory, the evolution of the quantum state can be expressed by the action of a timeindependent effective Hamiltonian H , defined by W = e −iH [52,53]. Due to the discrete spatial translational invariance implied by the lattice, the corresponding eigenstates are Bloch waves characterized by a quasimomentum k, which takes values within the Brillouin zone (−π/a,π/a] N . Likewise, the discreteness of the time evolution implies that the eigenvalues of the effective Hamiltonian H are quasienergies, denoted by , which in our notation take dimensionless values in the interval (−π,π]. Note that physical energy units can be restored trough multiplication by the quantity /T . In DTQWs, the quasienergy spectrum reveals a band structure with two bands resulting from the two internal states, as can be seen in Fig. 1(a), where we provide the quasienergy spectrum for the 1D split-step protocol with (θ 1 ,θ 2 ) = (π/2,0) (Hadamard walk). For a generic choice of the coin parameters, these two bands are gapped. The gapped spectrum relates quantum walks to static systems like insulator materials. However, unlike in static systems, the Floquet quasienergy spectrum can also have a gap at = π since quasienergies = −π and = π are identified. In addition, artificial electric [54,55] and magnetic (a) FIG. 1. Topological twist in the 1D split-step quantum walk with (θ 1 ,θ 2 ) = (π/2,0) (Hadamard walk). (a) Quasienergy spectrum with two energy gaps occurring at energy = 0 and = π . (b,c) The corresponding quasienergy eigenstates of the upper band in the two time frames, Eqs. (7) and (8), displayed on the Bloch sphere. Chiral symmetry constrains the eigenspinors to lie in a plane, x = 0, while the quasimomentum is varied across the Brillouin zone, performing a closed loop. The color gradient indicates the winding direction around the Brillouin zone. The (signed) winding number associated with transformation differs in the two time frames, ν = 1 in (b) and ν = 0 in (c). The topological invariants of the bulk are given by the sum and difference of the two winding numbers, (ν 0 ,ν π ) = (ν + ν ,ν − ν )/2 + 1/2. See also Fig. 2(a) for the related phase diagram. fields [56,57] can lead to a higher number of bands, which can possess nontrivial topological properties as well.
Adapting methods developed for static topological insulators to the effective Hamiltonian H , Kitagawa et al. [38] have shown that DTQWs can reproduce all ten classes of nontrivial topological phases in one and two dimensions for noninteracting particles [7,8]. Topological phases can be assigned to different realizations of the effective Hamiltonian, and the corresponding topological invariants occur in the form of winding numbers of the Bloch energy eigenstates [1].
However, a closer inspection of DTQWs reveals that their so-called Floquet topological phases exhibit an even richer structure, which can only be accessed by analyzing the full time evolution of the walk. This holds for both 1D and 2D DTQWs [42,46,58]. For instance, the topological phases of the 1D splitstep protocol originate from a special symmetry of the walk protocol, which is called chiral symmetry. A walk operator W exhibits chiral symmetry if a unitary operator exists, which transforms it as follows: Although the split-step walk operator W 1D defined in Eq. (5) does not have chiral symmetry, one can show that the two walk operators obtained through a cyclic permutation of the single walk operations, do exhibit chiral symmetry, with the symmetry operator being = σ 1 [59]. The cyclic permutation has split the coin operations into two parts, C(θ i ) = C(θ i /2) C(θ i /2), i = 1,2. Since the walk operations repeat themselves periodically, a cyclic permutation of these operations corresponds to a change of basis preserving the underlying topological structure. Likewise, cyclic permutations allowed identifying time-reversal symmetry in Floquet topological insulators [60]. Hence, the two walk operators in Eqs. (7) and (8) are chiralsymmetric representations of the same walk but expressed in two different time frames. It results from chiral symmetry that each eigenstate at quasienergy has a chiral-symmetric partner eigenstate at quasienergy − . In particular, if eigenstates exist with quasienergy either = 0 or = π , these states can be their own symmetry partners, i.e., be eigenstates of the symmetry operator . This characteristic ensures the robustness of TP edge states in the 1D split-step walk (see Sec. II C). We obtain a geometrical representation of the topological twist of the 1D split-step walk by displaying on the Bloch sphere the eigenspinors of the two chiral-symmetric walk operators defined in Eqs. (7) and (8). The eigenspinors ± n(k) with quasimomentum k are determined by the translationally invariant effective Hamiltonian, H = k (k) |k k| ⊗ n(k) · σ . It directly follows from chiral symmetry that the eigenspinors with quasienergy = 0, π lie in the plane x = 0. This holds true, in particular, for the bulk eigenstates, whose quasienergies lie outside of the gaps, as shown in Fig. 1(a). Hence, if we vary the quasimomentum k across the whole Brillouin zone, the eigenspinor rotates in the plane performing a closed trajectory, winding a (signed) number of times around the origin, as shown in Figs. 1(b) and 1(c). The difference and sum of the signed winding numbers associated with the two time frames yield a pair Z × Z of topological invariants [42,61,62]. For the derivation of the winding numbers, the reader is referred to Ref. [59].
These invariants classify the topological phases of the splitstep walk, and depend only on the coin angles (θ 1 ,θ 2 ), as shown by the phase diagram in Fig. 2(a). In essence, the pair of topological invariants (ν 0 ,ν π ) counts the minimal number of times the band gap closes at quasienergy = 0 and = π , respectively, as the walk is continuously transformed into the topological phase characterized by (0,0). Note, however, that the topological protection of these states holds only for perturbations that can be continuously contracted to unity. For noncontinuous perturbations, instead, the topological phase diagram relies on a single signed winding number, as recently demonstrated in Ref. [63].
In two dimensions, a Floquet topological invariant Z, the so-called Rudner winding number [46], identifies the topological phases of the 2D DTQW protocol [64]. The topological phase diagram is shown in Fig. 2 Topological invariants assigned to the coin angles of (a) the 1D split-step walk and (b) the 2D protocol. Due to the form of the coin operator C(θ ), the walk possesses a 4π periodicity in the coin angles. At the phase boundaries, the gap closes at quasienergy = 0 (dotted), = π (dashed), or both at = 0 and = π (dash-dotted). The coin angle pairs chosen in the numerical examples in this work and the corresponding phase transitions defined in Eqs. (9) and (10) are also displayed (line with stars). The 1D Hadamard walk (θ 1 ,θ 2 ) = (π/2,0), which is discussed in Fig. 1, is also shown (diamond).
of the coin angles. Remarkably, due to the Floquet character of the DTQW protocol, nontrivial topological phases exist even if the topological invariants assigned to the effective Hamiltonian (i.e., the Chern numbers) are zero. Moreover, we note that, unlike in one dimension, the 2D DTQW protocol possesses nontrivial topological phases without need for specific symmetries.
C. Topologically protected edge states
We consider a spatially inhomogeneous DTQW in which the coin angles depend on the position. The coin angles are allowed to assume any value inside a spatially confined region at the interface between bulk regions, where the coin angles are kept constant instead. When these bulk regions are associated with different topological invariants, TP edge states occur at energies lying in the gaps of the bulk insulators. More precisely, the bulk-boundary correspondence principle states that the minimum number of edge states is equal to the algebraic difference (in absolute value) between the topological invariants of the individual bulk phases.
For the investigation of TP edge states in the 1D protocol, we choose realizing two spatially adjacent topological phases with invariants (ν 0 ,ν π ) = (0,0) for x 0 and (1,0) for x 0, as delineated in Fig. 2(a). We thus expect a TP edge state with quasienergy = 0 to be localized at the boundary around the site x = 0. To account for realistic experimental conditions, we considered a regular variation of the coin angles over approximately two lattice sites, as displayed in Fig. 3(a), without abrupt changes. The width of the transition is related to the optical resolution of our experiment, introduced in Sec. IV. Under these conditions, we studied the time evolution of a walker initially prepared in the single-site state |ψ 0 = |0, ↓ . The results for the ideal situation without decoherence are presented in Fig. 3(b), where the spatial probability distribution is shown as a function of position x and number of steps n, P (x; n) = s∈{↑,↓} | x,s|ψ n | 2 . Because the initial state has a large overlap with the TP edge state ( 0.3 for the example shown in Fig. 3), the walker is trapped at the boundary with a high probability, yielding a peaked position distribution around the origin even in the long-time limit.
In the 2D walk protocol, the boundary between two distinct topological domains describes a 1D contour. Along this boundary, which can have, in general, any shape, TP edge states are expected to exist [65]. However, unlike in the 1D split-step walk, the wave function of the TP edge states is delocalized in space, extending along the whole length of the boundary. As a result of that, a walker in a superposition of TP edge states is no longer confined in the vicinity of the initial site but can propagate along the whole boundary. We gather further insight into the transport dynamics along edges by studying the propagation of a wave packet along a straight boundary, which we assume is oriented along, say, the x direction. The flatness of the boundary ensures that the quasimomentum in the boundary's direction k x is preserved, so that it can be used to derive the energy dispersion relation of the edge modes. Figure 4 shows the quasienergies as a function of the quasimomentum k x computed from the effective Hamiltonian for the case of horizontal boundaries between topological domains. The quasienergy spectrum shows edge modes present in the gaps of the bulk phases. Recalling the expression of the group velocity, v g (k) = ∂ (k x )/∂k x , characterizing the motion of a wave packet, we realize from the slope of the dispersion relations that the TP edge modes transport currents in a unidirectional manner. Moreover, for the specific situation of a straight horizontal boundary as considered in Fig. 4, it appears that the group velocity does not depend on k (i.e., dispersionless transport), being equal to ±1 site per step. We remark that dispersionless transport is not a topological feature but rather a quantum transport property of the specific DTQW protocol defined in Eq. (6).
With reference to the phase diagram in Fig. 2(b), this choice of angles is associated with Rudner invariants −1 inside and +1 outside. We have chosen to add a sharp corner on top of the topological island to test the robustness of the TP edge modes against irregularities of the boundary. As in the 1D case, we again consider a continuous variation of the coin angle at the boundary. Angles at the crossover between the inside and outside regions are varied along the line marked in the phase diagram in Fig. 2(b). Figure 5(a) shows the spatial probability density distribution P (x; n) as a function of position x and number of steps n. We initialize the walker in a single site near the boundary, so that its state has a significant overlap with the TP edge states, leading to a unidirectional propagation around the island. In the absence of 9) realizing two spatially adjacent, distinct topological domains with invariants (ν 0 ,ν π ) = (0,0) for x 0 and (1,0) for x 0. We use a smooth crossover transition corresponding to the diffraction-limited optical resolution of our imaging system (see Sec. IV for details). (b) Decoherence-free evolution of the spatial density distribution P (x; n) as a function of the number of steps n for a walker initially prepared in the single-site state |0, ↓ . The narrow peak located at the boundary near x = 0 indicates the component of the walker populating the TP edge state. (c) The same walk is subject to pure spin decoherence and pure spatial decoherence with increasing decoherence probabilities p S , p P . Insets: time dependence of the walker's probability P (x = 0; n) to be at the origin x = 0 in logarithmic scale. It exhibits an exponential decay for small amounts of decoherence but stays constant for the decoherence-free evolution. The time evolution is calculated for a large number of lattice sites (201) to prevent the walker from reaching the boundaries in the given maximum number of steps. decoherence effects, we observe that the edge current persists even after many revolutions around the island, indicating the presence of metallic edge states delocalized along the whole contour of the island. However, unlike for the straight boundary discussed in Fig. 4, which exhibits dispersionless transport, we observe for the droplet-shaped island that the wave packet's probability distribution spreads along the entire border after several revolutions. We attribute the observed dispersion to the short radius of curvature associated with the border.
A. Stroboscopic decoherence model
Quantum superposition states are fragile against decoherence, that is, disturbances caused by the surrounding environment onto the quantum system. The effect of decoherence on the quantum evolution can be effectively described as the projection of quantum states onto a particular basis of so-called pointer states [67], which are robust against decoherence. In quantum-walk experiments with neutral atoms, the pointer states are the spin |s , with s ∈ {↑, ↓}, and the position states |x with x ∈ Z N [48]. Assuming a small amount of decoherence per step, we can approximate the continuous-time decoherence process through a series of discrete measurement operations, which are applied stroboscopically after each unitary step of the walk. We assume that each measurement only resolves the walker's state with a certain decoherence probability 0 p 1. The walk's evolution is coherent for p = 0, while it describes a classical random walk for p = 1. Our model relies on the assumption of small decoherence to be accurate, p 1. Henceforth, we denote by p = p S and p = p P the decoherence probability related to the spin and position states, respectively.
We follow Ref. [48] to describe the nonunitary time evolution of the walker by means of the reduced-density-matrix formalism. As the walker is initially prepared in a pure state |ψ 0 , the initial density matrix is ρ 0 = |ψ 0 ψ 0 |. The density matrix ρ n+1 describing the walker at time t = (n + 1) T depends only on the state of the walker at time t = n T (Markovian assumption). Hence, ρ n+1 is obtained through the repetitive application of the linear superoperator E, which accounts for the effect of environment-induced decoherence at each step [68]: (11) where i ∈ {↑, ↓} for pure spin and i ∈ {x} for pure position decoherence. The projectors P i are defined as We found in a previous study that this simple model reproduces in a satisfactory manner the effects of decoherence occurring in our experiments with neutral atoms [48]. In particular, our previous analysis revealed that spin decoherence is the main mechanism responsible for the loss of coherence in the current 1D quantum-walk setup. We therefore focus in this work primarily on decoherence by spin dephasing. In addition, our numeric analyses assume a conservative decoherence probability of p S 0.05 per step, which is based on previous experimental results [48]. However, the construction of a new quantum-walk setup for 2D DTQWs is underway that promises decoherence probabilities as low as p S < 0.01 owing to a number of technical improvements, including, among others, shielding of stray magnetic fields and suppression of polarization distortions of the optical lattice laser beams.
B. Decoherence effects on TP edge states in 1D
We illustrate the effect of decoherence by analyzing the walk evolution of a 1D DTQW with two adjacent bulks with coin angles defined by Eq. (9). We again initialize the walker in a single-site state |0, ↓ near the boundary, so that the walker is able to populate the TP edge state.
In Fig. 3(c) we show the spatial probability distribution P (x; n) = s∈{↑,↓} x,s|ρ n |x,s obtained numerically using Eq. (11). The resulting distribution of the walk reflects two phenomena. First, the walker occupies the TP edge state, resulting in a narrow probability peak located around the crossover point at x = 0. Second, this peak stays nearly constant in position and shape but decays over time with a rate increasing with the decoherence strength p. On the other hand, the component of the walker's wave function that has no overlap with the TP edge state expands in the bulk. For small decoherence, the expansion preserves a ballisticlike behavior for many steps, resulting in the characteristic distribution with off-center peaks. The number of peaks and the direction of propagation depends on the initial state of the walker. For stronger decoherence, this expansion exhibits a diffusive behavior [48], with a distribution centered around the starting point, thus overlapping with the TP edge state. From our simulations, it results that experiments must be conducted under small-decoherence conditions, p < 0.05, in order for us to be able to detect the persistence of a sharply peaked distribution at the boundary, a signature of the TP edge state. It should be noted that the decoherence rate determines the point in time where the expansion changes from a ballistic spreading on a short time scale to a diffusive behavior for longer times [48].
The probability for the walker to remain in the origin, P (x = 0; n), is an indicator of the robustness of the TP edge state (see the insets in Fig. 3). It shows an oscillatory evolution for a short transient due to the dynamics of the walker's component overlapping with the bulk states, which is free to expand into the bulk. For longer times, the probability stays constant for the decoherence-free evolution but decays nearly exponentially for low decoherence rates. In the case of strong decoherence, the population of the TP edge state deviates from a simple exponential decay. In this regime, however, the assumption underlying our stroboscopic decoherence model, p 1, does not hold anymore (see Sec. III A). A more detailed discussion based on an analytic model is presented in Sec. III D.
C. Decoherence effects on TP edge states in 2D
The evolution of the 2D walk revolving around the droplet-shaped topological island in the presence of weak spin decoherence is presented in Fig. 5(b). The probability current along the boundary shows a slow decay over time. As an indicator of the population of the TP edge modes, we study the probability P (x ∈ F ; n) for the walker to be situated in a small band F around the edge, as shown in Fig. 6(a). For an initial transient period of 50 steps, the edge probability shows a decrease which is nearly independent of the decoherence probability and is attributed to the nonvanishing projection of the initial single-site state onto the bulk states. For the decoherence-free evolution, the probability tends, in the longtime limit, to a constant value, P (x ∈ F ; n 1) = 0.53. It is worth emphasizing that such a high probability is favorable for future experiments, which aim to detect matter waves trapped at the boundary. In the presence of decoherence, instead, we observe an approximately exponential decay in qualitative agreement with the results obtained in the 1D walk (see Sec. III B).
While decoherence reduces the probability current, it has no discernible effect on the propagation velocity of a wave packet along the boundary. The comparison between Figs. 5(a) and 5(b) shows, in fact, that the front of the wave packet moves, in both cases, with a speed of approximately one lattice site per step, regardless of whether the walker is subject to decoherence. This velocity is also in good agreement with that computed in Sec. II C from the energy dispersion relation of a flat boundary. Interestingly, the propagation along the boundary attains the highest velocity, one site per step, allowed by the 2D quantum walk protocol defined in Eq. (6) (i.e., attains the effective speed of light for the DTQW protocol). To gain further insight into the dynamics of the walker revolving around the island, we display in Fig. 6(b) the probability P (x ∈ L; n) for the walker to be in the lower half, L, of the boundary. This probability exhibits periodic oscillations in time with a period that is independent of the decoherence rate and approximately equal, in units of steps, to the length of the contour of the topological island. The period, in particular, corroborates our previous observation that the wave packet moves unidirectionally along the boundary with a velocity of nearly one site per step. We also observe that the oscillation amplitude is damped after several revolutions. We explain this damping as the result of the group velocity dispersion of the TP edge states, which make the wave packet spread along the entire boundary. In the presence of decoherence, the damping occurs on a much shorter time scale, presumably due to the walker's component that is diffused into the bulk but located inside the band L. For the unitary evolution, however, oscillations persist with the same periodicity for long times, as shown in the inset of Fig. 6(b). The modulation of the oscillation amplitude over long time scales is attributed to partial collapses and revivals since the time evolution is unitary and the edge of the topological island constitutes a finite Hilbert space with a discrete spectrum [69]. A detailed study of the residual oscillations would require further investigation.
D. Analytical model of the decay of TP edge states
We consider the 1D split-step walk protocol to derive a simple analytical model predicting the decay rate of TP edge states in the presence of decoherence. Assuming that the walker is initially in a TP edge state |E , we compute the probability (n) that it remains in the same state after n steps. Due to decoherence, the walker's wave function acquires a nonvanishing overlap with the continuum of the bulk states. In order to carry out the computation analytically, we assume that the walker's component coupled to the bulk rapidly leaves the boundary because of the nearly ballistic expansion without ever repopulating the TP edge state. Under this assumption, which is well justified in the regime of weak decoherence p 1, we find in the Appendix that the probability of occupying the edge state is where the decay rate γ depends on |E and is linear in p. For pure spin decoherence, the decay rate is given by A similar expression for the decay rate γ P for pure position decoherence is provided in the Appendix. Moreover, the expression in Eq. (14) can be written in a more compact form as γ S = p S (1 − s | s|s E | 4 ) by exploiting the factorization of 1D TP edge states into position and spin components, |E = |χ ⊗ |s E , as ensured by chiral symmetry (see Sec. II B). This simple model predicts an exponential decay of the edge-state population, which agrees well with the numerical simulations for short times and small decoherence, as shown in Fig. 7. In addition, we attribute deviations from the exponential decay model, observed for longer times, to a non-negligible probability that decoherence transfers the walker from the bulk states back to the TP edge state.
E. Limits of the stroboscopic decoherence model
In Sec. III A, we have modeled the effect of decoherence through a single measurement operation of either the spin or the position of the particle, applied after each coherent step of the walk W . This constitutes, in general, a good approximation of the actual dynamics, provided that the amount of decoherence is small (p 1), as is the case in ultracold-atom experiments (see Sec. IV).
However, situations exist where the stroboscopic application of decoherence can completely fail to describe the decay of a TP edge state. We would like to caution the reader about that by providing an explicit example, which is constructed ad hoc to prove the existence of a TP edge state that is robust against any amount of stroboscopic spin decoherence. Such a situation can occur when the quantum walk possesses a special symmetry (for example, chiral symmetry) that forces the spin component of the TP edge state to be oriented along a given direction, for example, along the z direction. It is evident in this case that spin measurements in the z basis leave the TP edge state unperturbed. This is confirmed by Eq. (14), predicting in this case a decay rate γ S = 0 for any p S . This can be realized by considering a unitary transformation of the walk operator in Eq. (7),W 1D = C(π/2) W 1D C(−π/2). This transformation is equivalent to a cyclic permutation, and it does not change the walk evolution in the bulk as well as the corresponding topological invariants. The chiral-symmetry operator of the transformed walk is σ z since σ zW1D σ z =W 1D † . Since the TP edge states are eigenstates of the symmetry operator (see Sec. II B), their spin must be either |↑ or |↓ , and projective measurements of the spin in the z basis leave the TP edge state unaffected. We note that an analogous situation can be reproduced in the Su-Schrieffer-Heeger topological model, where it is known that the sublattice symmetry (tantamount to chiral symmetry) forces the TP edge state to lie on either one of the two sublattices [9]. Hence, a quantum nondemolition measurement of the sublattice would leave, in like manner, the TP edge state unaffected.
A remedy to avoid such seemingly paradoxical situations, where TP edge states are left unmodified by environmentinduced decoherence, consists of modifying Eq. (11) to allow the decoherence Kraus operators to act after each discrete operation of the single step. Furthermore, identifying the exact operator-sum representation in terms of Kraus operators of the decohered coin operation would ultimately provide the most accurate modeling of decoherence effects [70].
A. Optical lattice experimental setup
We have shown in previous experiments [36] that an atomic quantum walk can be realized employing a single neutral cesium atom in an optical lattice at a specific wavelength λ L = 866 nm. The outermost hyperfine ground states, |↑ = |F = 4,m F = 4 and |↓ = |F = 3,m F = 3 , define the pseudo-spin-1/2 states of the quantum walker. Due to their different ac polarizabilities, each of these states experiences, to a large extent, only the trapping potential of either one of two distinct σ + -and σ − -circularly polarized optical lattices. The setup for spin-dependent shift operations in one dimension is depicted in Fig. 8(a), where two counterpropagating laser beams of linear polarization form a 1D optical lattice along the direction of the quantization axis. Spin-dependent shift operations are then realized by controlling the polarization and phase of just one of the two optical lattice beams (beam 1 in the figure). A rotation of its linear polarization, which is achieved through a shift of the relative phase between circular polarization components, displaces into opposite directions the two circularly polarized optical lattices and thereby atoms in different internal states. Previous implementations [71,72] of this concept based on an electro-optic device suffer from the shortcoming that shift operations are limited to a maximum distance of about one lattice site at a time and, most importantly, to only relative displacements between |↑ and |↓ spin components. Sole relative displacements are not sufficient to realize the S ↓ x and S ↑ x operations, which are required by the split-step walk protocol in Eq. (5). However, we recently demonstrated a different technique for precision polarization synthesis, which overlaps two fully independent laser beams with opposite polarizations to form a beam of arbitrary polarization and phase [73]. The new implementation of spin-dependent transport allows us to independently shift each individual spin component by an arbitrary distance, ultimately limited by the Rayleigh length.
We propose to extend the concept of spin-dependent transport, which has hitherto been demonstrated only in one dimension, to a square lattice in two dimensions. We employ three interfering laser beams with linear polarization, as illustrated in Fig. 8(b). With reference to the figure, the polarization of beams 1 and 2 can be rotated in time by angles φ 1 and φ 2 , respectively, employing our recently developed polarization-synthesis setup for each of the two beams. The polarization of beam 3 is instead fixed and orthogonal to the quantization axis, which is chosen along the direction of beams 1 and 2. In essence, a rotation of the two polarization angles results in a spin-dependent shift operation along one of the two diagonal directions, as shown in Fig. 8(c). This experimental scheme allows the precise control of discrete-time spin-dependent shift operations along the two main directions of a square lattice. We note that our scheme differs substantially from other experimental schemes 8. (a) One-dimensional lattice potentials created by two linearly polarized beams. A polarization rotation by φ leads to a relative displacement of the two optical potentials (orange and blue curves), which spin-dependently trap atoms in either the |↑ or |↓ internal state. The vector B represents the direction of the external magnetic field, which fixes the quantization axis. (b) Twodimensional lattice potentials created by three interfering laser beams for spin-dependent transport on a square lattice. The polarization of beam 3 points out of the plane, whereas the polarization of beams 1 and 2 can rotate, producing spin-dependent displacements along two diagonal directions at ±45 • relative to the quantization axis. Two counterpropagating beams (not shown) orthogonal to the plane provide the confinement in the third direction. (c) Potential depth of the two spin-dependent optical lattices (orange and blue) for different polarization angles, φ 1 and φ 2 .
for continuous-time spin-orbit coupling, which are based on either a dynamical rotation of the magnetic field (i.e., of the quantization axis) [74] or a dynamical modulation of a magnetic-field gradient [75,76].
The geometric arrangement of laser beams in Fig. 8(b) increases the spacing between adjacent lattice sites by a factor of √ 2 (thus, a = √ 2 λ L /2) compared to the 1D lattice presented in Fig. 8(a), constituting an advantage to optically address each lattice site individually. In addition, the concurrent interference of all three beams yields a trap depth that is 3/2 times as deep as that obtained by a 1D lattice for the same optical power. 9. The intensity of Raman lasers, utilized to implement the coin operation, is modulated in space to give rise to sharp topological phase boundaries. A spatial light modulator (SLM) creates a structured intensity pattern, which is imaged onto the optical lattice by a high-numerical-aperture (NA of 0.92) objective lens mounted in a 4f optical system.
The construction of the experimental apparatus is currently underway. An objective lens with large numerical aperture (NA), which is placed 150 μm in front of the 2D lattice, allows us to detect the location of atoms with single-site resolution by fluorescence imaging on the D 2 line at λ f = 852 nm [77], as well as to project a structured intensity pattern for local optical control of the coin operation. The coin operation can be implemented either through microwave radiation resonant with the hyperfine splitting at 9.2 GHz or through a pair of Raman laser beams with wavelength λ C = 894 nm slightly detuned from the D 1 line. Microwave pulses are most suited for driving coin operations with position-independent coin angles, while Raman laser pulses allow spatial variations of the coin angles by modulating their intensity. For the local control of the Raman laser intensity with single-site resolution, we propose the 4f optical system illustrated in Fig. 9. The coin rotation angle at a certain lattice site depends linearly on the intensity of Raman lasers illuminating that given site.
In the experiments, sharp crossovers between topological phases are preferable because their TP edge states are strongly localized in the proximity of the boundary, thereby avoiding slowly decaying tails in the direction of the bulk. This ensures a relatively high probability that an atom originally prepared in a single lattice site next to the boundary populates the edge state. Additionally, sharp boundaries make it less demanding for experiments to realize coherence lengths [78] longer than the size of TP edge states. However, there is a limit on how sharp crossovers between different topological domains can be, which is determined by diffraction in the optical system. For diffraction-limited optical systems, the sharpness of the phase crossover depends on the NA of the objective lens, the lattice constant a, and the wavelength λ C of the Raman lasers. Mathematically, the intensity profile experienced by atoms results from the convolution of the profile generated by the spatial light modulator (see Fig. 9) with the point-spread function (PSF) of the imaging system [77]. In the numerical simulations presented in this work, we approximated the experimentally measured Airy-disk-like PSF with a Gaussian function with standard deviation ( √ 2/π )R A , where R A = λ C /(2NA) is the Abbe radius. Hence, the unit step profile with coin angles θ L for x 0 and θ R for x > 0, which we considered for the 1D simulations, results, after the convolution, in where erf is the Gaussian error function. The present 1D quantum walk setup with NA = 0.22 [77] and a = λ L /2 allows only moderately sharp boundaries, R A 4.8a. The new 2D quantum walk setup, instead, features an objective lens with a higher numerical aperture, NA = 0.92, and a longer lattice constant, a = √ 2 λ L /2, resulting in R A 0.8a. This permits nearly abrupt phase boundaries, where the coin angle is varied across just approximately one lattice site.
B. Realization of topological phase boundaries
In order to obtain a quantitative relation between the optical resolution of the optical system and the shape of TP edge states, we numerically studied the phase crossover in the 1D protocol as a function of the ratio a/R A . As shown in Fig. 10, the size of the TP edge state decreases monotonically with the optical resolution until it attains a constant value around one lattice site. The figure also displays the probability P init = | E|x 0 ,s 0 | 2 to populate the TP edge state |E from the initial state |x 0 ,s 0 . In the experiments, it is important to maximize this probability by choosing a sharp boundary and the initial spin |s 0 such that it coincides with the spin of the edge state at position x 0 . The initial spin can be easily prepared by applying a suitable microwave pulse.
V. OUTLOOK AND DISCUSSION
In this paper, we have studied the robustness of TP against environment-induced decoherence, which causes dephasing of the quantum walk states. We have analyzed the effect of decoherence on the existence and form of TP edge states. We have found that decoherence of spin and position states leads, in both cases, to an approximately exponential decay of the TP edge state into the bulk states. A study of phase coherence properties of matter waves propagating along a quantum circuit of TP edge states will be the subject of future work, similar to that pursued in Ref. [79] with IQHE solid-state devices [13].
Our scheme for 2D spin-dependent transport combined with Raman laser pulses to drive the coin operation will allow us to realize arbitrary topological domains in 1D and 2D quantum walks under realistic decoherence conditions. Owing to a high numerical aperture, the diffraction-limited optical system utilized to project the Raman pulses reduces the size of the TP edge states to a minimum, yielding a high probability to populate them from a single site.
Exploring the limits of the stroboscopic decoherence model revealed that specific TP edge states can be unaffected by decoherence. In the future, we plan to build upon this result to construct Kraus operators that can pump the walker into a TP edge state when applied periodically in time. This would allow us to engineer dissipation to protect TP edge states not only from static disorder but also from a weak amount of environmental decoherence [80].
As yet, little is known about the role of interactions in topological insulators [81,82]. While topological phases of noninteracting systems are relatively well understood, the classification of interacting topological phases is in its infancy. The most promising direction of future quantum walk experiments with neutral atoms consists of exploiting the strong, controllable interactions between atoms in order to understand topological phases with interacting particles. Atoms have, in fact, the potential to shed new light on topological phases with strongly correlated particles, which go beyond a purely wave-mechanical picture such as that of noninteracting topological phases [31,34,35].
ACKNOWLEDGMENTS
We thank C. Robens, G. Moon, and M. Fleischhauer for insightful discussions. We acknowledge financial support from the Deutsche Forschungsgemeinschaft SFB project Oscar, the ERC grant DQSIM, and the EU project SIQS. We acknowledge support from the Hungarian Scientific Research Fund (OTKA) under Contract No. NN109651 and the Deutscher Akademischer Austauschdienst (TempusDAAD Project No. 65049). T.G. was supported by the Studienstiftung des deutschen Volkes. J.K.A. was supported by the Janos Bolyai Scholarship of the Hungarian Academy of Sciences.
APPENDIX: ANALYTICAL DECAY MODEL OF THE TP EDGE STATE UNDER DECOHERENCE, EQUATIONS (13) AND (14)
We derive an analytical model describing the decay of the TP edge state under pure spin decoherence. A model describing the decay under decoherence affecting only the position states can be derived analogously.
Let |E be a TP eigenstate of the walk operator W with quasienergy . The corresponding density matrix ρ 0 = |E E| is then invariant under application of the walk operator W : We consider the 1D walk evolution of this state under spin decoherence as defined by Eq. (11). After one step, the walker's state is described by where P s is the projector onto the spin state s, as defined in Eq. (12). The probability (1) to find the walker in the same state |E is given by x ,s| ρ 0 |x,s x,s| ρ 0 |x ,s where we used the orthogonality of the basis states |x,s as well as the purity of the initial state, tr(ρ 2 0 ) = 1. Hence, we obtain whereρ 1 describes a statistical mixture with no overlap with the initial state, tr(|E E|ρ 1 ) = 0. Assuming that |E will never be populated by the time evolution ofρ 1 , tr[|E E| E n (ρ 1 )] = 0 ∀ n > 0, the probability (n) to find the walker at time t = n T in the initial state is given by where the decay rate γ S is defined as For pure position decoherence, one analogously obtains where | 12,752.6 | 2016-05-11T00:00:00.000 | [
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Human Head and Helmet Interface Friction Coefficients with Biological Sex and Hair Property Comparisons
Dummy headforms used for impact testing have changed little over the years, and frictional characteristics are thought not to represent the human head accurately. The frictional interface between the helmet and head is an essential factor affecting impact response. However, few studies have evaluated the coefficient of friction (COF) between the human head and helmet surface. This study’s objectives were to quantify the human head’s static and dynamic COF and evaluate the effect of biological sex and hair properties. Seventy-four participants slid their heads along a piece of helmet foam backed by a fixed load cell at varying normal force levels. As normal force increased, static and dynamic human head COF decreased following power–law curves. At 80 N, the static COF is 0.32 (95% CI 0.30–0.34), and the dynamic friction coefficient is 0.27 (95% CI 0.26–0.28). Biological sex and hair properties were determined not to affect human head COF. The COFs between the head and helmet surface should be used to develop more biofidelic head impact testing methods, define boundary conditions for computer simulations, and aid decision-making for helmet designs.
Introduction
Linear and rotational head accelerations influence brain injury risk [9,22,23,28,29], and an emphasis on reducing rotational acceleration has driven new helmet design features.Bike helmet manufacturers have sought to decrease concussion risk by reducing the head's rotational acceleration upon impact using different rotation-mitigating technologies.These technologies include Multi-directional Impact Protection System (MIPS), WaveCel, POC Shearing Pads INside (SPIN), and 6D Omni-Directional Suspension (ODS) [10].MIPS is a technology that provides a slip plane for the head to slide independently from the helmet shell [7].POC SPIN technology uses silicone gel-filled pads to decouple the head from the helmet [8].In another approach, the WaveCel technology reduces head rotational acceleration through liner cells flexing and gliding [10].Like WaveCel, the 6D ODS does not use a slip plane but an elastomeric damper array between an inner and outer helmet layer [8].These new design developments highlight that interfacial properties, such as friction between the helmet and head, play a significant role in impact response.Reducing friction between the headform and helmet correlates with lower head rotational kinematics [1,13].Therefore, friction could Associate Editor Joel Stitzel oversaw the review of this article.
influence helmet testing and data interpretation when determining injury risk [14].
Despite the technological advances, dummy headforms implemented in head impact testing have changed little over the years and have known limitations to their biofidelity [36].Of note, the dummy headforms' friction characteristics are thought to not accurately represent the human head [1,11,19,35].The Hybrid III headform, developed for automotive crash testing but now also used in helmet testing, has a vinyl plastisol skin with a high friction coefficient [19,35].Some test methods cover the Hybrid III headform with a stocking to reduce friction and better simulate the human head's friction characteristics [12,32,34].Other helmet test methods use a National Operating Committee on Standards for Athletic Equipment (NOCSAE) headform.The NOCSAE headform was developed exclusively for helmet testing, and its outer layer is composed of polyurethane skin [11,16,18].Magnesium headforms, which are also commonly used in standards for helmet testing, have no outer layer and have been reported to have lower coefficients of friction than the Hybrid III [13,25,33].However, few studies have evaluated the coefficient of friction (COF) between the human head and helmet interior surface; therefore, the frictional biofidelity of these headforms is unknown [13,33].
The most relevant friction study, by Trotta et al., measured the friction between six cadaver heads and a liner material using a 20-mm probe on an Instron [33].This study found that the human head had a static COF between 0.21 and 0.35 and a dynamic COF between 0.20 and 0.32 for a normal force of 20-200 N, and that hair had no effect [33].However, the results were limited by the small sample size, only testing cadavers, and a small interacting surface area.Another study by Ebrahimi et al. found the human skin COF against helmet padding to be 0.683 using force measurements from ten trials at two different normal forces [13].Few details were provided describing the methods used to calculate COF.Ebrahimi et al. were limited by not specifying the area of skin, a small sample size, and not evaluating friction as a function of applied normal force instead of averaged across normal forces [13].
Human skin has viscoelastic properties [5,6,30] which may deviate from the classic Amonton and Coulomb friction law that indicates friction is proportional to normal force [26].To assess friction coefficients for human skin accurately, it is essential to consider the normal force since previous studies have demonstrated a decline in dynamic and static friction coefficients as the normal force increases for human skin [30].However, it should be noted that these studies were conducted on other areas of the skin [30].Similarly, Trotta et al. observed a reduction in human head COF when higher stroke frequencies (material moving over the head) and increased normal force were applied, indicating that there is a relationship between normal force and COF for the human head [33].The textile industry observed a comparable effect when evaluating viscoelastic materials and often quantifies this using a power-law relationship [15,27].Therefore, a power-law relationship could be necessary in describing the decrease in friction coefficients with increasing normal force when evaluating human head friction.
Our study objective was to evaluate the human head's static and dynamic friction coefficients against expanded polystyrene (EPS) helmet foam over varying normal force levels.Our approach included a larger sample size, a larger interacting surface area, and living participants, compared to the works of Trotta et al. and Ebrahimi et al.We also evaluated biological sex and hair properties' effects on friction coefficients.Defining the human head static and dynamic friction coefficients on a helmet surface can be used to develop more biofidelic dummy headforms, describe boundary conditions for computer-aided simulations, and aid decision-making for helmet designs.
Materials and Methods
We quantified human head friction coefficients using a rigidly mounted 3-axis load cell (Humanetics 2866 seat mount load cell; Farmington Hills, Minnesota, USA) with an EPS foam interface extracted from the crown of a Bell Vert 2.0 Bike/Skate helmet (Vista Outdoor; Rantoul, Illinois, USA).The EPS foam was 10.5 cm by 10.5 cm and had a measured density of 77 kg/m 3 .The EPS foam was securely attached to a plate using adhesive, which was then secured to the load cell interface according to manufacturer specifications.Through an Institutional Review Board-approved protocol, 74 participants were recruited, consented, and attended a single data collection session.
Participants' height, weight, biological sex, and hair properties (self-reported curl type, style at the time of participation, and tightness of style at participation) were recorded.Curl type was self-reported based on 4 defined categories: tight curls, curly, wavy, and straight.At the time of participation, participants were instructed to wear their hair as if they were going to wear a helmet.The styles at the time of participation included the following: shorter than one inch, longer than one inch but shorter than shoulder length, down, braided (any type of braid was included), bun, or ponytail.All participants that wore a ponytail or bun style tied their hair below the occipital bone indicating a low bun or low ponytail style.The tightness of the style was also recorded at the time of participation.A tight style indicated that the hair was tied into a bun, ponytail, or braid and had limited movement around the scalp.A loose style was indicated if the hair was tied in bun, ponytail, or braid, but much of the hair around the scalp was free moving.A free hair style was indicted if the participant did not tie up their hair in any fashion.Hair properties were recorded using a categorical approach (Table 1).
From a standing position and a comfortable distance, participants were asked to lean over, place a finger on their hairline, and then line up their finger with the bottom edge of the vertically mounted EPS foam.Participants were then instructed to remove their finger and press their head as much as possible to the EPS foam surface (Fig. 1).Once the participant's head was fully contacting the EPS foam, they were instructed to apply the appropriate normal force level.Each participant performed a total of nine sliding motions at three participant perceived applied normal force levels (low, medium, and high).Participants were instructed to apply force based on a self-perceived scale varying from 1 to 10, where 1 is barely touching, and 10 is the maximum force they could apply.Participants were instructed that a low applied normal force was two on the scale, the medium force was five to six, and the high normal force was eight to ten on the self-perceived scale.After the participant indicated that they reached the appropriate normal force, the study staff member would instruct the participant to rotate and move their head down to slide their heads along the contour of the padding until their heads are off the padding or the top of their head ends and they cannot slide their heads on the padding anymore.The participant was instructed to make the movement last 3 s, which was verified by a study staff member who would count out loud with a stopwatch.Each trial's sagittal view was also captured using a video camera.
The applied normal force was the force the subject exerted onto the device along the z-axis.The tangential force was defined as the measured x-and y-axis resultant force [20].After each participant, the EPS foam was checked for damage and cleaned with a dissentient cloth to remove any residue that may have transferred from the participant hair.
Normal and tangential forces were collected from the load cell during the nine trials at 20 kHz.The raw force data for each trial were then processed in MATLAB (Mathworks; Natick, Massachusetts, USA).The 3-axis force data were filtered using a 4-pole phaseless lowpass Butterworth filter with a 100 Hz cut-off frequency.Baseline offsets in the signal were corrected for, and the data were smoothed using a 50-ms moving average window (Fig. 2).
For each trial, the COF over time was estimated by dividing the tangential force by the normal force.The static COF was defined as the maximum COF value on the COF vs time trace after force application began just before the movement occurred.Movement was identified by a large decrease in the COF and was confirmed through video analysis.The dynamic COF was defined as the average COF of the plateau region during movement (Fig. 3).The plateau region was also indefinable by a large spike in COF toward the end of the trial that indicated the participant was no longer in contact with the EPS foam, and this was also confirmed with video analysis.
For each applied normal force level, the average static COF, dynamic COF, and applied normal force were computed across the three trials.Each trial was rated based on signal quality.Signals were rated as either low, acceptable, or high quality.A low-quality signal was defined as a signal where static and dynamic friction coefficient features could not be clearly identified from the force signatures or there was a large (5-10 N) drift in the normal force application by the participant.The clarity of the features was also used to define the acceptable, identifiable with video referencing, and high-quality signals, easily identifiable features.
Power-law curves were fit to model static and dynamic COF as a function of applied normal force between all participants, based on the known power-law relationship (Eq. 1) in RStudio (Version 1.2, RStudio; Boston, Massachusetts, USA) [2,21].We also fit static and dynamic COF power-law curves separately for males and females.95% confidence A biological sex-based effect was added to the exponent of the model to determine the impact of biological sex on model parameters (Eq.2).Data were fit using a nonlinear least squares regression to define the coefficients and corresponding p values and determine the statistical significance of biological sex on the model parameters.A threshold of p < 0.05 for the model's biological sex coefficient was used to determine if biological sex had a significant effect on friction coefficients.
Quantitative comparisons of hair properties (curl type, style at time of participation, and tightness of style) at high normal force level were conducted to determine their effect on static COF.Hair properties were compared for the high applied normal force and for only static COF, as real-world impacts occur at kN normal force levels and impact durations (2) COF = a * Applied Normal Force b+sex are approximately 10 ms [3,4,24].Therefore, comparing the asymptote of the curve at high normal forces for static friction is considered the most appropriate approach.
Results
The 74 participants ranged in age from 18 to 39 years (Table 2) and were 51% female.Most participants wore their hair in a low ponytail/bun (40%) or had a short hairstyle (45%).Of the 666 samples, 580 were considered acceptable or high quality and used in the analysis.Table 3 depicts the applied normal force levels, means, and standard deviation, for all participants and by biological sex.
Static and dynamic COF varied with normal force, and higher applied normal forces generated lower COF values (Fig. 4, Table 4).To highlight the decline in COF with normal force, we evaluated each measure at 50 N, the mean normal force applied, and 80 N, the mean high applied normal force.At 50 N, the human head and EPS foam static friction coefficient is 0.39 (95% CI 0.36-0.42),and the dynamic friction coefficient is 0.29 (95% CI 0.27-0.32).At 80 N, the Fig. 2 Normal (orange) and tangential (red) force verses time for a single trial.Just after 2.5 s, the participants head started to move along the foam indicating the static COF point.COF was calculated as the tangential force divide by the normal force.Calculated COF over time for a single trial Fig. 3 Calculated COF over time for a single trial corresponding data to Fig. 2. The shaded orange region is the start of applied force before movement occurs, and the shaded red region is the start of the sliding motion after overcoming the static COF static friction coefficient is 0.32 (95% CI 0.30-0.34)and the dynamic friction coefficient is 0.27 (95% CI 0.26-0.28).
While significant, the effect size was small when accounting for biological sex in the static (p = 0.006) and dynamic (p = 0.001) friction coefficient models.The static friction coefficient at 80 N for females is 0.34 (95% CI 0.30-0.38)and for males is 0.30 (95% CI 0.27-0.32),a difference of 0.04 with overlapping CI.The dynamic friction coefficient for females is 0.30 (95% CI 0.26-0.35),and for males is 0.24 (95% CI 0.21-0.27),a difference of only 0.06 with overlapping CI (Fig. 5).
Participant's hair properties, including curl type, style at the time of participation, and of style at participation, showed no effect on the static COF at the high applied normal force (Fig. 6).
Discussion
This study quantified the head and helmet interface static and dynamic COF relative to the normal force.Friction may significantly impact rotational acceleration and the resultant head injury prediction for the head impact test [1,13].Friction coefficients between the head and helmet interface have not been thoroughly characterized before, making it hard to determine if headform friction characteristics are biofidelic.Our data also show that biological sex and hair properties do not significantly affect head and helmet interface friction coefficients.
At the average high normal force level, 80 N, the human head had a static COF between 0.30 and 0.34 and a dynamic COF between 0.26 and 0.28.Trotta et al. reported that the static COF ranges between 0.21 and 0.35 averaged over Ebrahimi et al. reported a COF of 0.683 for skin against helmet material which is on the top end of the static COF we found at low applied normal force and over double the static and dynamic COF at 80 N [13].However, it is essential to note that this was also a different helmet material and further analysis would be needed to determine the difference in interacting materials that aaffect the human head COF.Ebrahimi et al. also did not report the two applied normal forces used, if the friction was static or dynamic, or if it was skin from the head, which made the comparisons to our results vague [13].
Trotta et al. also reported that at higher stroke frequencies (material moving over the head) when applied normal force increased, there was a reduction in COF [33].This study demonstrates that a power-law relationship can describe the decrease in friction coefficients with increasing normal force when evaluating human head friction coefficients.Seo et al. reported similar trends against other areas of the skin for both dynamic and static friction coefficients [30].This is likely due to the skin's viscoelastic properties [5,6,30], as viscoelastic textiles also display a power-law relationship between normal force and friction coefficients [15,27].Based upon this evidence, human head friction coefficients should be evaluated with respect to the normal force using a power-law relationship for dynamic and static friction coefficients.
Although statistically significant, at 80 N, the difference in COF between males and females is small.Only a 0.04 static COF and 0.06 dynamic COF difference was found between biological sexes at 80 N and both had overlapping CI.Furthermore, the variance in the mean static (0.04) and dynamic (0.06) COF between the biological sexes is within the normal variance expected in a human participant study.Given these points, it is probably not necessary to account for biological sex differences; however, the effect of altering COF by this small difference on linear and rotational kinematics during impact is unknown.This should be investigated before deciding how much fine-tuning of COF is required to reasonably recreate real-world impact events.The distribution of static COF overlapped considerably for all hair properties confirming Trotta et al. finding that hair did not affect COF [33].This study also determined that no specific hair property (curl, style at the time of participation, and tightness of style at the time of participation) affects the static COF.
This study had several limitations.One limitation is that the study population consisted of younger adults (18-39 years old), though age has been shown not to affect skin COF [31].Another study limitation is that we only evaluated the COF against EPS foam and not against comfort lining materials.Furthermore, in estimating dynamic COF, we did not consider the acceleration of the head during movement.Thus, the dynamic coefficient was an estimate based on normal and tangential force and could overestimate the actual dynamic friction coefficient when accounting for acceleration.However, head impacts in the real world typically last around 10 ms [4,17] and as a result, static friction would dominate the frictional response.Hence, considering the static friction coefficient is critical when evaluating the biofidelity of the dummy headform.For this study, participants were instructed to slide their heads along the foam for three to four seconds.Therefore, the accelerations had low magnitudes, and we suspect this would only introduce minor errors.
Finally, the main limitation of this study is that the normal applied force levels and strain rates are well below the forces experienced during an impact.Working with human participants, we could not enforce an applied normal force or strain rate close to the level of a head impact event as it may result in injury to the participant.Therefore, the highest normal force level of 80 ± 34 N is substantially below the approximate 5 kN normal force experienced during a bicycle impact [4,17].The strain rate used in our study was also comparatively longer, with a duration of 3 s, whereas real-world head impacts typically last around 10 ms [4,17].
Although the 80 N force is still well below the normal forces experienced by dummy headforms during impact testing, the published friction coefficients for dummy headforms do not state the normal force.Partly due to this, a wide range of COF is reported for dummy headforms.The COF reported for Hybrid III headforms is 1.07 [7] and 0.75 ± 0.06 [33], both well above the human head COF.When a stocking or hair is applied to the Hybrid III headform, Bonin et al. reported a COF of 0.26 or 0.17 [7].Therefore, the addition of a stocking cap to the Hybrid III headform reduces the COF into the range of the human head.The magnesium EN960 bare headform has reported COF of 0.23 [13], 0.16 ± 0.03 [33], and 0.20 [25].Based on these reported COF, the bare EN960 headform is slightly below the human head CI of the static or dynamic COF.However, when the EN960 headform is covered in silicon rubber, COF has been reported to increase from 0.78 to 0.81 causing the EN960s headforms friction to be well above the human heads [13,25].Currently, there are no reported friction coefficients for the NOCSAE headform.However, each headform COF was found using various testing methods, and there has not been any published COF vs. normal force curves for any headform.
This study compared human head COF across a range of normal forces and reported the power-law curve relationships for static and dynamic COF.Our evaluation of friction coefficients between the head and helmet interface included a larger living sample population and a larger interacting surface area compared to previous studies.Our findings also demonstrate that biological sex and hair properties have little effect on the frictional characteristics of the human head.This study can be used to compare the COF of dummy headforms with that of the human head at defined normal forces.The defined static and dynamic friction coefficients should be used to develop more realistic head impact testing methods, define helmet-head boundary conditions for computer-aided simulations, and aid the optimization and development of helmet designs.Future research should evaluate the COF of commonly used headforms in impact testing to determine their friction biofidelity against the COF found for the human head using similar testing methods.There also should be an evaluation of how headforms with different COF affect oblique impact testing results.
Fig. 1
Fig. 1 Participants slid their heads nine times along EPS foam while applying three different normal force loads (low, medium, high) to the foam.The EPS foam was rigidly mounted on a trial axial load cell that captured the normal and tangential forces during each trial
Fig. 4 Table 4
Fig.4 The static (orange) and dynamic (red) COF over applied normal force[N].Including a mean power-law curve (solid line) and 95% CI curves (dashed lines)
Fig. 5 Fig. 6
Fig.5 Biological sex comparison for static and dynamic COF vs. applied normal force.Including a mean power-law curve (solid line) and 95% CI curves (dashed lines)
Table 1
Each participant's hair was categorized by curl type, style at participation, and tightness of style at the time of participation
Table 2
The breakdown of participants by sex and hair properties
Table 3
Applied normal force levels | 5,248.6 | 2023-08-04T00:00:00.000 | [
"Biology",
"Engineering",
"Medicine"
] |
Successive minimum spanning trees
In a complete graph $K_n$ with edge weights drawn independently from a uniform distribution $U(0,1)$ (or alternatively an exponential distribution $\operatorname{Exp}(1)$), let $T_1$ be the MST (the spanning tree of minimum weight) and let $T_k$ be the MST after deletion of the edges of all previous trees $T_i$, $i<k$. We show that each tree's weight $w(T_k)$ converges in probability to a constant $\gamma_k$ with $2k-2\sqrt k<\gamma_k<2k+2\sqrt k$, and we conjecture that $\gamma_k = 2k-1+o(1)$. The problem is distinct from that of Frieze and Johansson (2018), finding $k$ MSTs of combined minimum weight, and for $k=2$ ours has strictly larger cost. Our results also hold (and mostly are derived) in a multigraph model where edge weights for each vertex pair follow a Poisson process; here we additionally have $\mathbb E(w(T_k)) \to \gamma_k$. Thinking of an edge of weight $w$ as arriving at time $t=n w$, Kruskal's algorithm defines forests $F_k(t)$, each initially empty and eventually equal to $T_k$, with each arriving edge added to the first $F_k(t)$ where it does not create a cycle. Using tools of inhomogeneous random graphs we obtain structural results including that $C_1(F_k(t))/n$, the fraction of vertices in the largest component of $F_k(t)$, converges in probability to a function $\rho_k(t)$, uniformly for all $t$, and that a giant component appears in $F_k(t)$ at a time $t=\sigma_k$. We conjecture that the functions $\rho_k$ tend to time translations of a single function, $\rho_k(2k+x)\to\rho_\infty(x)$ as $k \to \infty$, uniformly in $x\in \mathbb R$. Simulations and numerical computations give estimated values of $\gamma_k$ for small $k$, and support the conjectures just stated.
Introduction
1.1. Problem definition and main results. Consider the complete graph K n with edge costs that are i.i.d. random variables, with a uniform distribution U (0, 1) or, alternatively, an exponential distribution Exp (1). A wellknown problem is to find the minimum (cost) spanning tree T 1 , and its cost or "weight" w(T 1 ). A famous result by Frieze [10] shows that as n → ∞, w(T 1 ) converges in probability to ζ(3), in both the uniform and exponential cases.
Suppose now that we want a second spanning tree T 2 , edge-disjoint from the first, and that we do this in a greedy fashion by first finding the minimum spanning tree T 1 , and then the minimum spanning tree T 2 using only the remaining edges. (I.e., the minimum spanning tree in K n \ T 1 , meaning the graph with edge set E(K n ) \ E(T 1 ).) We then continue and define T 3 as the minimum spanning tree in K n \ (T 1 ∪ T 2 ), and so on. The main purpose of the present paper is to show that the costs w(T 2 ), w(T 3 ), . . . also converge in probability to some constants. Theorem 1.1. For each k 1, there exists a constant γ k such that, as n → ∞, w(T k ) p −→ γ k (for both uniform and exponential cost distributions).
The result extends easily to other distributions of the edge costs, see Remark 7.1, but we consider in this paper only the uniform and exponential cases.
A minor technical problem is that T 2 and subsequent trees do not always exist; it may happen that T 1 is a star and then K n \ T 1 is disconnected. This happens only with a small probability, and w.h.p. (with high probability, i.e., with probability 1 − o(1) as n → ∞) T k is defined for every fixed k, see Section 7. However, in the main part of the paper we avoid this problem completely by modifying the model: we assume that we have a multigraph, which we denote by K ∞ n , with an infinite number of copies of each edge in K n , and that each edge's copies' costs are given by the points in a Poisson process with intensity 1 on [0, ∞). (The Poisson processes for different edges are, of course, independent.) Note that when finding T 1 , we only care about the cheapest copy of each edge, and its cost has an Exp(1) distribution, so the problem for T 1 is the same as the original one. However, on K ∞ n we never run out of edges and we can define T k for all integers k = 1, 2, 3, . . . . Asymptotically, the three models are equivalent, as shown in Section 7, and Theorem 1.1 holds for any of the models. In particular: Theorem 1.2. For each k 1, as n → ∞, w(T k ) p −→ γ k also for the multigraph model with Poisson process costs.
Frieze [10] also proved that the expectation E w(T 1 ) converges to ζ (3). For the multigraph model just described, this too extends. Theorem 1.3. For the Poisson multigraph model, E w(T k ) → γ k for each k 1 as n → ∞.
It is well known that the minimum spanning tree (with any given costs, obtained randomly or deterministically) can be found by Kruskal's algorithm [21], which processes the edges in order of increasing cost and keeps those that join two different components in the forest obtained so far. (I.e., it keeps each edge that does not form a cycle together with previously chosen edges.) As in many other previous papers on the random minimum spanning tree problem, from [10] on, our proofs are based on analyzing the behavior of this algorithm.
Rescale to think of an edge of weight w as arriving at time t = nw. Kruskal's algorithm allows us to construct all trees T k simultaneously by growing forests F k (t), with F k (0) empty and F k (∞) = T k : taking the edges of K n (or K ∞ n ) in order of time arrival (increasing cost), an edge is added to the first forest F k where it does not create a cycle. We will also consider a sequence of graphs G k (t) ⊇ F k (t), where when we add an edge to F k we also add it to all the graphs G 1 , . . . , G k ; see Section 2.1 for details.
The proof of Theorem 1.1 is based on a detailed structural characterization of the graphs G k (t), given by Theorem 2.1 (too detailed to set forth here in full), relying heavily on the theory of inhomogeneous random graphs from [4] and related works. Where C 1 (G k (t)) denotes the number of vertices in the largest component of G k (t) (or equivalently of F k (t), as by construction they have the same components) Theorem 2.1 shows that C 1 (G k (t))/n converges in probability to some function ρ k (t), uniformly for all times t. Moreover, each G k has its own giant-component threshold: ρ k (t) is 0 until some time σ k , and strictly positive thereafter.
The functions ρ k (t) are of central interest. For one thing, an edge is rejected from F k , making it a candidate for F k+1 , precisely if its two endpoints are within the same component of F k , and it is shown (see Corollary 5.9) that this is essentially equivalent to the two endpoints both being within the largest component. This line of reasoning yields the constants γ k explicitly, see (6.23), albeit not in a form that is easily evaluated. We are able, at least, to re-prove (in Example 6.5) that γ 1 = ζ(3), as first shown in [10].
The functions ρ k also appear to have a beautiful structure, tending to time-translated copies of a single universal function: Conjecture 1.4. There exists a continuous increasing function ρ ∞ (x) : This suggests, though does not immediately imply, another conjecture. Conjecture 1.5. For some δ, as k → ∞, γ k = 2k + δ + o (1).
Although we cannot prove these conjectures, some bounds on γ k are obtained in Section 3 by a more elementary analysis of the sequence of forests F k . In particular, Theorem 3.1 and Corollary 3.2 lead to the following, implying that γ k ∼ 2k as k → ∞. Corollary 1.7. For every k 1, 2k − 2k 1/2 < γ k < 2k + 2k 1/2 . (1.1) See also the related Conjectures 3.5, 10.1 and 11.1.
Remark 1.8. For the simple graph K n with, say, exponential costs, there is as said above a small but positive probability that T k does not exist for k 2. Hence, either E w(T k ) is undefined for k 2, or we define w(T k ) = ∞ when T k does not exist, and then E w(T k ) = ∞ for k 2 and every n. This is no problem for the convergence in probability in Theorem 1.1, but it implies that Theorem 1.3 does not hold for simple graphs, and the multigraph model is essential for studying the expectation.
Remark 1.9. For the minimum spanning tree T 1 , various further results are known, including refined estimates for the expectation of the cost w(T 1 ) [8], a normal limit law [15], and asymptotics for the variance [15; 20; 30]. It seems challenging to show corresponding results for T 2 or later trees.
1.2.
Motivations. Frieze and Johansson [11] recently considered a related problem, where instead of choosing spanning trees T 1 , T 2 , . . . greedily one by one, they choose k edge-disjoint spanning trees with minimum total cost. It is easy to see, by small examples, that selecting k spanning trees greedily one by one does not always give a set of k edge-disjoint spanning trees with minimum cost, so the problems are different. We show in Theorem 9.3 that, at least for k = 2, the two problems also asymptotically have different answers, in the sense that the limiting values of the minimum cost -which exist for both problems -are different.
(Also, as discussed in Section 3.1, we improve on the upper bound from [11,Section 3] on the cost of the net cheapest k trees, since our upper bound (3.1) on the cost of the first k trees is smaller.) Both our question and that of Frieze and Johansson [11] are natural, both seem generally relevant to questions of robust network design, and both have mathematically interesting answers.
Another motivation for our question comes from Talwar's "frugality ratio" characterizing algorithmic mechanisms (auction procedures) [29]. The frugality ratio is the cost paid by a mechanism for a cheapest structure, divided by the nominal cost of the second-cheapest structure (in the sense of our T 2 ). Talwar showed that for any matroidal structure (such as our spanning trees), in the worst case over all cost assignments, the frugality ratio of the famous Vickrey-Clarke-Groves (VCG) auction is 1: the VCG cost lies between the nominal costs of T 1 and T 2 . It is natural to wonder, in our randomized setting, how these three costs compare.
Chebolu, Frieze, Melsted and Sorkin [7] show that in the present setting (MST in K n with i.i.d. U (0, 1) edge costs), the VCG cost is on average exactly 2 times the nominal cost of T 1 , and Janson and Sorkin [19] show that the VCG cost converges in probability to a limit, namely 2 times the limit ζ(3) of the cost of T 1 (with further results given for all graphs, and all matroids). Frieze and Johansson [11] show that the combined cost of the cheapest pair of trees converges in expectation to a constant which is numerically about 4.1704288, and Theorem 9.3 shows that the cost of T 1 +T 2 converges in probability to a value that is strictly larger. It follows that in this average-case setting, the frugality ratio converges in probability to some value smaller than (2ζ(3))/(4.1704288−ζ(3)), about 0.80991. So where Talwar found that the (worst-case) frugality ratio was at most 1 for matroids and could be larger in other cases, in the present setting it is considerably less than 1.
We use := as defining its left-hand side, and def = as a reminder that equality of the two sides is by definition. We write . = for numerical approximate equality, and ≈ for approximate equality in an asymptotic sense (details given where used).
We use "increasing" and "decreasing" in their weak senses; for example, a function f is increasing if f (x) f (y) whenever x y.
Unspecified limits are as n → ∞. As said above, w.h.p. means with probability 1 − o (1). Convergence in probability is denoted p −→. Furthermore, if X n are random variables and a n are positive constants, X n = o p (a n ) means, as usual, X n /a n p −→ 0; this is also equivalent to: for every ε > 0, w.h.p. |X n | < εa n .
Graph means, in general, multigraph. (It is usually clear from the context whether we consider a multigraph or simple graph.) If G is a multigraph, thenĠ denotes the simple graph obtained by merging parallel edges and deleting loops. (Loops do not appear in the present paper.) The number of vertices in a graph G is denoted by |G|, and the number of edges by e(G).
For a graph G, let C 1 (G), C 2 (G), . . . be the largest component, the second largest component, and so on, using any rule to break ties. (If there are less than k components, we define C k (G) = ∅.) Furthermore, let C i (G) := |C i (G)|; thus C 1 (G) is the the number of vertices in the largest component, and so on. We generally regard components of a graph G as sets of vertices.
Model.
We elaborate the multigraph model in the introduction.
We consider (random) (multi)graphs on the vertex set [n] := {1, . . . , n}; we usually omit n from the notation. The graphs will depend on time, and are denoted by G k (t) and F k (t), where k = 1, 2, 3, . . . and t ∈ [0, ∞]; they all start as empty at time t = 0 and grow as time increases. We will have G k (t) ⊇ G k+1 (t) and F k (t) ⊆ G k (t) for all k and t. Furthermore, F k (t) will be a forest. As t → ∞, F k (t) will eventually become a spanning tree, F k (∞), which is the kth spanning tree T k produced by the greedy algorithm in the introduction, operating on the multigraph G 1 (∞).
Since the vertex set is fixed, we may when convenient identify the multigraphs with sets of edges. We begin by defining G 1 (t) by letting edges arrive as independent Poisson processes with rate 1/n for each pair {i, j} of vertices; G 1 (t) consists of all edges that have arrived at or before time t. (This scaling of time turns out to be natural and useful. In essence this is because what is relevant is the cheapest edges on each vertex, and these have expected cost Θ(1/n) and thus appear at expected time Θ(1).) We define the cost of an edge arriving at time t to be t/n, and note that in G 1 (∞), the costs of the edges joining two vertices form a Poisson process with rate 1. Hence, G 1 (∞) is the multigraph model defined in Section 1.
Thus, for any fixed t 0, G 1 (t) is a multigraph where the number of edges between any two fixed vertices is Po(t/n), and these numbers are independent for different pairs of vertices. This is a natural multigraph version of the Erdős-Rényi graph G(n, t). (The process G 1 (t), t 0, is a continuous-time version of the multigraph process in e.g. [3] and [16, Section 1], ignoring loops.) Note thatĠ 1 (t), i.e., G 1 (t) with multiple edges merged, is simply the random graph G(n, p) with p = 1 − e −t/n . Next, we let F 1 (t) be the subgraph of G 1 (t) consisting of every edge that has arrived at some time s t and at that time joined two different components of G 1 (s). Thus, this is a subforest of G 1 (t), as stated above, and it is precisely the forest constructed by Kruskal's algorithm (recalled in the introduction) operating on G 1 (∞), at the time all edges with cost t/n have been considered. Hence, F 1 (∞) is the minimum spanning tree T 1 of i.e., the subgraph of G 1 (t) consisting of all edges rejected from F 1 (t); in other words G 2 (t) consists of the edges that, when they arrive to G 1 (t), have their endpoints in the same component.
We continue recursively. F k (t) is the subforest of G k (t) consisting of all edges in G k (t) that, when they arrived at some time s t, joined two different components in G k (s). And G k+1 (t) := G k (t) \ F k (t), consisting of the edges rejected from F k (t).
Hence, the kth spanning tree T k produced by Kruskal's algorithm equals F k (∞), as asserted above.
Note that F k (t) is a spanning subforest of G k (t), in other words, the components of F k (t) (regarded as vertex sets) are the same as the components of G k (t); this will be used frequently below. Moreover, each edge in G k+1 (t) has endpoints in the same component of G k (t); hence, each component of G k+1 (t) is a subset of a component of G k (t). It follows that an edge arriving to G 1 (t) will be passed through G 2 (t), . . . , G k (t) and to G k+1 (t) (and possibly further) if and only if its endpoints belong to the same component of G k (t), and thus if and only if its endpoints belong to the same component of F k (t).
2.2. More notation. We say that a component C of a graph G is the unique giant of G if |C| > |C | for every other component C ; if there is no such component (i.e., if the maximum size is tied), then we define the unique giant to be ∅.
We say that a component C of F k (t) is the permanent giant of F k (t) (or of G k (t)) if it is the unique giant of F k (t) and, furthermore, it is a subset of the unique giant of F k (u) for every u > t; if there is no such component then the permanent giant is defined to be ∅.
Let C * k (t) denote the permanent giant of F k (t). Note that the permanent giant either is empty or the largest component; thus |C * k (t)| is either 0 or C 1 (F k (t)) = C 1 (G k (t)). Note also that the permanent giant C * k (t) is an increasing function of t:
2.3.
A structure theorem. The basis of our proof of Theorems 1.1 and 1.2 is the following theorem on the structure of the components of G k (t).
Recall that F k (t) has the same components as G k (t), so the theorem applies as well to F k (t). The proof is given in Section 5. For k = 1, the theorem collects various known results for G(n, p). Our proof includes this case too, making the proof more self-contained.
Theorem 2.1. With the definitions above, the following hold for every fixed k 1 as n → ∞.
(i) There exists a continuous increasing function We note also a formula for the number of edges in G k (t), and two simple inequalities relating different k.
3. Bounds on the expected cost 3.1. Total cost of the first k trees. The following theorem gives lower and upper bounds on the total cost of the first k spanning trees.
be the total cost of the first k spanning trees, for every k 1, Comparing with Frieze and Johansson [11, Section 3], our upper bound is smaller than their k 2 + 3k 5/3 despite the fact that they considered a more relaxed minimization problem (see Section 9); as such ours is a strict improvement. In both cases the lower bound is simply the expected total cost of the cheapest k(n − 1) edges in G, with (3.2) matching [11, (3.1)].
Proof. The minimum possible cost of the k spanning trees is the cost of the cheapest k(n − 1) edges. Since each edge's costs (plural, in our model) are given by a Poisson process of rate 1, the set of all edge costs is given by a Poisson process of rate n 2 . Recall that in a Poisson process of rate λ, the interarrival times are independent exponential random variables with mean 1/λ, so that the ith arrival, at time Z i , has E Z i = i/λ. It follows in this case that W k We now prove the upper bound. An arriving edge is rejected from F i iff both endpoints lie within its "forbidden" set B i of edges, namely those edges with both endpoints in one component. The nesting property of the components means that B 1 ⊇ B 2 ⊇ · · · . An arriving edge e joins F k if it is rejected from all previous forests, i.e., e ∈ B k−1 (in which case by the nesting property, e also belongs to all earlier Bs) but can be accepted into F k , i.e., e / ∈ B k . The idea of the proof is to show that the first k forests fill reasonably quickly with n−1 edges each, and we will do this by coupling the forest-creation process (Kruskal's algorithm) to a simpler, easily analyzable random process.
Let s(τ ) = {s k (τ )} ∞ k=0 denote the vector of the sizes (number of edges) of each forest after arrival of the τ 'th edge; we may drop the argument τ when convenient. Let p k = |B k |/ n 2 , the rejection probability for F k . For any τ , by the nesting property of the components and in turn of the B k , The MST process can be simulated by using a sequence of i.i.d. random variables α(τ ) ∼ U (0, 1), incrementing s k (τ ) if both α(τ ) p k−1 (τ ) (so that e is rejected from F k−1 and thus from all previous forests too) and α(τ ) > p k (τ ) (so that e is accepted into F k ). We take the convention that p 0 (τ ) = 1 for all τ . For intuition, note that when s k = 0 an edge is never rejected from in F k (p k = 0, so α ∼ U (0, 1) is never smaller); when s k = 1 it is rejected with probability p k = 1/ n 2 ; and when s k = n − 1 it is always rejected (|B k | must be n 2 , so p k = 1). Given the size is maximized (thus so is p k ) when all the edges are in one component, i.e., The size vector s(τ ) thus determines the valuesp k (τ ) for all k. Let r(τ ) denote a vector analogous to s(τ ), but with By construction, For intuition, here note that when r k = 0 an arrival is never rejected from r k (p k = 0); when s k = 1 it is rejected with probabilityp k = 1/(n − 1) > p k = 1/ n 2 ; and when s k = n − 1 it is always rejected (p k = 1). Figure 1. Coupling of the forests' sizes s(τ ) to a simply analyzable random process r(τ ), showing the structure of the inductive proof (on τ ) that s(τ ) majorizes r(τ ).
Taking each F i (0) to be an empty forest (n isolated vertices, no edges) and accordingly s(0) to be an infinite-dimensional 0 vector, and taking r(0) to be the same 0 vector, we claim that for all τ , s(τ ) majorizes r(τ ), which we will write as s(τ ) r(τ ). That is, the prefix sums of s dominate those of r: for all τ and k, . We first prove this; then use it to argue that edge arrivals to the first k forests, i.e., to s, can only precede arrivals to the first k elements of r; and finally analyze the arrival times of all k(n − 1) elements to the latter to arrive at an upper bound on the total cost of the first k trees.
We prove s(τ ) r(τ ) by induction on τ , the base case with τ = 0 being trivial. Figure 1 may be helpful in illustrating the structure of this inductive proof. Suppose the claim holds for τ . The probabilities p k (τ ) are used to determine the forests F k (τ +1) and in turn the size vector s(τ +1). Consider an intermediate object s (τ + 1), the size vector that would be given by incrementing s(τ ) using the upper-bound valuesp k (τ ) taken from s(τ ) by (3.5). Then, s i (τ + 1) receives the increment if p i−1 α > p i , and s j (τ + 1) receives the increment ifp j−1 α >p j ; hence, fromp i−1 p i−1 α it is immediate that i j and thus s(τ + 1) s (τ + 1).
It suffices then to show that s (τ + 1) r(τ + 1). These two vectors are obtained respectively from s(τ ) and r(τ ), with s(τ ) r(τ ) by the inductive hypothesis, using probability thresholdsp k (τ ) = f (s k (τ )) and p k (τ ) = f (r k (τ )) respectively, applied to the common random variable α, where f (s) = s/(n − 1) (but all that is important is that f is a monotone function of s). Suppose that so that elements i in s and j in r are incremented. If i j, we are done. (Prefix sums of s(τ ) dominated those of r(τ ), and an earlier element is incremented in s (τ + 1) than r(τ + 1), thus prefix sums of s (τ + 1) dominate those of r(τ + 1).) Consider then the case that i > j. In both processes the increment falls between indices j and i, so the k-prefix sum inequality continues to hold for k < j and k i. Thus, for j k < i, from which it follows that s (τ + 1) r(τ + 1), completing the inductive proof that s(τ ) r(τ ).
Having shown that the vector s(τ ) of component sizes majorizes r(τ ), it suffices to analyze the latter. Until this point we could have used (3.4) rather than (3.5) to definep k ,p k , and the function f , but now we take advantage of the particularly simple nature of the process governing r(τ ). Recall that a new edge increments r i for the first i for which the U (0, 1) "coin toss" α(τ ) has α(τ ) >p i def = r i /(n − 1). Equivalently, consider an array of cells n − 1 rows high and infinitely many columns wide, generate an "arrival" at a random row or "height" X(τ ) uniform on 1, . . . , n − 1, and let this arrival occupy the first unoccupied cell i at this height, thus incrementing the occupancy r i of column i. This is equivalent because if r i of the n − 1 cells in column i are occupied, the chance that i is rejected -that X(τ ) falls into this set and thus the arrival moves along to test the next column i + 1 -is r i /(n − 1), matching (3.6).
Recalling that the cost of an edge arriving at time t is t/n in the original graph problem, the combined cost W k of the first k spanning trees is 1/n times the sum of the arrival times of their k(n − 1) edges. The majorization means that the 'th arrival to the first k forests comes no later than the 'th arrival to the first k columns of the cell array. Thus, the cost W k of the first k trees is at most 1/n times the sum of the times of the k(n − 1) arrivals to the array's first k columns.
The continuous-time edge arrivals are a Poisson process with intensity 1/n on each of the n 2 edges, thus intensity (n − 1)/2 in all; it is at the Poisson arrival times that the discrete time τ is incremented and X(τ ) is generated. Subdivide the "X" process into the n − 1 possible values that X may take on, so that arrivals at each value (row in the cell array) are a Poisson process of intensity λ = 1 2 . The sum of the first k arrival times in a row is the sum of the first k arrival times in its Poisson process. The ith such arrival time is the sum of i exponential random variables, and has expectation i/λ. The expected sum of k arrival times of a line is thus k+1 2 /λ = k(k + 1), and (remembering that cost is time divided by n), the expected total cost of all n − 1 lines is n − 1 n k(k + 1), yielding the upper bound in (3.1) and completing the proof of the theorem.
Then, for every k 1, Proof. Immediate from Theorems 3.1 and 1.3.
Proof of Corollary 1.7. For the upper bound, we note that obviously γ 1 γ 2 . . . , and thus, for any 1, using both the upper and lower bound in (3.11), and hence and hence Choosing, again, = √ k gives the lower bound in (1.1).
Besides these rigorous results, taking increments of the left and right-hand sides of (3.11) also suggests the following conjecture.
3.3. Improved upper bounds. The upper bounds in Theorem 3.1 and Corollary 3.2 were proved using the bound (3.5). A stronger, but less explicit, bound can be proved by using instead the sharper (3.4). That is, we consider the random vectors r(τ ) defined as above but with (3.6) replaced byp As remarked before (3.4), this approximation comes from imagining all edges in each F k to be in a single component; this overestimates the probability that an arriving edge is rejected from F k and, as developed in the previous subsection, gives s(τ ) r(τ ) just as whenp k was defined by (3.5).
Using for consistency our usual time scaling in which edges arrive at rate (n − 1)/2, by a standard martingale argument one can show that, for each k 1, uniformly for t 0, (3.17) for some continuously differentiable functions g k (t) satisfying the differential equations, with g 0 (t) := 1, Moreover, using s(τ ) r(τ ) and taking limits, it can be shown that We omit the details, but roughly, in time dt, 1 2 n dt edges arrive, all costing about t/n, and a g k (t) 2 fraction of them pass beyond the first k graphs (to the degree that we are now modeling graphs). Compare (3.19) with (6.19), with reference to (6.3).
For k = 1, (3.18) has the solution g 1 (t) = tanh(t/2), and (3.19) yields the bound Γ 1 = γ 1 2 ln 2 . = 1.386. This is better than the bound 2 given by (3.11), but still far from precise since γ 1 = ζ(3) . = 1.202. For k 2 we do not know any exact solution to (3.18), but numerical solution of (3.18) and calculation of (3.19) (see Section 11.3) suggests that Γ k < k 2 + 1. We leave the proof of this as an open problem. If proved, this would be a marked improvement on Γ k k 2 + k, which was the exact expectation of the random process given by (3.5) (that part of the analysis was tight). In particular, it would establish that 2k − 2 γ k 2k; see Conjecture 11.1.
For k = 2, the numerical calculations in Section 11.3 give γ 1 + γ 2 4.554 2 . . . (see Table 2) and thus γ 2 3.352 1 . . .. The same value was also obtained using Maple's numerical differential equation solver, with Maple giving greater precision but the two methods agreeing in the digits shown here.
4. Preliminaries and more notation 4.1. Some random graphs. For a symmetric array (p ij ) n i,j=1 of probabilities in [0, 1], let G(n, (p ij )) be the random (simple) graph on the vertex set [n] := {1, . . . , n} where the edge ij appears with probability p ij , for i < j, and these n 2 events are independent. We extend this (in a trivial way) by defining G(n, A) = G(n, (a ij )) := G(n, (a ij ∧ 1) n i,j=1 ) for any symmetric non-negative n × n matrix A = (a ij ) n i,j=1 . Moreover, the matrix A can be a random, in which case G(n, A) is defined by first conditioning on A. (Hence, edges appear conditionally independently, given A.) Note that we do not allow loops, so the diagonal entries p ii or a ii are ignored, and may be assumed to be 0 without loss of generality.
4.2.
Susceptibility. The susceptibility χ(G) of a (deterministic or random) graph G of order n = |G| is defined by can be interpreted as the mean size of the component containing a random vertex, see [18]. We also exclude the first term in the sum and define (This is particularly interesting for a graph G with a single giant component of order Θ(n), when the sum in (4.1) is dominated by the first term.) Viewing each term in the sums (4.1)-(4.2) as ( C i (G)/n = 1 each sum can be viewed as a weighted sum of the sizes C i (G) with the weights summing to at most 1, so Let π(G) be the probability that two randomly chosen distinct vertices in G belong to the same component. Then 4.3. Kernels and an integral operator. A kernel, or graphon, is a nonnegative symmetric measurable function κ : S 2 → [0, ∞), where (in a common abuse of notation) S = (S, F, µ) is a probability space. Given a kernel κ on a probability space S, let T κ be the integral operator defined by (for suitable functions f on S), and let Φ κ be the non-linear operator In our cases, the kernel κ is bounded, and then T κ is a compact (in fact, Hilbert-Schmidt) operator on L 2 (S, µ). Since furthermore κ 0, it follows that there exists an eigenfunction ψ 0 on S with eigenvalue T k , see [4,Lemma 5.15], where T κ denotes the operator norm of T k as an operator on L 2 (S, µ).
4.4.
Branching processes. Given a kernel κ on a probability space (S, F, µ), as in [4] let X κ (x) be the multi-type Galton-Watson branching process with type space S, starting with a single particle of type x ∈ S, and where in each generation a particle of type y is replaced by its children, consisting of a set of particles distributed as a Poisson process on S with intensity κ(y, z) dµ(z). Let further X κ be the same branching process started with a particle of random type, distributed as µ.
(i) The function ρ κ is a fixed point of Φ κ , i.e., it satisfies the equation The proof of Theorem 2.1 is based on induction; we assume throughout this section that, for k 1, Theorem 2.1 holds for k − 1 and show that it holds for k.
For convenience, we define F 0 (t) := G 0 (t) := K n for every t 0; this enables us to consider G 1 (t) together with G k (t) for k > 1. (Alternatively, we could refer to known results for the random graph process G 1 (t).) Note that Theorem 2.1 then trivially holds for k = 0, with ρ 0 (t) = 1 for all t and σ 0 = 0, except that (iii) has to be modified (since ρ 0 is constant). There are some trivial modifications below in the case k = 1 (and also some, more or less important, simplifications); we leave these to the reader.
Thus, fix k 1, assume that Theorem 2.1 holds for k − 1 and consider the evolution of G k (t). Essentially everything in this proof depends on k, but we often omit it from the notation. (Recall that we also usually omit n.) We condition on the entire process (F k−1 (s)) s 0 . For two distinct vertices i, j ∈ [n], let τ (i, j) = τ k−1 (i, j) be the time that i and j become members of the same component in F k−1 (t). This is the time when edges ij start to be passed to G k (t), and it follows that, conditionally on (F k−1 (s)) s 0 , the process G k (t), t 0, can be described as G 1 (t) above (Section 2), except that for each pair {i, j} of vertices, edges appear according to a Poisson process on (τ (i, j), ∞). In particular, for a fixed time t (a value, independent of n) and conditioned on (F k−1 (s)) s 0 , in the multigraph G k (t), the number of edges ij is Po (t − τ (i, j)) + /n , and these numbers are (conditionally) independent for different pairs {i, j}. Hence, if we merge multiple edges and obtain the simple graphĠ k (t), we see thaṫ the random graph defined in Section 4.1 with when i = j, and (for completeness) p ii = 0. Note that the probabilities p ij depend on (F k−1 (s)) s 0 and thus are random, and recall that therefore i.e., the first time that vertex i belongs to the permanent giant of 4) but strict inequality is possible since i and j may both belong to a component of F k−1 (t) that is not the permanent giant. We shall see that this does not happen very often, and one of the ideas in the proof is that we may regard the inequality (5.4) as an approximate equality. This is formalized in the following lemma, and leads to a more tractable graph defined in (5.22) and compared withĠ k (t) in Lemma 5.3.
Proof. Fix ε > 0, let L := t/ε and let t : Note that, using (5.4), for any pair (i, j), and for a good pair (i.e., a pair that is not bad), By the induction hypothesis Theorem 2.1(v), w.h.p. G k−1 (t 1 ) has a permanent giant, so we may assume that this holds. (Failures contribute o p (n 2 ) to the right-hand side of (5.5).) In the first case, i and j belong to the same component in G k−1 (σ k−1 − ε), and in the second case they belong to the same component in G k−1 (t ), but not to the largest one, since that is assumed to be the permanent giant. Hence, for any t, the number of bad pairs (i, j) is at most, using the definitions (4.1)-(4.2), (5.9) By (4.3) and the induction hypothesis (i) and (iii), 10) and similarly for every , by (4.4) and the induction hypothesis (ii), By (5.9)-(5.11), the number of bad pairs is o p (n 2 ). Hence, using (5.7) and 12) and the result follows since ε is arbitrary.
We use the machinery and notation in Bollobás, Janson and Riordan [4, in particular Section 2], and make the following definitions: • µ k−1 is the probability measure on S with distribution function • ν n is a probability measure given by where δ x is the point mass (Dirac delta) at x. (In other words, ν n is the empirical distribution of {x 1 , . . . , x n }. Put yet another way, for any set A ⊂ S, ν n (A) := 1 n {i : x i ∈ A} .) Note that x n and ν n are random, and determined by (F k−1 (s)) s 0 .
Proof. The claim is equivalent to In the terminology of [4, Section 2], (S, µ k−1 ) is a ground space and, by Lemma 5.2, is a vertex space, meaning that the number of vertices x i appearing by time t is governed by µ k−1 , as made precise by (5.18). We define also, for every t 0, the kernel Note that, for fixed t, the kernel κ t is bounded and continuous; hence κ t is a graphical kernel [4, Definition 2.7, Remark 2.8 and Lemma 8.1]. Furthermore, κ t is strictly positive, and thus irreducible, on [0, t)×[0, t), and 0 on the As detailed in [4, Section 2], specifically near its (2.3), these ingredients define a random graph G V (n, κ t ). (5.21) Recall that in our case the kernel κ t is given by (5.20) while the vertex space V is given by (5.19), in turn with S and µ k−1 given by (5.13) and (5.14), and x n given by (5.15). In general, G V (n, κ t ) denotes a random graph with vertices arriving at random times x n , vertices i and j joined with probability κ t (x i , x j ), and [4] describes the behavior of such an inhomogeneous random graph. It suffices to think of G V (n, κ t ) in terms of S, µ k−1 , and κ t , because as shown in [4] the particulars of x n are irrelevant as long as x n is consistent with µ k−1 in the sense of (5.18) and (5.16), this consistency following from the fact that V is a vertex space (see (5.19) and the line following it).
Here, G V (n, κ t ) is the random graph alluded to after (5.4), a proxy for G k (t) with the difference that it is based on the times τ (i) of vertices joining the permanent giant of F k−1 , rather than the more complicated two-variable times τ (i, j) of two vertices first belonging to a common component. Concretely, when i = j, and (for completeness) p − ii = 0. We assume throughout that n t, so that p − ij ∈ [0, 1]; this is not an issue since t is fixed while n → ∞.
Note that by (5.2) and (5.5), Recall that both p ij and p − ij depend on (F k−1 (s)) s 0 , and thus are random. By (5.1) and (5.22),Ġ k (t) = G(n, (p ij )) and G V (n, κ t ) = G(n, (p − ij )), so by making the obvious maximal coupling of G(n, (p ij )) and G(n, (p − ij )) conditionally on (F k−1 (s)) s 0 , we obtain a coupling ofĠ k (t) and is the number of edges that are present in one of the graphs but not in the other, then Then, using Markov's inequality, for any δ > 0, P X n > εn P(Y n > δn) + E P(X n > εn | Y n δn) P(Y n > δn) + δn εn .
5.2.
Towards part (i). The following lemma establishes (2.1) of Theorem 2.1(i) for any fixed t 0; doing so uniformly for all t 0, as the theorem states, follows later. Here we rely on [4, Theorem 3.1], which, roughly speaking, relates the size of the largest component of a random graph G V (n, κ t ), to the survival probability of the branching process defined by the same kernel κ t and the measure (here µ k−1 ) comprised by the vertex space V. By Lemma 5.3, the graphĠ k (t) of interest differs from G V (n, κ t ) in only o p (n) edges, and the stability theorem [4,Theorem 3.9] shows that the size of the largest component ofĠ k (t) is about the same as that of G V (n, κ t ).
Let X t = X t,k := X κt be the branching process defined in Section 4.4 for the kernel κ t and the measure µ k−1 , and (recalling (4.8)) let ρ(κ t ) def = ρ(κ t ; µ k−1 ) be its survival probability.
the survival probability of the branching process X t .
Hence we may in the rest of the proof assume t > σ k−1 and thus µ k−1 (t) = ρ k−1 (t) > 0. As noted after (5.20) above, the kernel κ t then is quasiirreducible. Hence, it follows from [4, Theorem 3.1] that We have shown in Lemma 5.3 thatĠ k (t) differs from G V (n, κ t ) by only o p (n) edges, and we appeal to the stability theorem [4, Theorem 3.9] to show that largest components of these two graphs have essentially the same size.
(Alternatively, we could use [5, Theorem 1.1].) A minor technical problem is that this theorem is stated for irreducible kernels, while κ t is only quasiirreducible. We can extend the theorem (in a standard way) by considering only the vertices i with x i = τ k−1 (i) t, i.e., the vertices i in the permanent giant C * k−1 (t) of G k−1 (t), see (5.3). This defines a generalized vertex space [4, Section 2] V = (S , µ k−1 , (x n ) n 1 ), where S := [0, t], µ k−1 is the restriction of µ k−1 to S , and x n is the subsequence of x n = (x 1 , . . . , x n ) consisting of all x i ∈ S . The kernel κ t is strictly positive a.e. on S × S , and is thus irreducible.
Thus, we may take G n in [4, Theorem 3.9] to be G n := G V (n, κ t ), (5.30) which may be thought of as the restriction of G V (n, κ t ) to C * k−1 (t). Take the theorem's G n to be the restriction ofĠ k (t) to C * k−1 (t). For any δ > 0, from Lemma 5.3, w.h.p.
δn. Restricting each of these graphs to C * k−1 (t), it follows that w.h.p. e(G n G n ) δn. (5.32) Thus, G n and G n fulfill the theorem's hypotheses. For any ε > 0, we may choose δ > 0 per the theorem's hypotheses, and it follows from the theorem and (5.29) that w.h.p.
Our aim is to establish (2.2), which is (5.33) with C 1 (G k (t)) in lieu of C 1 (G n ). Each component C of G k (t) (or equivalently ofĠ k (t)) is a subset of some component of G k−1 (t), either C 1 (G k−1 (t)) or some other component. Since t > σ k−1 and by the induction hypothesis (v) of Theorem 2.1, w.h.p. C * k−1 (t) = ∅ and thus C 1 (G k−1 (t)) = C * k−1 (t). Thus, components of G k (t) contained in C 1 (G k−1 (t)) are also contained in G n , and the largest such component is governed by (5.33). Components of G k (t) contained in a smaller component of G k−1 (t) have size at most C 2 (G k−1 (t)), which by the induction hypothesis (ii) is w.h.p. smaller than any constant times n, and thus smaller than the component described by (5.33). Consequently, w.h.p. C 1 (G k (t)) = C 1 (G n ), and thus (5.33) implies (2.2) w.h.p., for every ε > 0, which is equivalent to (2.1).
5.3.
Towards part (ii). The next lemma establishes something like Theorem 2.1 (ii), but only for any fixed t 0; extending this to the supremum follows later.
Proof. We use the notation of the proof of Lemma 5.4, specifically (5.30) and (5.31). Let G † n be the graph G n with a single edge added such that the two largest components C 1 (G n ) and C 2 (G n ) are joined and let ε > 0. (If C 2 (G n ) = ∅, let G † n := G n .) Since w.h.p. the analog of (5.32) holds also for G † n , [4, Theorem 3.9] applies also to G n and G † n and shows that w.h.p.
Furthermore, as shown in the proof of Lemma 5.4, w.h.p. every component of G k (t) that is not part of G n has size at most C 2 (G k−1 (t)), which w.h.p. is εn by the induction hypothesis. Consequently, w.h.p.
which completes the proof.
Let T t = T t,k := T κt be the integral operator defined by (4.6) with the measure µ k−1 . We regard T t as an operator on L 2 (S, µ k−1 ), and recall that (since κ t is bounded) T t is a bounded and compact operator for every t 0.
Proofs of parts (iii) and (iv).
Proof of Theorem 2.1(iii). By Lemma 5.6, there exists a unique σ k > 0 such that where the last equivalence follows from [4, Theorem 3.1], establishing T t > 1 as a necessary and sufficient condition for the existence of a giant component, and providing its size. In order to see that ρ k is strictly increasing on [σ k , ∞), let σ k < t < u. Since κ u (x, y) κ t (x, y) for all x, y ∈ S, we may couple the branching processes X t = X κt and X u = X κu such that X u is obtained from X t by adding extra children to some individuals. (Each individual of type x gets extra children of type y distributed as a Poisson process with intensity (κ u (x, y)−κ t (x, y)) dµ k−1 (y), independent of everything else.) Then clearly X u survives if X t does, so ρ k (u) := ρ(κ u ) ρ(κ t ) = ρ k (t). (See [4, Lemma 6.3].) Moreover, there is a positive probability that X t dies out but X u survives, for example because the initial particle has no children in X t but at least one in X u , and this child starts a surviving branching process. Hence ρ k (u) > ρ k (t).
We next prove Theorem 2.1(iv). A simple lemma will be useful here and subsequently.
Consider the process defined in Section 2 of all graphs G j (t), j 1 and t 0, under some edge-arrival process; consider also a similar set of graphs G j (t) coming from a second arrival process thicker than the first (i.e., containing the same arrivals and possibly others).
Lemma 5.7. The thicker process yields larger graphs, i.e., G j (t) ⊆ G j (t) for all j and t. Also, any edge e present in both arrival processes, if contained in F 1 (t) ∪ · · · ∪ F j (t), is also contained in F 1 (t) ∪ · · · ∪ F j (t).
Proof. It is easy to see that adding edges can only make G 1 larger, i.e., that G 1 (t) ⊇ G 1 (t). Thus any edge originally passed on to G 2 (t) will still be passed on, plus perhaps some others; by induction on j, any G j (t) can only increase, i.e., G j (t) ⊇ G j (t). This proves the first assertion. The second assertion follows from the first. If e is not contained in F 1 (t) ∪ · · · ∪ F j (t) then it is passed on to G j+1 (t), and hence, as just shown, it belongs also to G j+1 (t) and therefore not to F 1 (t) ∪ · · · ∪ F j (t).
Let q n (t) be the probability that two fixed, distinct, vertices in G k (t) belong to the same component. By symmetry, this is the same for any pair of vertices, and thus also for a random pair of distinct vertices. Hence, recalling (4.5), q n (t) = E π(G k (t)). (5.43) Lemma 5.8. There exist constants b k , B k > 0 such that, for every n 2, Proof. Fix some t 0 > σ k ; thus ρ k (t 0 ) > 0 by (iii). Then, cf. (4.5), writing . lim Let q := ρ k (t 0 ) 2 /2, say. Then (5.46) shows that if n is large enough, q n (t 0 ) > q. By reducing q, if necessary, we may assume that this holds for every n, since obviously q n (t 0 ) > 0 for every fixed n 2.
For an integer m 0, consider the process defined in Section 2 of all graphs G j (t), j 1 and t 0, but erase all edges and restart at mt 0 ; denote the resulting random graphs by G = G k (t 0 ); furthermore, the random graphs G k,m , m = 0, 1, . . . , are independent, since they depend on edges arriving in disjoint time intervals.
Consider the process at times i t 0 for integers i. By Lemma 5.7, G k (i t 0 ) dominates what it would have been had no edges arrived by (i − 1)t 0 , which, for i 2, is simply an independent copy of G k (t 0 ) (that is, independent of G k (t 0 ) but identically distributed). Consequently, for any integer M , vertices x and y can be in different components of G k (M t 0 ) only if they are in different components in each of the M copies of G k (t 0 ). Thinking of all values i 1 at once, these copies of G k (t 0 ) are all independent, as they depend on edge arrivals in disjoint time intervals (i − 1)t 0 , i t 0 . Thus, (5.47) Thus, for any t 0, taking M := t/t 0 , which shows (5.44). (In fact, we get B k = e q < e; we can take q arbitrarily small and thus B k arbitrarily close to 1, at the expense of decreasing b k .) Proof of Theorem 2.1(iv). Let C 1 (t) be the component of G k (t) that contains vertex 1. Then, by Lemma 5.8, Furthermore, by Lemma 5.4 and dominated convergence, E C 1 (G k (t))/n → ρ k (t) as n → ∞. Hence, (5.49) implies ρ k (t) 1 − B k e −b k t , which is (2.3).
for every j N . (The case j = N is trivial, since G k (∞) a.s. is connected.) Then, for every j = 1, . . . , N and every t ∈ [t j−1 , t j ], 52) which together with a similar lower bound shows that w.h.p. |C 1 G k (t) /n− ρ k (t)| 2ε for all t 0. Since ε is arbitrary, this shows (2.2).
Assume (5.51) and (5.53) for every j N , and also that C 2 G k (t) > 3εn for some t 0. Choose j with 1 j N such that t ∈ [t j−1 , t j ]. If C 2 (G k (t)) has not merged with C 1 (G k (t)) by time t j , then which contradicts (5.53). If on the other hand these two components have merged, then, using (5.51) and (from (5.50)) that ρ k (t j−1 ) ρ k (t j ) − ε, which contradicts (5.51). Consequently, w.h.p. sup t C 2 G k (t) 3εn.
Proof of Theorem 2.1(v). If t > σ k , then ρ k (t) > 0 by Theorem 2.1(iii). Let δ = ρ k (t)/2. Then, by (i) and (ii), w.h.p. C 1 (G k (t)) > δn, and, simultaneously for every u 0, C 2 (G k (u)) < δn. Assume that these inequalities hold. Then, in particular, the largest component of G k (t) is a unique giant. (Recall the definition from Section 2.2.) Moreover, for every u t, the component C of G k (u) that contains the largest component of G k (t) then satisfies |C| C 1 (G k (t)) > δn > C 2 (G k (u)), (5.56) showing that C is the unique giant of G k (u). Hence, the largest component of G k (t) is w.h.p. a permanent giant. Consequently, if t > σ k , then w.h.p. |C * k (t)| = C 1 (G k (t)) and (2.4) follows from (2.1). On the other hand, if t σ k , then (2.1) and (iii) yield This completes the proof of Theorem 2.1.
5.6.
A corollary. We note the following corollary. , it is not difficult to prove the much stronger results that if t < σ k is fixed, then there exists a finite constant χ k (t) such that χ(G k (t)) p −→ χ k (t), and if t = σ k is fixed, then there exists a finite constant χ k (t) such that χ(G k (t)) p −→ χ k (t). Furthermore, these limits can be calculated from the branching process X t = X κt on (S, µ k−1 ): if we let |X t | be the total population of the branching process, then χ k (t) = E(|X t |) and χ k (t) = E |X t | 1{|X t | < ∞} . We omit the details.
Proof of Theorem 2.3. Since κ t (x, y) = 0 for every y when x t, a particle of type x t will not get any children at all in the branching process X t,k = X κt , hence has survival probability ρ κ (x) = 0. Thus, recalling (4.9) and (5.14), the survival probability Moreover, even if x < t, there is a positive probability that x has no children in X t,k , and thus there is strict inequality in (5.61) whenever ρ k−1 (t) > 0.
An alternative view of the last part is that, asymptotically, no edges arrive in G k (t) until t = σ k−1 , and even if all edges were passed on to G k (t) from that instant, G k (t) would thenceforth evolve as a simple Erdős-Rényi random graph, developing a giant component only 1 unit of time later, at t = σ k−1 + 1.
Proof of Theorem 1.2
For a and b with 0 a < b ∞, let N k (a, b) be the number of edges that arrive to G 1 (t) during the interval (a, b] and are not passed on to G k+1 (t); furthermore, let W k (a, b) be their total cost. In other words, we consider the edges, arriving in (a, b], that end up in one of T 1 = F 1 (∞), . . . , T k = F k (∞). In particular, for 0 t ∞, and thus Since an edge arriving at time t has cost t/n, we have Lemma 6.1. Let 0 a < b ∞ and k 1. For any ε > 0, w.h.p.
Let F t be the σ-field generated by everything that has happened up to time t. At time t, the fraction of edges arriving to G 1 (t) that are rejected by all of F 1 (t), . . . , F k (t) is simply the fraction lying within a component of F k (t), namely π(G k (t)) (see (4.5)). Since edges arrive to G 1 (t) at a total rate 1 n n 2 = n−1 2 , conditioned on F t , edges are added to F 1 (t) ∪ · · · ∪ F k (t) at a rate, using (4.5), (6.6) By Corollary 5.9, for every fixed t, Condition on the event r k (a) 1 − ρ k (a) 2 + ε n/2, which by (6.7) occurs w.h.p. Then, since r k (t) is a decreasing function of t, the process of edges that are added to F 1 (t) ∪ · · · ∪ F k (t) can for t a be coupled with a Poisson process with constant intensity 1−ρ k (a) 2 +ε n/2 that is thicker (in the sense defined just before Lemma 5.7). Thus, letting Z be the number arriving in the latter process in (a, b], we have w.h.p.
Furthermore, by the law of large numbers, w.h.p.
For the lower bound, we stop the entire process as soon as r k (t) < 1 2 1 − ρ k (b) 2 − ε n. Since r k (t) is decreasing, if the stopping condition does not hold at time t = b then it also does not hold at any earlier time, so by (6.7), w.h.p. we do not stop before b. As long as we have not stopped, we can couple with a Poisson process with constant intensity 1 − ρ k (b) 2 − ε n/2 that is thinner (i.e., opposite to thicker), and we obtain the lower bound in (6.5) in an analogous way as the upper bound.
Proof. Let N 1 and define t j := jb/N . By (6.4) and Lemma 6.1, for every j ∈ [N ], w.h.p. (6.11) where we define the piecewise-constant function f N by Consequently, w.h.p., (6.14) We obtain a corresponding lower bound similarly, using the lower bounds in (6.4) and (6.5).
, which is (6.10). We want to extend Lemma 6.2 to b = ∞. This will be Lemma 6.4, but to prove it we need the following lemma. Lemma 6.3. For any k 1 there exist constants b k , B k > 0 such that, for all t 0, Proof. For any t, recalling that N k counts edges arriving at rate r k (t) and that r k (t) is a decreasing function, we obtain by (6.6), (5.43), and Lemma 5.8, Thus, by (6.4), for b k := b k /2 and some B k < ∞, Hence, for some B k < ∞ and all t 0, 2B k e −b k t by Theorem 2.1(iv), establishing that the integral converges.
Proof of Theorem 1.2. By (6.3) and Lemma 6.4 (with W 0 (0, ∞) = 0), (6.23) Example 6.5. The limit γ k in Theorem 1.2 is thus given by the integral in (6.23). Unfortunately, we do not know how to calculate this, even numerically, for k 2. However, we can illustrate the result with the case k = 1. In this case, ρ 1 (t) is the asymptotic relative size of the giant component in G(n, t/n), and as is well-known, and follows from (5.28) and (4.10) noting that κ t (x, y) = t, σ 1 = 1 and for t > 1, ρ 1 (t) = 1 − e −tρ 1 (t) . The latter function has the inverse t(ρ) = − log(1 − ρ)/ρ, ρ ∈ (0, 1). Hence, by an integration by parts and two changes of variables, with ρ = 1 − e −x , where the final integral can be evaluated using a series expansion. Hence we recover the limit ζ(3) found by Frieze [10].
Remark 6.6. An argument similar to the proofs of Lemmas 6.2 and 6.4 shows that However, since T k has n − 1 edges, we trivially have N k (0, ∞) = k(n − 1) a.s. Hence, for any k 1, (This is easily verified for the case k = 1, by calculations similar to (6.24).) Equivalently, for any k 1 (since (6.26) holds trivially for k = 0 too), Proof of Theorem 1.3. It follows from (6.1) that N k (0, t) k(n − 1) and thus, using also (6.4), W k (0, b) kb. Consequently, Lemma 6.2 and dominated convergence yield, for every b < ∞, (6.28) Hence, (6.28) holds for b = ∞ too by the following routine three-epsilon argument: We have (6.29) where, for any ε > 0, we can make all three terms on the right-hand side less than ε (in absolute value) by choosing first b and then n large enough. The result follows since w(T k ) = W k (0, ∞) − W k−1 (0, ∞), cf. (6.23).
We can now prove Theorem 2.2.
Proof of Theorem 2.2. Let 0 a < b ∞, and let N (a, b) be the total number of edges arriving to G 1 (s) in the interval s ∈ (a, b]. Then N (a, b) ∼ Po n 2 1 n (b − a) , and by the law of large numbers, for any ε > 0, w.h.p.
The number of edges passed to 1 (a, b), and thus it follows from (6.30) and (6.5) that for any ε > 0, w.h.p. In the Poisson (process) model studied so far, we have a multigraph with an infinite number of parallel edges (with increasing costs) between each pair of vertices.
It is also of interest to consider the simple graph K n with a single edge (with random cost) between each pair of vertices, with the costs i.i.d. random variables. We consider two cases, the exponential model with costs Exp(1) and the uniform model with costs U (0, 1). When necessary, we distinguish the three models by superscripts P, E, and U.
We use the standard coupling of the exponential and uniform models: if X E ij ∼ Exp(1) is the cost of edge ij in the exponential model, then the costs are i.i.d. and U (0, 1), and thus yield the uniform model. Since the mapping X E ij → X U ij is monotone, the Kruskal algorithm selects the same set of edges for both models, and thus the trees T 1 , T 2 , . . . (as long as they exist) are the same for both models; the edge costs are different, but since we select edges with small costs, X U ij ≈ X E ij for all edges in T k and thus w(T U k ) ≈ w(T E k ); se Lemma 7.4 for a precise statement. Remark 7.1. We can in the same way couple the exponential (or uniform) model with a model with i.i.d. edge costs with any given distribution. It is easily seen, by the proof below and arguments as in Frieze [10] or Steele [28] for T 1 , that Theorem 1.1 extends to any edge costs X ij that have a continuous distribution on [0, ∞) with the distribution function F (x) having a right derivative F (0+) = 1 (for example, an absolutely continuous distribution with a density function f (x) that is right-continuous at 0 with f (0+) = 1); if F (0+) = a > 0, we obtain instead w(T k ) p −→ γ k /a. This involves no new arguments, so we confine ourselves to the important models above as an illustration, and leave the general case to the reader.
Moreover, we obtain the exponential model from the Poisson model by keeping only the first (cheapest) edge for each pair of vertices. We assume throughout the section this coupling of the two models. We regard also the exponential model as evolving in time, and define G E k (t) and F E k (t) recursively as we did G k (t) and F k (t) in Section 2, starting with G E 1 (t) := G 1 (t), the simple subgraph of K n obtained by merging parallel edges and giving the merged edge the smallest cost of the edges (which is the same as keeping just the first edge between each pair of vertices).
Recall from the introduction that while in the Poisson model every T k exists a.s., in the exponential and uniform models there is a positive probability that T k does not exist, for any k 2 and any n 2. (In this case we define w(T k ) := ∞.) The next lemma shows, in particular, that this probability is o(1) as n → ∞. (The estimates in this and the following lemma are not best possible and can easily be improved.) Lemma 7.2. In any of the three models and for any fixed k 1, w.h.p. T k exists and, moreover, uses only edges of costs 2k log n/n.
Proof. Consider the exponential model; the result for the other two models is an immediate consequence by the couplings above (or by trivial modifications of the proof). The result then says that w.h.p. G E k (2k log n) is connected.
By induction, we may for k 1 assume that the result holds for k − 1. Thus, w.h.p., G E k−1 2(k − 1) log n is connected, and then all later edges are passed to G E k (t). Consider now the edges arriving in (2(k − 1) log n, 2k log n]. They form a random graph G(n, p) with p = e −2(k−1) log n/n − e −2k log n/n = e −2k log n/n e 2 log n/n − 1 As is well-known since the beginning of random graph theory [9], see e.g. [2], such a random graph G(n, p) is w.h.p. connected. We have also seen that w.h.p. this graph G(n, p) is a subgraph of G E k (2k log n). Hence, G E k (2k log n) is w.h.p. connected, which completes the induction. Proof. Since the exponential model is obtained from the Poisson model by deleting some edges, we have by Lemma 5.7 that every edge contained in both processes and contained in F 1 (t)∪· · ·∪F k (t) is also contained in F E 1 (t)∪ · · · ∪ F E k (t); the only edges "missing" from the latter are those that were repeat edges in the Poisson model.
At time t k := 2k log n, how many repeat edges are there? For two given vertices i and j, the number of parallel edges is Po(t k /n), so the probability that it is two or more is p 2 (t k ) := P(Po(t k /n) 2) (t k /n) 2 /2. (We use that the kth factorial moment of Po(λ) is λ k , and Markov's inequality.) Hence, the number of pairs {i, j} with more than one edge is Bi( n 2 , p 2 (t k )), which is stochastically smaller than Bi(n 2 , (t k /n) 2 ), which by Chebyshev's inequality w.h.p. is 2t 2 k = 8k 2 log 2 n. Similarly, the probability that i and j have three or more parallel edges is (t k /n) 3 /6 and thus w.h.p. there are no triple edges in G 1 (t k ). By Lemma 7.2, w.h.p. T P 1 ∪· · ·∪T P k = F 1 (t k )∪· · ·∪F k (t k ), and we have just established that w.h.p. all but at most 2t 2 k of the edges in Since each spanning tree has exactly n − 1 edges, the missing edges are replaced by the same number of other edges, which by Lemma 7.2 w.h.p. also have cost t k /n each, thus total cost at most 2t 3 k = 16k 3 log 3 n/n. Consequently, w.h.p., Having additional edges can never hurt (in this matroidal context), so This yields the first inequality in (7.3), while the second follows from (7.4) together with (7.5) for j k − 1.
Lemma 7.4. For each fixed k, Proof. As said above, T E k and T U k consist of the same edges, with edge costs related by (7.1). Since (7.1) implies 0 2k log n n 2 .
(7.7)
Proof of Theorem 1.1. It follows from Theorem 1.2 and Lemma 7.3 that for each fixed k, w(T E k ) p −→ γ k , and then from Lemma 7.4 that w(T U k ) p −→ γ k , which is Theorem 1.1.
Recall that the corresponding statement for the expectation is false, as E w(T E k ) = E w(T U k ) = ∞ for k 2; see Remark 1.8.
The second threshold
As noted in Example 6.5 we do not know how to calculate the limit γ 2 . However, we can find the threshold σ 2 . In principle, the method works for σ k for any k 2, provided we know ρ k−1 , so we will explain the method for general k. However, we will assume the following: This is, we think, not a serious restriction, for the following reasons. First, (8.1) is easily verified for k = 2, since we know ρ 1 explicitly (see Example 6.5), so the calculation of σ 2 is rigorous. Second, we conjecture that (8.1) holds for all k 2, although we have not proved this. (Cf. what we have proved in Theorem 2.1.) Third, even if this conjecture is wrong and (8.1) does not hold for some k, we believe that the result below is true, and can be shown by suitable modifications of the argument and perhaps replacing ρ k−1 by suitable approximations.
A related problem by Frieze and Johansson
As said in the introduction, Frieze and Johansson [11] recently considered the problem of finding the minimum total cost of k edge-disjoint spanning trees in K n , for a fixed integer k 2. (They used random costs with the uniform model, see Section 7; we may consider all three models used above.) We denote this minimum cost by mst k , following [11] (which uses mst k (K n , X) for the random variable, where X is the vector of random edge costs, and uses mst k (K n ) for its expectation). Trivially, (9.1) and as said in the introduction, it is easy to see that strict inequality may hold when k 2, i.e., that our greedy procedure of choosing T 1 , T 2 , . . . successively does not yield the minimum cost set of k disjoint spanning trees.
We assume in this section that n 2k; then k edge-disjoint spanning trees exist and thus mst k < ∞. (Indeed, K 2k can be decomposed into k Hamilton paths, as shown in 1892 by Lucas [24, pp. 162-164] using a construction he attributes to Walecki. 1 ) Remark 9.1. As observed by Frieze and Johansson [11], the problem is equivalent to finding the minimum cost of a basis in the matroid M k , defined as the union matroid of k copies of the cycle matroid of K n . This means that the elements of M k are the edges in K n , and a set of edges is independent in M k if and only if it can be written as the union of k forests, see e.g. [32,Chapter 8.3]. (Hence, the bases, i.e., the maximal independent sets, are precisely the unions of k edge-disjoint spanning trees. For the multigraph version in the Poisson model, of course we use instead the union matroid of k copies of the cycle matroid of K ∞ n ; we use the same notation M k .) We write r k for rank in this matroid.
Kruskal's algorithm, recapitulated in the introduction, is valid for finding a minimum cost basis in any matroid; see e.g. [32,Chapter 19.1]. In the present case it means that we process the edges in order of increasing cost and keep the ones that are not dependent (in M k ) on the ones already selected; equivalently, we keep the next edge e if r k (S ∪ {e}) > r k (S), where r k is the rank function in M k and S is the set of edges already selected.
Remark 9.2. It follows that the largest individual edge cost for the optimal set of k edge-disjoint spanning trees is at most the largest edge cost for any given set of k edge-disjoint spanning trees. Hence, it follows from Lemma 7.2 that for the random models studied here, the optimal k spanning trees w.h.p. use only edges of cost 2k log n/n. It follows, with only minor modifications of the proofs, that analogues of Lemmas 7.3 and 7.4 hold for mst k for the three different models. Hence, for limits in probability, the three models are equivalent for mst k too.
Moreover, one can similarly show that for any b > 0 there is a constant B such that with probability at least 1 − n −b , the optimal k spanning trees w.h.p. use only edges of cost Bk log n/n. One can then argue as for the minimum spanning tree, see e.g. [12], [25,Section 4.2.3] or [6,Example 3.15], and obtain strong concentration of mst k for any of the three models; in particular Var(mst k ) = o(1), and thus convergence of the expectation E(mst k ) is equivalent to convergence in probability of mst k .
Frieze and Johansson [11] stated their results for the expectation E mst k (for the uniform model), but the results thus hold also for convergence in probability (and for any of the three models).
For k = 2, Frieze and Johansson [11] show that the expectation This is strictly smaller than our estimate for the total cost of two edgedisjoint spanning trees chosen successively, γ 1 + γ 2 . = 1.202 . . . + 3.09 . . . > 1 Lucas introduces the problem as one of "Les Jeux de Demoiselles", namely "Les Rondes Enfantines", a game of children holding hands in a circle repeatedly, never repeating a partner. The conversion between the Hamilton cycles of the game and the Hamilton paths serving as our spanning trees is simple, and Walecki's construction is more naturally viewed in terms of Hamilton paths. For much stronger recent results on Hamilton decompositions, see for example [22]. Tables 1 and 3. This would show that choosing minimum spanning trees one by one is not optimal, even asymptotically, except that our estimates are not rigorous. The following theorem is less precise but establishes rigorously (subject to the numerical solution to (8.24) giving σ 2 as in (8.26)) that the values are indeed different.
With µ 2 defined by the limit in (9.2), this can be restated in the following equivalent form. The proof of the theorem is based on the fact that many edges are rejected from T 1 and T 2 after time σ 2 , but none is rejected from the union matroid until a time c 3 , and c 3 (which we will show is the threshold for appearance of a 3-core in a random graph) is later than σ 2 .
We begin with three elementary lemmas that are deterministic, and do not assume any particular distribution of edge costs; nevertheless, we use the same scaling of time as before, and say that an edge with cost w is born at time nw. (Lemma 9.5 has been used in several works, including [11], in the study of minimum spanning trees.) Lemma 9.5. Suppose that we select N edges e 1 , . . . , e N , by any procedure, and that e i has cost w i . Let N (t) := |{i : w i t/n}|, the number of selected edges born at or before time t. Then the total cost is For the next lemma, recall from Remark 9.1 that r k is rank in the union matroid M k . We consider several (multi)graphs with the same vertex set [n], and we define the intersection G ∩ H of two such graphs by E(G ∩ H) := E(G) ∩ E(H). (We regard the multigraphs as having labelled edges, so parallel edges are distinguishable.) Note too that the trees T i in the lemma are arbitrary, not necessarily the trees T i defined in Section 2.1.
Lemma 9.6. Consider K ∞ n with any costs w e 0. Suppose that T 1 , . . . , T k are any k edge-disjoint spanning trees. For t 0, let G(t) be the graph with edge set {e ∈ E(K ∞ n ) : w e t/n}, and let N (t) := e G(t) ∩ (T 1 ∪ · · · ∪ T k ) . Then, N (t) r k (G(t)) for every t, and Proof. First, N (t) is by definition the number of edges in E G(t) ∩ (T 1 ∪ · · ·∪T k ) , an independent (with respect to M k ) subset of E(G(t)), and thus N (t) r k (G(t)), as asserted. Now apply Lemma 9.5, taking N = k(n − 1), taking the edges e 1 , . . . , e N to be the N edges in T 1 ∪ · · · ∪ T k , and noting that the definition of N (t) in Lemma 9.5 matches that here. This yields Next, as a special case, consider a collection of k spanning treesT 1 , . . . ,T k with minimum total cost. (Since we are in a deterministic setting, such a collection may not be unique.) We may assume that they are found by Kruskal's algorithm, and thus, for every t, the set of edges in G(t)∩(T 1 ∪· · ·∪ T k ) is a maximal set of independent edges in G(t) (independent with respect to M k ), hence the number of these edges is N (t) = r k (G(t)). Consequently, Lemma 9.5 yields The result (9.4) follows by subtracting (9.5) from (9.6).
Lemma 9.7. Let the multigraph G be a subgraph of K ∞ n and assume that the (k + 1)-core of G is empty for some k 1. Then the edge set E(G) is a union of k disjoint forests. In other words, r k (G) = e(G).
The properties in two last sentences are equivalent by Remark 9.1.
Proof. We use induction on |G|; the base case |G| = 1 is trivial.
If |G| > 1 and |G| has an empty (k + 1)-core, then there exists a vertex v in G of degree d(v) k. Let G be G with v and its incident edges deleted. By the induction hypothesis, E(G ) is the union of k edge-disjoint forests F 1 , . . . , F k . These forests do not contain any edge with v as an endpoint, so we may simply add the first edge of v to F 1 , the second to F 2 , and so on, to obtain the desired decomposition of E(G).
Alternatively, the lemma follows easily from a multigraph version of a theorem of Nash-Williams [26], appearing also as [32,Theorem 8.4.4]; specifically, the matroidal proof in [32] extends to multigraphs. This theorem hypothesizes that G is "sparse", meaning that for every vertex subset A, e(G[A]) k(|A| − 1), but this follows from our hypothesis. If G has empty core, so does G[A], thus G[A] has a vertex v of degree k, whose deletion leaves another such vertex, and so on until there are no edges, showing that e(G[A]) k(|A| − 1).
Proof of Theorem 9.3. By Lemmas 7.3-7.4 and Remark 9.2, the choice of model does not matter; for convenience we again take the Poisson model.
10. Conjectured asymptotics of ρ k (t) As discussed in Section 3, γ k ∼ 2k for large k, see for example Corollary 1.7. Moreover, simulations (see Section 11) suggest that the functions ρ k (t) converge, after suitable translations. If so, and assuming suitable tail bounds, (6.26) implies that the translations should be by 2k, up to an arbitrary constant plus o(1); this is formalized in Conjecture 1.4.
It is easy to see that this, together with suitable tail bounds justifying dominated convergence, by (6.23) and (6.27) would imply Recall that ρ k (t) is given by Lemma 5.4 as the survival probability of the branching process X t defined in Section 4.4 with kernel κ t (x, y) on the probability space (R + , µ k−1 ) where µ k−1 has the distribution function ρ k−1 (t). More generally, we could start with any distribution function F (t) on R + and the corresponding probability measure µ and define a new distribution function Ψ(F )(t) as the survival probability ρ(κ t ; µ). This defines a map from the set of distribution functions (or probability measures) on [0, ∞) into itself, and we have ρ k = Ψ(ρ k−1 ). If one could show that Ψ is a contraction for some complete metric (perhaps on some suitable subset of distribution functions), then Banach's fixed point theorem would imply the existence of a unique fixed point ρ ∞ , and convergence of ρ k to it. However, the mapping Ψ is quite complicated, and we leave the possible construction of such a metric as an open problem.
Recall also that t = σ k is where ρ k (t) becomes non-zero, see Theorem 2.1(iii). Hence, Conjecture 1.4 suggests also the following, related conjecture.
Conjecture 10.1. There exists a real constant σ ∞ such that as k → ∞, In particular,
Computational results
11.1. Naive simulations. For intuition and as a sanity check on all calculations, we first directly simulate the problem described in the introduction's Poisson edge-weight model. Specifically, we take a graph with n vertices and random edge weights (i.i.d.exponential random variables with mean 1), find the MST, add fresh exponentials to the weights of the MST edges, and repeat to get the second and subsequent MSTs. For each MST, we plot each edge's rank within the MST, divided by n (so, 1/n for the first edge, up to (n − 1)/n for the last) on the vertical axis, against the edge's weight (multiplied by n in accordance with our time scaling) on the horizontal axis.
The results are shown in Figure 2. The corresponding estimates of γ k , for k up to 5, are 1.197, 3.055, 5.035, 7.086, 9.100. This was done for just a single graph with n = 4 000, not averaged over several graphs. For a sense of the limited accuracy of the estimates, remember that γ 1 = ζ(3) = 1.2020 . . ..
Better simulations.
Better simulations can be done with reference to the model introduced in Section 2.1 and used throughout. We begin with k empty graphs of order n. At each step we introduce a random edge e and, in the first graph G i for which e does not lie within a component, we merge the two components given by its endpoints. (If this does not occur within the k graphs under consideration, we do nothing, just move on to the next edge.) For each graph we simulate only the components (i.e., the sets of vertices comprised by each component); there is no need for any more detailed structure. The edge arrivals should be regarded as occurring as a Poisson process of intensity (n − 1)/2 but instead we simply treat them as arriving at times 2/n, 4/n, etc. Figure 3 depicts the result of a single such simulation with n = 1 000 000, showing for each k from 1 to 5 the size of the largest component of G k (as a fraction of n) against time.
A larger simulation, using 10 simulations each with n =10M, and up to time t = 40 (i.e., 200M steps), supports Conjecture 1.6 that γ k = 2k − 1 + o(1); see Figure 4. 11.3. Estimates of the improved upper bound. The differential equation system (3.18), giving the improved upper bound of Section 3.3, is easy to solve numerically. We did so as a discrete-time approximation, setting g k (t + ∆t) = g k (t) + 1 2 ∆ g k−1 (t) 2 − g k (t) 2 , using ∆t = 0.000 01 and considering k up to 50. Figure 5 shows the results up to time t = 10. Because g k (t) pertains to a model in which all edges of F k are imagined to be in a single component, this plot is comparable both to that in Figure 2 (which counts all edges) and to those in Figure 3 (which counts edges in the largest component) and Figure 7 (the theoretical giant-component size).
Figure 5.
Values g k (t) plotted against t. The function g 7 (t) is just rising from 0 within the plot range; the values of g k (t) for larger k are too close to 0 to be seen. Table 2 and Figure 6 show the corresponding upper bounds on Γ k . Specifically, the bound on Γ k from (3.19), call it Γ k , is estimated as Γ k . = 1 2 ∆ t∈T t(1 − g k (t) 2 ) where T = {0, ∆, 2∆, . . .}. Since we cannot sum to infinity, we terminate when the final g k under consideration is judged sufficiently close to 1, specifically within 0.000 000 1 of 1. It appears experimentally that the gap 1−g k (t) decreases exponentially fast (very plausible in light of (2.3)) so termination should not be a large concern; see also (6.15). Table 2. Upper bounds on Γ k obtained from numerical solution of (3.19). Figure 6 suggests that the gaps Γ k − k 2 level off at about 0.743. (Beyond about k = 25 the gaps decrease, but using ∆t = 0.000 1 they continued to increase, and in either case the degree of change is comparable with ∆t and thus numerically unreliable.) This suggests the following conjecture. (Recall from (3.11) that Γ k k 2 .) Conjecture 11.1. For every k 1, Γ k Γ k k 2 +δ for some constantδ. We established in Section 3.3 that Γ k Γ k , so only Γ k k 2 +δ is conjectural. If the conjecture holds, then it follows, using also (3.11), that γ k = Γ k − Γ k−1 (k 2 ) − ((k − 1) 2 +δ) = 2k − 1 −δ and γ k = Γ k − Γ k−1 (k 2 +δ) − (k − 1) 2 = 2k − 1 +δ. Hence, the conjecture would imply 2k − 1 −δ γ k 2k − 1 +δ. (11.1) In particular, if Conjecture 11.1 holds withδ 1 as it appears, then 2k−2 γ k 2k.
11.4.
Estimates of the fixed-point distributions ρ k . We also numerically estimated the distributions ρ k ; recall from Theorem 2.1 that C 1 (G k (t))/n p −→ ρ k (t). We may begin with either ρ 0 (t), which is 0 for t < 0 and 1 for t 0, or with ρ 1 (t), which as described in Example 6.5 is the inverse function of − log(1 − ρ)/ρ. (Both choices gave similar results, the latter being slightly preferable numerically.) We use ρ k−1 to obtain ρ k , following the branching process described in Section 4.4. The survival probability ρ t (x) at time t of a particle born at time x in the branching process equivalent of G k is given by the function ρ t = ρ κ which (see (4.10)) is the largest fixed point of (11.2) (the time t is implicit in the kernel κ = kk t thus in the operators Φ κ and T κ ), where (see (4.6)) T κ is given by T κ f (x) = S κ(x, y)f (y) dµ(y). With reference to the kernel κ defined in (5.20), T κ f (x) = 0 for x > t, while otherwise, with µ = ρ k−1 as in (5.14), Given t, to find ρ t numerically we iterate (11.2), starting with some f known to be larger than ρ t and repeatedly setting f (x) equal to Φ κ f (x); this gives a sequence of functions that converges to the desired largest fixed point ρ t , cf. [4,Lemma 5.6]. We will estimate ρ t for times i ∆t, for ∆t some small constant and i = 0, . . . , I, with I∆t judged to be sufficient time to observe all relevant behavior. We initialize with f ≡ 1 to find ρ I∆t , then iteratively initialize with f = ρ i∆t to find ρ (i−1)∆t . Since the branching process is monotone in t -each vertex can only have more children by a later time t -so is the survival probability, thus ρ i∆t is larger than ρ (i−1)∆t and therefore a suitable starting estimate. In practice we find that the process converges in 20 iterations or so even for ρ I∆t , and less for subsequent functions ρ i∆t , with convergence defined as two iterates differing by at most 10 −8 for any x.
For each k in turn, we do the above for all times t, whereupon the desired function ρ k (t) def = ρ(κ) = ρ(κ t ) is given by (see (4.9) and (5.28)) ρ k (t) = ∞ 0 ρ t (x) dρ k−1 (x). (11.4) Do not confuse ρ t of (11.2) and ρ k of (11.4), respectively the ρ κ and ρ of (4.8); see also (5.28) and the comment following it. All the calculations were performed with time (t, x, and y) discretized to multiples of ∆t = 0.01 and restricted to the interval [0, 10]. For a fixed t, the calculation in (11.3) can be done efficiently for all x. The derivative of (11.3) with respect to x is − x 0 f (y) dρ k−1 (y) (cf. (8.3) and (8.4)). So, given the value of (11.3) for some x, that at the next discrete x is the discrete sum corresponding to this integral, and in one pass we can compute these integrals (discretized to summations) for all x. Each computed ρ k (t) is translated by 2k to keep the functions' interesting regimes within the time range [0, 10], before doing the computations for k + 1, but these translations are reversed before interpreting the results.
The first observation is that the estimates of ρ k are consistent with Conjecture 1.4. As shown in Figure 7, even the first few functions ρ k have visually very similar forms.
To make a more precise comparison, we time-shift each function ρ k so that it reaches the value 1 − e −1 at time t = 4 (arbitrarily chosen). Figure 8 shows the thus-superposed curves for ρ 1 , ρ 2 , and ρ 1 000 ; the curve ρ 5 (not shown) is already visually indistinguishable from ρ 1 000 .
Estimates for γ k , obtained from those for ρ k via (6.23), are shown in Table 3. Estimates of γ k for large k were deemed numerically unreliable for two reasons. First, discretization of time to intervals of size ∆t = 0.01 is problematic: the timing of ρ 1 is uncertain to this order, that of ρ 2 additionally uncertain by the same amount, and so on, and translation of ρ k directly affects the corresponding estimate of γ k . Second, the time range t ∈ [0, 10] (translated as appropriate) used in the computations proved to be too narrow, in that for large k the maximum value of ρ k observed only about 0.9975, and the gap between this and 1 may be enough to throw off the estimates of γ k perceptibly. Table 3. Estimates of γ k from (6.23).
Open questions
We would be delighted to confirm the various conjectures above, in particular Conjectures 1.4-1.6, and get a better understanding of (and ideally a closed form for) ρ ∞ (provided it exists).
It is also of natural interest to ask this kth-minimum question for structures other than spanning trees. Subsequent to this work, the length of the kth shortest s-t path in a complete graph with random edge weights has been studied in [13]. The behavior is quite different: the first few paths cost nearly identical amounts, while [13] gives results for all k from 1 to n − 1.
The "random assignment problem" is to determine the cost of a minimumcost perfect matching in a complete bipartite graph with random edge weights, and a great deal is known about it, by a variety of methods; for one relatively recent work, with references to others, see [31]. It would be interesting to understand the kth cheapest matching.
It could also be interesting to consider other variants of all these questions. One, in the vein of [11], is to consider the k disjoint structures which together have the smallest possible total cost. Another is to consider a second structure not disjoint from the first, but differing in at least one element, either of our choice or as specified by an adversary. | 23,091.6 | 2019-06-04T00:00:00.000 | [
"Mathematics"
] |
A Data-Driven Method for the Estimation of Truck-State Parameters and Braking Force Distribution
In the study of braking force distribution of trucks, the accurate estimation of the state parameters of the vehicle is very critical. However, during the braking process, the state parameters of the vehicle present a highly nonlinear relationship that is difficult to estimate accurately and that seriously affects the accuracy of the braking force distribution strategy. To solve this problem, this paper proposes a machine-learning-based state-parameter estimation method to provide a solid data base for the braking force distribution strategy of the vehicle. Firstly, the actual collected complete vehicle information is processed for data; secondly, random forest is applied for the feature screening of data to reduce the data dimensionality; subsequently, the generalized regression neural network (GRNN) model is trained offline, and the vehicle state parameters are estimated online; the estimated parameters are used to implement the four-wheel braking force distribution strategy; finally, the effectiveness of the method is verified by joint simulation using MATLAB/Simulink and TruckSim.
Introduction
Economic development has placed stricter demands on the transportation industry, and the increased use of commercial vehicle transportation as a mode of road transportation for the transport of goods and passengers has played a vital role in easing the pressure on transportation and increasing the productivity of various industries [1][2][3]. Among them, the braking of commercial vehicles is an important basis for ensuring the safety of vehicle driving and the development of active safety technology, and the emergence of electro-mechanical brake (EMB), which is responsive, easy to realize active braking, and offers more accurate control of braking force, provides a strong hardware basis for intelligent vehicles [4,5]. EMB provides executable prerequisites for the intelligent braking of the vehicle under different working conditions to ensure driving safety [6,7].
In terms of active safety functions, the anti-lock brake system (ABS), which actively intervenes in the braking force, plays an important role in improving the car's wheel adhesion capacity and driving stability during heavy braking, and the control strategy of ABS can be mainly divided into rule-based control strategy [8][9][10] and model-based control strategy [11][12][13]. Among them, the rule-based control strategy considers the state of the vehicle driving with the slip rate as the limit and also considers the angular deceleration rate for the decision of discontinuous control such as increase, pressure preservation, and decompression. This control method is computationally small, the technology is relatively mature, and the accuracy requirement for the state observation of the vehicle is small, and owing to the high stability of this control method, this method is commonly used in various ABS strategy development. However, due to the inability to directly measure the slip rate, the accuracy of vehicle observation of slip rate, and the limitation of non-continuous control, the method can only perform suboptimal control in practice, and does not take advantage of EMB's precise control of each wheel braking force. Therefore, the traditional rule-based control strategy is difficult to balance the control adaptability and real-time control effect.
In the research on model predictive control strategy, the application of the MPC method of ABS control is gradually becoming a research hotspot, which requires fewer calibration parameters compared with the traditional controller, thus shortening the development time, and the method can adjust the vehicle braking torque in real time by following the vehicle slip rate, which can precisely control the braking force of each wheel under the vehicle braking torque distribution strategy. However, due to the huge computational volume of the model predictive control, it is difficult to meet the requirements of real-time control due to the limitation of the computing power of the automotive computing platform, so the optimization of this method is also being carried out gradually [14,15].
The tire force is the fundamental cause of changing the vehicle motion state, the tire force is the basis for controlling the vehicle state, and there is a transparent mapping relationship between the tire force and the vehicle state [16,17]. There are three main traditional methods for tire force observation: filter-based methods [18,19], mathematical model-based methods [20,21], and sensor-based observation methods [22][23][24]. The filterbased methods are mainly Kalman filter and least squares [24,25], but this method is significantly affected by environmental factors in practical application, and the observation accuracy depends on the accuracy of the specified tire model. The mathematical modelbased method is mainly the Romberg method [26]; the accuracy of tire characteristic parameters is required by this method. The sensor-based observation methods are very expensive, easy to be affected by the motion state of the vehicle and has poor robustness.
The problem of observing the tire force can be transferred to the solution of obtaining the mapping relationship between the vehicle motion state and the running attitude and the tire force. Because of the highly nonlinear relationship between them, the highly nonlinear solver has become an important way to build a high-precision tire force observer [27,28]. Among them, machine learning has become a critical approach to solving the problem due to its powerful generalization and inference regression capabilities. Machine learning already has a wide range of applications in the field of state observation. For example, battery SOC state observation [29,30], future vehicle speed prediction [31,32], and torque observation of key power components of hybrid vehicles [33,34]. Therefore, this method has good observation accuracy in performing state observation.
In summary, this paper proposes an improved ABS control strategy based on a highprecision state observer. In the control strategy, the wheel force high-precision state observer is integrated with the ABS control strategy to map high-precision tire force to provide an accurate reference for vehicle ABS control. The independent distribution of multi-wheel braking pressure provides a guarantee to enhance the braking efficiency of the vehicle. Finally, the joint simulation verifies wheel force state observation and vehicle ABS control accuracy.
Innovation point:
1.
For the component parameters of four-wheeled trucks, which are difficult to observe accurately due to their complex nonlinear variations, this paper proposes a data-driven machine learning estimation method to accurately estimate the vehicle parameters (this parameter specifically refers to the four-wheeled vertical force) 2.
According to the estimated four-wheel force, the braking force is distributed according to the proportion of the force.
3.
By collecting the operating data of the vehicle under Changchun City working conditions, the data were interpolated and filtered to eliminate component signal frequency inconsistencies, noise, and anomalies, and to construct a machine learning model dataset.
The Model Construction of Truck
The main research object of this paper is a four-wheel truck whose structure is shown in Figure 1. This vehicle consists of the engine, clutch, transmission, drive axle, and other components. The engine is the only power source to provide the vehicle driving energy. The vehicle is equipped with a six-speed gearbox to realize everyday driving under multiple working conditions according to information such as vehicle speed and power while improving the engine's working point and optimizing the engine's efficiency to a certain extent. Table 1 shows the information on the vehicle parameters of the four-wheeled truck. frequency inconsistencies, noise, and anomalies, and to construct a machine learning model dataset.
The Model Construction of Truck
The main research object of this paper is a four-wheel truck whose structure is shown in Figure 1. This vehicle consists of the engine, clutch, transmission, drive axle, and other components. The engine is the only power source to provide the vehicle driving energy. The vehicle is equipped with a six-speed gearbox to realize everyday driving under multiple working conditions according to information such as vehicle speed and power while improving the engine's working point and optimizing the engine's efficiency to a certain extent. Table 1 shows the information on the vehicle parameters of the four-wheeled truck.
Mathematic Model of Truck
In the actual drive-over driving process of the vehicle, to realize the normal driving of the vehicle, the power provided by the vehicle must overcome the rolling resistance, air resistance, slope resistance, and acceleration resistance, the driving force, and power balance equation expression as shown in Equations (1) (1)
Mathematic Model of Truck
In the actual drive-over driving process of the vehicle, to realize the normal driving of the vehicle, the power provided by the vehicle must overcome the rolling resistance, air resistance, slope resistance, and acceleration resistance, the driving force, and power balance equation expression as shown in Equations (1) and (2): where F t is the tangential driving force generated by the driving wheels; m is the vehicle mass; g is gravitational acceleration; f is rolling resistance coefficient; α slope is the road slope; C D is the air resistance coefficient; A is the windward area; δ is the rotating mass conversion factor; v is the vehicle speed; T req is the demand torque; r is the wheel rolling radius, the relevant parameter values are shown in Table 2; η t is the transfer efficiency.
Engine Model
As the only power source of the vehicle, the maximum torque of the engine can reach 740.6 Nm. According to the experimental data, the external characteristics and efficiency map of the engine are established, as shown in Figure 2.
where t F is the tangential driving force generated by the driving wheels; m is the hicle mass; g is gravitational acceleration; f is rolling resistance coefficient; slop α the road slope; D C is the air resistance coefficient; A is the windward area; δ is the ro ing mass conversion factor; vis the vehicle speed; req T is the demand torque; r is the wh rolling radius, the relevant parameter values are shown in Table 2; t η is the transfer e ciency.
Engine Model
As the only power source of the vehicle, the maximum torque of the engine can re 740.6 Nm. According to the experimental data, the external characteristics and efficie map of the engine are established, as shown in Figure 2.
Pneumatic ABS Solenoid Valve Model
The EBS system in this paper uses dual-channel control for the rear axle and a sin channel control and ABS solenoid junction for the front axle. The ABS solenoid valv used to control the braking pressure of the left and right wheels of the front axle se rately, the braking pressure of all four wheels of the EBS system can be controlled in pendently. Additionally, the ABS solenoid valve consists of a booster valve and a p sure-reducing valve, of which the booster valve is a normally open solenoid valve. structure diagram of ABS solenoid valve is shown in Figure 3 and the operating cha teristics of ABS solenoid valve are shown in Table 3.
Pneumatic ABS Solenoid Valve Model
The EBS system in this paper uses dual-channel control for the rear axle and a singlechannel control and ABS solenoid junction for the front axle. The ABS solenoid valve is used to control the braking pressure of the left and right wheels of the front axle separately, the braking pressure of all four wheels of the EBS system can be controlled independently. Additionally, the ABS solenoid valve consists of a booster valve and a pressure-reducing valve, of which the booster valve is a normally open solenoid valve. The structure diagram of ABS solenoid valve is shown in Figure 3 and the operating characteristics of ABS solenoid valve are shown in Table 3.
Brake Model
High-pressure gas from the storage cylinder through the EBS system actuators finally reaches the brake chamber to produce braking pressure, so the EBS can control the braking pressure of the brake chamber. While in ABS and regenerative braking control strategy, the final given is the braking force or braking torque of the wheels, which requires key conversion components of brakes. Brakes are mainly divided into disc brakes and drum brakes.
Disc brakes use a disc-shaped brake disc as the rotating element in the frictional vice. Disc brakes are small in size, light in mass, have good resistance to heat recession, and are commonly used in passenger cars. Drum brakes use a brake drum as the rotating element in the frictional vice. The braking torque generated by the brake is mainly related to the brake chamber pressure, brake contact area, braking efficiency, brake friction coefficient, effective braking radius, and brake coefficient, so the braking torque generated by the brake is shown in the following Equation (3): where P b is braking pressure; A b braking contact area; η b braking efficiency; µ b braking friction coefficient; r b effective braking radius; c b is brake coefficient.
where K b is the brake conversion factor, Table 4 gives the brake related parameter settings in the simulation, the units are all international system units, and we can calculate the brake conversion factor K b = 0.0022. Table 4. Brake related parameter setting.
Tire Model
Tires are the only vehicle part that contacts the ground and transmits forces and moments. The longitudinal force, lateral force, and return torque to the vehicle are all generated by the contact between the tires and the ground, so the accuracy of the tire model is critical to the overall vehicle model. Nowadays, the mainstream tire models are divided into three categories: theoretical models, semi-empirical models, and empirical models. In order to improve the applicability of the model, the theoretical model, the GIM tire model, is chosen [35,36]. The GIM tire model has a high accuracy for the calculation of lateral and longitudinal forces and the model parameters are easily measured to meet the requirements of state estimation in this paper. a.
Slip rate calculation The slip rate indicates the sliding ratio's share in the overall vehicle form process. During the braking process, as the braking intensity increases, the rolling component of the wheel becomes less and less, while the sliding component becomes more and more. The formula for calculating the longitudinal slip rate is shown in Equation (5).
Dynamic load calculation model The slip rate indicates the sliding component's share in the overall vehicle form process. During the braking process, as the braking intensity increases, the rolling component of the wheel becomes less and less. In contrast, the load of the four wheels remains unchanged during everyday driving. However, when the vehicle is braking, longitudinal axle load transfer occurs, at which time the vertical load (normal force) of each wheel is calculated as shown in the Equations (6)- (9).
where F z f l is front left wheel vertical load; F z f r is front right wheel vertical load; F zrl is rear left wheel vertical load; F zrr is rear right wheel vertical load; M is the mass; L is the axle distance; a is the distance from center of mass to front axle; b is the distance from center of mass to rear axle; h g is the height of car center of mass; a x is the longitudinal acceleration; a y is the lateral acceleration; d f is the front wheelbase; d r is the rear wheelbase.
Methodology
For the complex braking force system of four-wheeled trucks and the state of the vehicle and the working state of components present complex nonlinear operating characteristics, this paper proposes a machine-learning-based regression of the vehicle parameters to achieve the accurate estimation of the complex nonlinear parameters of the vehicle and improve the accuracy of the vehicle in the braking decision to give full play to the potential of the independent braking force. The architecture diagram is shown in Figure 4. Firstly, the CANoe adopted to collect information in the actual driving process of the vehicle to establish the data module. Secondly, a large number of data sets for the subsequent machine learning model training brings a huge amount of computation, the use of random forest (RF) method for the data set feature screening to reduce the dimensionality of the data and reduce the computational load. Finally, the estimation of complex nonlinear parameters of the vehicle are achieved by using generalized regression neural network (GRNN). Through the data-driven approach, the accurate estimation of the vehicle state parameters of the truck is realized, and the potential of the independent braking of the truck is fully utilized to improve the stability and safety. subsequent machine learning model training brings a huge amount of computation, the use of random forest (RF) method for the data set feature screening to reduce the dimensionality of the data and reduce the computational load. Finally, the estimation of complex nonlinear parameters of the vehicle are achieved by using generalized regression neural network (GRNN). Through the data-driven approach, the accurate estimation of the vehicle state parameters of the truck is realized, and the potential of the independent braking of the truck is fully utilized to improve the stability and safety.
Data Processing
In the actual driving process of the vehicle, the collected data need to be processed because of factors such as signal frequency disparity, signal noise, and abnormal data points in the collected information of the vehicle components. In this paper, Newton's interpolation method is adopted to achieve uniformity in the time-to-time dimension of the collected data for specific differences in the signal frequencies of the collected components. In addition, the first order low-pass filtering method is adopted to process the noise and anomalies of the signals to establish an effective data set.
a. Newton interpolation
The inheritance of the Newton interpolation method can use the results of previous operations to reduce the number of operations when adding additional interpolation points. It has a more significant advantage in the process of interpolation calculation for a large amount of data. Let the time point in the original sampling frequency be less than the nearest point of the interpolated time point, marked as β. The data value obtained by interpolation is the average of the The 0 1 , ,..., n x x x are 1 n + non-coincident points, then the following linearly independent Newton polynomial is shown in Equation (10).
Data Processing
In the actual driving process of the vehicle, the collected data need to be processed because of factors such as signal frequency disparity, signal noise, and abnormal data points in the collected information of the vehicle components. In this paper, Newton's interpolation method is adopted to achieve uniformity in the time-to-time dimension of the collected data for specific differences in the signal frequencies of the collected components. In addition, the first order low-pass filtering method is adopted to process the noise and anomalies of the signals to establish an effective data set. a.
Newton interpolation The inheritance of the Newton interpolation method can use the results of previous operations to reduce the number of operations when adding additional interpolation points. It has a more significant advantage in the process of interpolation calculation for a large amount of data. Let the time point in the original sampling frequency be less than the nearest point of the interpolated time point, marked as β. The data value obtained by interpolation is the average of the β − (α/2 − 1) data to β + α/2 data in the original sampling value.
The x 0 , x 1 , . . . , x n are n + 1 non-coincident points, then the following linearly independent Newton polynomial is shown in Equation (10).
Given the function value of f (x i ) exist a unique polynomial satisfying p n (x i ) = f (x i ), as shown in Equation (11).
b. First order low-pass filter The low-pass filter achieves the characteristic is 'pass low frequency and block high frequency', allowing signals below the cutoff frequency to pass while signals above the cutoff frequency are blocked. This paper uses the first order low-pass filter to process the signal, and its transfer function is shown in Equation (12).
where T is the time constant; f c is the cutoff frequency, when the input signal is certain, the smaller the cutoff frequency fc is, the less signal the low-pass filter allows to pass, and the better the suppression of fluctuation. The larger the fc is, the more signal the low-pass filter allows to pass, and the greater the fluctuation. If you use a filter with a fixed cutoff frequency, you need to set the cutoff frequency fc of the low-pass filter in advance, and if it is set too high, the low-pass filter cannot play the role of filtering well.
In addition, the first order low-pass digital filtering formula is shown in Equation (13).
where f (x) is the filter coefficient function one; g(x) is the filter function two, the actual value of the functions depends on the filter time constant and the sampling period; X n is the input value at the n-th sampling; Y n is the output value at the nth sampling, and Y n−1 is the output value at the previous sampling. The first order low-pass filtering method uses the weighting of the current sampling value with the last filtered output value to obtain a practical filtered value, which makes the output have a feedback effect on the input. The filtering effect is mainly influenced by the filter function f (x) and the filter function g(x), and there is a certain relationship between f (x) and g(x). When the actual value of f (x) is larger at a certain moment, the actual value of g(x) will decrease accordingly, and the smaller f (x) is, the smoother the filtering effect will be, and the larger f (x) is, the more unstable the filtering effect will be, with great sensitivity.
The data processing through data interpolation and filtering solves the inconsistency of data in the time dimension, eliminates the noise and anomalies of the signal, makes the data more rational and more convincing, and provides a solid basis for the establishment of data sets as well as data applications.
RF-Based Feature Screening
Random forest is integrated learning based on decision trees, which essentially addresses the inherent shortcomings of individual models as integrated learning algorithms and integrates individual regression models to form better models. On the basis of a large amount of data, random forest can play a better feature screening property. The feature selection in a random forest is similar to the random selection of datasets, where the decision tree in a random forest randomly selects certain features from all the features to be selected and does not use all the data features in the data. In the process of random forest feature selection, the features are selected based on the principle of the magnitude of the contribution of each feature to achieve dimensionality reduction of the data.
In the process of model training, RF adopts a bagging framework to generate m training sets by the bootstrap method. Each decision tree has inconsistencies in training samples, and the characteristics of the samples are extracted from various aspects. The sampling formula is shown in Equation (14). Input samples α have a total of n data samples in the bootstrap, and a training sample β is obtained from random sampling n times of replacement in the N samples, so a number of samples have not been collected. In order to reduce the phenomenon of over-fitting, an "out-of-bag estimate" is performed on the generalization error of the decision tree by using the original samples that are not selected. The out-of-bag estimate of samples is shown in Equation (16).
where α are the input samples; β are the training samples; N is the number of input samples; n is the number of training samples; D is the number of input samples features; d is the number of training samples features; H oob (x) is the out-of-bag estimate of sample x; h t is the t-th decision tree; T is the total number of decision trees; y is the featured item in the sample feature set.
Then the out-of-bag estimate of bagging generalization error is shown in Equation (17).
In the actual application of RF, the result of the decision trees output adopts the mean value method to obtain the final prediction result of RF, as shown in Equation (18).
where v t is the speed information output by the t-th decision tree; P t is the probability distribution of the output speed information of the t-th decision tree.
The out-of-bag data error rate evaluates the importance of different features in the dataset. The dimensionality of the high-dimensional data is reduced by selecting the data with higher importance and excluding the data with lower importance.
GRNN-Based Parameter Estimation
Generalized Regression Neural Network (GRNN) as a radial-based neural network structure has strong nonlinear insertion ability as well as high fault tolerance and robustness and has a good performance in the nonlinear solution process. The theoretical basis of generalized regression neural networks is nonlinear regression analysis, where the regression analysis of the non-independent variable Y with respect to the independent variable X is actually the calculation of y with a maximum probability value, then the regression of y with respect to X (i.e., the conditional mean) is shown in Equation (19).
where Y is the predicted output of Y given the input X; f (X, y) is the joint probability density function of the random variable x and the random variable y; and X is the observed value. Applying the Parzen nonparametric estimation, the density function can be estimated from the sample data set, as shown in Equation (20).
where X i , Y i are the sample observations of the random variables; n is the sample size; p is the dimensionality of the random variable; and δ is the width coefficient of the Gaussian function, here called the smooth factor. The output of the network is Y.
The GRNN network structure has four different layers: the input layer, pattern layer, summation layer and output layer, and the network structure is shown in Figure 5. p is the dimensionality of the random variable; and δ is the w Gaussian function, here called the smooth factor. The output of th The GRNN network structure has four different layers: the inp summation layer and output layer, and the network structure is sh
a. The input layer
The number of neurons in the input layer is equal to the dimen input, and the distribution of each neural unit is simple. The inpu passed to the pattern layer.
b. The pattern layer
The pattern layer is fully connected to the input layer, and between the inner layers. The number of neurons in the mode laye input samples, and the transfer function is expressed in the ex squared Euclid distance, as shown in Equation (21).
where X is the network input variable; i X is the learning samp i-th neuron.
c. The summation layer
The summation layer has two different ways of summing th summation calculation is the arithmetic sum of the output of the nection weight of 1 for the mode layer and each neuron. The transf Equation (22). The other type of summation is calculated as a weigh in the mode layer, and the transfer function is shown in Equation a.
The input layer The number of neurons in the input layer is equal to the dimensionality of the sample input, and the distribution of each neural unit is simple. The input variables are directly passed to the pattern layer. b.
The pattern layer The pattern layer is fully connected to the input layer, and there is no connection between the inner layers. The number of neurons in the mode layer equals the number of input samples, and the transfer function is expressed in the exponential form of the squared Euclid distance, as shown in Equation (21).
where X is the network input variable; X i is the learning sample corresponding to the i-th neuron.
c. The summation layer The summation layer has two different ways of summing the neurons. One type of summation calculation is the arithmetic sum of the output of the mode layer with a connection weight of 1 for the mode layer and each neuron. The transfer function is shown in Equation (22). The other type of summation is calculated as a weighted sum of the neurons in the mode layer, and the transfer function is shown in Equation (23).
where q ij is the weight value of the ith neuron in the model layer and the jth neuron in the summation layer; The output of the output layer node is equal to the output of the corresponding summation layer divided by the output of the first node of the summation layer. The relationship is shown in Equation (24).
In the process of practical application, the information of the vehicle presents the characteristics of high dimensionality and multiple noise points. GRNN has high fault tolerance and robustness, and has high accuracy in the process of nonlinear parameter estimation of the vehicle.
Braking Force Distribution Strategy Based on Weight Coefficients
During the vehicle's braking process, the wheels' vertical pressure directly affects the amount of ground braking force. In the actual driving process, the reasonable distribution of braking pressure is carried out according to the estimated values of four-wheel vertical pressure (as shown in Algorithm 1).
Algorithm 1 Online control algorithm of braking force distribution strategy.
Input: T Brake_All , F F_L , F F_R , F R_L , F R_R , S Brake Output: result Initialize: result = [] Notations: T Brake_All is total braking force F F_L is the vertical force of the left front wheel F F_R is the vertical force of the right front wheel F R_L is the vertical force of the left rear wheel F R_R is the vertical force of the right rear wheel T F_L is the braking force of the left front wheel T F_R is the braking force of the right front wheel T R_L is the braking force of the left right wheel T R_R is the braking force of the right rear wheel S Brake is the brake signal 1: while S Brake > 0 do 2: Load_1 = F F_L /(F F_L + F F_R + F R_L + F R_R ); 3: Load_2 = F F_R /(F F_L + F F_R + F R_L + F R_R ); 4: Load_3 = F R_L /(F F_L + F F_R + F R_L + F R_R ); 5: Load_4 = F R_R /(F F_L + F F_R + F R_L + F R_R );
Simulation and Experimentation
In this section, wheel slip rate is mainly used as the criterion for judging the merits of the vehicle braking force distribution strategy. In order to verify the rationality of the braking force distribution strategy proposed in this paper, the vehicle model of the four-wheeled truck is established by MATLAB/Simulink and TruckSim, and simulated and verified under FTP25 working conditions. In this paper, Changchun city road is used as the driving condition, and CANoe is used for the vehicle data acquisition, and a total of 56 data items, such as longitudinal vehicle speed and side/longitudinal speed of the mass on the spring are collected. The random forest algorithm with decision tree as 500 was used to filter the features among 56 data items, and a total of 26 data items (Longitudinal acceleration, vertical velocity of sprung mass and other parameters) with the greatest correlation with the four-wheel vertical force were filtered out to realize the dimensionality reduction of the data. By analyzing and comparing the simulation results of different parameter estimation methods and the braking distribution strategy of the vehicle, the GRNN strategy based on machine learning can achieve an accurate estimation of the nonlinear parameters of the vehicle, which provides a robust data basis for the braking force distribution and improves the safety and smoothness of the braking process of the vehicle. Please note that the simulations are performed on a computer equipped with an Intel i7-12700H processor and 16 GB of RAM.
Complete Vehicle Data Acquisition
According to the requirements of the data set parameters and the preliminary analysis of the data quality, the CANoe tool is used to collect the data information of the vehicle. The test hardware scheme and the physical hardware are shown in Figures 6 and 7, respectively. rs 2022, 22, x FOR PEER REVIEW 12 of correlation with the four-wheel vertical force were filtered out to realize the dimension ity reduction of the data. By analyzing and comparing the simulation results of differe parameter estimation methods and the braking distribution strategy of the vehicle, t GRNN strategy based on machine learning can achieve an accurate estimation of the no linear parameters of the vehicle, which provides a robust data basis for the braking for distribution and improves the safety and smoothness of the braking process of the vehic Please note that the simulations are performed on a computer equipped with an Intel 12700H processor and 16 GB of RAM.
Complete Vehicle Data Acquisition
According to the requirements of the data set parameters and the preliminary anal sis of the data quality, the CANoe tool is used to collect the data information of the vehic The test hardware scheme and the physical hardware are shown in Figures 6 and 7, r spectively. The experimental data collection of the vehicle is carried out with Changchun ro conditions as the main driving conditions. The road map of Changchun conditions shown in Figure 8. The collected information of individual parameters of the vehicle saved and exported, and the interpolation and filtering processes are carried out to co struct a reasonable data set. correlation with the four-wheel vertical force were filtered out to realize the dimensionality reduction of the data. By analyzing and comparing the simulation results of different parameter estimation methods and the braking distribution strategy of the vehicle, the GRNN strategy based on machine learning can achieve an accurate estimation of the nonlinear parameters of the vehicle, which provides a robust data basis for the braking force distribution and improves the safety and smoothness of the braking process of the vehicle. Please note that the simulations are performed on a computer equipped with an Intel i7-12700H processor and 16 GB of RAM.
Complete Vehicle Data Acquisition
According to the requirements of the data set parameters and the preliminary analysis of the data quality, the CANoe tool is used to collect the data information of the vehicle. The test hardware scheme and the physical hardware are shown in Figures 6 and 7, respectively. The experimental data collection of the vehicle is carried out with Changchun road conditions as the main driving conditions. The road map of Changchun conditions is shown in Figure 8. The collected information of individual parameters of the vehicle is saved and exported, and the interpolation and filtering processes are carried out to construct a reasonable data set. The experimental data collection of the vehicle is carried out with Changchun road conditions as the main driving conditions. The road map of Changchun conditions is shown in Figure 8. The collected information of individual parameters of the vehicle is saved and exported, and the interpolation and filtering processes are carried out to construct a reasonable data set. ity reduction of the data. By analyzing and comparing the simulation results of differe parameter estimation methods and the braking distribution strategy of the vehicle, t GRNN strategy based on machine learning can achieve an accurate estimation of the no linear parameters of the vehicle, which provides a robust data basis for the braking fo distribution and improves the safety and smoothness of the braking process of the vehic Please note that the simulations are performed on a computer equipped with an Intel 12700H processor and 16 GB of RAM.
Complete Vehicle Data Acquisition
According to the requirements of the data set parameters and the preliminary ana sis of the data quality, the CANoe tool is used to collect the data information of the vehic The test hardware scheme and the physical hardware are shown in Figures 6 and 7, spectively. The experimental data collection of the vehicle is carried out with Changchun ro conditions as the main driving conditions. The road map of Changchun conditions shown in Figure 8. The collected information of individual parameters of the vehicle saved and exported, and the interpolation and filtering processes are carried out to co struct a reasonable data set.
Comparison of the Results of Estimation of Four-Wheel Vertical Force Parameters Based on GRNN
In the actual driving process, the vertical force situation of the four wheels directly affects the efficiency of the vehicle braking in order to give full play to the effect of the vehicle braking force and prevent the vehicle ABS from triggering leading to wheel locking, which affects the safety and smoothness of the vehicle. Among them, Longitudinal acceleration, vertical velocity of sprung mass and other parameters directly affect the force situation of the four wheels of the vehicle, and the force state of the four wheels presents complex nonlinear changes in the time dimension, which is difficult to be estimated accurately. This paper uses MATLAB/Simulink and TruckSim for joint simulation, and FTP72 is the simulation driving condition, as is shown in Figure 9. In the actual driving process, the vertical force situation of the four wheels directly affects the efficiency of the vehicle braking in order to give full play to the effect of the vehicle braking force and prevent the vehicle ABS from triggering leading to wheel locking, which affects the safety and smoothness of the vehicle. Among them, Longitudinal acceleration, vertical velocity of sprung mass and other parameters directly affect the force situation of the four wheels of the vehicle, and the force state of the four wheels presents complex nonlinear changes in the time dimension, which is difficult to be estimated accurately. This paper uses MATLAB/Simulink and TruckSim for joint simulation, and FTP72 is the simulation driving condition, as is shown in Figure 9. In this paper, the GRNN machine learning method (L-Method) is used for the estimation of the four-wheel force state parameters. To better illustrate the superiority of the data-driven method proposed in this paper, the more traditional moment Torque-balance method (T-Method) is used to estimate the four-wheel parameters. In the actual driving process of the vehicle, a time interval of 0.1 s is adopted to estimate once, and the parameter estimation results are shown in Figures 10-13. In this paper, the GRNN machine learning method (L-Method) is used for the estimation of the four-wheel force state parameters. To better illustrate the superiority of the data-driven method proposed in this paper, the more traditional moment Torque-balance method (T-Method) is used to estimate the four-wheel parameters. In the actual driving process of the vehicle, a time interval of 0.1 s is adopted to estimate once, and the parameter estimation results are shown in Figures 10-13. In the actual driving process, the vertical force situation of the four wheels directly affects the efficiency of the vehicle braking in order to give full play to the effect of the vehicle braking force and prevent the vehicle ABS from triggering leading to wheel locking, which affects the safety and smoothness of the vehicle. Among them, Longitudinal acceleration, vertical velocity of sprung mass and other parameters directly affect the force situation of the four wheels of the vehicle, and the force state of the four wheels presents complex nonlinear changes in the time dimension, which is difficult to be estimated accurately. This paper uses MATLAB/Simulink and TruckSim for joint simulation, and FTP72 is the simulation driving condition, as is shown in Figure 9. In this paper, the GRNN machine learning method (L-Method) is used for the estimation of the four-wheel force state parameters. To better illustrate the superiority of the data-driven method proposed in this paper, the more traditional moment Torque-balance method (T-Method) is used to estimate the four-wheel parameters. In the actual driving process of the vehicle, a time interval of 0.1 s is adopted to estimate once, and the parameter estimation results are shown in Figures 10-13. In Figures 10-13, the parameter estimation of the four wheels presents different effects under different strategies. In Figures 10 and 11, it can be seen that the overall vertical In Figures 10-13, the parameter estimation of the four wheels presents different effects under different strategies. In Figures 10 and 11, it can be seen that the overall vertical In Figures 10-13, the parameter estimation of the four wheels presents different effects under different strategies. In Figures 10 and 11, it can be seen that the overall vertical In Figures 10-13, the parameter estimation of the four wheels presents different effects under different strategies. In Figures 10 and 11, it can be seen that the overall vertical force of the left-front wheel is larger than that of the left-rear wheel during braking. In addition, the right-front and right-rear wheels in Figures 12 and 13 exhibit the same characteristics. The reason for this is that the focus of the vehicle shifts forward during the braking process, resulting in the front wheels taking on more vertical force, yet the rear wheels have less vertical force. With the different braking intensities, the front and rear wheels' vertical force changes out of different characteristics. From the above graph, it can be seen that in the 800.0 s-900.0 s interval, the variation of the vertical force of the four wheels is small. However, in the 1010.0 s-1030.0 s, it can be seen that the vertical force of the front and rear wheels exhibit a large variation due to the greater braking intensity.
In the above simulation results, the parameters estimation of the four-wheel vertical force of the vehicle based on the data-driven machine learning has perfect estimation accuracy, and it can be seen from Figures 11-13 that the parameters estimation method based on the L-Method performs significantly during the driving process, and the trend of the estimated four-wheel vertical force is highly consistent with the actual four-wheel vertical force of the vehicle. Then, the T-Method has a relatively large error in the estimation of the four-wheel vertical force of the vehicle, and the estimation effect has low accuracy. In the 80.0 s-110.0 s interval, the four-wheel vertical force exhibits a certain amplitude of vibration due to the suspension of the vehicle. In the interval of 800.0 s-900.0 s, the four-wheel vertical forces of the vehicle have a small up-and-down amplitude, and the T-Method has the phenomenon of up-and-down vibration with large error. However, the L-Method shows a better estimation accuracy. In the 1010.0 s-1030.0 s, the L-Method also shows a high estimation accuracy.
Through the analysis of the above simulation results, the L-Method can accurately estimate the four-wheel vertical force values from the state information of the vehicle. Its change trend shows a high consistency with the real data. Accurately estimating the four-wheel vertical force of the vehicle provides a strong data base for the braking force distribution of the vehicle and improves control accuracy.
Braking Force Distribution Results Comparison
In order to deeply analyze the reasonableness of braking force distribution based on four-wheel state observation, give full play to the braking capacity of four-wheeled trucks and ensure the smoothness and safety of the vehicle. Slip rate is a direct manifestation of wheel clamping, and the braking force distribution strategy keeps the slip rate of four wheels of the truck within a reasonable range to prevent the wheels from reaching the clamping threshold, which affects the stability and safety of the vehicle. In this paper, the slip rate distribution is taken as the criterion for the superiority of the braking force distribution of the vehicle. In the braking process of the vehicle, in order to give full play to the braking efficiency of the vehicle, it is necessary to ensure that the slip rate of the four wheels is kept within a reasonable range. If the slip rate is too high, the ABS function will be triggered to keep the slip rate of the four wheels within a reasonable range of 15-20%. In order to further investigate the superiority of the proposed braking distribution control strategy of the vehicle, the slip rate of the four wheels of the vehicle is analyzed and compared. In this paper, the distribution of the slip rate of the vehicle is divided into four grade ranges, which are [10-15%), [15-20%], and (20-100%]. Among them, the slip rate is kept at [15-20%], and the vehicle can be fully braked with a better braking effect. In this paper, the slip rate distribution of four wheels is shown in Figures 14-17 Figure 14, the percentage of slip rate of the left-front wheel in the range of [15-20%] is 18.1% based on the T-Method. However, the percentage of slip rate of the left-front wheel in the range of [15-20%] is 19.9% based on the L-Method strategy, which has a better braking force effect. The slip rate in (25-100%] indicates that the wheel has obvious slippage, which seriously affects the braking effect of the vehicle, and the left-front wheel slip rate in the T-Method-based method occupies 30.3% in this interval. In contrast, based on the L-Method only occupies 9.1% in this interval, the braking force distribution strategy performs better. In addition, in the interval [20-25%], the percentage of left front wheel slip under the L-Method-based approach is still higher than that under the T-Method strategy.
As shown in Figure 15, the left-rear wheel still has a high percentage of 17.4% in the interval [15-20%] of the slip rate based on the L-Method. The left-rear wheel has 11% of the slip rate in the interval [15-20%] and 62.3% in the interval (25-100%), and the slip phenomenon of the left-rear wheel appears more frequently, and the braking effect is poor in the T-Method. In the interval (20-25%) of the slip rate, the proportion of the T-Method is higher than that of the L-Method, which is only 2.1% higher. On the whole, the braking force distribution strategy based on the L-Method shows a better control effect in the process of vehicle braking than that based on the T-Method. Figures 16 and 17 show the distribution of the slip rate of the right-front wheel and the right-rear wheel under different control strategies. From Figure 16, the slip rate of the right-front wheel under the T-Method is 17.2% in the interval of [15-20%]. However, the percentage of the L-Method is 16.7% in the interval of [15-20%]. In the interval of (25-100%), the both control strategies show similar control effects, and the percentage of the L-Method and T-Method are 32.6% and 32%, respectively. In the [10-15%) and (20-25%] slip rate intervals, the right-front wheel under both control strategies has similar percentage cases. As can be seen from Figure 17, the right-rear wheel shares of the L-Method is significantly higher than that of the T-Method in the [15-20%] slip rate interval, with the shares of 16.6% and 11.6%, respectively. In both the [10-15%) and (20-25%] slip rate intervals, the right-rear wheel shares under the L-Method is significantly higher than that under the T-Method.
Through the analysis and comparison of the above results, the braking force distribution strategy based on the L-Method proposed in this paper has a better effect, which can be more distributed in the interval of [15-20%] and less distributed in the interval of [25-100%] for the four wheels of the vehicle, which can effectively avoid the phenomenon of the vehicle slipping several times during the braking process and can give full play to the braking potential of the vehicle.
Conclusions
In this paper, a braking force distribution strategy is proposed for a four-wheel truck to fully utilize the braking potential. In order to better realize the accurate estimation of the high nonlinear parameters in the vehicle, a machine learning method is used for the accurate estimation of the four-wheel vertical force parameters of the vehicle to provide accurate data for the braking force distribution of the four wheels. The method in this paper provides a new method for the current research of vehicle parameter estimation. In order to verify that the proposed method can have the correct estimation of the four-wheel pendant force values of the vehicle and the reasonable distribution of braking force, a joint simulation was conducted using MATLAB/Simulink and TruckSim, and through the comparison and analysis of the simulation results, the L-Method was able to keep the wheel slip rate within a reasonable range and give full play to the braking potential of the vehicle.
In the study of this paper, the method is suitable for the same type of trucks, the application range is narrow. In the future research, the new method will be explored for more models. Meanwhile, in the process of braking force distribution, the accuracy of vehicle state parameter estimation directly affects the control effect. The estimation accuracy of complex nonlinear parameters of the vehicle will be further improved to provide more accurate parameters of the vehicle for the control of the braking force, and further develop the braking potential of the vehicle. | 11,417 | 2022-10-31T00:00:00.000 | [
"Engineering"
] |
Synthesis, Characterization, Conformation in Solution, and Thermoresponsiveness of Polymer Brushes of methoxy[oligo (propylene glycol)-block-oligo(ethylene glycol)]methacrylate and N-[3-(dimethylamino)propyl]methacrylamide Obtained via RAFT Polymerization
The thermo- and pH-responsive polymer brushes based on methoxy[oligo(propyleneglycol)8-block-oligo(ethyleneglycol)8]methacrylate with different concentrations of N-[3-(dimethylamino)propyl]methacrylamide (from 0% to 20%) were synthesized via RAFT polymerization. The “grafting-through” approach was used to prepare the low-molar-mass dispersion samples (Mw/Mn ≈ 1.3). Molar masses and hydrodynamic characteristics were obtained using static and dynamic light scattering and viscometry. The solvents used were acetonitrile, DMFA, and water. The molar masses of the prepared samples ranged from 40,000 to 60,000 g·mol–1. The macromolecules of these polymer brushes were modeled using a prolate revolution ellipsoid or a cylinder with spherical ends. In water, micelle-like aggregates were formed. Critical micelle concentrations decreased with the content of N-[3-(dimethylamino)propyl]methacrylamide. Molecular brushes demonstrated thermo- and pH-responsiveness in water–salt solutions. It was shown that at a given molecular mass and at close pH values, the increase in the number of N-[3-(dimethylamino)propyl]methacrylamide units led to an increase in phase separation temperatures.
Introduction
In recent decades, for the controlled delivery of various medicinal substances to diseased organs, various polymeric forms such as hydrogel nanocapsules, micelles, dendrimers, etc. have been proposed and intensively studied [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. One of the most promising means of delivery is the micelles of polymers, in the hydrophobic core of which the drugs poorly soluble in water are retained, which are then released due to diffusion or destruction of micelles under external influence.
One convenient way to create a shell for polymer nanoparticles is using thermo-and pH-responsive polymers. One of them is polyethylene glycol (PEG) [16,17]. It allows the particle to circulate through the circulatory system for a long time and penetrate through various membranes and the blood-brain barrier [18]. The most rapidly developing method of obtaining polymer particles with a surface from polyethylene glycol fragments is the use of macromonomers, namely the derivatives of (meth)acrylic acid with ethylene glycol groups in the substituent [19,20]. Amphiphilic (co)polymers methoxiolygoethylenglycolmethacrylate (MOEGM) have good biocompatibility and low toxicity, are susceptible to biodegradation, and have low critical solution temperature, which is close to human body temperature. In [21], a series of novel temperature-responsive copolymer brushes with P-(2-(2-methoxyethoxy)ethyl methacrylate)-co-acrylamide) (P-(OEGMA188-co-AAm)) chains grafted from glass surfaces functionalized with (3-aminopropyl)triethoxysilane followed by the ATRP initiator were synthesized. P(OEGMA188-co-AAm) with a high mole fraction of AAm demonstrates "schizophrenic" behavior in wettability after immersion in pH buffer solutions, with transitions that mimic LCST and UCST for pH = 3, LCST for pH = 5 and 7, and temperature-induced transitions blocked for pH = 9.
The effect of temperature and buffer solutions with different pH on the behavior of poly(oligo(ethylene glycol) methacrylate) (POEGMA) brush coatings, synthesized without the incorporation of the functional groups, was studied for the first time in detail using water contact angle measurements and atomic force microscopy. The thermoresponsiveness of the grafted brush coatings based on POEGMAs is driven by the LCST phenomenon. The obtained AFM results suggest a strong impact of the buffer solutions on the values of LCST transition and contact angle ranges, as well as on the morphology of the coatings. The ellipsometry data reflect the penetration of salt ions from buffer solutions into the brush coatings. In contrast to the "typical" behavior of POEGMA coatings in water, the different mechanisms available below LCST in the buffer solutions destroy the hydrated layers surrounding POEGMA macromolecules, leading to their collapse [28].
To summarize, it should be noted that research is actively underway on the development of new types of biocompatible polymeric stimulus-sensitive molecular brushes with controlled conformational and phase transitions in aqueous solutions, whose micelles can be used as nanocontainers for the delivery of hydrophobic drugs. In this regard, new water-soluble macromonomers, such as the esters of methacrylic acid with a diblock alcohol moiety containing hydrophilic oligoethylene glycol and hydrophobic oligopropylene glycol blocks, were used to synthesize polymer brushes. A distinctive feature of such macromonomers is the possibility of the fine regulation of their amphiphilic nature by varying the length and arrangement of hydrophilic and hydrophobic blocks, which should be expressed in the manifestation of the amphiphilic properties of polymers.
In previous studies [29,30], we have investigated polymethacrylic molecular brushes with oligo(ethylene glycol)-block-oligo(propylene glycol) side chains, which were obtained via conventional radical polymerization. In thermodynamically good solvents, namely acetonitrile, the investigated copolymers had a high intramolecular density, and the shape of their molecules resembled a star-shaped macromolecule. Phase separation temperatures were reduced with an increase in the content of the oligo(propylene glycol) block.
To assess pH responsitivity, N- [3-(dimethylamino) propyl]methacrylamide (DMAPMA) was introduced into the polymer chain. DMAPMA is very hydrophilic and does not show thermosensitivity; therefore, the DMAPMA monomer increases the phase separation temperatures of copolymer solutions. The aim of the present work is to investigate the effect of the content of N- [3-(dimethylamino)propyl]methacrylamide on the hydrodynamic and conformational characteristics of thermoresponsive methoxy [oligo(propyleneglycol) 8 -blockoligo(ethyleneglycol) 8 ] methacrylate and N- [3-(dimethylamino)propyl]methacrylamide (polyOPG 8 OEG 8 MA-DMAPMA) in dilute solutions. The structural formulae of homo-and copolymers are presented in Figure 1.
blocks, which should be expressed in the manifestation of the amphiphilic properties of polymers.
In previous studies [29,30], we have investigated polymethacrylic molecular brushes with oligo(ethylene glycol)-block-oligo(propylene glycol) side chains, which were obtained via conventional radical polymerization. In thermodynamically good solvents, namely acetonitrile, the investigated copolymers had a high intramolecular density, and the shape of their molecules resembled a star-shaped macromolecule. Phase separation temperatures were reduced with an increase in the content of the oligo(propylene glycol) block.
To assess pH responsitivity, N- [3-(dimethylamino) propyl]methacrylamide (DMAPMA) was introduced into the polymer chain. DMAPMA is very hydrophilic and does not show thermosensitivity; therefore, the DMAPMA monomer increases the phase separation temperatures of copolymer solutions. The aim of the present work is to investigate the effect of the content of N- [3-(dimethylamino)propyl]methacrylamide on the hydrodynamic and conformational characteristics of thermoresponsive methoxy [oligo(propyleneglycol)8-block-oligo(ethyleneglycol) 8] methacrylate and N- [3-(dimethylamino)propyl]methacrylamide (polyOPG8OEG8MA-DMAPMA) in dilute solutions. The structural formulae of homo-and copolymers are presented in Figure 1.
Materials and Methods of Synthesis
The "grafting-through" method was used to produce polymers with a brush structure.
The synthesis of the polymer brushes using this approach involves a one-step process using macromonomers capable of radical polymerization. The macromonomer methoxy[oligo(propylene glycol)-block-oligo(ethylene glycol)] methacrylate with average lengths of oligo(propylene glycol) (p) and oligo(ethylene glycol) (e) fragments equal p = 7.9 and e = 8.2 was used to obtain the polymers.
Materials and Methods of Synthesis
The "grafting-through" method was used to produce polymers with a brush structure. The synthesis of the polymer brushes using this approach involves a one-step process using macromonomers capable of radical polymerization.
For the synthesis of the macromonomers, a previously described method involving involves the esterification of methacrylic acid with methoxy oligo(alkylene glycol)s [31,32] was used. The synthesis was carried out at a temperature of 120-125 • C in 30 wt% toluene solution in the presence of 2 wt% of p-toluene sulfonic acid as a catalyst and 0.3 wt% of hydroquinone as a polymerization inhibitor. Previous to polymerization, the macromonomer was passed through a basic alumina column to remove inhibitors.
The Determination of CMC
The critical micelle concentrations (CMCs) of copolymers were determined via fluorimetry using pyrene as a fluorescent probe [33,34]. The steady-state fluorescence spectra were recorded on a Shimadzu RF-6000 spectrofluorimeter (Shimadzu, Kyoto, Japan) at the temperature of 25 • C.
For the solutions investigated in acetonitrile and DMFA, the distribution of the light scattering intensity I over the hydrodynamic radii R h-D (c) of scattering objects was unimodal. The values of R h-D (c) were determined in the wide concentration range and extrapolated to zero concentration to obtain the hydrodynamic radius R h-D of macromolecules. As is well known, the translation diffusion coefficients D 0 and the friction coefficient f of macromolecules are related to R h-D , which is defined using Stokes-Einstein equations [35][36][37]: where k B is Boltzmann's constant and T is the absolute temperature. SLS measurements were performed at the angle of 90 • since no angular dependence of the scattered light was observed. The obtained results were analyzed according to the Debye method, and the values of the weight-average molar masses M w and the second virial coefficient A 2 were calculated using the following formula: where H is the optical constant.
Here, I 90 is the excessive intensity of light scattered at an angle of 90 • , N A is Avogadro's number, and dn/dc is the refractive index increment. The values of dn/dc were determined using an RA-620 refractometer (Shimadzu, Kyoto, Japan) with a wavelength λ 0 = 589.3 nm. The values of dn/dc were calculated from the slope of concentration dependence on the difference between the refractive indexes of the solution n and the solvent n 0 (∆n = n − n 0 ).
The viscometry experiments were performed using an Ostwald-type Cannon-Manning capillary viscometer (Cannon Instrument Company Inc., State College, PA, USA). The de-pendencies of the reduced viscosity η sp /c on the concentration were analyzed using the Huggins equation: where [η] is the intrinsic viscosity, and k H is the Huggins constant. Light scattering, viscometry, and refractometry experiments were carried out at 21 • C. Millipore filters (Millipore Corp., Billerica, MA, USA) with a PTFE membrane with a pore size of 0.20 nm were used.
Investigation of Self-Assembly of polyOPG 8 OEG 8 MA-DMAPMA in Aqueous Solutions
The aqueous solutions of the copolymers were investigated using the methods of light scattering and turbidimetry with the Photocor Complex described above, which is also equipped with a Photocor-PD detection device for measuring the transmitted light intensity. The solution temperature T was changed discretely, with the step ranging from 1.0 to 5.0 • C. At steady-state conditions, i.e., when the solution parameters do not depend on time, the hydrodynamic radii R h of scattering species and their contribution S i to the integral scattering intensity were determined. S i was estimated using the values of the areas under the curve of the corresponding R h distribution peak. For all copolymers, the polymer concentration was c = 0.0050 g·cm −3 , and polyOPG 8 OEG 8 MA-DMAPMA 90:10 was investigated in the concentration range from c = 0.0025 to 0.0100 g·cm −3 .
A phase transition temperature (T ph ) was determined from the temperature dependence of optical transmittance.
The acidity of the pH medium varied from 3.6 to 12.4 in buffer solutions (pH 3.6, 6.86, 12.4, Hanna Instruments) and the pH of the water solution was determined using a pH meter (Sartorius, Finland) and pH-meter-ionomer Expert-001 (Russia). The samples of the copolymers were synthesized using RAFT polymerization. Their structure was confirmed using NMR spectroscopy and GPC (Figures 2 and 3). The values of the refractive index increments increased with an increase in the number of DMAPMA units. Moreover, in both acetonitrile and DMFA, the dn/dc dependencies on DMAPMA fractions were well illustrated in a straight line. Therefore, for the studied samples, the principle of the additivity of the refractive index increments of monomeric units was considered.
Results and Discussion
According to the chromatography method, the polydispersity indexes Đ = Mw/Mn of the prepared samples were close (Table 1). On the other hand, the values of molar masses obtained using GPC and SLS did not coincide. This difference is likely due to the fact that the GPC method does not allow one to obtain correct values for polymers with complex architecture, in particular molecular brushes. The values of the refractive index increments increased with an increase in the number of DMAPMA units. Moreover, in both acetonitrile and DMFA, the dn/dc dependencies on DMAPMA fractions were well illustrated in a straight line. Therefore, for the studied samples, the principle of the additivity of the refractive index increments of monomeric units was considered.
According to the chromatography method, the polydispersity indexes Ð = M w /M n of the prepared samples were close (Table 1). On the other hand, the values of molar masses obtained using GPC and SLS did not coincide. This difference is likely due to the fact that the GPC method does not allow one to obtain correct values for polymers with complex architecture, in particular molecular brushes. The molar masses of the investigated polymers were determined in acetonitrile. Unfortunately, it was not possible to measure the MM in DMF, due to the low value of the refractive index increment dn/dc, which ranged from 0.03 to 0.037 cm 3 ·g -1 . In acetonitrile, dn/dc changed from 0.120 to 0.137 cm 3 ·g -1 . It is worth noting that the M w values of copolymer samples differed insignificantly.
Using the MM values, it is easy to calculate the polymerization degree N b of the backbone of the copolymers according to the following equation: where M 0-cp values indicate the molar masses of the repeating units of polyOPG 8 The N b values are listed in Table 2. Table 2 also presents the average values of the length L b = N b ·λ 0-b of the backbone. Length L b is calculated under the assumption that all valence bonds have the same length of 0.14 nm and that the valence angles are tetrahedral. Consequently, the length of the repeating unit of the main chain was λ 0-b = 0.25 nm. The L b values were only 2-3 times greater than the length L sc = 6.4 nm of the side chain of the OPG 8 OEG 8 MA monomer. The chains of the second component were much shorter, and their length was L DMAPMA = 0.9 nm. The L sc and L DMAPMA values were calculated using the described assumptions. Notably, when N b and L b were estimated, the molar masses of the terminal groups of the main chain and their length were not taken into account. The MM of these groups was about 460 g·mol −1 , which was about 1 percent of the MM of the lowest molecular weight sample polyOPG 8 OEG 8 MA-DMAPMA 95:5. Accordingly, the actual value of N b of the studied samples differed from the values presented in Table 2 by less than one percent. The total length of the end groups was about 2.8. nm, i.e., two times less than L sc .
The obtained structural parameters allowed us to make preliminary assumptions about the shape of the copolymer macromolecules. Figure 3 shows a simplified molecular schema polyOPG 8 OEG 8 MA-DMAPMA 80:20. It is clearly seen that the transverse and longitudinal dimensions did not significantly differ. The "diameter" L ⊥ = 2L sc of the macromolecule was determined by the length L sc of the OPG8OEG8MA side chains and did not exceed 13 nm. The largest longitudinal dimension L was equal to the sum of the backbone length and twice the side chain length L b + 2L sc . This conformation of the macromolecule was realized in the "ideal" case, when both the main and side chains were in a fully extended trans-conformation. Naturally, the real situation was somewhat different. Indeed, the side chains were quite long, and they were most likely more or less folded. For steric reasons, the side chains located near the terminal groups were probably folded much more strongly than the chains located in the central part of the backbone. Accordingly, ∆ ≤ δ < L sc (Figure 4). romolecule was realized in the "ideal" case, when both the main and side chains were in a fully extended trans-conformation. Naturally, the real situation was somewhat different. Indeed, the side chains were quite long, and they were most likely more or less folded. For steric reasons, the side chains located near the terminal groups were probably folded much more strongly than the chains located in the central part of the backbone. Accordingly, Δ ≤ δ ˂ Lsc (Figure 4). In the first approximation, the macromolecules were modeled using a revolution prolate ellipsoid or a cylinder with spherical ends. The asymmetry parameter p or the ratio of longitudinal to transverse dimensions is determined by the following equation: p = L /L⊥ = (Lb+2Δ)/2 δ ˂ Lb/2Lsc + Δ/δ (7) where the ratio Δ/δ is less than unity. For the studied copolymers, the value of Lb/2Lsc ranged from 0.9 for polyOPG8OEG8MA-DMAPMA 95:5 to 1.4 poly-OPG8OEG8MA-DMAPMA 80:20. Accordingly, for all the studied samples, p < 2.4.
For the studied polymers, low experimental values of both the intrinsic viscosity and hydrodynamic radii of macromolecules were obtained. In principle, this could be expected since the macromolecules of the copolymers under consideration had a dense structure. On the other hand, the calculations using the formulas for a rigid ellipsoid of revolution and a cylinder (see monograph [35] and the references in it) and the obtained structural parameters Lb and Lsc resulted in the values of [η] and Rh-D, which strongly differed from the experimental values of these characteristics. Therefore, for the studied copolymers, the use of the rigid particle models for the analysis of hydrodynamic characteristics is incorrect, although these models quite often adequately describe the hydrodynamic behavior of polymers with complex architecture in dilute solutions [35]. It can be assumed that, in this case, an important role is played not only by the permeability of macromolecules but also by the change in their shape due to the difference in the real In the first approximation, the macromolecules were modeled using a revolution prolate ellipsoid or a cylinder with spherical ends. The asymmetry parameter p or the ratio of longitudinal to transverse dimensions is determined by the following equation: where the ratio ∆/δ is less than unity. For the studied copolymers, the value of L b /2L sc ranged from 0.9 for polyOPG 8 For the studied polymers, low experimental values of both the intrinsic viscosity and hydrodynamic radii of macromolecules were obtained. In principle, this could be expected since the macromolecules of the copolymers under consideration had a dense structure. On the other hand, the calculations using the formulas for a rigid ellipsoid of revolution and a cylinder (see monograph [35] and the references in it) and the obtained structural parameters L b and L sc resulted in the values of [η] and R h-D , which strongly differed from the experimental values of these characteristics. Therefore, for the studied copolymers, the use of the rigid particle models for the analysis of hydrodynamic characteristics is incorrect, although these models quite often adequately describe the hydrodynamic behavior of polymers with complex architecture in dilute solutions [35]. It can be assumed that, in this case, an important role is played not only by the permeability of macromolecules but also by the change in their shape due to the difference in the real conformation of the side chains from the conformation of the trans-chain. Analyzing Figure 3, one would expect that an increase in the DMAPMA units should not lead to a significant decrease in intramolecular density. However, the observed changes in these characteristics were sufficient to change the hydrodynamic invariant A 0 , which was calculated using the formula in [35,38,39]. This characteristic is determined with the experimental values of molar mass M, intrinsic viscosity [η], and translation diffusion coefficient D 0 as follows: where η 0 is the viscosity of the solvent, and T is the absolute temperature. As can be seen from Table 1, A 0 values increased from 2.4 to 3.2 × 10 10 , erg·K −1 mol −1/3 with increasing DMAPMA content, i.e., a decrease in intramolecular density. Similar behavior was previously observed in the homologous series of star-shaped four-armed poly-2-ethyl-2-oxazine [40]. Note that low values of A 0 ≤ 2.8, i.e., lower than the theoretically predicted value for a hard sphere, are typical for polymers with complex architecture, such as molecular brushes, as well as hyperbranched and star-shaped polymers [41][42][43][44].
Characteristics of polyOPG 8 OEG 8 MA-DMAPMA in Aqueous Solutions at Room Temperatures
At 21 • C, two modes were detected using DLS for the aqueous solutions of the investigated polymer brushes. For all samples at all concentrations, on average, the hydrodynamic radii R h-f (Table 3) of the particles responsible for fast mode exceeded the hydrodynamic radius R h-D of macromolecules determined in acetonitrile, by 30 percent (Table 2). Therefore, the species with radius R h-f had supramolecular structures. This fact can be explained by the formation of micelles in water. The CMC values for polymers in aqueous solutions are presented in Table 3. Note that an increase in the DMAPMA fraction led to an increase in the CMC, i.e., the introduction of more hydrophilic DMAPMA units reduced the tendency of the polymer to aggregate due to changing the hydrophilic-hydrophobic balance of the molecules. However, the change in CMC values was not significant. Table 3. Characteristics of solutions of polyOPG 8 OEG 8 MA-DMAPMA at c = 0.005 g·cm −3 in water.
Samples
pH The objects responsible for the slow mode were aggregates with hydrodynamic radius R h-s . The hydrodynamic radii of supramolecular structures R h-s were more than an order of magnitude greater than the size of the isolated macromolecules R h-D and micelles R h-f . This fact indicates that a very large number of polymer molecules were combined into aggregates. Note that for homo polyOPG 6.6 OEG 8.3 MA obtained using radical polymerization, the aqueous solutions, or more precisely, only the micelles in them, were unimodal [30]. Hence, it can be assumed that the terminal groups of the copolymers obtained via RAFT polymerization play a significant role in the formation of large aggregates. The relative weight concentration (c s ) of large aggregates was much less than the concentration (c f ) of micelles. Indeed, the estimate in terms of hard-sphere models for micelles and coil for large aggregates revealed that c s was less than 10 percent (Table 3). Similar dependencies were obtained for all the studied samples at all concentrations. Several temperature intervals can be distinguished on these dependencies. The first of them occurred at T ≤ T 1 , when the optical transmission did not depend on the temperature. At T 1, a sharp decline in I* was observed. Accordingly, T 1 marked the onset of the phase separation interval. In the third temperature interval at T ≤ T 2 , I* = 0, and T 2 was considered the temperature of the finishing phase transition.
The temperatures of phase separation were determined by analyzing the dependencies of I on T. At the temperature of the phase separation onset, a sharp increase in the light scattering intensity was observed. I reached the maximum value at the temperature of the finishing phase transition. Further heating was accompanied by a decrease in the I value. The phase transition temperatures determined via turbidimetry and SLS coincided with an accuracy of one degree. Figure 5 shows the temperature dependencies of the relative light scattering sity I/I21 and transmitted intensity I*/I*21, the hydrodynamic radii, and ratio Ss/Sf aqueous solution polyOPG8OEG8MA-DMAPMA 90:10. (I21 and I*21 are light sca intensity and optical transmission at 21 °C, and Ss and Sf are contributions of lar gregates and micelles to the integral light scattering intensity of the solution.) Similar dependencies were obtained for all the studied samples at all concentr Several temperature intervals can be distinguished on these dependencies. The f them occurred at T ≤ T1, when the optical transmission did not depend on the tem ture. At T1, a sharp decline in I* was observed. Accordingly, T1 marked the onset phase separation interval. In the third temperature interval at T ≤ T2, I* = 0, and considered the temperature of the finishing phase transition.
The temperatures of phase separation were determined by analyzing the de encies of I on T. At the temperature of the phase separation onset, a sharp increase light scattering intensity was observed. I reached the maximum value at the tempe of the finishing phase transition. Further heating was accompanied by a decrease i value. The phase transition temperatures determined via turbidimetry and SLS coin with an accuracy of one degree.
In the first temperature interval, the I values decreased, which was caused by a change in the hydrodynamic radii Rh-s of the aggregates ( Figure 5). This is probably the partial dehydration of the side chains and the formation of intramolecular bond increasing temperature. It can be assumed that a similar process also occurred celles. However, their small size did not allow one to record the changes using DL at T ≤ T1, no change was observed in the hydrodynamic radius Rh-f. Corresponding contribution of the aggregates to the integral intensity of the scattered light dec (Figure 3). In the first temperature interval, the I values decreased, which was caused by a slight change in the hydrodynamic radii R h-s of the aggregates ( Figure 5). This is probably due to the partial dehydration of the side chains and the formation of intramolecular bonds with increasing temperature. It can be assumed that a similar process also occurred in micelles. However, their small size did not allow one to record the changes using DLS, and at T ≤ T 1 , no change was observed in the hydrodynamic radius R h-f . Correspondingly, the contribution of the aggregates to the integral intensity of the scattered light decreased (Figure 3).
At T 1 ≤ T ≤ T 2 , the size of the aggregates strongly increased, while micelles were no longer visible using DLS. Therefore, in the phase separation interval, aggregation occurred, and hydrodynamic radii exceeded one micron. At T ≥ T 2 , the light scattering intensity and hydrodynamic radii of the aggregates decreased, which was caused by the precipitation of the part of the polymer in the sediment. Table 4 presents the phase separation temperatures for a solution of polyOPG 8 OEG 8 MA 90:10 with a concentration ranging from 0.0025 g·cm −3 to 0.01 g·cm −3 . It was found that with an increase in concentration, the phase separation temperatures decreased, i.d. with dilution, and the quality of the solvent improved the size of formed aggregates at room temperature and at temperature T 1 decreased; that is, the limits of solubility increased. We did not observe any change in macromolecule radii, since they were small. The aggregates decreased with dilution. Similar behavior has been reported for other thermo-and pH-sensitive polymers [23].
The Influence of Composition of Copolymers on Phase Separation Temperatures at Fixed Concentration and pH Solutions
The influence of the composition in a wide range of water solutions at c = 0.005 g·cm −3 on the properties of solutions of polyOPG 8 OEG 8 MA-DMAPMA was observed at room temperature. The size of fast and slow modes with a decrease in the DMAPMA content grew.
The molar masses of the investigated copolymers, pH, and concentration (0.005 g·cm −3 ) of solutions changed insignificantly in the series of copolymers; it became possible to compare the phase separation temperatures.
It was found that with the increase in the number of DMAPMA units, the temperatures significantly increased at pH 3.56, slightly increased at pH 6.86, and did not change at pH = 12.43.
Note that polyOPG 8 OEG 8 MA is not pH-sensitive, but the determined phase separation temperatures at different pH values did not coincide. This fact is related to the effect of salting out, which occurs to a noticeable extent at low contents of ionogenic monomer. In the case of a greater number of DMAPMA units, as expected, the phase separation temperatures decreased with increasing pH (Table 5).
Conclusions
The thermo-and pH-responsive polymer brushes based on methoxy[oligo (propyleneglycol) 8 -block-oligo(ethyleneglycol) 8 ]methacrylate with different concentrations of N- [3-(dimethylamino)propyl]methacrylamide (from 0% to 20%) were successfully synthesized via RAFT polymerization. The "grafting-through" approach was used to prepare the low-molecular-weight dispersion samples (M w /M n ≈ 1.3). Molar masses and hydrodynamic characteristics were obtained using static and dynamic light scattering and viscometry. The solvents used were acetonitrile, DMFA, and water. The solutions in acetonitrile were molecularly dispersed. The molar masses of the prepared samples ranged from 40,000 to 60,000 g·mol -1 . It was established that for all copolymers, the side chains of N- [3-(dimethylamino)propyl] methacrylamide shield the backbone and decrease intermolecular density. Analyzing characteristics such as molar masses, hydrodynamic radius (diffusion coefficient), and intrinsic viscosity, we concluded that, in the first approximation, the macromolecules of polymer brushes based on methoxy[oligo(propyleneglycol) 8 -block-oligo(ethyleneglycol) 8 ]methacrylate with different concentrations of N- [3-(dimethylamino)propyl]methacrylamide could be modeled using a prolate revolution ellipsoid or a cylinder with spherical ends. In water, micelle-like aggregates were formed. Critical micelle concentrations decreased with the content of N- [3-(dimethylamino)propyl]methacrylamide. Molecular brushes demonstrated thermo-and pH-responsiveness in water-salt solutions. Our findings reveal that at a given molecular | 6,675.2 | 2023-03-25T00:00:00.000 | [
"Chemistry"
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Vestibular Facilitation of Optic Flow Parsing
Simultaneous object motion and self-motion give rise to complex patterns of retinal image motion. In order to estimate object motion accurately, the brain must parse this complex retinal motion into self-motion and object motion components. Although this computational problem can be solved, in principle, through purely visual mechanisms, extra-retinal information that arises from the vestibular system during self-motion may also play an important role. Here we investigate whether combining vestibular and visual self-motion information improves the precision of object motion estimates. Subjects were asked to discriminate the direction of object motion in the presence of simultaneous self-motion, depicted either by visual cues alone (i.e. optic flow) or by combined visual/vestibular stimuli. We report a small but significant improvement in object motion discrimination thresholds with the addition of vestibular cues. This improvement was greatest for eccentric heading directions and negligible for forward movement, a finding that could reflect increased relative reliability of vestibular versus visual cues for eccentric heading directions. Overall, these results are consistent with the hypothesis that vestibular inputs can help parse retinal image motion into self-motion and object motion components.
Introduction
Accurate and precise estimation of object motion during selfmotion is important for survival, because moving organisms must often simultaneously monitor other moving agents, including predators, prey and potential mates. Self-motion relative to a stationary environment produces a globally consistent pattern of visual motion on the retina, whereas independently moving objects give rise to local motion signals that are inconsistent with the global pattern. Thus, estimating object motion during selfmotion can potentially be achieved by comparing local retinal motion signals to the global flow pattern. Indeed, visual psychophysical studies in humans have shown that the brain parses retinal image motion into object and self-motion components based on global flow computations [1][2][3][4][5][6][7][8][9]. This body of research has focused on two related topics: 1) estimating heading (i.e., direction of self-translation) in the presence of moving objects [1,3,10,11], and 2) estimating object motion during self-motion [2,[4][5][6][7][8][9]12,13].
These studies, however, have primarily focused on biases introduced by interactions between object motion and background motion due to self-translation, and have not generally considered how these interactions affect perceptual sensitivity. Furthermore, while some prior studies have investigated perception of object motion during real physical self-motion [14,15], other studies that have focused on the specific question of optic flow parsing have largely ignored non-visual (e.g., vestibular and proprioceptive) cues that could help to disambiguate retinal image motion. In particular, vestibular sensory signals play a vital role in heading perception, leading to more precise heading estimates when both visual and vestibular cues are available [16][17][18][19]. Given these interactions between self-motion and object motion perception, as documented previously, we hypothesized that vestibular signals may also influence the precision with which subjects judge object motion during self-motion.
To test this hypothesis, we asked subjects to discriminate object motion during simulated self-motion in the presence and absence of scene-consistent vestibular stimulation. Our rationale is as follows: combined visual/vestibular stimulation leads to improved heading perception [16][17][18][19] and thus presumably improved flow estimation at the object location, and may therefore also lead to improved flow parsing ability and object motion discrimination. The vestibular contribution to heading perception depends on the relative reliability of visual and vestibular cues, so we hypothesized that the same should hold for flow-parsing and object motion discrimination. Relative reliability was manipulated by varying heading eccentricity (i.e., heading direction relative to straight ahead). Relative reliability of vestibular cues increases with eccentricity because visual heading discrimination thresholds increase more steeply with eccentricity than vestibular thresholds [20,21]. Therefore we expected that improvement in object motion discrimination thresholds during the combined visualvestibular stimulation would be more pronounced for eccentric rather than forward heading directions. Preliminary aspects of this work were presented in abstract form [22,23].
Ethics Statement
Eight human subjects (3 female) participated in this study. Informed consent was obtained from all participants and all procedures were reviewed and approved by the human subjects committee of Washington University.
Setup
Subjects were seated in a padded racing seat mounted on a 6degree-of-freedom Moogß motion platform. A 3-chip DLP projector (Galaxy 6; Barco, Kortrijk, Belgium) was also mounted on the motion platform behind the subject and front-projected images onto a large (1496127 cm) projection screen via a mirror mounted above the subject's head. The projection screen was located ,70 cm in front of the eyes, thus allowing for a visual angle of ,94u684u. A 5-point harness held subjects' bodies securely in place and a custom-fitted plastic mask secured the head against a cushioned head mount thereby holding head position fixed relative to the chair. Subjects were enclosed in a black aluminum superstructure, such that only the display screen was visible in the darkened room. Subjects also wore active stereo shutter glasses (CrystalEyes 3; RealD, Beverly Hills, CA), thereby restricting the field of view to ,90u670u. Eye position was recorded for both eyes at 600 Hz via a video-based eye-tracking system (ISCANß) attached to the stereo glasses and subjects were instructed to look at a centrally-located, head-fixed target throughout each trial. Sounds from the platform were masked by playing white noise through headphones. Behavioral tasks and data acquisition were controlled by Matlab and responses were collected using a button box. Additional details specific to the human apparatus can be found in recent publications [18,21,24].
Experimental Protocol: Main Experiment
The visual scene consisted of a 3-dimensional (3D) starfield composed of randomly placed triangles with base and height of 1 cm. The triangles filled a volume 170 cm wide 6170 cm tall6 100 cm deep and the 3D density of triangles was 0.001 triangles/ cm 3 . With this density and viewing frustum, ,1000 triangles were rendered on a given frame. The nearest and farthest rendered triangles subtended ,3u and ,0.6u, respectively. A spherical object (diameter of 10 cm, i.e., ,8u) was rendered at the same depth as the screen, and located to the left of the fixation point, ,27 cm (,21u) away. The object was also composed of random triangles and the density of triangles within the volume of the object was the same as for the starfield, such that the object was distinguished only by its velocity relative to the background motion. Given the volume of the sphere and its density, ,4 triangles were rendered within the sphere on a given video frame. Motion coherence of the starfield and object was set to 70% and the elements of the scene were limited-lifetime (1 sec). Note, reduced motion coherence was used to make the relative reliabilities of the visual and vestibular self-motion cues more equal [17,18], and to allow comparison with heading discrimination data collected under the same conditions with a range of heading eccentricities [21]. To prevent pop-out of the object relative to the background, object motion coherence matched coherence of the background star field.
Each trial simulated a 13cm, 1s translation of the subject relative to the starfield and object. The object was simultaneously displaced either upward or downward relative to the starfield and the subject's task was to indicate whether the object moved upward or downward relative to the world (Fig. 1A). Note that we did not attempt to evaluate whether subjects made their judgments in world or screen coordinates. However, regardless of the coordinate frame of the judgment, subjects had to parse the optic flow field to perform the task. Thus, for this task, we do not suspect that the basic conclusions of the present study would change depending on the strategy used by the subjects.
The simulated self-motion and object motion followed synchronized Gaussian velocity profiles, such that the object could not be distinguished simply by having a different temporal profile of motion than the background. Given this velocity profile, the peak simulated visual and vestibular speed of self-motion was 30 cm/s and peak acceleration/deceleration was 1.13 m/s 2 . This dynamic stimulus was chosen because: (1) it is a smooth, transient, natural stimulus, (2) it evokes robust visual and vestibular responses in cortical multisensory neurons (e.g., areas MSTd and VIP; both visual and vestibular responses tend to reflect stimulus velocity more than acceleration [25][26][27][28]), (3) it results in near-optimal multisensory integration, both at the level of behavior [17][18][19] and at the level of single neurons [17,19,29].
Due to the independent object motion in the scene, the retinal image motion associated with the object deviated from that of the surrounding optic flow (Fig. 1B). Deviation angle was varied from trial to trial according to a staircase procedure. The staircase began at the largest deviation angle and possible deviation angles were +/2 [80u 64u 48u 32u 16u 8u 4u 2u 1u 0.5u 0.25u]. The deviation angle was reduced 30% of the time after correct responses and was increased 80% of the time after incorrect responses. This staircase rule converges to the 73% point of the psychometric function. The deviation angle was positive (upward) on 50% of trials and negative (downward) on the other 50%.
The angle of deviation is given byd~tan where v s and v o , respectively, are the independent velocity components (in screen coordinates) associated with self-motion and object motion, respectively (Fig. 1B). The self-motion component (v s ) depended on heading angle but was constant for a given heading (peak velocity of 10.2u/s, 20.7u/s, 24.0u/s, and 20.8u/s for headings of 0u, 30u, 60u, and 90u, respectively). Deviation angle (d) for a given trial was specified by the staircase procedure. Object speed on the screen (v o ) was therefore constrained to satisfy the above equation.
Four different heading directions were examined (0u, 30u, 60u, and 90u from straight ahead, Fig. 1C-F), with data for each heading angle collected in a separate block of trials. Trials for visual-only and combined (visual/vestibular) conditions were interleaved within a given block (200 trials/block, lasting ,25 min). This made for a total of 8 stimulus conditions in the Main Experiment. At least 800 trials per condition per subject (6 subjects, S1-S6) were collected.
Experimental Protocol: Eye-movement Control
Because no eye movement data were recorded initially, we repeated the visual-only and combined protocols in a second experiment for the lateral (90u) heading only, while recording eye movements. This was necessary to verify that subjects maintained fixation equally well during both visual-only and combined visualvestibular trials. At least 500 trials per subject per condition were collected in 5 subjects (S4-S8) for the second experiment.
Experimental Protocol: Retinal-speed Control
Finally, in a third experiment, observers were presented with visual-only trials, as described above, except that the simulated distance of translation was reduced to ,13cm (6.75, 5.56, and 6.13 cm for heading directions of 30u, 60u and 90u, respectively) in order to achieve the same retinal image speed (v s in Fig. 1B) at the eccentric location where the moving object was presented (v s equal to 10.2u/s for all headings). This control experiment was necessary to examine to what extent the observed dependence of object motion discrimination thresholds on heading direction was simply a result of changes in retinal speed. Because translation distance was fixed in the first experiment, v s increases with eccentricity, such that effects of heading eccentricity (i.e. flow-field geometry) and retinal speed are confounded. At least 600 trials per subject per condition were collected in 5 subjects (S4-S8) for the third experiment.
Data Analysis
For each subject and each condition we plotted the proportion of 'upward' responses as a function of object deviation angle and a cumulative Gaussian function was fit to these data using psignifit software [30,31]. Threshold is given by the standard deviation of the fitted function. A two-factor repeated measures ANOVA was performed on threshold data from the Main Experiment to examine the effect of heading eccentricity (0u, 30u, 60u, 90u), the effect of condition (visual-only, combined), and their interaction. Data were further examined using paired t-tests. Threshold data from the Retinal-speed Control experiment were analyzed with a one-factor repeated measures ANOVA to examine the effect of heading eccentricity (0u, 30u, 60u, 90u) when retinal speed at the object location was matched across headings.
To analyze eye movement data, horizontal eye position traces were first smoothed by applying a boxcar filter and then differentiated to obtain eye velocity traces for both eyes. From these traces we calculated mean eye velocity during the stimulus presentation (1s) on each trial and then examined how psychophysical threshold changed as a function of mean eye velocity for each subject. Over the entire range of mean eye velocities, we used a sliding window 1u/s wide, and fit a psychometric function to all trials within that window, provided that a minimum of 150 trials were available in a given velocity window. Window position was increased from the minimum to the maximum mean velocity at 0.1u/s intervals, so that a different threshold was calculated for each window position (i.e., each mean eye velocity). A regression line was fit to the resulting data and the slope and significance of the regression were used to evaluate the influence of mean eye velocity on discrimination performance.
Results
In these experiments, optic flow simulated observer translation through a starfield, while simultaneously an object moved up or down in the world (Fig. 1A). The subject's task was to indicate the object's motion direction (up/down) in the world during trials in which self-motion was cued by either optic flow alone (visual-only condition) or optic flow combined with platform motion (combined condition). The object was transparent, composed of random dots with the same density as the starfield, and was distinguished from the starfield only by the relative velocity of its movement. Starfield and object velocity followed synchronized Gaussian velocity profiles. Object motion amplitude (i.e., total displacement), and thus angle of deviation of the object motion relative to the background (Fig. 1B), was varied from trial to trial using a staircase procedure. Subjects were instructed to maintain visual fixation on a central, head-fixed target to cancel reflexive eye movements. In each block of trials, the heading was fixed, but it differed across blocks such that data were collected separately for forward (0u), lateral (rightward, 90u) and intermediate (30u and 60u) directions (Fig. 1).
Main Experiment
Subject-by-subject thresholds for both the visual-only and combined conditions are displayed in Fig. 2 (blue and red bars, respectively). For most subjects and most headings, it can be observed that combined thresholds are slightly lower than those in the visual-only condition; this effect was significant. Across all heading eccentricities, the mean object discrimination threshold is lower in the combined condition compared to the visual-only condition (p = 0.011; paired t-test), consistent with the hypothesis that vestibular cues facilitate optic flow parsing. A separate analysis also revealed a significant effect of stimulus condition on threshold improvement (combined vs. visual-only: F(1,5) = 7.40, p = 0.04, repeated measures ANOVA).
Closer examination of Fig. 2 reveals that the improvement in object discrimination thresholds in the combined condition depends on heading eccentricity, and this effect was also significant (F(3,5) = 3.78, p = 0.03, interaction term of repeated measures ANOVA). This dependence of vestibular facilitation on heading eccentricity is further illustrated in Fig. 3, which plots the percentage decrease in object discrimination thresholds in the combined condition, relative to that in the visual-only condition, for subjects that participated in all conditions of the main experiment (S1-S6). For the forward (0u) heading, there was no significant improvement in object discrimination thresholds when vestibular cues were present (p = 0.58; paired t-test). In contrast, for headings 30u, 60u, and 90u, the improvement was either significant or approaching significance (p = 0.02, p = 0.12, p = 0.04, respectively; paired t-test). Pooling across all non-zero heading directions, the improvement was highly significant (p,0.001; paired t-test).
As shown in Fig. 3, vestibular facilitation was least for heading 0 deg, greatest for heading 90 deg, and moderate for intermediate heading angles. The corresponding mean percentage decreases in the combined condition were 23.1%, 9.7%, 6.7%, and 17.0% for headings 0u, 30u, 60u, and 90u, respectively. While we do not expect vestibular facilitation to depend linearly on heading eccentricity, the data suggests a trend for vestibular facilitation to increase with heading eccentricity. Therefore, using the data presented in Fig. 3, we conducted a non-parametric (rank-based) correlation analysis in order to evaluate the significance of this trend. This revealed a significant positive correlation between heading eccentricity and percent decrease in combined threshold (p = 0.007, Spearman's rho = 0.53).
Eye-movement Control
A potentially trivial explanation for this finding is that incomplete suppression of the translational vestibulo-ocular reflex (TVOR) improves nulling of retinal slip in the combined condition compared to the visual-only condition. In this scenario, a residual TVOR during combined stimulation would physically (rather than computationally through flow parsing) cancel more of the background motion on the retina, thus reducing the speed of the starfield motion and making it easier to discriminate the direction of object motion. Indeed, prior research has shown that the TVOR is more effective in canceling retinal slip during lateral than during forward movements [32][33][34], consistent with the improvement we observed during lateral self-motion. We therefore repeated the experiment for the lateral (90u) heading in a subset of subjects (S4-S8) while recording eye movements, in order to monitor fixation and identify differences in residual eye velocity between visual-only and combined conditions.
Distributions of mean eye velocity (for the left eye) are illustrated in Fig. 4, left column (blue: visual-only condition; red: combined condition). Because the self-motion direction was rightward in these experiments, an unsuppressed TVOR would elicit leftward (negative) eye velocities. All histograms peaked near zero with only one subject (S6) exhibiting mean eye velocity significantly different from zero (t-test, visual-only p,0.001, combined p = 0.01). Importantly, visual-only and combined histograms were largely overlapping; there was no significant difference in the distribution of eye velocity between combined and visual-only conditions, and this was true for all subjects (ttest, p.0.05). To further investigate the relationship between eye movements and object discrimination performance, we also examined how object discrimination thresholds changed as a function of mean eye velocity for each subject. To do this, we binned trials according to mean eye velocity and we fitted psychometric functions to behavioral data for each bin (see Methods for details). If a residual TVOR facilitates object motion discrimination in the combined condition (red), there should be a positive correlation between mean eye velocity and discrimination performance (i.e., leftward (negative) eye velocity should be associated with lower thresholds).
Only one subject (S6) exhibited a significant positive correlation between eye velocity and discrimination threshold in the combined condition (r = 0.85, p,0.001). However, visual-only and combined thresholds were virtually identical for this subject (Fig. 2, S6, Heading = 90u). On the other hand, subjects who exhibited the largest decrease in threshold for the combined relative to the visual-only condition (e.g. S5 or S7) showed a negative correlation for the combined condition in Fig. 4 (larger leftward eye velocities were associated with worse discrimination performance; S5, r = 20.76, p = 0.001; S7, r = 20.82, p,0.001). Moreover, S7 showed a significant positive correlation between threshold and eye velocity for the visual-only condition (r = 0.90, p,0.001), suggesting that unsuppressed (perhaps optokinetic) eye movements led to improved performance in the visual-only but not in the combined condition. Yet this subject performed better in the combined that the visual-only condition, suggesting that these correlations cannot explain the behavioral results. Thus, in summary, we found no evidence that the improvement in object discrimination thresholds in the combined condition is due to Figure 2. Summary of discrimination thresholds. Each panel shows the data from a different subject. Error bars represent 95% confidence intervals. Subjects S1-S6 participated in the main experiment, so visual-only (blue bars) and combined (red bars) thresholds were measured at all heading eccentricities. Subjects S4-S8 participated in the retinal speed (RS) control experiment (green bars). Note that subjects S7 and S8 were only tested with the 90u heading in the eye movement control experiment (lateral motion). doi:10.1371/journal.pone.0040264.g002 a physical cancellation of the optic flow by unsuppressed, reflexive eye movements.
Retinal-speed Control
The data from the visual-only and combined conditions of the Main Experiment (Figs. 2 and 3, S1-S6) show a significant (F(3,5) = 28.25, p,0.001) overall effect of heading direction: object discrimination thresholds were consistently greatest for the 0u heading. We hypothesized that this dependence was predominantly due to differences in the self-motion-related component of retinal speed at the object location (v s ) across headings. Specifically, as heading direction is shifted from forward toward lateral, the expected retinal image motion due to self-motion at the location of the object (v s in Fig. 1B) increases. We therefore repeated the experiment for a subset of subjects while matching optic flow speed at the object location (v s ) across heading directions. This was done by changing the amplitude of self-motion as a function of heading. With the selfmotion component of retinal speed (v s ) matched at the location of the object, any remaining effect of heading direction would suggest some dependence of flow-parsing on flow field geometry. In particular, for heading 0, the flow field is radial and there is considerable divergence at the location of the object motion (Fig. 1C). For heading 90, on the other hand, the flow field is laminar and divergence at the location of object motion is minimal (Fig. 1F).
Results from this experiment are illustrated by the green bars in Fig. 2 (S4-S8). When the retinal speed of optic flow at the object location (v s ) was matched across headings, there was no significant influence of heading direction on object discrimination thresholds (F(3,4) = 1.34, p = 0.31). Thus, the overall effect of heading eccentricity on discrimination thresholds in the first experiment appears to result primarily from associated changes in retinal speed. Prior research has demonstrated the dependence of flow parsing on global flow properties [2]. However, given our limited investigation of this question, we did not find evidence that flowparsing depended on the degree of divergence in the flow field at the location of the object motion. . Summary of eye movement analysis. Each row summarizes data from one subject. Only left eye (LE) velocities were used for these analyses; conducting the same analyses using right eye velocities yielded similar results. Left column shows histograms of mean eye velocities from all trials for both the Visual-only (blue) and Combined (red) conditions. Right column shows Visual-only (blue) and Combined (red) thresholds as a function of mean eye velocity, along with regression lines fit to these data (see text for details). doi:10.1371/journal.pone.0040264.g004
Discussion
Estimation of self-motion and object motion are reciprocal parts of the flow-parsing problem, so factors influencing estimation of self-motion may also influence observers' ability to estimate object motion during self-motion. We examined the influence of vestibular stimulation and heading direction on observers' ability to discriminate the direction of object motion in the world. Similar manipulations were shown previously to influence heading discrimination [19][20][21], and here we have shown that they also influence object motion discrimination. We found that object discrimination thresholds during self-motion generally decreased when congruent vestibular stimulation accompanied background optic flow, suggesting that vestibular inputs can help parse retinal image motion into self-motion and object motion components.
Vestibular Facilitation of Optic Flow Parsing
Although the observed effect was small, this is not surprising considering the processes that are likely to be involved. We assume (at least) a two-stage process in which 1) the nervous systems generates a multisensory estimate of self-motion, and 2) uses this estimate to recover object motion in the world by canceling the expected visual consequences of self-motion. Any facilitation due to vestibular stimuli will most likely act by reducing the variability of the multisensory estimate of self-motion described in stage one above. We have studied visual-vestibular heading estimation extensively [17][18][19] and have found that the standard predictions of the Maximum-likelihood Estimation (MLE) model of cue integration are upheld [35]. The predicted improvement in combined heading estimation relative to visual-only is at most ,!2, and this should occur when visual and vestibular heading estimates are approximately equally reliable.
Over the range of headings investigated here, previous measurements indicate that the reliabilities of visual and vestibular heading estimates vary considerably [21]. For discrimination around a straight forward heading reference, visual heading discrimination thresholds are much more reliable than vestibular thresholds. However, visual heading thresholds increase approximately 5-fold as reference eccentricity increases toward lateral heading directions [ Fig. 2B of 21]. Vestibular heading discrimination thresholds also increase with eccentricity of the reference heading, but only approximately 2-fold, for lateral as compared to forward heading directions [ Fig. 2A of 21]. Vestibular heading thresholds were never lower than visual thresholds, but were approximately equal for the lateral (90u) heading eccentricity.
Consequently, it is reasonable to expect that vestibular cues are weighted more heavily for eccentric heading directions where their relative reliability is more comparable to that of visual heading cues. By this logic, we expect to see larger vestibular-facilitated decreases in object motion discrimination thresholds for eccentric rather than forward heading directions. Our results are consistent with this hypothesis. Subjects showed little or no improvement in object motion discrimination in the combined condition for forward heading (0u) and the largest improvement for lateral (90u) heading (Fig. 3B). Indeed, the maximum improvement predicted by the MLE model is ,!2, which is of the same order of magnitude as the largest observed improvements in our experiment (,20-30%, Fig. 3B).
Note that direct extension of MLE cue integration predictions to our object motion task requires some assumptions. First, the estimate of self-motion should be unbiased, or the bias should remain fairly constant for a given heading direction. Second, the operation that cancels the expected visual consequences of self-motion (described as stage two, above) should introduce little noise into the object motion estimate. If either of these assumptions is substantially violated, the expected improvement in performance in the combined condition will be reduced relative to the MLE-prediction.
While the present results are suggestive, they do not prove conclusively that object motion perception depends directly on heading recovery. Recent work with visual-only stimuli has aimed to test the hypothesis that object motion estimates can be predicted directly from heading estimates in response to an illusory optic flow stimulus [36]. Results of that study are inconsistent with predictions of the strict self-motion-cancellation hypothesis, suggesting that flow parsing does not necessarily depend on heading recovery. Clearly, further research is needed on this topic.
Importantly, an alternative explanation of our results based on a residual TVOR, which might cause a physical (rather than computational) reduction of background optic flow, is inconsistent with our data. Mean eye velocity was small on most trials and was similar for visual-only and combined conditions. We calculated object discrimination thresholds as a function of mean eye velocity and this analysis confirmed that the vestibular facilitation of object discriminability could not be attributed to reflexive eye movements. We suggest instead that vestibular self-motion signals contribute to optic flow parsing computations. Note, however, that a more complete understanding of the role of vestibular signals in flow parsing will require experiments that also measure biases in perceived object motion trajectory due to self-motion. Future studies should examine how vestibular signals modulate the ability of subjects to accurately judge the direction of object motion (relative to the world) in the presence of self-motion.
Neurophysiological Implications
Given the above considerations, it is striking that we observed an overall decrease in thresholds in the combined condition. Although modest, the improvements in object motion discrimination thresholds that we have observed are likely to be functionally relevant. Moreover, it is possible that the same cortical areas with convergent optic flow and vestibular inputs (e.g., areas MSTd and VIP) [25,26,28,37,38], which have been implicated in mediating the improvement in heading discrimination thresholds [17][18][19], also mediate improved object motion discrimination during simultaneous vestibular stimulation. Particularly relevant might be a group of cortical multisensory neurons with incongruent visual and vestibular preferences [26,28,39]. These cells are sub-optimally stimulated when visual and vestibular signals are congruent, as during selfmotion relative to a stationary visual environment in the absence of object motion. On the other hand, they are maximally stimulated by incongruent optic flow and vestibular signals [28,29], and are therefore ideally suited to signal instances when visual motion does not match the optic flow that might be expected based on vestibular input. This is precisely what occurs during independent object motion. As Wallach proposed [40], the visual system could better estimate object motion during self-motion by 'canceling' the effects of self-motion and it is possible that incongruent cells contribute to implementing this cancellation process, such that object motion may be estimated more precisely [41]. | 6,679.4 | 2010-09-03T00:00:00.000 | [
"Biology",
"Psychology"
] |
Design of Travel Route Identification and Scheduling System Based on Artificial Intelligence-Aided Image Segmentation
This study designs a travel recognition and scheduling system using artificial intelligence and image segmentation techniques. To address the problem of low division quality of current point division algorithms, this study proposes a streaming graph division model based on a sliding window (GraphWin), which dynamically adjusts the amount of information (vertex degree information and adjacency information) referenced at each division according to the current division quality and division time by introducing a sliding window mechanism, to achieve the highest possible division while allowing loss of certain division efficiency. The goal is to improve the division quality as much as possible while allowing a certain loss of division efficiency. To meet the user's need to travel through multiple destinations with the shortest route, this thesis proposes a deep reinforcement learning actor-critic (AC)-based multiobjective point path planning algorithm. The algorithm builds a strategy network and an evaluation network based on actor-critic's multiobjective point path planning, updates the strategy network and evaluation network parameters using AC optimization training, reduces the reliance of the algorithm model on a large amount of high-quality label data, and speeds up the convergence speed of the deep reinforcement learning algorithm by pretraining, finally completing the multiobjective point access sequential path planning task. Finally, the personalized travel recommendation system is designed and implemented, and the system performance analysis is conducted to clarify the system requirements in terms of functional and nonfunctional aspects: the system architecture, system functional modules, and database tables are designed to conduct use case testing of the main functional modules of the system, and the usability of the attraction recommendation algorithm is verified through the concrete implementation of the functional modules such as attraction recommendation in the system.
Introduction
With the popularization of smart mobile devices, the development of unlimited communication technology, and the establishment of the mobile APP ecosystem, the mobile Internet has become the main platform for people's information interaction [1]. Web3.0 era, the convenience of a handful of smartphones and unlimited communication networks, has made mobile travel recommendation replace the traditional recommendation method into the mainstream and brought new changes to the tourism industry [2]. For example, tourists are increasingly inclined to plan their attractions and routes for flexible self-help travel, tourism application services are gradually transferred to mobile, and smart tourism is deepening and expanding. To achieve efficient and accurate mobile travel recommendation service and improve user experience, in addition to users' personal information and interest preferences, mobile travel recommendation also needs to pay attention to the condition of attractions, geographic location, situational factors, and contextual information in real time, to facilitate tourists to make route changes at any time [3]. Touring is the core part of the travel recommendation service. How to plan travel routes to allow tourists to visit as many attractions as possible that match their interest preferences, and to achieve real-time adjustment of mobile travel route recommendation services based on geographic location and user choice is the focus of travel recommendation research.
For travel research, route planning is crucial. Map navigation mobile applications represented by Baidu Maps and Gaode Map, as well as travel mobile applications represented by Drop Taxi provide users with relevant services, such as travel planning, displaying congested road sections, avoiding obstacle sections, and real-time navigation [4]. Nevertheless, the safety and comfort of the route are still difficult to be guaranteed. However, safety and comfort on the road are key indicators of overall travel satisfaction. Researchers in the USA interviewed 4,872 women and found that 85 percent took a different route home or to their destination to avoid potential harassment or assault, and many women would choose a longer route than the one recommended by their navigation software for greater safety [5]. In addition, for visitors new to a city, travel satisfaction depends not only on the beauty of the scenery but also on the safety and comfort on the road. erefore, planning a safe and convenient route becomes especially important. How to ensure convenient transportation and at the same time improve the overall satisfaction of travelers has become a pressing issue for the tourism service and transportation sector.
Once the offset field portion is recovered and removed from the image, leaving only the reflected portion, the image will mitigate grayscale nonuniformities. Since the "Year of Intelligent Tourism" in 2014, the development and popularization of artificial intelligence technology based on the era of big data have injected new vitality into the travel industry and promoted the development of the tourism industry in the direction of intelligence, thus promoting the sustainable economic development of the country's tertiary service industry and ultimately driving the healthy growth of the national economy and further solving the traditional tourism industry existing in the backward equipment, low management level, and other problems [6]. erefore, it is an important new proposition to realize the redevelopment of the tourism industry with the power of artificial intelligence. At this stage, artificial intelligence has been successfully applied to many fields, while the tourism industry has been criticized for its single route design, the lack of independent choice of tourists, and travel safety. e introduction of artificial intelligence technology in travel planning can provide accurate suggestions according to the user's situation so that the user can get a more personalized travel plan; at the same time, it can predict and control the focus of tourism and accelerate the development of tourism [7]. is study establishes the importance and relevance of artificial intelligence in the field of tourism by analyzing the model of integrating artificial intelligence and image segmentation technology with tourism route planning. e principle of image segmentation is to divide an image into subregions with feature consistency according to different characteristics of the image (such as grayscale, color, texture, and structure) or actual production and life needs, and then extract the interesting features target area.
Related Works
e development of AI (artificial intelligence) has experienced three major difficulties in the past, and with the continuous improvement of new computer computing power and hardware infrastructure, AI technology has become a hot spot for worldwide pursuit with unprecedented development. Many scholars and scientists have become very interested in the field of AI, and related applications and theoretical studies have emerged [8]. Different scholars have different understandings of AI. Pamela McCurdock wrote in her book "Machine inking" that AI should not only think like a human but also in the future development process will surpass human intelligence, thus replacing human thinking and becoming a "thinking machine" [9]. Professor Winston of MIT considers AI as an intelligent operating system, and Professor Naudé W of Stanford University defines AI as a discipline that learns how to express, acquire, and use knowledge [10]. Liu X and Deng Z proposed that AI is a technology that can exhibit a similar level of cognitive, thinking, and acting abilities as human beings in a specific application environment created with the help of a corresponding vehicle for achieving specific task goals [11]. Zhou Z et al. (2019) suggest that artificial intelligence is a "complementary" alternative to the current social environment, which is facing the status quo of an aging society and fewer children and is also necessary to meet people's aspirations for a better life and the pursuit of high-quality employment [12].
Path planning problem as an optimization problem has been in nature for a long time, and the design of flexible path planning algorithms for different path planning scenarios has become an urgent need for the intelligent travel and electronic navigation industry, and coupled with the development of artificial intelligence AI technology, intelligent path planning is the realization of intelligent travel and intelligent tourism route recommendation [13]. e necessary conditions: in recent years, with the maturity of artificial intelligence algorithms, the popularity of intelligent life services, personalized path planning research gradually expanded to the application level, and for the provision of travel services, intelligent personalized path planning function become the key to the absolute competitiveness of enterprises in the market, with the advantage of autonomy of reinforcement learning algorithms through continuous interaction with the environment to complete specific goals to achieve intelligent. Ghosh S et al. propose to enhance recommendation systems through a collaborative relationship between context-aware computing and collaborative filtering, specifically based on the cooperation between soft computing and data mining techniques, integrating user profiles, social network history data, and attraction data, and defining collaborative filtering methods for historical data for meaningful interest point extraction [14]. Gu Z et al. provide statistics on travel recommendation systems using artificial intelligence techniques and analyze the interfaces, functions, recommendation mechanisms, and artificial intelligence methods employed [15]. Vijayakumar V et al. propose a location-based personalized traveler recommendation system that uses user information, attraction information, and user-attraction interaction information to provide users with personalized travel [16]. Du S et al. proposed a travel intelligent recommendation system. e integration of heterogeneous online travel information was achieved through a travel ontology. A complete knowledge process was developed to ensure the whole engineering process [17]. e system is based on web technology and uses the user's interactive behavior to recommend tourism resources to the user. e experiment compares and analyzes the results of the label weight coefficient α, the weighted centrality coefficient β, and the label weight diffusion coefficient c under different values and their correlations, and determines the optimal ratio by combining the advantages of the three coefficients.
Artificial Intelligence-Aided Image
Segmentation Model Design e principle of image segmentation is to divide an image into various subregions with consistent features according to different features of the image (such as grayscale, color, texture, and structure) or actual production and life needs and then extract the target region of interest. Image segmentation methods can be broadly divided into two categories: traditional image segmentation methods and image segmentation methods based on a specific theory [18]. Traditional image segmentation methods mainly include threshold-based segmentation, edge-based segmentation, and region-based segmentation methods. e image segmentation methods based on a specific theorem mainly include segmentation methods based on fuzzy theory, segmentation methods based on Retinex theory, segmentation methods based on level set theory, segmentation methods based on genetic coding, segmentation methods based on wavelet variation, segmentation methods based on neural networks, segmentation methods based on machine learning, and so on. So far, there is no general segmentation method for image segmentation. For images with complex structures, human assistance is often required to complete the segmentation, so researchers have added the a priori information of images to the segmentation process to improve the accuracy of image segmentation.
is chapter classifies the numerous methods for grayscale inhomogeneous image segmentation based on the nature of the image a priori information utilized in the segmentation process. e human visual system can recognize and match the same color under multiple lighting conditions, a phenomenon known as "color constancy." Land used the Retinex theory to propose an explanation for this perceptual phenomenon. However, color camera images depend on illumination, and Retinex theory suggests that a grayscale inhomogeneous image i can be decomposed as the product of the illumination factor b and the reflection s l , i.e., i � 2b × s l . (1) Let I � logi, B � linb, S � logs, then we have where B denotes the offset field portion of the image and S denotes the real image. e essence of the so-called Retinex problem is to recover the offset field portion from the grayscale inhomogeneous image, which will mitigate the grayscale inhomogeneity once the offset field portion is recovered and removed from the image, leaving only the reflected portion. erefore, the Retinex theory can be applied to grayscale inhomogeneous image segmentation. Coupled with the development of artificial intelligence (AI) technology, intelligent route planning is an inevitable condition for the realization of smart travel and smart tourism route recommendation. Many problems can be abstracted as graph partitioning problems. Graph partitioning can decompose the original problem into multiple smaller problems and then solve each smaller problem separately, which can further improve the processing efficiency. It is worth noting that graph partitioning can be divided into point partitioning and edge partitioning according to the partitioning method, this section focuses on the definition of edge partitioning, point partitioning is like edge partitioning, and point partitioning needs to meet the load balancing and minimization of replication points [19]. e difference between the two is mainly as follows: edge partitioning is to make cuts to the edges in the graph, and the cut edges are copied to different partitions, while point partitioning is to make cuts to the vertices in the graph, and the cut vertices are copied to each partition. e advantage of the edge partitioning method is that it saves storage space, and the disadvantage is that when performing edge-based computation on the graph, for one edge two vertices are partitioned to different machines, and cross-machine communication is costly; the advantage of the point partitioning method is that it significantly reduces the amount of communication between machines, but increases the storage overhead. With the decline in disk prices, storage space is no longer an issue, and inter-cluster communication has still not made a breakthrough, so most of the currently distributed computing platforms' underlying division methods are mostly pointed division.
At present, with the emergence of big data, the graph data scale is getting larger and larger, and many online applications such as WeChat, Weibo, and Google need a real-time response. e graph data of these online applications are changing every moment, and the topology of the graph data will also change, so the traditional graph partitioning methods are no longer applicable to this scenario. To solve this problem, many online graph partitioning algorithms have emerged, among which the streaming graph partitioning method proposed by Stanton in 2012 is the most famous, and many excellent online graph partitioning algorithms are based on this algorithm for improvement [20]. e reward signal reflects the pros and cons of the agent's behavioral strategy and provides guidance for the subsequent behavioral strategy, which is the direct and decisive feature of the agent's completion of the target task. Streaming graph partitioning algorithms usually load edges or vertices of graph data into the data stream according to certain rules (random ordering, breadth-first strategy, and depth-first strategy) and partition one vertex or one edge at a Computational Intelligence and Neuroscience time. According to the different division strategies, stream graph division algorithms can be divided into hash-based (Hash) division algorithms, division algorithms with constraints, and greedy division algorithms, as shown in Figure 1.
Reinforcement learning is the algorithm in machine learning that most closely resembles the human learning process, aiming at achieving a specific goal by an intelligent being (agent) by interacting with its environment and learning in the process, continuously updating its strategy to reach the maximum reward. In recent years, with the continuous exploration and implementation by many researchers, reinforcement learning has played an important role in various fields. Among them, in games such as robot obstacle avoidance and maze walking, reinforcement learning possesses the advantage of being able to make effective decisions when some information about the environment is unknown, demonstrating the unprecedented competitiveness of reinforcement learning algorithms and providing a good model for integrating them into smart travel scenarios to solve practical path planning problems [21]. When an intelligent body completes a task, it first senses the environment to obtain the current state S t and interacts with the environment through action a t , under the joint action a t and the environment, the intelligent body gets a new state S t+1 with probability P(S t /S t+1 , a t ), while the environment gives an immediate reward r t back to the intelligent body and then enters the next round of interaction cycle. e reward signal represents the goal of the reinforcement learning problem and is generally represented by the scalar r. At each moment when intelligence makes an action, the environment sends a value defined as the reward to the intelligence whose only goal is to maximize the total reward it obtains overall. us, the reward signal reflects the merit of the intelligence's behavioral strategy, provides guidance for subsequent behavioral strategies, and is a direct and decisive feature of the intelligence's ability to accomplish its goal task. In general, the reward signal may be a stochastic function of the state of the environment and the action taken. e value function, also known as the value function or evaluation function, is generally denoted by V (s) . Value functions differ from rewards in that rewards represent the superiority or inferiority of intelligence's behavioral strategy in a direct sense, whereas value functions represent superiority or inferiority in a long-term sense. While rewards reflect the direct, intrinsic desirability of intelligence's behavioral strategies, value functions consider changes in the environment after an intelligence makes action and the effects on the subsequent state of the intelligence in the environment, pointing to the long-term desirability of these behavioral strategies.
From the above analysis, it is easy to see that rewards are in some sense primary, while the value function as a prediction of rewards is secondary. Without rewards, there is no value, and at the same time, the only purpose of using the value function for prediction is to obtain more rewards. However, the value function is crucial when selecting strategies and evaluating decisions. In an optimization problem, the intelligence makes action choices based on the value function, seeking the action that brings the highest value rather than the highest reward.
Construction of Tourist Route Identification and Scheduling System
e development of the system is based on six principles: security, comprehensiveness, stability, adaptability, legality, and convenience. e main reasons are the security of the system is fundamental to providing reliable services. First, we must ensure that all users' information is true and reliable, so we must consider how reliable the identity verification is, and all users' information should be well preserved and not leak data. e development of the system must follow six principles, which are security, comprehensiveness, stability, adaptability, legality, and convenience. e comprehensiveness of the system is mainly reflected in two aspects: the first is that the system is designed with full consideration of the entire system operation involved in the institutional sector; at the same time, the second aspect is that the system needs to be continuously maintained and modified in the process of application, so in the process of program design, the use of good comment writing specifications is to ensure a certain space to ensure the expansion of the system [22]. e stability of the system directly determines whether the system is available or not and whether there will be no running errors during the use by users and administrators. e purpose of this system is to provide users with a lot of conveniences and promote certain economic development, while following the relevant regulations of the state in the design process, and must strictly follow the strict national emphasis on information security, which ensures the privacy and security of users. According to the system development principles, the system architecture design and database design are required before the system development.
Mobile travel route recommendation requires obtaining mobile travel-related data from multiple data sources and tracking mobile context and context in real time: first, obtaining user personal information such as name, age, and gender from the registration form; second, obtaining time, geographic location, and location-related context information from the mobile travel platform; and furthermore, obtaining user-attraction association information from the database such as the time of user's choice of attraction. Finally, we extract the existing association rules and classification trees from the external knowledge base as the basis of association rule recommendation. Based on the above important influencing factors, the T-ARC-based mobile travel route recommendation model is established. e travel route mapped by the income iteration index of the smallest route is the optimal travel route. In this study, the travel recommendation system adopts the current mainstream front-end and back-end separated development model, which can make the front-end and back-end development completely decoupled, the front-end and backend developers only need to define the interface documents, and then they can synchronize the development without interfering with each other, improving the quality and speed of development [23].
e system uses the Spring Boot framework for back-end development, the Vue framework for front-end development, TensorFlow for model training, and Redis for feature data caching. Based on the functional requirements of the system, this section designs the specific functional modules of the system, which are mainly divided into four parts: home page, attraction recommendation, trip planning, and personal homepage. e specific functions of each part are shown in Figure 2.
Deep learning is based on big data and cannot be separated from the creation of a database after the collection of a large amount of data. e use of artificial intelligence for the development and upgrading of tourism requires the creation of databases for both users and tourism elements. e database for the user is a collection and aggregation of information generated by the user so that the data can be called and processed. In this way, it is possible to gradually add and modify the description and characterization of the selected object over time, and through the collection of data over a long period, it is possible to achieve an exact match with the user's characteristics, so this method is the most common method of database creation. For users, the most important factor at the level of tourism planning is targeted recommendation, and through the establishment of a personal database, the information provided by deep learning also tends to be more personalized and humanized. For tourism resources (such as hotels and attractions), the establishment of a database is a statistical regression on parameters such as the number of user retrievals, hotness, and user feedback, to explore the commonalities and characteristics among attractions [24]. e search for commonality can facilitate the classification of tourism resources, and the search for characteristics can be based on the user database for further recommendations for individuals. Moreover, the feedback on the attention of attractions by the above method can make timely arithmetic processing to predict the crowding level of different attractions. In this process, the crowding level appears as a new parameter to further improve the accuracy of recommendations; at the same time, it can be used as a basis to modify the recommendations for different users, to reasonably allocate and balance the flow of people in scenic spots, avoiding the unbalanced situation of crowding in some scenic spots and scarcity of visitors in others. e establishment of the database is slow to fast and then accurate process, as shown in Figure 3, the system gradually stabilizes after the initial model is established, and the cost of data supplementation and adjustment at a later stage is very low. In summary, the establishment of the personalized database can achieve a fast, accurate, and stable number in tourism design and tourism project recommendation.
Starting from the accommodation center M, we visit the seed tourist attractions of the tourist route plan in order and finally return to the accommodation center M, forming a closed-loop process, setting the number of tourist attractions visited as φ, φ � m k�1 a wk . With M determined, there are many tourist routes, but not every route maximizes the iterative value of tourist benefits for tourists, and the purpose of this study is to identify the optimal and suboptimal routes for tourists to choose from. e attractiveness and benefit of a certain tourist route to tourists depend on the influence of all factors on that tourist route, including the influence factors α and β in the actual trip. α and β are extracted from the Baidu Maps and Gaode Map, and their benefit iteration functions are constructed. e function has the same initial gain iteration value I O between every two subnodes, i.e., the initialization value I O is the same when calculating M points to other optimal travel seed nodes. Substituting the positive influence factor α and the negative influence factor β for iteration, the final gain values of the subnodes are output. In a closed-loop structure, the benefit iteration index L remains a monotonically increasing function, which increases with the number of visited attractions and finally outputs a Computational Intelligence and Neuroscience After completing the above process, the system outputs an ascending vector O i of the iterative index of return L of a route. According to the above definition, the tour route mapped by the smallest iterative index of the route is the best tour route. Because its output route's gain iteration index sum is the smallest, it means that its gain function value is the largest for all its subnode intervals, representing that tourist can get a better travel experience than other visit orders through the route planning's attraction visit order. In terms of comprehensive output results, the optimal travel route performs best in terms of tourist attraction classification, distance, time, budget expenditure, transportation information service, and tourist attraction star rating. At the same time, the recommendation system also recommends the second-best route and provides visualization of the route for tourists to choose.
Artificial Intelligence-Aided Image Model Performance Tests
Safety and comfort during travel are also key indicators of comprehensive travel satisfaction. e core of the UPST-TB mobile recommendation algorithm lies in the processing of interest tag sets and the mining of mobile user-interest tag-attraction correlations, and different tag weight preprocessing methods produce different recommendation results, so it is necessary to explore the weighting ratio of the three tag analysis methods in the algorithm. e default rating value of unrated data is 2.5 (on a 5-point scale), the time weight coefficient ξ is 0.5, and the minimum similarity between users and attractions φ is 0.0001. Calculating the similarity between the user label weight vector U → x and the attraction label weight vector S → y , U x S y is used to construct a similarity matrix to achieve tourist attraction recommendations. To increase the rationality and interpretability of the algorithm, the experiments were conducted by comparing and analyzing the results of the label weight coefficient α, the weighted centrality coefficient β, and the label weight diffusion coefficient c at different values and their correlations, and by combining the advantages of the three coefficients, the optimal ratios were determined, as shown in Figure 4.
From Figure 4, the accuracy and recall of the recommendations increase with the increase of c and β values and decrease with the decrease of α value; the coverage increases with the increase of α value and decreases with the decrease of β, and c values decrease with the decrease of β value, and the change with β value is not obvious in the above three figures. It can be determined that the α value is positively correlated with the c value and negatively correlated with the β value. erefore, it is not difficult to analyze and obtain that the interesting label weighting coefficients are not highly targeted and have weak performance in accuracy recommendation; the weighted centrality coefficient and label weight diffusion coefficient have better performance in accuracy/recall index, but the recommendation results are too concentrated and inferior to the interesting label weighting coefficients in coverage index, i.e., diversity recommendation. Overall, the evaluation results of all three indicators are better when the value of c is large, and as the coefficient that makes the most use of mobile data, it can be more comprehensive in mining and analyzing user preferences and item attributes. Among them, the weighted centrality coefficient prefers popular tags, the tag weight diffusion coefficient focuses on cold recommendations, the interest tag weight coefficient helps the diversity of recommendations, and the comprehensive performance of the algorithm is improved by combining the three-weight coefficient tuning. Mobile travel recommendation also needs to pay attention to the status of scenic spots, geographical location, situational factors, and contextual information in real time, so as to facilitate tourists to change routes at any time.
e UPST-TB interest label optimization algorithm outperforms both the FolkRank algorithm and UCF algorithm in terms of accuracy and recall metrics for different n values and has good performance in accuracy recommendation. Although the accuracy of the UPST-TB algorithm is significantly closer to that of the FolkRank algorithm at n � 30, the performance of the UPST-TB algorithm is still clearly superior2. e UCF algorithm based on user preferences is like the FolkRank tag recommendation algorithm in terms of coverage metrics and is always superior, while the UPST-TB algorithm is deficient in diversity recommendation, although it is better at 3. e limitation of collaborative filtering is that it is difficult to handle multidimensional data information, so the UCF algorithm has the worst recommendation effect; the classical FolkRank tag recommendation algorithm is based on the three-part graph and focuses on the correlation between user-tag-item, which is better than the UCF algorithm; the UPST-TB algorithm combines the strengths of both algorithms. Tourists are more inclined to self-planned attractions and routes for flexible self-help travel, tourism application services are gradually transferred to mobile terminals, and smart tourism is deepening and expanding. e UPST-TB algorithm combines the strengths of both algorithms and combines multidimensional data such as user preferences and social tags to make recommendations, which has certain superiority in recommendation performance. Although the label weight diffusion factor is used to mine cold labels and optimize their diversity based on the TF-IDF method, the UPST-TB algorithm still favors popular recommendations and is deficient in diversity recommendations.
Computational Intelligence and Neuroscience
To verify the effectiveness of the algorithm, this group of experiments compares the parameter-tuned UPST-TB algorithm with the classical tag recommendation algorithm FolkRank and the user-based collaborative filtering (UCF) algorithm through the core subset of location-set based on tourist attraction recommendations, and the structure is shown in Figure 5.
Experiments prove that the UPST-TB algorithm has advantages in accuracy recommendation, normalizing important mobile information from multiple data sources into interest labels helps improve recommendation performance, and weighting analysis and tuning of the user-interest label set can further optimize the performance of mobile recommendation. e time complexity of the UPST-TB algorithm is O, which is the same as that of the classical algorithm. e UPST-TB algorithm has good performance in the field of mobile travel route recommendation for attraction selection and recommendation. When the number of target points is 10, compared with the d2m-greedy method and the genetic algorithm, the total length of the safe path planned by the MDRP-AC algorithm proposed in this chapter is reduced by 12.00% and 3.11%, respectively. e runtimes of the graph division for the ParMetis algorithm, GP-Metis algorithm, GraphHash model, and GraphGPU model on each of the three datasets are labeled above the bar graphs. In particular, the runtimes of the exchange optimization phase are marked in square brackets on the bar graphs of the GraphHash and GraphGPU models. e results are shown in Figure 6. e GraphGPU model runs 1.7-2.5 times faster than the ParMetis algorithm and 1.1-1.47 times faster than the GP-Metis algorithm. e algorithms stop the coarsening operation too early in the coarsening phase when dividing large-sized graphs, making the final coarsened graphs too large. In the longitudinal comparison with GraphHash, the GraphGPU optimization phase takes significantly less time than the GraphHash algorithm because the barrel-optimized exchange algorithm in GraphGPU converges in 4-7 iterations, while GraphHash requires 8-13 iterations to converge, which also reflects the effectiveness of the GraphGPU initial clustering division algorithm.
Simulation Experiment of Travel Route
Identification and Scheduling System e system development process uses the Spring Boot framework for back-end development, Vue framework for front-end, and Python 3.6 language and TensorFlow framework for attraction recommendation service, and the purpose of system functional testing is to detect the operation of each function in the system through test cases. e system is tested and evaluated through the system functional test case table to ensure that the system runs without abnormalities. e test case table contains the case number, name, and prediction result. It mainly tests the functions in the home page, attraction recommendation, itinerary planning, and personal homepage of the travel recommendation system. In the actual multiobjective path planning scenario, the road network information is complex and diverse, and the user needs are different. To make the multiobjective path planning results more suitable for the user's requirements on the safety of travel routes, we use the safety distance between two target points as the distance weight between two target points and verify the effectiveness of the MDRP-AC algorithm proposed in this chapter in the actual. Based on the safe path planning dataset created in Chapter 3 of this thesis, we verify the effectiveness of the proposed MDRP-AC algorithm in urban scenarios. e UPST-TB interest tag optimization algorithm is better than the FolkRank algorithm and the UCF algorithm in terms of precision and recall in different n values, and has good performance in accuracy recommendation. e MDRP-AC algorithm proposed in this chapter models the multiobjective path planning problem as a sequence-to-sequence-based TSP problem constructs an A-Ptr network based on a pointer network specifically designed for solving the TSP problem, and optimizes the parameters of the A-Ptr network by combining the actor-critic algorithm in deep reinforcement learning techniques through the interaction training between the intelligence and the environment to achieve the goal of the shortest total distance of multiobjective point visits. e goal is to predict the output of the sequence and then to achieve the shortest total travel distance of the multiple target points represented by the sequence.
e MDRP-AC algorithm, the d2m-greedy method, and the genetic algorithm can obtain good results when the number of target points is 5. As the number of target points increases, the advantage of the MDRP-AC algorithm proposed in this chapter becomes obvious. When the number of target points is 10, compared with the d2mgreedy method and the genetic algorithm, the total length of safe paths planned by the MDRP-AC algorithm in this chapter is reduced by 12.00% and 3.11%; when the number of target points is 20, compared with the d2m-greedy method and the genetic algorithm, the total length of safe paths planned by the MDRP-AC algorithm in this chapter is reduced by 2.98%. e total length of safe paths planned by the MDRP-AC algorithm is reduced by 2.98% and 0.14% compared with the d2m-greedy method and the genetic algorithm, respectively. e results of the safe travel routes corresponding to the three multiobjective point path planning algorithms are shown in Figure 7. From Figure 7, the MDRP-AC algorithm proposed in this chapter effectively reduces the number of users repeatedly passing through the same street in the road network based on the reduction of the total length of the safe path.
From the above experimental results, it can be concluded that the MDRP-AC algorithm proposed in this chapter effectively shortens the total length of multitarget point travel paths, uses the interaction trajectory data obtained from the interaction between the intelligent body and the environment, uses the actor-critic reinforcement learning method to train the pointer network, overcomes the problem of high data cost, reduces the high dependence of network performance on labeled data, and provides a feasible method for multitarget point path planning. Next, we apply the MDRP-AC algorithm to a practical smart travel scenario, design and implement a travel route planning scheme based on the MDRP-AC algorithm, and provide users with personalized path planning recommendations for multiple attractions.
is section designs and implements a travel route planning scheme to be applied to various travel mobile applications. e scheme is based on the MDRP-AC algorithm proposed in this chapter, which uses the shortest distance or safe distance as the distance weight between two target points to achieve the multitarget point access path planning function, i.e., to plan a travel access route based on multiple destinations inputted by the user, and to accomplish the goal of "multisite day trip" travel route planning. Based on the input K destination locations and the user's performance requirements for the path planning results, the distance weights between each two target points are determined by obtaining information about the surrounding streets, intersections, and safety hazard areas from the database. If the user selects the shortest path requirement, task one is executed. e shortest path planning is performed according to the Dijkstra algorithm, and the shortest path planning result of K(K-1)/2 paths is obtained; if the user chooses the safe path demand, task 2 is executed, and the safe path planning is performed according to the Q-SRP algorithm based on the policy guidance mechanism proposed in Chapter 3, 800 iterations of learning are performed according to the starting and ending points of the path, and the safe path planning result of K(K-1)/2 paths is obtained. e path planning result is obtained. e path planning results are stored as sequences in the order of traveling nodes, which can be directly called by the multidestination access path planning task to obtain the distance weights between two destinations. After that, the K destination sequences are input into the AC optimization model containing the A-Ptr network and CL network, 1000 rounds of iterative learning are performed according to the MDRP-AC algorithm process, and finally, the multitarget access sequences are output to obtain the full path planning results, as shown in Figure 8.
We first execute task 2 to get the secure path between every two attractions by Q-SRP algorithm based on the policy-guided mechanism for user B's self-selected multitarget points and the requirement of ensuring path security,
Conclusion
is study focuses on the establishment of user-interest sets and deep mining of user-interest tag-item correlation and proposes the UPST-TB mobile recommendation algorithm based on interest tags. By using various data preprocessing methods to weight the interest tags, the quality of tags is further optimized, and the three-part graph data of mobile recommendation are processed in the way of social tag recommendation. An actor-critic-based multitarget point path planning algorithm is proposed. In the multitarget point access sequential path planning task, we want to achieve the optimization objective that multiple target points are all visited once and the total path length is the shortest. Experimental results show that our algorithm results in shorter total path lengths for a larger number of target points compared to distance matrix mapping methods and genetic algorithms used for multiobjective path planning. Finally, the MDRP-AC algorithm is applied to a real travel scenario, and a travel route planning scheme based on the MDRP-AC algorithm is designed and implemented to recommend personalized multispot optimized path planning results for users. In the process of this study, there are still many shortcomings; for example, there are many factors that affect the location recommended routes; in this study, we mainly use user check-in data and attraction review information; in addition to text data, there are weather, time, money, and some other modal data (pictures and audio) that affect the location recommendation, these factors can be incorporated into the model system in future research, and the recommendation mechanism will be more in line with the actual needs.
Data Availability e datasets used and analyzed during the current study are available from the corresponding author upon request.
Conflicts of Interest
e author declares that there are no conflicts of interest. | 9,184 | 2022-07-04T00:00:00.000 | [
"Computer Science"
] |
Generalized Parton Distributions from Lattice QCD with Asymmetric Momentum Transfer: Axial-vector case
Recently, we made significant advancements in improving the computational efficiency of lattice QCD calculations for Generalized Parton Distributions (GPDs). This progress was achieved by adopting calculations of matrix elements in asymmetric frames, deviating from the computationally-expensive symmetric frame typically used, and allowing freedom in the choice for the distribution of the momentum transfer between the initial and final states. A crucial aspect of this approach involves the adoption of a Lorentz covariant parameterization for the matrix elements, introducing Lorentz-invariant amplitudes. This approach also allows us to propose an alternative definition of quasi-GPDs, ensuring frame independence and potentially reduce power corrections in matching to light-cone GPDs. In our previous work, we presented lattice QCD results for twist-2 unpolarized GPDs ($H$ and $E$) of quarks obtained from calculations performed in asymmetric frames at zero skewness. Building upon this work, we now introduce a novel Lorentz covariant parameterization for the axial-vector matrix elements. We employ this parameterization to compute the axial-vector GPD $\widetilde{H}$ at zero skewness, using an $N_f=2+1+1$ ensemble of twisted mass fermions with clover improvement. The light-quark masses employed in our calculations correspond to a pion mass of approximately 260 MeV.
I. INTRODUCTION
Parton distribution functions (PDFs) play a crucial role in understanding the quark and gluon structure of strongly interacting systems [1].These functions, measurable in processes such as inclusive deep-inelastic lepton-nucleon scattering, provide valuable insights into the distribution of partons within hadrons as a function of their momentum fraction, denoted as x.PDFs are defined through matrix elements of bi-local operators, where the parton fields are separated by a light-like interval, and the operators are evaluated for the same initial and final hadron states.Generalized parton distributions (GPDs) extend the concept of PDFs by considering light-like parton operators computed for different initial and final states [2][3][4].GPDs introduce additional dependencies on the longitudinal momentum transfer (ξ) and the invariant momentum transfer (t) to the target, in addition to the parton momentum fraction (x).While this multi-variable nature makes GPDs more complex, they offer a wealth of information beyond PDFs.In particular, GPDs provide three-dimensional images of hadrons [5][6][7][8], enable access to the angular momenta of partons [3], and offer insights into the pressure and shear forces within hadrons [9][10][11].Recently, it has been discovered that GPDs exhibit chiral and trace anomaly poles, which provide insights into phenomena such as mass generation in QCD, chiral symmetry breaking, and confinement [12][13][14].Understanding these imprints can offer valuable insights into fundamental aspects of QCD.We also refer the reader to several other review articles that extensively discuss the physics of GPDs [15][16][17][18][19][20][21][22].
In our recent publication of Ref. [85] 1 , we achieved significant advancements in enhancing the computational efficiency of lattice QCD calculations for off-forward matrix elements.The work was also extended to calculate the Mellin moments of the unpolarized GPDs [89], including high moments enabling a physical picture of quark distribution in the transverse plane.In these calculations, we employed a unique approach using asymmetric frames, which differ from the more commonly used symmetric frames.In this approach, the entire momentum transfer ∆ is applied to the initial state (source) of the nucleon.This choice not only reduces the computational cost but also offers the advantage of covering a broader range in t ≡ ∆ 2 , enabling us to effectively map the GPDs across a larger t-space.In our previous work, our focus was on unpolarized quark GPDs (H and E) at zero skewness.We introduced a novel Lorentz-covariant parameterization for the vector matrix element in terms of Lorentz-invariant amplitudes.This also allowed us to establish connections between matrix elements from any two kinematic frames.Additionally, we employed this amplitude-based approach to propose a frame-independent definition of quasi-GPDs and demonstrated that these definitions can potentially result in reduced power corrections in the matching relations to light-cone GPDs.In this work, we extend the amplitude-based approach to compute the axial-vector GPD H at zero skewness.For a comprehensive discussion on the inaccessibility of E at ξ = 0, we refer to Sec.II, where we discuss the intricacies and reasons behind this limitation.
The paper is structured as follows.In Section II, we begin by presenting the definitions of axial-vector light-cone and quasi-GPDs.We then shift our focus towards discussing the Lorentz-covariant decomposition of axial-vector matrix elements in terms of the Lorentz-invariant amplitudes.Furthermore, we establish the relations between these amplitudes and the GPDs H and E. Based on these amplitudes, we propose a few potential candidates for a new, frame-independent definition of quasi-GPDs under the constraints of finite boost momentum.We thoroughly explore the interpretations of these new definitions, carefully examining the subtleties involved while also addressing the important issue of uniqueness/non-uniqueness in their formulation.In Section III, we provide the Euclidean decompositions of lattice-calculable matrix elements in terms of these amplitudes.We also outline our lattice setup for the calculations in position space.Section IV is dedicated to our numerical results, accompanied by a detailed comparison between the symmetric and asymmetric frames at different stages, both in coordinate space and momentum space.Notably, we provide numerical results for the invariant amplitudes and the twist-2 light-cone GPD H, specifically for ξ = 0. Finally, in Section V, we conclude our findings and discuss potential future prospects for further research and exploration in this field.
II. STRATEGY OF FRAME TRANSFORMATION
Computing GPDs in the symmetric frame presents significant challenges in lattice QCD.Extracting a range of momentum transfers requires separate calculations for each ∆, severely limiting the accessible momentum transfer range.This prompts the question of calculating GPDs in computationally advantageous asymmetric frames.One approach, as outlined in our previous work [85], establishes a connection between the symmetric and asymmetric frames through a suitable Lorentz transformation.Employing a Lorentz transformation along the z-direction does not work since a spatial operator distance will receive a nonzero temporal component, which cannot be dealt with in lattice-QCD calculations.In contrast, transverse Lorentz transformations ("transverse boosts") preserve the spatial operator distance.In our second approach, we have developed a Lorentz covariant formalism that allows calculations in any frame.By parameterizing the relevant matrix element using Lorentz-invariant (frame-independent) amplitudes, we establish connections between different frames.In the following sections, we will explore this approach and its implications for computing axial-vector GPDs in asymmetric frames.
A. Definitions of GPDs
To begin, let us revisit the definition of light-cone quark GPDs for a spin-1/2 hadron.In position space, GPDs characterize non-local quark field matrix elements, which are defined as follows: where Γ represents a gamma matrix.The gauge invariance of this correlator is ensured by the presence of the Wilson line In Eq. ( 2), the parameter g represents the strong coupling constant, while A + denotes the plus-component of the gluon field on the light cone.The initial (final) hadronic state in Eq. ( 1) is described by its 4-momentum p i (p f ) and helicity λ (λ ′ ).We introduce the following kinematic variables: the average 4-momentum of the hadrons P , the (aforementioned) 4-momentum transfer ∆, the skewness ξ (which is defined for hadrons with a large light-cone plusmomentum and represents the longitudinal momentum transfer to the hadron), and the (aforementioned) invariant squared 4-momentum transfer t, We use the definitions in Eq. ( 3) in both the symmetric and asymmetric frames.At twist-2, the correlator with Γ = γ + γ 5 in Eq. ( 1) can be characterized by two distinct axial-vector GPDs, H and E. In position space, the expression is given by [16] For the expression corresponding to Eq. ( 1) in momentum space, the Fourier transform is taken with respect to P • z while keeping P + fixed, leading to Now, let us redirect our focus to quasi-GPDs, which are defined in position space through the equal-time correlator [61] Here, the Wilson line is given by For Γ = γ 3 γ 5 , one finds with the quasi-GPDs H 3 (z 3 , ξ, t; P 3 ) and E 3 (z 3 , ξ, t; P 3 ).Eq. ( 8) is the quasi-GPD counterpart of Eq. ( 4).For the expression corresponding to Eq. ( 8) in momentum space, we perform a Fourier transform with respect to P • z while keeping P 3 fixed, yielding In Ref. [90], it was proposed to define the quasi-counterpart of the light-cone GPDs H and E using Γ = γ 3 γ 5 , as presented in Eq. ( 8).The rationale for selecting γ 3 γ 5 instead of, for instance, γ 0 γ 5 is the absence of mixing with other operators under renormalization, where this mixing is regarded as a lattice artifact caused by chiral symmetry breaking [90].Furthermore, Ref. [72] argues that, for this definition, it becomes necessary to substitute γ + γ 5 /P + with γ 3 γ 5 /P 0 in the prefactor of H to ensure consistency with the forward limit.The definition in Eq. ( 9) also produces the correct local limit when integrated with respect to x.
B. Parameterization of an axial-vector matrix element
Now, let us discuss the Lorentz-covariant decomposition of the axial-vector matrix elements, specifically Eq. ( 1) with Γ = γ µ γ 5 , for spin-1/2 particles in position space.By incorporating parity constraints, we establish that the axial-vector matrix element can be expressed as a combination of eight distinct Dirac structures, each multiplied by a corresponding Lorentz-invariant amplitude.The choice of basis for the amplitudes is not unique, and here we employ where ϵ µP z∆ = ϵ µαβγ P α z β ∆ γ .We note that the above equation holds for a general value of z and has a smooth z → 0 limit.The amplitudes A i are frame-independent, while the basis vectors are generally frame-dependent.Note also that the basis vectors in Eq. (10) do not contain factors of z2 .(For example, such factors can occur when working with an orthogonal set of basis vectors.)For the amplitudes, we adopt the concise notation A i ≡ A i (z • P, z • ∆, ∆ 2 , z 2 ) for brevity.The procedure of deriving these results closely follows the steps outlined in Ref. [91], with a similar treatment found in Ref. [92] where the matrix element was parameterized in momentum space using a straight Wilson line.It is worth noting that the number of amplitudes is the same as for the vector current (Γ = γ µ ) discussed in Ref. [85].
While it is possible to work with alternative sets of basis vectors, the number of independent amplitudes will remain unchanged, requiring eight independent lattice matrix elements to disentangle all the amplitudes.Furthermore, in Appendix B, we present a comprehensive discussion on the symmetry properties of the amplitudes implied by Hermiticity and the time-reversal transformation.In particular, the relations in Eq. (B3) imply that the amplitudes A 3 , A 4 , and A 8 are odd in ξ.This symmetry behavior, plus the requirement of a well-defined forward limit of the matrix element in Eq. ( 10), leads us to conclude that these three amplitudes vanish for ξ = 0.In the analysis of the lattice data presented in this work, we first kept those amplitudes as nonzero and indeed found them numerically to be compatible with zero.More discussion can be found in Sec.IV.
We will now establish connections between the light-cone GPDs and the amplitudes.As certain quantities depend on the kinematic frame, it becomes crucial to differentiate and specify the relevant frame.To achieve this distinction, we employ superscripts s and a to denote the symmetric and asymmetric frames, respectively.We note that in the symmetric frame, the momentum transfer is equally distributed between the initial and final states, while any other distribution is considered asymmetric.After substituting µ = + in Eq. ( 10), we can apply a basis transformation to relate the A i 's in the resulting expression to the GPDs in Eq. ( 4): where the A i 's are evaluated at z 2 = 0. We emphasize that in the aforementioned equations, we have expressed the kinematic variables multiplying the amplitudes using Lorentz-invariant scalars.It is crucial to note that this particular re-writing is unique.Furthermore, as evident now, these equations exhibit the property of Lorentz invariance, which guarantees their validity and applicability across different reference frames.It is worth noting that due to the prefactor ∆ + , E drops out of the parametrization, Eq. ( 4), at ξ = 0. Upon first look the expression for E, Eq. ( 12), seems only valid for ξ ̸ = 0.However, based on symmetry arguments (as discussed before and given in Appendix B), A 3 is odd in ξ and vanishes at ξ = 0.One can therefore reliably determine the zero-skewness limit of A 3 /ξ (and of E) by calculating A 3 for nonzero ξ and extrapolating the r.h.s. of Eq. ( 12) to ξ = 0. Note that a recent work has unveiled the possibility of obtaining a glimpse into E at ξ = 0 by studying a specific twist-3 GPD [93].Now, we shift our focus to quasi-GPDs.As highlighted in Ref. [85], one plausible approach to define the quasi-GPDs is by starting from the Lorentz-invariant light-cone definitions in Eqs.(11) and (12) to incorporate z 2 ̸ = 0. Throughout our discussions, we will refer to this definition as the Lorentz-invariant (LI) quasi-GPD: where now the A i are evaluated at z 2 ̸ = 0 2 .In simple words, this definition of the quasi-GPD is based on the same functional form in terms of the A i as the light-cone GPD (see Eq. (11) and Eq. ( 12)).One finds that this definition is given by an operator which combines (γ 0 , γ 1 , γ 2 )γ 5 , rather than the conventional operator γ 3 γ 5 (further explained in the subsequent paragraph and sections).Because of this operator structure, a different matching coefficient is required compared to the one used for γ 3 γ 5 .Specifically, one can disregard the contributions from the operators γ 1 γ 5 and γ 2 γ 5 as they are relatively suppressed by a factor of 1/(P 3 ) 2 .In our numerical results, we chose to implement the matching for γ 3 γ 5 (see Ref. [71] and also Eq. ( 81)) due to the unavailability of the matching kernel for γ 0 γ 5 in the literature.Consequently, this necessitates a new calculation for both the matching and the renormalization of the γ 0 γ 5 operator, along with addressing its mixing effects.Note also that the difference between results with matching for γ 0 γ 5 and γ 3 γ 5 is finite and is expected numerically to be very small.
We now turn to the set of quasi-GPDs already introduced in Eq. (8).By setting µ = 3 in Eq. ( 10), we can perform a change of basis to transform the resulting expression and establish a mapping between the A i and the quasi-GPDs defined in Eq. (8).The relations are as follows: Similar to the light-cone case, it is important to note that there are no divergences arising from the terms A 3 /ξ and A 4 /ξ as ξ → 0 in Eq. ( 16).We iterate that the reason for the well-behaved ξ → 0 limit is the fact that these amplitudes are odd in ξ and vanish for ξ → 0 (see also Appendix B).Moreover, if one intends to calculate the value of E at ξ = 0 using Eq. ( 16), extrapolation from nonzero ξ values becomes necessary.Now, let us examine the frame (in)dependence of Eqs. ( 15)-( 16).It is noteworthy that these equations hold true in both symmetric and asymmetric frames, which is why we have refrained from using explicit "s/a" superscripts to denote the GPDs.The kinematical prefactor of the amplitudes can (again) be uniquely expressed through Lorentz scalars: In our previous study [85], we emphasized the frame-dependence of the conventional definitions of unpolarized quasi-GPDs that employ γ 0 .In contrast, we observe that the helicity quasi-GPDs defined through γ 3 γ 5 are the same in the symmetric and non-symmetric frames.This can be understood since the two frames are connected through a transverse boost which preserves the 3-component.By applying the same reasoning, it can be inferred that quasi-GPDs defined using γ 0 γ 5 will exhibit frame dependence.Furthermore, given the ability to reformulate the traditional definition involving γ 3 γ 5 in a Lorentz-invariant manner, it is clear that it emerges as an additional contender for a Lorentzinvariant definition.Consequently, this example explicitly demonstrates the lack of uniqueness in Lorentz-invariant definitions for quasi-GPDs.The distinction between the Lorentz-invariant definitions presented in Eqs. ( 13)-( 14) and Eqs. ( 17)-( 18) can be attributed to terms proportional to z 2 associated with the amplitudes A 4 and A 7 .
We repeat that the two sets of quasi-GPDs discussed above are not equivalent, as they differ in the contributing amplitudes and both explicit and implicit power corrections.Henceforth, when referring to power corrections, we specifically denote corrections that are proportional to z 2 .The additional amplitudes in Eqs. ( 17)-( 18) can be interpreted as contamination arising from explicit power corrections, which could potentially be suppressed by considering higher values of the momentum.One may therefore speculate that Eqs. ( 13)-( 14) converge faster compared to Eqs. ( 17)- (18).However, it is essential to acknowledge that the amplitudes themselves also contain implicit power corrections, so the above statement should be examined case by case.(The presence of additional amplitudes could potentially mitigate the implicit power corrections inherent in the amplitudes stated in Eqs. ( 13)-( 14).)Ultimately, the actual convergence of the different quasi-GPD definitions is determined by the underlying non-perturbative dynamics.Therefore, it is important to perform numerical comparisons to assess the convergence behavior of these definitions and gain insights into the relative magnitude of power corrections in each case.
We conclude this section by briefly discussing the symmetry properties of H (and E) in position space, as these properties play a crucial role in leveraging symmetries to improve statistical precision in lattice calculations.The Hermiticity constraint provides the symmetries of GPDs under the transformation P 3 → −P 3 for a fixed value of z 3 .Similarly, for a fixed P 3 and with ∆ → −∆, the Hermiticity constraint unveils the symmetries of GPDs under the transformation z 3 → −z 3 .Notably, we find that the real part of H satisfies H(−P 3 ) = + H(P 3 ) (and likewise for E).Furthermore, we observe H(−z 3 ) = + H(z 3 ) (and likewise for E).(The imaginary parts of the GPDs satisfy the same constraints as their real parts, with the exception of a negative sign.)Finally, we would like to reiterate that a comprehensive analysis of the symmetries at the level of amplitudes is provided in Appendix B.
III. LATTICE CALCULATION A. Methodology
In this section, we present a synopsis of the methodology for the lattice QCD calculation of proton matrix elements using the axial-vector operator.All expressions here are presented in Euclidean space, where we use lower indices in P and ∆ to avoid confusion in the expressions given previously in Minkowski space.The goal of this calculation is twofold: (a) compare the Lorentz invariant amplitudes extracted from different frames; (b) present results for the H GPD at multiple values of t.We note that our calculation is performed at zero skewness and, thus, E is inaccessible from the matrix elements.The two frames we employ are the symmetric and an asymmetric in which the final state does not contain the momentum transfer In the above equations, a factor of 2π L (L: spatial extent of the lattice) is implied in ⃗ ∆ and P 3 .Note that ⃗ ∆ is the same in both frames, however, differs due to the term containing the energies.In each kinematic frame, we parametrize the lattice matrix elements using the trace where F [γµγ5] is given in Eq. ( 10).We use four parity projectors; the unpolarized, Γ 0 , and the three polarized, Γ k , defined as K is a kinematic factor that has been obtained based on the normalization of the proton state, As we will demonstrate below, the combination of the four projectors and the four directions of the axial-vector operator can disentangle all eight A i for any kinematic setup.
Next, we focus on the ground-state contribution to the matrix elements that we will denote as Π s/a µ (Γ κ ) (µ, κ : 0, 1, 2, 3).We note that the operator γ j γ 5 (j ̸ = 3) has a finite mixing under renormalization for lattice regularizations with chiral symmetry breaking [47,90,94,95].Such mixing is not included in the renormalization analysis in this calculation, as it would require the matrix elements of the tensor operator.However, the effect is found to be small for the twisted mass formulation with a clover term [47,90].The general expressions for Eq. ( 21) in the symmetric frame for zero skewness are Π s 3 (Γ 0 ) = 0 (37) where K simplifies to 2m 2 /(E(E + m)), due to E i = E f ≡ E in the symmetric frame when ξ = 0.It is interesting to observe that A 7 appears only in Eq. (40).In general, we find fourteen nonzero equations, some of which are linearly dependent.For instance, Eqs. ( 26) and ( 27) have the same numerical value besides a multiplicative factor of ∆ 1 and ∆ 2 , respectively.Still, there are eight linearly independent matrix elements that allow one to disentangle all amplitudes A i .Another observation is that the amplitudes A 3 , A 4 , A 8 are decoupled from the other ones.This is an important aspect, as these amplitudes are expected to be zero at ξ = 0 due to theoretical arguments.In Sec.IV, we will comment more about how one can incorporate this information into the analysis.
The trace algebra of Eq. ( 21) in the asymmetric frame of Eq. ( 20) leads to more complicated kinematic coefficients mainly because E i ̸ = E f , as well as the lack of symmetry between p f and p i .At zero skewness, we obtain To summarize our findings, Eqs. ( 25) - (40) and Eqs. ( 41) -( 56) are sufficient to disentangle the A i in the symmetric and asymmetric frame, respectively.This task can be done analytically by inverting the equations, which, however, leads to very complicated general expressions; it is practically more convenient to implement a numerical inversion of the 8 × 8 system for each value of P and ⃗ ∆.Here, we give the expressions for A i using ⃗ ∆ = (∆, 0, 0) as an example.We use a superscript s and a in the matrix elements to differentiate between the two frames; A i are frame-independent and do not carry such an index.The expressions for the symmetric frame take the form and for the asymmetric frame at ⃗ ∆ = (∆, 0, 0), one obtains The use of the amplitudes A i is a pathway to extracting the quasi-GPDs using lattice data from any kinematic frame.Here, we present two approaches to relate the A i to the quasi-GPDs: (a) the standard γ 3 γ 5 operator (Eq.( 73)); (b) an alternative Lorentz-invariant definition (Eq.( 75)).Our focus is on zero skewness, which only gives access to the H GPD; the kinematic coefficient of E in Eq. ( 8) becomes zero due to the factor ∆ 3 .For the same reason, E does not appear in the parametrization of the matrix elements in the forward limit.In fact, to obtain E-GPD at t = 0, one must parametrize its t dependence, and, similarly, its estimate at zero skewness could be obtained by a fit using ξ ̸ = 0 values.Below, we give the relation between the quasi-GPD of H at zero skewness using the γ 3 γ 5 definition.We note that the standard definition of Eq. ( 73) is Lorentz invariant, and therefore, it is the same in both frames, as discussed in Sec.II B. At zero skewness, one obtains For simplicity, we only show two arguments for H 3 , that is, A i to indicate the frame used in the calculation and z to explicitly show that the relation for quasi-GPDs is given in coordinate space.To keep the expressions compact, we suppress the arguments of the amplitudes A i .It is useful to rewrite Eq. ( 73) in terms of matrix elements in the symmetric frame for the special case ⃗ ∆ = (∆, 0, 0), for which we find As expected, Eq. ( 74) is the usual expression extracted from the matrix elements of the γ 3 γ 5 operator previously used for the helicity GPDs [77].With the A i being frame-invariant, one can use either A s i or A a i in Eq. ( 73); calculating A a i is computationally less costly and, thus, more optimal for lattice QCD calculations.
An alternative approach to extract the light-cone GPDs is through a Lorentz-invariant definition of choice for the quasi-GPDs H and E, as given in Eqs. ( 17) - (18), where H( , by construction.The expression for H at zero skewness simplifies giving For completeness, we provide the expressions of H using matrix elements in each frame.As above, we use as an example the case ⃗ ∆ = (∆, 0, 0) to write H in terms of matrix elements, that is This alternative definition of H can be interpreted as the construction of a new operator that is a combination of γ µ γ 5 with µ = 0, 1, 2, 3, as given in the example of Eqs. ( 76) - (77).We note, however, that in the case of the helicity, the matrix elements γ k γ 5 with k = 0, 1, 2 (k ̸ = 3) have finite mixing in lattice regularization [90], which affects H.In Sec.IV, we will compare the two definitions of H 3 and H and discuss their merits.
B. Computational setup
The proton matrix elements entering Eq. ( 21) (F [γµγ5] ) use a non-local axial-vector operator containing spatiallyseparated quark fields in the ẑ direction.The Wilson line and the momentum boost are also along the ẑ direction.The matrix elements have momentum transfer between the initial and final state, ⃗ ∆ = ⃗ p f − ⃗ p i , and can be written as |N (p i )⟩ and |N (p f )⟩ are the initial (source) and final (sink) states of the proton, while the remaining variables are defined previously.We use momentum smearing [96] to improve the overlap with the proton ground state and suppress gauge noise; Ref. [97] demonstrated that the method is essential for non-local operators.It was also found that the statistical noise is z-dependent and reduces by a factor of 4-5 in the real part and 2-3 in the imaginary part of the quasi-GPDs calculated in a previous work [77].In addition, we use five steps of stout smearing [98] to the gauge links of the operator with parameter ρ = 0.15, to further suppress gauge noise, as demonstrated in Refs.[99,100].We note that the stout smearing changes both the matrix elements and the renormalization function, but the renormalized matrix elements should remain independent of the stout smearing.Indeed, in Ref. [101] it was examines the effect of the number of stout smearing steps (0, 5, 10, 15, 20) and shows that the renormalized matrix elements are stoutsmearing independent; the test was performed at ⃗ ∆ = 0 and a physical pion mass ensemble.The same conclusions were reached in the case of the gluon PDF [102] calculated using the same ensemble as this work.The matrix element is extracted from the ratio where C 2pt and C 3pt , are the two-and three-point correlation functions.τ is the current insertion time, and t s is the source-sink time separation; the source is taken at zero timeslice.As shown in Table II, we implement all kinematically equivalent momenta that lead to the same value of p 2 i , p 2 f .Thus, to increase statistical accuracy, we average C 2pt for all possible values.We extract the ground-state contribution to F [γµγ5] from R µ by taking a plateau fit with respect to τ in a region of convergence.Here, we indicate the ground state by Π µ (Γ κ ), and their decomposition is given in Eqs. ( 25) - (56).For simplicity, the dependence on z, p f , and p i is not shown explicitly in the matrix elements Π j (Γ κ ).
The calculation is performed on a gauge ensemble of N f = 2 + 1 + 1 twisted-mass fermions, including a clover term [103].The gluon part of the action is Iwasaki-improved.The volume of the ensemble is 32 3 × 64, and its lattice spacing, a, is 0.093 fm.The quark masses correspond to a pion mass of 260 MeV.The ensemble parameters are given in Table I.Using this ensemble, we obtain the matrix elements at a source-sink time separation of t s = 10a = 0.934 fm, a choice made to effectively manage statistical uncertainties in the matrix elements.The study of excited states via calculations of multiple time separations lies outside the scope of the current project.Details regarding the statistics of the calculation in both the symmetric and asymmetric frames are provided in Table II.In summary, for P 3 = 1.25 GeV we analyze three different values of −t in the symmetric frame.These are complemented by seven values of −t in the asymmetric frame, which significantly enhances computational efficiency.The majority of the values are within the range −t ∈ [0.17 − 1.50] GeV.To examine dependence on the momentum boost, we focus on −t s = 0.69 GeV 2 , where we use three values of P 3 , that is 0.83, 1.25, and 1.67 GeV.Notably, the asymmetric frame offers a computationally advantageous approach, as it enables the acquisition of multiple values of ⃗ ∆ within the same computational cost.To elaborate, while each value of t in the symmetric frame requires a separate calculation, the data production in the asymmetric frame is divided into two groups: one for (±∆ x , 0, 0) and its permutations and another for (±∆ x , ±∆ y , 0) and their permutations.The benefits of acquiring the data summarized in Table II are three-fold, as it allows: -Comparison of results on the three values of P 3 at fixed −t to assess P 3 dependence; -Comparison of the estimates for A i in the two frames using −t s = 0.69 GeV 2 and −t a = 0.65 GeV 2 .
-Extraction of the −t dependence of the GPDs and apply parametrizations.
In comparing A i between frames, it's worth noting that although t s and t a are not precisely identical, they are closely aligned, differing by only 5%, which allows for a meaningful and reliable comparison.
A. Comparison of kinematic frame
In this section, we focus on the setup with P 3 = ±1.25 GeV and ⃗ ∆ = { 2π L (±2, 0, 0), 2π L (0, ±2, 0)}, implemented in both the symmetric and asymmetric frames.This setup gives −t s = 0.69 GeV 2 in the symmetric frame, and −t a = 0.65 GeV 2 in the asymmetric frame.Our first goal is to compare the A i between the two frames, in a similar fashion as our previous work for the unpolarized GPDs [85].Once agreement is established between the A i from the two frames, all data from Table II will be analyzed to extract the −t dependence of GPDs.
Before presenting the matrix elements, we show the ratio of Eq. ( 79) for two representative cases, R 3 (Γ 3 ) and R 2 (Γ 2 ) and P 3 = 1.25 GeV and ⃗ ∆ = 2π L (2, 0, 0).For better clarity, we use the symmetric frame in which the data have less statistical fluctuations.We choose [3a − 7a] for the fit with respect to the insertion time We remind the reader that the data of Figs. 1 -2 are only one of the eight kinematically equivalent cases.These are averaged at the amplitude level according to the symmetry properties of the latter.Below we present selected matrix elements in the two frames.Although direct numerical comparisons of these values may not yield direct physical insights, they do prove invaluable in assessing the signal quality and the extent of symmetry breaking concerning the sign of P 3 and z.In Fig. 3, we show the real and imaginary parts of the bare matrix element Π 3 (Γ 3 ) for the eight combinations of aP 3 = ± 2π L 3 and a ⃗ ∆ = 2π L (±2, 0, 0), 2π L (0, ±2, 0).Similarly, Figs. 4 -6 show Π 0 (Γ 0 ), Π j (Γ j ; ∆ j = 0), and Π j (Γ j ; ∆ j ̸ = 0) (j = 1, 2), respectively.Note that Π j (Γ j ) leads to independent equations for ∆ j = 0 and ∆ j ̸ = 0 (see, e.g., Eq. ( 30)).All the plots presented in this section offer side-byside comparisons between the symmetric and asymmetric frame data.It is essential to underline that the numerical values of matrix elements in these two frames should not be directly compared.This is because the parametrization of a matrix element for a given operator and parity projector differs between frames in terms of the involved A i and their associated kinematic coefficients.For example, Π s 3 (Γ 3 ) contains information on A 2 , A 6 , and A 7 , while Π a 3 (Γ 3 ) decomposes into A 2 , A 3 , A 4 , A 6 , and A 7 , as can be seen in Eqs. ( 40), (56).Comparison of Π 3 (Γ 3 ) from Fig. 3 in the two frames reveals two features: (a) the matrix elements in the symmetric frame are less noisy than in the asymmetric frame; and (b) the variation of the data between the eight different classes of ±P 3 and ±z is smaller in the symmetric frame.The latter is due to the fact that symmetries in the matrix elements with respect to ±P 3 and ±z are only present in the symmetric frame.Nevertheless, the asymmetry in ±P 3 and ±z is found to be small for this kinematic setup in the asymmetric frame.Similar observations hold for Π 0 (Γ 0 ) and Π 1,2 (Γ 1,2 ), which are not shown here.In the light cone limit, the operators γ 0 γ 5 and γ 3 γ 5 are the components of γ + γ 5 , and, thus, lead to the standard helicity GPDs, H and E. This justifies the large magnitude observed in Figs. 3 -4.However, γ 0 γ 5 has finite mixing under renormalization, while γ 3 γ 5 does not [90].The mixing was previously investigated numerically for twisted mass fermions [90,104] and was found that the inclusion of a clover term in the fermion action suppresses the mixing significantly.To extract the amplitudes A i , we utilize the matrix elements obtained from all possible combinations of operators and projectors, as detailed in Section III A. For each A i , we combine the positive and negative values of P 3 , ⃗ ∆, and z according to their respective symmetry properties, as outlined in Eqs.(B3).Upon averaging the data for A i , we proceed to compare their estimated values in the two frames.This comparison serves as a numerical assessment of their agreement, essentially acting as a consistency check for the lattice estimates of A i .The degree of agreement observed between the two frames offers an assessment of systematic effects, such as those stemming from finite lattice spacing, that may affect the results.
, and A a 7 remain consistent, regardless of whether we include A 3 , A 4 , and A 8 in the analysis or not.This consistency provides additional validation for the results obtained.
In Figs. 7 -8 we present a comparison of the amplitudes using our data obtained with P 3 = ±1.25 GeV and ⃗ ∆ = { 2π L (±2, 0, 0), 2π L (0, ±2, 0)} for both frames (−t s = 0.69 GeV 2 and −t a = 0.65 GeV 2 ).This comparison takes into account all eight combinations of ±P 3 and ± ⃗ ∆.Among the amplitudes, we observe that A 5 has the largest magnitude both in the real and the imaginary parts, followed by A 2 .The remaining amplitudes are notably small or negligible, which can be attributed to the small signal for certain matrix elements.Encouragingly, we find a very good agreement between the two frames for each A i up to statistical fluctiations, as expected given their Lorentz-invariant definition.As previously mentioned, the small differences observed may be associated with the approximately 5% discrepancy between t s and t a , as well as potential systematic uncertainties that have yet to be determined.Regarding the amplitudes A 1 , A 6 , and A 7 , they cannot be directly accessed at z = 0 because their associated kinematic coefficients in Eqs. ( 25) -( 56) become zero.Nevertheless, one may perform extrapolations on their z dependence to estimate A i (z = 0).These findings collectively provide valuable insights into the behavior of the amplitudes under various conditions and kinematic setups.An insightful exploration of the amplitudes involves examining their dependence on momentum transfer.To illustrate this, we will focus on the substantial amplitudes, A 2 and A 5 , and analyze their t dependence.The results for these amplitudes are presented in Fig. 9 and Fig. 10, respectively.We use all the data obtained in this work that covers the range −t ∈ [0.17 − 2.77] GeV 2 .Importantly, since the amplitudes are frame invariant, a single function can describe the data from any frame.This feature allows for a direct comparison of the data, ensuring consistency in the analysis of the two frames.Our observations reveal that as −t increases, both the real and imaginary parts of the amplitudes decrease in magnitude.It is noteworthy that, based on our findings, these amplitudes continue to exhibit non-zero values even at −t beyond 2 GeV 2 .However, it is essential to exercise caution in this high-momentum transfer region.The calculations may suffer from systematic uncertainties and higher-twist contamination, rendering this region less reliable for precise conclusions.It is worth noting that the presence of the pion pole discussed in Refs.[12,13] is argued to extend to the GPD E in the isovector channel, where As discussed in Appendix C, the trace of this pole should be evident in A 5 .By comparing the t-dependence of A 5 with, example, A 2 around z = 0, we can infer that the lattice results for A 5 contains a pion pole behavior, and so should its Mellin moments, for example g P .It is worth highlighting that this z = 0 scenario aligns with our previously established anticipations for the pseudo-scalar form factor exhibiting a pole, as discussed in Ref. [106].The significance of this finding is underscored by the considerably steeper rise of A 5 compared to the other amplitudes.For instance, as observed from the plots in this section, in the t range of [−0.65, −0.17], GeV 2 , the rise factor is approximately 2.7 for A 5 , while for A 2 it is around 1.3.Similarly, in the t range of [−2.29, −0.17], GeV 2 , the rise factor is roughly 15 for A 5 , whereas it is about 2.7 for A 2 .These findings collectively support the notion that the detection of this pole does not necessitate a full calculation of E.
In the near future, we intend to thoroughly investigate this phenomenon in conjunction with the examination of the manifestation of the pole within the z-dependence of the amplitude.Such extension of our analysis aims to provide a deeper understanding of the pole's influence beyond the context of moments to a broader and more holistic understanding of its impact on the physics under consideration.
B. Quasi-GPDs in coordinate space
Our attention now shifts to the quasi-GPDs, which are renormalized in coordinate space using the RI ′ prescription developed and refined in Refs.[90,101,104].We refer the reader to these publications for more details, as well as the previous work of Ref. [85].In Sec.II B, we discussed that the definition of quasi-GPDs is not unique.In this context, we will consider the standard γ 3 γ 5 definition, denoted as H 3 , as well as an alternative definition that is constructed to be Lorentz invariant, termed H.As mentioned above, H 3 also exhibits frame independence, in contrast to the case of the unpolarized GPDs.This frame independence is linked to the fact that the indices of the axial operator align with the direction of the momentum boost, a point we discussed in detail in Section II B. The relations between the quasi-H GPD and the amplitudes are provided in Eq. ( 73) and Eq. ( 75), for H 3 and H, respectively.To enable the comparison of momentum boost dependence, we utilize the data in the symmetric frame at −t s = 0.69 GeV for all cases.Although there is a slight difference in the imaginary part for intermediate values of z at P 3 = 1.25 GeV, overall, the two definitions remain consistent.In terms of the P 3 dependence, we find that, as P 3 increases, the real part approaches zero at smaller values of z.On the other hand, the imaginary part is enhanced for higher P 3 , a feature also observed in PDFs.This trend suggests a strong link between the behavior of quasi-GPDs and PDFs in response to varying value for the momentum boost.To investigate whether the similarity between the two definitions of quasi-H GPD is specific to the particular −t = 0.69 GeV 2 , we extend the analysis to other values of t.We compare the two definitions for all the data in both the symmetric frame (Fig. 12) and the asymmetric frame (Figs. 13 -14).Remarkably, we consistently find agreement between the two definitions across both frames.This agreement is noteworthy because, theoretically, quasi-GPD definitions are not unique, and one might expect variations in the results.The level of agreement observed suggests a robustness in the analysis and interpretation of these GPDs, despite the lack of a unique definition.In Figs. 15 -16, we present the −t dependence of H 3 and H in coordinate space to provide a comprehensive overview.The shapes of these functions exhibit striking similarities, as previously discussed.However, there are notable distinctions worth highlighting.For the real part, at −t = 0.69GeV 2 , H 3 maintains an equidistant relationship from both H 3 (−t = 0.34GeV 2 ) and H 3 (−t = 0.81GeV 2 ).In contrast, H(−t = 0.69GeV 2 ) shifts closer to H 3 (−t = 0.34GeV 2 ).The difference between the pair H 3 (−t = 1.24GeV 2 ), H 3 (−t = 1.38GeV 2 ) and H 3 (−t = 1.52GeV 2 ) is more pronounced compared to the analogous comparison in the H definition.For the imaginary part, H 3 (−t = 0.34GeV 2 ) demonstrates compatibility with H 3 (−t = 0.69GeV 2 ).In the case of H, there is a discernible difference.
C. Light-cone GPDs
The reconstruction of the x dependence of the quasi-GPDs is not unique for a finite number of discrete data, as the standard Fourier transform suffers from the so-called inverse problem3 , which intensifies in the small-x region.In this work, we employ the Backus-Gilbert (BG) reconstruction method [108], which offers a solution to the inverse problem.This approach is based on a model-independent criterion to choose the light-cone reconstructed GPDs from the infinite set of possible solutions to the inverse problem.The criterion employed is that the variance of the solution with respect to the statistical variation of the input data should be minimal.Despite the model independence of the Backus-Gilbert method, its reliable applicability may be limited by the small number of lattice data sets that enter the reconstruction.An approach to assess the consistency and reliability of our reconstruction is to conduct a sensitivity test by varying the number of input data used in the Backus-Gilbert method.Specifically, we test for different values of z max , namely z max = 9a, 11a, 13a.Furthermore, the functions H 3 (z) and H(z) for z > z max are assumed to be zero.This assumption helps establish a condition for the reconstruction and is a practical choice for such cases where data beyond this limit are either unavailable or less reliable.Fig. 17 shows the x dependence of the quasi-GPD for the three values of z max .It is found that, for all z max values, there is compatibility for the H quasi-GPD up to x = 0.7, as well as consistency between z max = 11a and z max = 13a up to x = 1.With that, z max = 11a has been chosen for the quasi-GPD to proceed with the matching to the light-cone GPDs.For the latter, we use the one-loop equations of Ref. [71] at ξ → 0, which we include here for completeness.
x−1 ln y y−1 − 1 y < 0 , In the above equations, q denoted a general quasi-GPD, q is the corresponding light-cone GPD, and f 1 is the matching kernel.Since quasi-GPDs are defined in the RI scheme, the kernel contains the so-called RI counterterms in addition to f 1 .The expressions are lengthy and can be found in Ref. [109].The matching formalism is constructed with the quasi-GPDs being defined in RI scheme at a scale of 1.2 GeV, while the light-cone GPDs are in the MS scheme at a renormalization scale of 2 GeV.We have conducted a series of investigations for quasi-GPDs, which can also be performed for the light-cone cases.In this section, we provide a comparison between the two definitions for H, examining their P 3 dependence where data is available, as well as their behavior with respect to −t.Fig. 18 illustrates the momentum boost dependence for both definitions, H 3 and H, specifically for the symmetric-frame data at −t = 0.69 GeV 2 .We observe some residual dependence between the two, albeit it is important to note that the difference between P 3 = 1.25GeV and P 3 = 1.67GeV is expected to be well within unquantified systematic uncertainties.The behavior of the two definitions for H GPD is remarkably similar, with only minor distinctions between P 3 = 1.25GeV and P 3 = 1.67GeV.It is worth emphasizing that although the two definitions are different, they both possess Lorentz invariance.Consequently, each definition offers a unique function that is applicable in any frame.Turning to Fig. 19, we shift our focus to the −t dependence of H 3 and H at |P 3 | = 1.25 GeV, where we have a substantial amount of data.Numerical values and statistical uncertainties are found to be similar for both definitions.This result is somewhat expected, as the difference between the two definitions is proportionally tied to A 7 , which is found to be very small.The GPDs exhibit a decaying behavior as −t increases, which parallels the behavior of the form factors. Notably, for −t > 1.5 GeV 2 , we observe a negligible dependence on −t, where the GPDs become of similar magnitude.It is important to recognize that this observation is qualitative in nature, as at such values of −t and for P 3 = 1.25 GeV, the lattice results have increased higher-twist contamination.Nevertheless, we have included this data, as it was obtained at no additional computational cost due to the use of an asymmetric kinematic frame.To conclude this discussion, we provide the data of Fig. 19 in a three-dimensional plot to demonstrate both the −t and x dependence of H GPD. For completeness, we show both definitions we explored in this work.
V. SUMMARY AND FUTURE PROSPECTS
This work builds upon recent advancements that enable the extraction of the x dependence of GPDs from lattice QCD matrix elements calculated in any kinematic frame [85].The main motivation is to efficiently compute GPDs across a range of −t values with efficient use of computational resources, a task that proves challenging in the symmetric kinematic frame.Our approach hinges on the decomposition of matrix elements into Lorentz invariant amplitudes, which can then be related to the quasi-GPDs.In this work, we concentrate on the axial-vector case for the proton, providing a detailed framework to extract the helicity GPDs, H and E. To illustrate our methodology, we present a proof-of-concept calculation, where we obtain the matrix element in the standard symmetric frame, as well as an asymmetric frame, in which the momentum transfer is assigned to the initial state of the proton; the parameters are chosen to lead to a very similar value of −t.The calculation is performed at zero skewness, which has the limitation that the E cannot be obtained directly from the lattice data.Our analysis involves a comparison of lattice data for the Lorentz invariant amplitudes, A i , which confirms the theoretical expectations that the amplitudes are frame independent.Such a finding paves the way for a complete asymmetric frame calculation to obtain the light-cone GPD H at multiple values of −t.In our work, we employ two definitions for the quasi-GPDs, namely the standard definition of γ 3 γ 5 , as well as a Lorentz invariant definition that is based on the same functional form in terms of the A i as the light-cone GPDs.Our observations suggest that both definitions yield comparable numerical results.However, it is important to highlight that the constructed Lorentz invariant definition receives contributions from finite mixing of different operators under renormalization due to chiral symmetry breaking [90].
Our final results for the GPDs are presented in the MS scheme at a scale of 2 GeV and are summarized in Figs.19 -20 for various −t values covering the range [0.17, 2.77] GeV 2 .While we have achieved a robust signal, reducing statistical noise further proves to be a formidable challenge for off-forward matrix elements.Considering the fact that systematic uncertainties are still unquantified for GPDs, aiming for high statistical accuracy falls outside the scope of this work.In the future, we anticipate a deeper exploration of systematic uncertainties, including the effects of eliminating excited states, as well as the impact of volume and discretization effects.We also aim to investigate the dependence on the pion mass and other systematic factors tied to the quasi-distribution approach, such as finite momentum boost and limitations of the one-loop formalism.There is also the potential for parameterizing the −t dependence and exploring the impact-parameter space across a broad range of −t values.Another avenue is introducing nonzero skewness, which would facilitate the direct extraction of E from lattice data and allow for extrapolation to ξ = 0.In summary, this study underscores the significant potential for advancing lattice QCD calculations with regard to generalized parton distributions.These advances promise precision calculations that will contribute to developing a framework of global analysis of both current and forthcoming experimental data, in which incorporating lattice data is possible.
5 FIG. 7 .
FIG. 7. Comparison of bare values of A2 and A5 in the symmetric (filled symbols) and asymmetric (open symbols) frame.The real (imaginary) part of each quantity is shown in the left (right) column.The data correspond to |P3| = 1.25 GeV and −t = 0.69 GeV 2 (−t = 0.65 GeV 2 ) for the symmetric (asymmetric) frame.
FIG. 8 .
FIG. 8. Comparison of bare values of z A1, z A6, and z 2 A7 in the symmetric (filled symbols) and asymmetric (open symbols) frame.The notation is the same as Fig. 7. 0
TABLE I .
Parameters of the ensemble used in this work.
TABLE II .
Statistics for the symmetric and asymmetric frame matrix elements are shown.The momentum unit 2π/L is 0.417 GeV.NME, N confs , Nsrc and N total are the number of matrix elements, configurations, source positions per configuration and total statistics, respectively.
FIG.9.The amplitude A2 for all values of −t given in TableII.
FIG.10.The amplitudes A5 for all values of −t given in TableII.
15G.15.The quasi-GPD H3 for several values of the momentum transfer squared, −t in coordinate space.
16G.16.The quasi-GPD H for various values of the momentum transfer squared, −t in coordinate space. | 12,164.6 | 2023-10-19T00:00:00.000 | [
"Physics"
] |
Risk Stratification for ECMO Requirement in COVID-19 ICU Patients Using Quantitative Imaging Features in CT Scans on Admission
(1) Background: Extracorporeal membrane oxygenation (ECMO) therapy in intensive care units (ICUs) remains the last treatment option for Coronavirus disease 2019 (COVID-19) patients with severely affected lungs but is highly resource demanding. Early risk stratification for the need of ECMO therapy upon admission to the hospital using artificial intelligence (AI)-based computed tomography (CT) assessment and clinical scores is beneficial for patient assessment and resource management; (2) Methods: Retrospective single-center study with 95 confirmed COVID-19 patients admitted to the participating ICUs. Patients requiring ECMO therapy (n = 14) during ICU stay versus patients without ECMO treatment (n = 81) were evaluated for discriminative clinical prediction parameters and AI-based CT imaging features and their diagnostic potential to predict ECMO therapy. Reported patient data include clinical scores, AI-based CT findings and patient outcomes; (3) Results: Patients subsequently allocated to ECMO therapy had significantly higher sequential organ failure (SOFA) scores (p < 0.001) and significantly lower oxygenation indices on admission (p = 0.009) than patients with standard ICU therapy. The median time from hospital admission to ECMO placement was 1.4 days (IQR 0.2–4.0). The percentage of lung involvement on AI-based CT assessment on admission to the hospital was significantly higher in ECMO patients (p < 0.001). In binary logistic regression analyses for ECMO prediction including age, sex, body mass index (BMI), SOFA score on admission, lactate on admission and percentage of lung involvement on admission CTs, only SOFA score (OR 1.32, 95% CI 1.08–1.62) and lung involvement (OR 1.06, 95% CI 1.01–1.11) were significantly associated with subsequent ECMO allocation. Receiver operating characteristic (ROC) curves showed an area under the curve (AUC) of 0.83 (95% CI 0.73–0.94) for lung involvement on admission CT and 0.82 (95% CI 0.72–0.91) for SOFA scores on ICU admission. A combined parameter of SOFA on ICU admission and lung involvement on admission CT yielded an AUC of 0.91 (0.84–0.97) with a sensitivity of 0.93 and a specificity of 0.84 for ECMO prediction; (4) Conclusions: AI-based assessment of lung involvement on CT scans on admission to the hospital and SOFA scoring, especially if combined, can be used as risk stratification tools for subsequent requirement for ECMO therapy in patients with severe COVID-19 disease to improve resource management in ICU settings.
Introduction
Since its onset in December 2019, the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic has become a global challenge for healthcare systems, particularly due to limited resources of intensive care units (ICU). In 2020, Coronavirus disease 2019 disease climbed to the third leading cause of death in the US according to the Centers for Disease Control [1]. Around 15-30% of COVID-19 inpatients require intensive care treatment, 15-20% require intubation and a substantial subpopulation of around three quarters of ICU patients develop respiratory failure such as acute respiratory distress syndrome (ARDS) [2][3][4][5][6][7][8]. In severe hypoxemic respiratory failure, extracorporeal membrane oxygenation (ECMO) can be a valuable lifesaving bridging technique providing time for potential organ recovery or, in rare cases, lung transplant [9][10][11][12]. Veno-venous ECMO (VV-ECMO) is indicated in severe hypoxemic respiratory failure refractory to conventional respiratory support such as low pressure and low tidal volume mechanical ventilation with optimal positive end expiratory pressure (PEEP), neuromuscular blockade and prone positioning [13][14][15]. Patients exhibiting cardiac or circulatory failure might be assigned to veno-arterial ECMO (VA-ECMO) for additional circulatory support independent of the extent of respiratory failure.
In severe cases of COVID-19 with refractory hypoxemia the use of ECMO as a rescue therapy has been advocated [16][17][18]. Published ECMO mortality rates have ranged widely from around 40 to as high as 90% or above, whereas increasing evidence suggests that COVID-19 ECMO mortality might be similar to known ARDS ECMO mortality rates of around 40-60% and might not be significantly different to overall COVID-19 ICU mortality [2,8,12,[17][18][19][20][21][22][23]. Because ECMO therapy might reduce mortality and outcome is likely to improve when therapy is applied early in severe ARDS, early risk stratification and patient allocation is crucial [17,[24][25][26]. This might also be applicable for patients with severe COVID-19 pneumonia. In this study we evaluated the potential of clinical parameters on ICU admission as well as AI-based CT imaging features on hospital admission for risk stratification of ECMO therapy in critically ill COVID-19 patients.
Patient Data
Our retrospective single-center study was approved by the local institutional review board. All COVID-19 patients (n = 95) admitted from 03/2020 until 01/2021 and already discharged or deceased by end of January 2021 with positive SARS-CoV-2 PCR testing and computed tomography (CT) scans within 48 h of hospital admission to the two participating ICUs, which have been dedicated to exclusive COVID-19 care during the pandemic, were included in the study ( Figure 1). Patient data were collected retrospectively and extracted from our digital patient information system (QCare PDMS, Health Information Management GmbH, Bad Homburg, Germany), which is routinely used at the corresponding ICUs: e.g., age, gender, body mass index (BMI), length of stay on ICU, hospital discharge or death, hours of invasive and non-invasive ventilation, re-intubation, sequential organ failure (SOFA) score, respiratory data as oxygenation indices, lung compliances and PEEP values. Chest X-ray (CXR) and chest CTs were extracted from the digital radiologic information system (RIS) and picture archiving and communication system (PACS). test between 2nd of March 2020 and 26th of January 2021, who were discharged or deceased and received a computed tomography (CT) scan of the thorax on admission, were included. Extracorporeal membrane oxygenation, ECMO.
Image Acquisition
CT scans (n = 91) were performed using CT scanners of our emergency department (Siemens Somatom Force, Somatom AS+ and GE Optima 660), either as non-contrast high-resolution scan or with contrast-enhanced pulmonary embolism protocol with the patient in supine position. Image acquisition was modulated between 80 and 120 kVp with adaptive tube current (mAS). All images were reconstructed with slice thicknesses of 1.00 mm or 1.25 mm. Multiplanar reconstruction methods were performed on all images. CT scans for n = 4 patients were performed at external hospitals before transfer to our hospital for ICU therapy with comparable scanning parameters. The datasets were suitable for AI-assessment and included in the present study.
Artificial Intelligence Based Quantification of Lung Involvement
The CAD4COVID CT report tool (Thirona B.V., Nijmegen, The Netherlands) was used for the quantification of CT lung involvement under the supervision of two radiologists with 4 and 7 years of clinical experience, respectively. CAD4COVID provides segmentation of lung lobes and displays them through a colored heatmap. The affected lung volume is quantified as percentage of the total lung volume (0-100%) and a score is generated ranging between 0 and 25 which indicates the extent of COVID-19 related abnormalities on the CT scan (0-5 points per lobe, maximum score 25 overall, Figure 2). The performance of the CAD4COVID method in the detection of COVID-19 was rated comparable with that of human readers, as shown in an evaluation study [27]. CAD4COVID is a freely usable CE-certified tool (class II, CE 0344) and access can be requested via the Thirona website (URL Thirona website). It is made available free-of-charge to support healthcare facilities during the pandemic. Axial lung kernel CT scans can be uploaded in DICOM file format after anonymization.
Prediction Parameters for the Regression Analysis
The demographic characteristics age, sex and body mass index (BMI) have been shown to be significant risk factors for disease severity and were therefore included in our regression model [6,28]. As ECMO represents a rescue therapy for patients with severely disturbed blood oxygenation capabilities due to lung damage, the oxygenation index on admission was also selected as an important admission parameter for evaluation. Lactate on admission as a general parameter for shock and the SOFA score on admission as a multiparametric indicator of organ failure were included in the analyses. SOFA score rates six different organ systems on a scale of zero to four points (range 0 to 24 points). Additionally, the overall affected area as a percentage of the total lung volume of the CAD4COVID tool was used as imaging features for the prediction model.
Statistical Analysis
All statistical analyses were performed with SPSS software (version 26.0, IBM). Continuous variables are reported as median with interquartile ranges (IQR). Mann-Whitney-U for continuous variables and Chi-square test or Fisher's exact test for categorical variables were applied to test for differences between the standard ICU therapy and the ECMO therapy groups. Significance was defined as a two-sided p-value < 0.05. Binary logistic regression for the prediction of allocation to ECMO therapy was performed adjusting for multiple covariates. Odds ratios with 95% confidence intervals are shown. Receiver operating characteristic (ROC) analyses using exact binomial confidence intervals (CI) were used to compare the predictive performance of parameters and the area under the curve (AUC) was calculated. Ideal discriminative values were determined using maximization of the Youden index and sensitivity as well as specificity are reported.
Differences between the ECMO Group and ICU Standard Therapy Group
Fourteen of the 95 COVID-19 patients (14.7%) required ECMO therapy, 12 patients were allocated to VV-ECMO (86%) and 2 patients to VA-ECMO (14%). Patients treated with ECMO had a median age of 62 years (IQR 55-68) vs. 68 years (IQR 55-75) in the standard ICU therapy group, p = 0.164. Sex was equally distributed between the groups with 79.0% male in the ECMO group versus 71.4% male in the standard ICU group, p = 0.528. BMI was significantly higher in the ECMO group with a median of 31 (IQR 27-37) vs. 27 .0) in the standard ICU therapy group, no statistically significant differences were detected. In the ECMO group, SOFA score on admission, mean SOFA score during stay and maximum SOFA score during stay were significantly higher than in the standard ICU therapy group (12 (IQR 10-14) vs. 8 (IQR 4-11), p < 0.001, Figure 3A; 14.5 (IQR 12.5-18.8) vs. 7.5 (IQR 5.1-10.6), p < 0.001 and 18 (IQR 15-22) vs. 12 (IQR 8-15), p < 0.001, respectively). Further, the oxygenation index was significantly lower in the ECMO group on admission (110 (IQR 90-161) vs. 178 (IQR 121-232), p = 0.009). Imaging on hospital admission showed a significantly higher severity score (21)(22) vs. 14 (IQR 10-19), p < 0.001) and significantly higher lung volume involvement (66% (IQR 49-72) vs. 30% (IQR 17-53), p < 0.001, Figure 3B) in the AI based CT assessment. Patients in the ECMO therapy group exhibited a significantly longer time interval from admission to the time point of maximum SOFA score (13 days (IQR 2-15) vs. 2 days (IQR 1-8) in the standard ICU therapy group, p = 0.012). This might be explained by a longer disease progression reaching significantly higher SOFA scores during the course of the disease for patients in the ECMO therapy group. The increase of SOFA score per day until reaching the maximum SOFA score did not differ significantly between groups (p = 0.836). Time from admission to death did not differ significantly between groups for non-survivors (p = 0.932). Median time from admission to ECMO allocation and placement was 1.4 days (IQR 0.2-4.0). The in-hospital mortality differed significantly between groups with 85.7% non-survivors in the ECMO therapy group vs. 29.6% non-survivors in the standard ICU therapy groups, mirroring the significant clinical differences on admission and confirming the use of ECMO therapy as a last resort for patients with the most severe COVID-19 disease progression. In multivariate binary logistic regression for mortality, the ECMO group was not significantly associated with a higher mortality after adjustment for clinical and demographic parameters (Supplementary Table S1). All results of the comparison between groups with corresponding p-values can be obtained from Table 2.
Risk Stratification for ECMO Therapy
In multivariate binary logistic regression analysis for the prediction of allocation to ECMO therapy during treatment on ICU including the parameters age, sex, BMI, SOFA score, lactate, oxygenation index and AI based assessment of CT imaging on hospital admission, only SOFA score and CT imaging findings on hospital admission were significantly associated with ECMO allocation during the subsequent treatment in ICU (odds ratio for SOFA score 1.32 (95% CI 1.08-1.62), p = 0.008 and for lung involvement on CT 1.06 (95% CI 1.01-1.11), p = 0.011), results are shown in Table 3. Additionally, we performed a multivariate binary logistic regression analysis for the prediction of allocation to ECMO therapy excluding the two patients with VA-ECMO yielding similar results (Supplementary Table S2). We also evaluated the predictive potential of comorbidities for ECMO therapy allocation but did not find a significant association (Supplementary Table S3). Using receiver operating characteristic (ROC) curves, we found an area under the curve (AUC) of 0.83 (95% CI 0.73-0.94) for lung involvement in percent of total lung volume on CT imaging on admission and an AUC of 0.82 (95% CI 0.72-0.91) for SOFA score on ICU admission (Figure 4). A combined parameter (multiplication of SOFA score on admission with percentage of lung involvement on admission CT) yielded the best predictive results with an AUC of 0.91 (95% CI 0.84-0.97, Figure 4). For a combination score of 435 (best discriminative value) we calculated a Youden index of 0.77 with a sensitivity of 93% and a specificity of 84% (Table 4).
Discussion
Early identification of ECMO therapy requirements for COVID-19 patients with insufficient oxygenation capacity might reduce mortality and improve outcome after hospitalization, especially when applied timely during disease progression [17,[24][25][26]. Accessible and reliable risk stratification as early as possible is crucial for further ICU therapy planning and effective resource management to assure optimal treatment for severely affected COVID-19 patients. However, as ECMO is an immensely resourceintensive approach and requires scarce capacities in specialized maximum care centers at high expenses, adequate triage of patients is of utmost importance and must meet high requirements [29,30].
We analyzed clinical data and quantitative CT imaging features of 95 SARS-CoV-2 PCR-positive ICU patients at our hospital. AI-based quantification of lung involvement as percentage of the total lung volume in COVID-19 ICU patients on admission CT could predict ECMO requirement with an AUC of 0.83 (CI 0.73-0.94). Further, the SOFA score on admission as a parameter for organ failure showed a substantial predictive power yielding an AUC of 0.82 (95% CI 0.72-0.91). As ECMO is a bridging technique for patients with severe oxygenation impairment and severe COVID-19 often manifests with ARDS it is comprehensible that lung involvement is a decisive factor. When the SOFA score on admission, as a measure for multi organ function, was taken into account and severity of lung involvement was weighted with the SOFA score in a combined prediction model, predictive capability could even be improved. The combined parameter (multiplication of SOFA on ICU admission and lung involvement on admission CT) showed the best discriminative potential with an AUC of 0.91 (95% CI 0.84-0.97) and a sensitivity of 0.93 and a specificity of 0.84 was calculated with a Youden index of 0.77. While lung involvement alone showed a high specificity whereas SOFA scoring alone displayed a high sensitivity, specificity could substantially be increased by quantitative CT imaging features in the combined model while a high sensitivity was preserved. Other parameters included in the analyses that have previously been associated with increased risk for a severe course of the disease such as age, gender and body mass index did not show discriminative power for allocation to ECMO therapy [6,28].
The role of CT in diagnosis, triage and allocation purposes for COVID-19 patients was acknowledged early in the pandemic [31]. CT scans as a noninvasive and widely available tool have been shown to be of value in risk stratification in COVID-19 [32][33][34][35]. However, reading of CT scans is often done manually by radiologists which is time consuming, especially if segmentation and quantitative evaluation needs to be done, and is subjective with an inter-as well as intra-observer variability. Artificial intelligence (AI) is therefore increasingly important for supporting radiologic workups and has been shown to promisingly derive quantitative CT imaging features. In previous studies AI has been shown to accurately predict lung cancer [36,37] and outcomes of ARDS [38]. In COVID-19 pneumonia, deep learning was used to differentiate COVID-19 disease from communityacquired pneumonia [39] and CT quantification of pneumonia lesions in COVID-19 CT features was used to predict severe disease course based on changes in chest CT scans from day 0 to day 4 [40]. However, risk stratification for ECMO therapy based on chest CT scans on hospital admission in combination with clinical features has not yet been reported and seems promising, as AI-derived features from CTs at an early stage of COVID-19 can be used to predict progression to severe oxygenation impairment with the requirement of a potentially lifesaving bridging therapy. A recent multi-center study with a larger VV-ECMO COVID-19 patient cohort (exclusively investigating VV-ECMO patients) found that the SOFA score was not predictive for survival of patients when collected right before initiation of the VV-ECMO and thus at a very critical stage of the disease course with severe oxygenation impairment [41]. In our study, the SOFA score on admission was not predictive for in-hospital mortality in the overall group. However, our results indicate that the SOFA score on admission to ICU is valuable for the assessment of the COVID-19 patient's risk for ECMO therapy.
Limitations
First, this study is a retrospective analysis with a limited sample size due to a finite number of COVID-19 patients with severe disease that could be treated in our hospital on the participating ICUs. Furthermore, discharged patients were not followed up beyond their hospital stay. Nevertheless, our hospital represents one of the largest maximum care university hospitals in Europe and 95 patients with severe COVID-19 disease were included in this single center analysis. The study results need further investigation, ideally on larger external validation cohorts. Second, the overall in-hospital mortality and particularly for patients allocated to ECMO therapy was very high in this study. This might be explained by a cohort with unusually high disease severity (high clinical scores for disease severity on admission). In order to transfer results from our study to other ICU settings and hospitals, an external validation cohort including less severe COVID-19 ICU patients is desirable.
Conclusions
AI-based quantitative assessment of lung volume involvement on admission CT, particularly if combined with the sequential organ failure assessment score, is a noninvasive and easily accessible tool to support risk stratification of ECMO requirements in severely ill COVID-19 patients upon ICU admission and can assist in early patient assessment and resource management. Informed Consent Statement: Patient consent was waived as this was a retrospective data analysis with completely anonymized data sets.
Data Availability Statement:
The datasets analyzed during the current study are available from the corresponding author on reasonable request. The used CAD4COVID tool to analyze the CT data sets is a CE-certified tool which is made available freely by Thirona B.V., Nijmegen, Netherlands (URL https://thirona.eu/cad4covid/, accessed on 3 June 2021). | 4,389 | 2021-06-01T00:00:00.000 | [
"Medicine",
"Computer Science"
] |
Schema Playground: a tool for authoring, extending, and using metadata schemas to improve FAIRness of biomedical data
Background Biomedical researchers are strongly encouraged to make their research outputs more Findable, Accessible, Interoperable, and Reusable (FAIR). While many biomedical research outputs are more readily accessible through open data efforts, finding relevant outputs remains a significant challenge. Schema.org is a metadata vocabulary standardization project that enables web content creators to make their content more FAIR. Leveraging Schema.org could benefit biomedical research resource providers, but it can be challenging to apply Schema.org standards to biomedical research outputs. We created an online browser-based tool that empowers researchers and repository developers to utilize Schema.org or other biomedical schema projects. Results Our browser-based tool includes features which can help address many of the barriers towards Schema.org-compliance such as: The ability to easily browse for relevant Schema.org classes, the ability to extend and customize a class to be more suitable for biomedical research outputs, the ability to create data validation to ensure adherence of a research output to a customized class, and the ability to register a custom class to our schema registry enabling others to search and re-use it. We demonstrate the use of our tool with the creation of the Outbreak.info schema—a large multi-class schema for harmonizing various COVID-19 related resources. Conclusions We have created a browser-based tool to empower biomedical research resource providers to leverage Schema.org classes to make their research outputs more FAIR. Supplementary Information The online version contains supplementary material available at 10.1186/s12859-023-05258-4.
Background
Funding agencies, international consortia, institutional policies, and publisher requirements have helped promote the adoption of the FAIR (Findability, Accessibility, Interoperability, and Reusability) guiding principles [4,41] for biomedical research data sharing to varying degrees of success.While it is now standard to make datasets accessible and potentially reusable via deposition of the dataset in a repository, metadata *Correspondence<EMAIL_ADDRESS>issues (i.e.-lack of standardization in how datasets are described) continue to make it challenging for researchers to make datasets findable, interoperable, and reusable.To address these issues, domain experts and data stewards have been inspecting the gap between principle and practice [23]; extending [19], adapting [15], and adopting the principles [12]; creating their own metadata standards [6] and data schemas [12,16,29].However a large gap remains between the communities that develop standards and the adoption of these standards by data and resource providers due to issues in communication, education/training, incentives, and the availability of supportive tools [14,17].For example, the Dublin Core Metadata Initiative (DCMI) provides a metadata ontology (i.e.-a structured vocabulary for classifying and describing metadata): terms and data elements (Dublin Core Metadata Initiative [9], two generaluse schema classes (i.e.-sets of metadata vocabulary used to describe a conceptual entity): core and qualified, and a thorough guide for utilizing their ontology with their model-based framework for creating schemas: the Dublin Core Application Profile (DCAP) guide [8].The DCAP guide was intended to empower data providers to mix and match Dublin Core (and other) metadata terms/elements (properties) to create new application profiles (schemas) to suit their needs.While the core (data element) schema has been widely-adopted, the lack of authoring tools to help create more type/conceptspecific schemas and the lack of tools for transforming schemas into working formats for consumption and implementation has hampered the adoption and implementation of DCAP [1].Even after standardization communities successfully introduce standards, their adoption, modification, and implementation are frequently defined by widely used tools or repositories within a specific community [12].
Schema.org is a metadata vocabulary standardization project founded by the major search engine companies such as Google, Microsoft, Yahoo, and Yandex.It is an open source, collaborative initiative that develops metadata standards for improved searchability.While domain-neutral, Schema.orgwelcomes proposals and discussions of new properties and classes from anyone, including domain-specific ontology or schema development groups, via participation in their W3C group [38].Members of metadata ontology development communities (including the aforementioned DCMI, as well as LRMI, and other W3C groups) [3,39] have been involved with, have influenced, and have successfully integrated some of their vocabulary into Schema.org[2,32].Schema.org already includes some biomedically relevant classes (i.e.-conceptual entities) like Datasets and Medical Study, and applying Schema.orgclasses to biomedical research resources would improve interoperability, enabling researchers readily ingest existing resources and to leverage search engine-based solutions (like Google Dataset Search) to find resources of interest.Furthermore, the hierarchical nature of schemas from Schema.org allows for inheritance of vocabulary sets (sets of properties) from parent schemas.Although there have been some efforts to leverage Schema.org to improve findability of scientific research data [20,29,31] Bioschemas is an open and collaborative effort that has been actively promoting the use of Schema.org in the life sciences by serving as a hub for researchers to create new biomedically relevant classes with the goal of refining and proposing these classes to Schema.org[11], Profiti et al. [30], and by raising awareness about the usefulness of metadata schemas.The Bioschemas community has also identified the need for easy-to-use tools to help improve public accessibility and participation in the schema development process.
Here, we describe the Data Discovery Engine's (DDE) Schema Playground, a webbased tool that improves the ease of using any registered schema or Schema.orgclasses.Our tool allows users to easily find and visualize relevant classes from Schema.org,Bioschemas, BioLink [5], and others, extend them; create JSON schema validation rules [22]; and save/share the newly created classes for others to reuse.Our tool expresses schemas in JSON-LD format, improving interoperability of schemas which might normally otherwise be viewed as HTML tables.Our tool also includes a framework for building data registries and creating guides for data submission; however, the implementation and integration of these features on our site is restricted to partner organizations.We introduce the features of this tool, review its value to different types of users, demonstrate its application towards the creation of a new schema for COVID-19-related resources, and discuss its adoption by the Bioschemas metadata standardization community.
Implementation
The Data Discovery Engine's Schema Playground is a browser-based tool built with Vue.js [43], Python/Tornado [35], and the BioThings Software Development Toolkit [25].Schemas from Schema.org and other consortia/projects are stored and made searchable using MongoDB [27] and Elasticsearch [34].The code for the Schema Playground can be found at https:// github.com/ bioth ings/ disco very-app and is free to use under the Apache License 2.0.The schema generated by the DDE are exported as JSON-LD files [21], following RDF schema specifications [40] with embedded JSON Schema metadata validation rules [22].The COVID-19 Outbreak.inforesource schemas were developed by comparing metadata properties across multiple type-specific repositories to identify properties in common.For example, metadata from LitCovid/PubMed, BioRxiv/ MedRxiv, various journals like JAME, NEJM and others, and the metadata from publications found on Zenodo, Figshare and others were compared in order to identify a suitable schema for COVID-19-related publications.Similarly, protocols from protocols.ioand the BioSchemas LabProtocol class were compared to develop a schema for COVID-19-related protocols.Once the desired properties and structure for each class of COVID-19-related resource was identified, the schemas were created by extending existing Schema.orgclasses using the DDE Schema Playground.
Results
The DDE Schema Playground consists of two standard (and fully-accessible) components and two related, custom (limited-access) components (Fig. 1).The standard components improve the ease of use of schemas and classes, while the custom components help communities to reap the benefits of their use.The Schema Editor allows users to import community standard schemas like Schema.org and customize them for biomedical purposes.These extended schemas can then be shared in the Schema Registry, which allows users to view the schemas and reuse them.When used in conjunction with Data Portals built with BioThings SDK [25], The DDE Schema Playground can automatically generate data submission forms known as Data Guides.
To understand how the Schema Playground might help to bridge the gap between data standardization communities and data resource providers, we identified potential utility and value of each of the DDE Schema Playground components for different types of users in our partner communities (Fig. 2).
Any data portals and guides can be used by anyone with sufficient access rights, but the creation of a data portal or data guide requires partnerships with our team to actualize.For the outbreak portal, data submission via the guide is open to all and utilizes GitHub for authentication.For other portals, access may be restricted as required by the responsible partner organization.The data portal and data guides allow data providers and data consumers to collect, share, and use data.Since the data guide converts a custom schema into a web-based data submission form, it enables data consumers and data standardizers to visually inspect and understand the burden of structure.
The schema registry and editor allows data providers and/or standardization communities to find, customize, and share schemas.Sharing schemas via the registry will make it easier for data consumers to understand how to consume data from a data provider and to create data validation if one is not available from the data provider.For example, data-use restrictions usually require a data consumer to create an account with the data provider in order to access data.However, data consumers cannot easily determine whether the data locked behind the account-creation process will actually be useful prior to creating an account.Sharing the data schema via the DDE registry could address this issue by allowing data consumers to understand what's available without actually displaying any restricted-access data.Having a central location for schemas submitted by data providers will also make it easier for data standardization communities to evaluate the needs of the biomedical research community.To our knowledge, the DDE's schema registry is the only crowd-sourced registry for type/concept-specific schemas created specifically for the biological and biomedical research space.To further illustrate the value of the schema registry and editor, we compare and detail the features of the DDE Schema Playground with available tools for creating, applying, and consuming other major schemas such as Schema.organd Bioschemas.
Schema.org, Bioschemas and other data standardization efforts have built strong communities to generate consensus on data modeling for the creation of new schemas or the improvement of existing schemas.Hence, there are extensive processes in place (but few tools) for the creation of a new schema based on Schema.org or any other schemas.Because of its widespread adoption, there are third party tools available for utilizing and consuming markup from Schema.org.The Bioschemas community has developed a process for defining new classes and has a set of tools which cover both the creation of a new schema (google spreadsheet conversion), utilization of a schema (markup generation), and evaluation of use (markup validation, scraping), but these tools vary in usability based on the users programming experience.In contrast to Schema.org,Bioschemas also defines cardinality (allowable number of values per property) and marginality (optional vs required value) in its profile schemas as these are important to the life sciences research community.Although the DDE schema playground was developed independently from the Bioschemas community, our interests aligned and we sought to provide complimentary schema tools to facilitate biomedical schema development and adoption.To do this, we identified schema tools and features available directly from the Schema.organd Bioschemas communities.We expanded the list of tools by searching for "Schema.orgtools", "schema generation tools", "schema creation tools", "schema editing tools", "schema validation tools", "bioschemas tools" in Google and in bio.tools).Bio.tools yielded two relevant results (biovalidator and ObjTables), while Google yielded multiple tool reviews/lists which generally featured similar sets of tools.Most user-friendly tools were aimed towards the generation, extraction, or validation of schema-compatible markup rather than the development of schemas themselves (Additional file 2: Supplemental Table 1).The Bioschemas community has a few well-documented tools for schema development, but many of those tools were only available as source code and required basic programming experience.We focused our efforts on features for which userfriendly tools for schema creation and reuse, resulting in a web-based application that empowers individual data resource providers to utilize and customize existing schemas from Schema.org and other similar efforts.As seen in Table 1, these features include:
Searching and viewing schemas from Schema.org and other metadata standardization efforts
The DDE Schema Playground allows for the visualization of JSON-LD-formatted schemas hosted online either on GitHub or elsewhere (Additional file 1: Supplemental Figure 1A).This allows users who are familiar with Schema.org to review their compliant schema in a more human readable format.The DDE Schema Playground also has a searchable registry of classes from Schema.org,BioLink, BioThings, Bioschemas, and others.Users may browse and visualize the schemas for various classes from these sources to identify the classes of most interest to them (Additional file 1: Supplemental Figure 1B).If a community like Bioschemas or consortia like the National COVID Cohort Collaborative (N3C) [13] is interested in making a new schema available for searching and viewing, they can import and register their JSON-LD-formatted schema.The DDE Schema Playground also enables users to compare up to four schemas.For example, there are multiple Dataset schemas available in the registry, and users can compare them to see what properties are unique to each and what properties they share (Additional file 1: Supplemental Figure 1C).
Extending and customizing a pre-existing schema for a particular use
The ability to browse and inspect pre-existing schemas makes it easier for a user to customize or extend the schema to suit their own purpose.All the properties from the pre-existing schema will be inherited in the extended schema; however, the user may select properties for which validation is desirable.The user can also create new properties to be included in the extended schema.For example, the Dataset class from Schema.org serves as a potential foundation, but a schema focused on COVID-19-related datasets may need additional fields (e.g., infectiousAgent).To tailor the Dataset schema, we find and extend it from the registry (Additional file 1: Supplemental Figure 2A).After we create a name for our schema (the namespace) and the class, we can customize it.We can select to include any property that is available from the schema we are extending (Additional file 1: Supplemental Figure 2B), and we can create new properties (e.g., infectiousAgent) that are tailored to our needs (Additional file 1: Supplemental Figure 2C).This feature also serves as an easy way to maintain Bioschemas profiles as users can update a registered profile by extending from it, making the necessary changes, and pushing them back to Bioschemas.Outside the tool, there is only manual writing/editing of JSON-LD, YAML, TTL, SHACL, ShEx, or other file types and running command-line tools for customizing an existing schema in an interoperable format and making it human-friendly viewable online.
Creating validation for the schema for data quality enforcement
Marginality (whether a property is required or not) and cardinality (whether a property can have one or multiple values) are two aspects of schema properties that are not expressed well by Schema.orgbut are desirable to biomedical researchers (Additional file 1: Supplemental Figure 3A and 3C).In the DDE Schema Playground, this is handled via the creation of JSON Schema validation rules, and the DDE's Schema Validation Editor provides a simple drag and drop mechanism to create straightforward validations (Additional file 1: Supplemental Figure 3B).For slightly more complex validations, the user can edit the validation rule before dragging and dropping it into the property of interest.In our example Dataset schema, we may want to restrict the values for our new property (infectiousAgent) such that they map to and are standardized by an ontology.We edit the example JSON schema validation rules for an ontology to tailor it to the NCBI Taxon ontology (Additional file 1: Supplemental Figure 3D).Schema development working groups often leverage the work done by ontology groups to ensure that the values of a property are standardized.Once these JSON schema validation rules have been created, they can be used to test the validity of JSON-LD-formatted metadata using any of the many third party metadata validation tools and program libraries that are already available.Future features of the DDE will include a built-in metadata validation tool.
Exporting and saving a schema generated by the Schema Playground editor
The DDE Schema Playground allows you to export/download your newly created schema locally and it is also integrated with GitHub, allowing users to save to their GitHub repository (Additional file 1: Supplemental Figure 4A-C).The integration with GitHub allows the edits to the schema to be made by multiple parties and provides the schema owner the option of pulling changes to the schema.Additionally, the schema can be forked and edited/customized allowing for re-use of the schemas which in turn improves findability and reusability of resources which follow the schemas.
Registering a newly created schema in the DDE schema registry to facilitate its extension and re-use
Once saved in GitHub, users can review their schema with the schema viewer and add it to the registry to enable others to easily re-use it (Additional file 1: Supplemental Figure 1A).This provides a user-friendly interface for editing, customizing, and re-using schemas for those who prefer not to manually edit text and format in JSON-LD.
The DDE Schema Playground offers any user the ability to reuse and extend existing schemas.This tool is primarily to assist in the authoring of schemas for use in other applications.In addition, we have converted three Dataset schemas into "guides", which are web-based forms for annotating resources using schemas authored in the DDE Schema Playground.Annotations created using these guides are stored within a resource registry hosted within the DDE.There are currently three public guides based on the Dataset schemas for the Outbreak.infoweb application [28], the N3C initiative, and the CD2H consortium [7].While the creation of guides from schemas is not a fully-automated feature that is available to all users, most of the underlying components are reusable, additional guides can be constructed and hosted within the DDE through collaboration.The Bioschemas community has integrated the DDE schema playground as part of its schema creation and update process to improve participation by members who lack the programming expertise needed to participate via their previous pipeline.
Creating the COVID-19 Outbreak schema using the Schema Playground
Schema.org classes are often simultaneously too broad (lacking properties needed) and too narrow (including too many irrelevant properties) for a specific research purpose.For this reason, it becomes necessary to adapt schemas to suit needs of a biomedical research project.Outbreak.info is a project from the Su, Wu, and Andersen labs at Scripps Research to unify COVID-19 and SARS-CoV-2 epidemiology and genomic data, published research, and other resources [10,37].The standardization of published research and other resources was accomplished by creating a single, multiclass schema to harmonize the metadata: The COVID-19 Outbreak schema.This schema can be found in the DDE registry at https:// disco very.bioth ings.io/ view/ outbr eak/ and was built via the DDE Schema Playground with some manual editing (for merging all the classes into a single schema).There are six principal classes in the Outbreak schema (Analysis, Dataset, Clini-calTrial, ComputationalTool, Protocol, Publication) and many subclasses to support the principal classes.As seen in Table 2, the classes in the Outbreak schema were extended from related Schema.orgclasses (whenever available) and were created based on metadata comparisons from a variety of related sources.By extending from existing schemas, we reuse existing metadata properties when appropriate, and create new properties only when necessary.
For example, the level of detail provided by Protocol Registration System (PRS) schema used by the National Clinical Trial (NCT) registry is more granular than Schema.org'sMedicalStudy class, but broad enough that it encompasses properties from both child classes of MedicalStudy (MedicalTrial and MedicalObservationalStudy).The child classes of MedicalStudy only differ in the property name for the study design (tri-alDesign vs studyDesign), and this property is not delineated in PRS.Further, the PRS includes many properties not currently available in any of these Schema.orgclasses.Adopting the PRS directly was also problematic as we planned to ingest records from other registries like the World Health Organization's Clinical Trial registry (WHOCT), and the PRS was also more granular than WHOCT.For this reason, the Outbreak.infoClinicalTrial class was created by using the DDE to extend from Schema.org, leveraging the PRS-WHO crosswalk [42], and creating properties that could help with issues previously identified [26].In addition to adapting Schema.orgclasses to normalize record data from multiple sources within a class, Outbreak.infoneeded to normalize common metadata properties between different classes.The hierarchical nature of Schema.orgclasses simplified this process, as many derivative classes inherit properties from the Thing class.For example, the Protocol class in the Outbreak schema was extended from the HowTo class in Schema.organd was based on properties identified from available metadata in protocols.ioand the LabProtocol profile from Bioschemas.Since both the Schema.orgclasses, MedicalStudy and HowTo, are derivatives of Thing, the Outbreak schema naturally has properties in common across multiple classes and can normalize the metadata across these classes allowing for cleaner query design and improved search functionality.This schema is currently used to harmonize and improve FAIRness of metadata from over 300,000 resource entries in the Outbreak.inforesearch library at https:// outbr eak.info/ resou rces.
Adoption of the Schema Playground into the Bioschemas schema development and maintenance pipeline
Previously, the pipeline for updating a Bioschemas specification involved the use of a google spreadsheet for attaining community consensus, a command-line tool for converting the CSV from the spreadsheet to yaml, cloning the Bioschemas website repository and copying/editing HTML and YAML files, running Jekyll to test the changes, editing example files in the Bioschemas specifications repository, and creating pull requests for the Bioschemas website repository once everything had performed as tested.The level of expertise needed in order to update a specification has been discussed in multiple Bioschemas community calls as a potential barrier to participation.After initial tests during and after Biohackathon 2021, the Bioschemas community has decided to adopt the DDE into its schema development and maintenance pipeline.Manuals for using the DDE to create or update Bioschemas specifications have been developed, and automated scripts using GitHub actions have been developed to more tightly integrate the tool into the pipeline.As seen in Fig. 3, the process for updating Fig. 3 The Bioschemas profile update process before (left) and after (right) the inclusion of the DDE a Bioschemas profile requires less technical expertise after the integration of the DDE.While the process prior to and after the DDE still requires the ability to edit a YAML/ JSON file (brown) and the ability to use GitHub (black), the DDE-based process does not require the user to have the technical knowledge needed to run tools via the command line (green), or to use Jekyll (blue).
Discussion
In an effort to make scientific resources more FAIR, communities in the biological sciences (Bioschemas), earth sciences (ESIP's Science on Schema.orgcluster), and more are working diligently to align and influence Schema.org to suit the needs of the scientific research community [11,33].These communities serve as an important bridge between domain-specific ontology development groups and the domain-neutral Schema.orgby introducing Schema.org to the scientific research resource providers, identifying existing ontologies to leverage, and creating tailored schemas more suitable for the research community.For example, ontology development groups, like PPEO/MIAPPE [24] and EDAM [18], have been consulted or have participated in the development of the Sample and ComputationalWorkflow schemas by the corresponding Bioschemas working groups.A term from PPEO/MIAPPE was included as a property in the Sample schema, while JSON schema validation rules enforce the use of terms from EDAM as values for certain properties in the ComputationalWorkflow schema.
Although communities like Bioschemas have helped to create more relevant classes or improve existing classes, it is difficult to push these suggestions to Schema.orgwithout compelling use cases or widespread adoption of these tailored classes.For example, the Bioschemas community first developed the Gene class (with input from gene resource providers, Gene Ontology proponents and gene resource consumers) in 2018.However, it was not included as a pending class in Schema.orguntil 2021 due to a lack of widespread adoption.The Bioschemas community spent considerable time and effort on education and training in order to increase the adoption of Bioschemas classes; however, participation in the development of the classes was hampered by the technological expertise needed in order to update a Bioschemas class.The availability of user-friendly tools can make it easier to find and use Schema.organd other community-driven schema classes, and empower data providers and researchers to engage in schema authoring and sharing.
Most tools for utilizing existing Schema.orgclasses focus on the utilization of an existing schema (such as markup generation) and lack the ability to customize the schema in a Schema.org-compliantway.Tools that do allow customizing/creating a schema (e.g., Bioschemas GoWeb) often require some degree of programming.The DDE Schema Playground is a browser-based tool that enables members of the research community to easily adapt schemas to suit their need and to enable community re-use of their schemas through the DDE schema registry.This encourages and empowers researchers to structure their data in a Schema.org-compliantfashion earlier on in the scientific research process rather than as an afterthought.The schema authoring by the research community, for the research community will encourage the creation and adoption of new classes and properties, which may have previously been neglected due to the absence of representation (e.g., volunteers with subject matter expertise) in data standardization communities.In this fashion, the DDE Schema Playground allows for researchers to express and share their data structuring needs with the data standardization community without diverting attention away from their primary research efforts.Data standardization communities also benefit because their volunteer time can be concentrated on classes already in use by researchers (but could benefit from some standardization), and diverted away from classes which lack interest/support from the research community at large.
There are many ways to express schemas (i.e., SHACL, ShEx), but the DDE only supports the expression of schemas in JSON-LD/JSON Schema format due to the widespread adoption of the JSON-LD format by resource providers and library/tool developers.In addition to this restriction, there are important limitations as to what can or cannot be registered into the DDE schema registry.Schema registration in the DDE is currently limited class-based schema (i.e., classes described by sets of properties) rooted in Schema.org,while many well-used, domain-neutral metadata ontologies (such as DCMI) and schema have properties that are not necessarily tied to any class.These classless metadata vocabularies intentionally do not group the properties into classes in order to encourage the mix-and-match of properties.Although classless metadata vocabularies cannot be registered in their entirety as classless properties in the DDE at this time, the DDE can flexibly ingest properties from any metadata vocabulary (whether or not they are class-based) as long as it is properly formatted (i.e., conforms to JSON-LD/JSON Schema formatting).This means that users can build their schema by extending from Schema.org,Bioschemas, or any registered schema, and incorporate properties from OWL, DCMI, or any other accessible vocabulary as needed.For example, all Bioschemas profile classes also include the conformsTo property from DCMI, and the NIAID Dataset schema [36] also leverages properties from OWL.In theory, classes inheriting just a single property from a Schema.orgclass, but otherwise built entirely from other metadata ontologies can be viewed and registered in the DDE.
We tested the use of the DDE Schema Playground to create customized Schema.orgcompliantclasses that could be used to normalize metadata between multiple types (datasets, clinical trials, publications, etc.) of COVID-19-related resources and applied these schemas towards a searchable resource site (https:// outbr eak.info).The Outbreak resource schema is available in the DDE schema registry which is also includes schemas from Schema.org,Bioschemas, BioLink, the National COVID Cohort Collaborative (N3C), the National Institute of Allergy and Infectious Diseases (NIAID) and more.We hope others will join us in making their open data more interpretable, interoperable, and reusable by adding their schemas to the schema registry.
Conclusion
We have created a user-friendly browser-based tool which facilitates the application of Schema.orgtowards biomedical research outputs.We demonstrate its use with the creation of the Outbreak.infoschema, its adoption into the Bioschemas schema development pipeline, and we encourage others to register and reuse Schema.org-compliantschemas.We welcome user feedback which has and continues to help identify desirable new features and tools (i.e., metadata validation tools) which will be added in the near future.
and many generic repositories (like Figshare and Zenodo) are compliant, Schema.orgremains largely underutilized by the biomedical research community.
Fig. 1 Fig. 2
Fig. 1 Components of the DDE Schema Playground and how they work together
Table 1
Comparison of Schema.org,Bioschemas, and DDE Schema Playground ✓ available, separate tools available, *process in place, **feature exists, but not generally available
Table 2
Classes in the Outbreak schema and how they were created and used | 6,528.2 | 2021-09-03T00:00:00.000 | [
"Computer Science",
"Medicine"
] |
Orbital dynamics in 2D topological and Chern insulators
Within a relativistic quantum formalism we examine the role of second-order corrections caused by the application of magnetic fields in two-dimensional topological and Chern insulators. This allows to reach analytical expressions for the change of the Berry curvature, orbital magnetic moment, density of states and energy determining their canonical grand potential and transport properties. The present corrections, which become relevant at relatively low fields due to the small gap characterizing these systems, unveil a zero-field diamagnetic susceptibility which can be tuned by the external magnetic field.
One of the most special features of the topological insulators (TIs) is the presence of protected helical states on their boundaries which are responsible for their singular transport properties [1,2]. Just as their robustness against non-magnetic impurities or external fields, the quantization of their transport properties also depend directly on the topology by means of a topological invariant which can be defined according to the intrinsic symmetries of the system and its dimensionality [3][4][5][6]. In time-reversal symmetry broken systems as well as in two-dimensional topological insulators this invariant is the first Chern number C obtained throughout the integral of the Berry curvature over the momentum space [7][8][9]. Besides the well-known relation between the electric conductivity and polarization with the topological invariant [10][11][12], great and original advances have been done to address the thermoelectric response of systems with non-zero Berry curvature in presence of electric and magnetic fields [13][14][15][16][17][18]. These studies take the semiclassical equations of motion for the Bloch electrons or a non-relativistic quantum formalism to derive magnetization and electric and thermal currents for a wide variety of compounds. These are the bases used to study planar Hall and chiral anomaly effects in topological insulators and Weyl semimetals through Boltzmann transport equation with in-plane magnetic fields [19,20].
Recently, the original studies have been extended by addressing second-order corrections through the Lagrangian formalism [21,22]. However, determining these quantities in a purely quantum way for the special case of topological insulators and Chern insulators, which present a non-trivial Berry curvature, involves some difficulties. First, we have to deal with a relativistic system described through a Dirac Hamiltonian [9,23], where spin and angular momentum are no longer good quantum numbers of the system and the velocity differs from the momentum as in their usual non-relativistic form v = p/m. Secondly, the evolution of eigenstates needs to be considered adiabatically; i.e., keeping the final and initial states of the system the same along the perturbation to preserve Berry phase effects. This leads us to treat with gauge dependent and divergent corrections to the system eigenstates that are identified and removed to get the usual equations of motion for non-zero Berry curvature systems but now in the proper relativistic context of these materials at low energies.
With this approach, we give analytical expressions to show how the introduction of a perpendicular magnetic field in 2DTIs and Chern insulators produces a modulation of the Berry curvature, which can affect its shape dramatically, but keeping the Chern number C of the system invariant. This effect is independent of the magnitude and time dependence of the magnetic field B at least until adiabaticity is lost or other effects such as the Zeeman splitting need to be considered. Behind these results, we can find the additional contributions to the density of states, orbital magnetic moment and energy corresponding to second-order corrections in perturbation theory. These terms must be taken into account at relatively low external magnetic fields due to the small topological gap characterizing these systems. In particular, we show that for the energy only those terms coming from the modified orbital magnetic moment, which are associated with the correction to the Berry potential, are necessary, while the other obtained with the semiclassical Lagrangian formalism in a relativistic particlehole symmetric system vanish [22]. Additionally, we observe a modified density of states that is strongly sensitive to the sign of the magnetic field and whose dispersion differs substantially from its first-order expansion [13]. These results can be directly introduced to determine explicitly the thermodynamic grand potential and hence the transport magnitudes in such systems, or in the Dirac oscillator Hamiltonian, as an argument to demonstrate how certain type of chiral photons or phonons can couple to the topological electrons preserving their topology and time-reversal symmetryT necessary for the presence of Kramer's pairs [24][25][26][27].
The quantum-materials version of the Dirac equation substitutes the light velocity c of the particle by the Fermi velocity of the electrons, as well as in some cases it incorporates a momentum dependence in the mass associated arXiv:2104.05126v1 [cond-mat.mes-hall] 11 Apr 2021 with the k-dependent energy dispersion [28], where γ µ are the gamma matrices, µ = 1, 2, 3, 4 and ∂ µ is the 4-gradient. In two-dimensional systems, where the term proportional to p z disappears, the Dirac Hamiltonian can be decoupled into two time-reversal symmetryrelated copies of a two-level Dirac Hamiltonian which is appropriate to introduce us to the non-trivial topological formalism [9,29].
Here v F is the Fermi velocity, is the reduced Planck constant, k ± = k x ± ik y and k = k 2 x + k 2 y . The term M (k) = M − Bk 2 , representing the gap (2M ) in the center of the Brillouin zone and its parabolic dependence, breaks the time-reversal symmetry of the system allowing a suitable characterization of the topology by means of the topological invariant Chern number C derived from the integral of the Berry curvature; i.e., C = 1/(2π) Ω n (k)dk being Ω n = −2Im ∂ kx n ∂ ky n ẑ the Berry curvature of the eigenstate n. As it is known, to get a non-zero Chern number C = ±1, M and B must have the same relative signs (M B > 0), implying that the incorporation of a spin-orbit coupling gets crucial to produce the crossing between the bands that precede the non-trivial topological regime [9,10]. The introduction of a magnetic field B = (0, 0, B) in the z-direction breaks the translational symmetry in x and y directions, which is evident by choosing an axial gauge A = (−By/2, Bx/2, 0) to enter the perturbation in the Hamiltonian through the Peierls substitution p → p + eA, being −e the electron charge. In such situation, the correction to the eigenstates by a perturbation, which corrects the particle momentum, has the following form up to first order [28] |n → |n − i being i the imaginary number, j = x, y denoting the spatial coordinates and |n and |m the eigenstates of the system. Let's label |+ and |− the eigenstates with en- . The presence of a field B implies the existence of a Lorentz force in the system which for the x and y directions is the velocity operator in the j direction, we have taken ξ + − ξ − = 2ξ provided that H is particle-hole symmetric and where the system eigenstates can be found to be being φ = arctan(k y /k x ). For simplicity, we proceed by setting the Hamiltonian parameter B as zero. As it seems logical, it is worthy to note that the corrections in Eq. (4) are proportional to the product of the magnetic field with the z-component of orbital magnetic moment m z = −e/2(xv y −ŷv x ) of the Bloch electrons [16,30,31].
However, in order to get a proper definition of the angular momentum and orbital magnetic moment on the band n, the previous expression needs to be corrected by where v n = n| v n |n = −1 ∂ k ξ n is the average velocity of the electrons in band n. This is equivalent to the addition of the center-of-mass position r c and its velocity in the Lagrangian formalism [21,22]. In this way, we can define properly the orbital magnetic moment [13,14,16,31], which results to be m n z = −1 eξ n Ω n for a twodimensional system as Eq. (2), and the first-order corrections to the energy ξ n 1 = −m · B. Nevertheless, the difficulties arise in Eq. (4) when one computes the matrix elements where it appears a divergence at zero particle momentum after gauge dependent terms have been removed. This behaviour is also present when computing velocity corrections and hence this contribution must be unphysical given that the force exerted by a magnetic field on a particle at rest is zero. We can solve this problem by decoupling the different contributions produced by the perturbation through the other definition of the velocity operator −1 ∂ k H. In this way, we can identify the ill-defined terms and properly obtain the corrections for the electron's velocity in topological systems. Rewriting Eq. (4) by using that m| ∂ kj H |∂ k l n = it can be shown that the third term is purely gauge dependent by rotations e iφ of the eigenstates, i.e. for |n = e −iφ |n and |m = e −iφ |m it changes its sign, and thus we can set one in which this term goes to zero. On the other hand, the first and second terms give a contribution equal to − eBΩ the Berry curvature of the conduction band of Hamiltonian (2) and leading their sum to Eq. (9) after rearranging terms.
Working with free divergent terms, i.e. the first, which must be considered twice due to the redefinition of the orbital magnetic moment, we can now easily compute velocity corrections in both directions. In fact, it is straightforward to see that corrections due to transverse components disappear and only longitudinal terms remain. Thus, we obtain the following corrections to the velocity which apply to both conduction and valence band by substituting their associated energy and curvature, where v n j = n|v j |n the average velocity in the band n for the component j and O(B 2 ) = −1/(4 ) ∂ kj ξ n (eBΩ/ ) 2 2 v 2 F k 2 /M 2 second-order corrections. In a simple way, we are observing the coupling effects between the magnetic field and the Berry curvature, which can be viewed like a magnetic field in the k-space on each band of Hamiltonian (2). Thus, introducing a perpendicular B in these systems enhances or decreases the field felt by their electrons depending on the relative sign between B and Ω. For instance, the conduction band of Hamiltonian (2) for M < 0 has a positive Berry curvature in the z direction and therefore an opposite magnetic field will decrease the velocity of their electrons and the Berry curvature even doing it zero or changing its sign. Given that the Lorentz force is radial this process causes an accommodation of the charge without involving any net current, as it can be checked by computing the integral of the previous expression. This is intrinsically related to the renormalization process affecting the phase-space volume and density of states for non-zero Berry curvature systems as we are going to show [13,14,21,32].
Complementing these effects, we can also consider contributions associated with a slow time dependence for B which incorporates a transverse term that can be easily transformed through Faraday's law into the wellknown anomalous velocity using that E x = 1 2 ∂B ∂t y and E y = − 1 2 ∂B ∂t x. The obtained expression up to first-order v n j → v n j 1 + eB · Ω + e (E × Ω n ) j represents the velocity of the electrons in the band n of a Chern insulator Eq. (2) or in one of the two branches of a two-dimensional topological insulator in a slowly variant time-dependent magnetic field. In contrast to the first contribution, the second term is associated with the electromotive force E generated by the variation of B which couples to the Berry curvature to produce a transverse and non-zero electric current. Setting aside this latter case, we wondered, as we postulated before if one of the crucial magnitudes for the topology and the transport, the Berry curvature, has experimented changes under this procedure. For the calculation it is convenient to employ an axial gauge A = (−By/2, Bx/2, 0) from which, as we showed, we are able to write the correction to the eigenstates in an easy to handle form Once we formulated the correction of the eigenstates the calculation of the Berry curvature corrections for the conduction band can be achieved by applying −2Im ∂ kx + ∂ ky + or ∂ kx A y − ∂ ky A x in Eq. (13), being A i = i +|∂ ki + the Berry potential and |+ the modified eigenstate. In fact, it is straightforward to show that the obtained corrections to the Berry potential are the same as the theoretically presented in ref. [21]. After some algebra, it can be proved that Berry curvature turns out in the following form demonstrating how a perpendicular magnetic field B modulates the Berry curvature and the field seen by the electrons in these topological systems. Besides the familiar first term in Eq. (14) we have obtained a second contribution in the corrections which affects the Berry curvature at k out of k = 0. This term is important at intermediate values whereas it falls to zero when k → ∞ and k = 0, although it can be shown to be tuned and even to disappear if we consider some energy dependence in the field B.
Since the Berry curvature has been modified, the next step is to compute the first Chern number C given its relation to the transport and hence with different physical observables. With this purpose, we can consider a uniform magnetic field of the form B ∝ m 2 e v 2 F /( e) just like in ref. [27], where the translation of the Berry curvature into a real field b was made using the magnetic flux quantization of helical orbits in terms of the Chern. As it has been analyzed, this field is closely related to the critical field B c needed to create electron-hole Schwinger pairs in the vacuum. However, this consideration is not necessary and one can also proceed equally by extracting B from the integral and computing it numerically ( Fig. 1(a)). Choosing the first option, the term 2eB ·Ω/ can be written as −M 3 /ξ 3 given that M = m e v 2 F and hence (15) where dk = 2πkdk. By using that Ω ± = ±∂/∂k 2 (M/ξ) it is straightforward to see that the sum of second and third terms in the integral cancel As consequence, the Chern number of the band does not change even though the Berry curvature does it. This occurs independently of the magnitude and time dependence of B until higher-order effects need to be considered or adiabaticity is lost and it is consistent with the preservation of quantized conductivities in the quantum Hall regime. These calculations can also be derived for non-zero but small B values (v 2 F >> 2BM/ 2 ). In this case, after neglecting terms in the energy derivative ∂ kj ξ in Eq. (10), the curvature corrections turn out into a more tedious expression but for which the Chern number C is constant and well-defined by an integer value, i.e. ±1 if M B > 0 and 0 if M B < 0 ( Fig. 1(b)). Notice that here Ω + = − 2 v 2 F (M + Bk 2 )/(2ξ 3 ). In both cases, there is a value (B ≈ −2.5T for the values of M and v F taken) for which the Berry curvature falls to 0 at the Γ point. This value is not other than the one delimited by the equation e v 2 F /( e) in ref. [27] with a difference of a factor 1/2 which comes from the redefinition of the orbital magnetic moment. This opens the possibility to enter in a regime where electron-hole pair creation might be experimentally accessible for certain k values. In contrast, we find that the case with eBΩ/ = −1 making zero the density of states D which arises when considering constant the Berry curvature [13], actually does not take place for k = 0. For these values of B, second-order corrections need to be taken into account and the density of states writes as D = 1 + eBΩ * / with Ω * the modified Berry curvature displayed in Eq. (14) or (16) [21,22]. This function has a minimum at k = 0 (Fig. 2) which can be tuned by B becoming zero for sufficiently high magnetic fields.
Furthermore, we are also in position to write secondorder corrections to the energy given that the matrix element −| ∆H |+ = −B −| m z |+ has been computed before. Then, we directly obtain that where −m · B is the well-known first-order response and the third term comes from second-order effects. This formula seems to enter in conflict with the one obtained from a semi-classical Lagrangian theory [22], in which the energy up to second-order for a relativistic particle-hole symmetric system as Eq. (2) is where g ij = Re ∂ i n|∂ j n − ∂ i n|n n|∂ j n is the quantum metric in the k-space, α kl = ∂ kl ξ 0 / 2 the inverse of the effective mass tensor, v 0 = −1 ∂ k ξ and A * j = − eBΩ v F k M i n|∂ j m is the j component of the modified Berry potential. By computing g ij and α kl for the positive energy eigenstate it is worthy to show that actually, the third and fourth terms cancel and only the one coming from the corrections to the Berry potential holds, recovering the energy dispersion presented in Eq. (18). In this way, we can reach the grand potential F determining the transport properties of the TIs in presence of perpendicular magnetic fields which incorporates the modified density of states and energy obtained with the changes of the Berry curvature and orbital magnetic moment. From here, we can compute the different transport magnitudes and coefficients such as, for instance, the system orbital magnetization M and susceptibility χ. Thus, for µ = 0 and zero temperature, it is immediate to obtain the dependency of M with the external magnetic field B (21) and the orbital magnetic susceptibility χ = −(∂ 2 F/∂B 2 ) with no more ingredients as their band gap 2M and Fermi velocity. Remarkably, we find a diamagnetic zero field susceptibility χ = −e 2 v 2 F /(6π|M |), which is identical to that obtained in ref. [22] (χ/χ 0 = −9π 2 t/(6π|M |) with t the first-neighbor hopping parameter), plus additional B-dependent terms which are not negligible for systems with small M . Notice that for zero gap systems (M = 0) these corrections are not well-defined since the Berry curvature vanishes. One outstanding application behind this relativistic formalism is its implementation to study thermoelectric features of TIs. In this case, it might not be desirable to introduce magnetic fields given that they break the time-reversal symmetry necessary for the preservation of Kramer's pairs, which are responsible for their high efficient thermoelectric response [33,34]. Notice that the Hamiltonian of a 2DTI is formed by two timereversal copies of Hamiltonian (2), and introducing the same field on both non-interacting systems implies the breakdown of temporal invariance. However, there exists an equivalent form to introduce these interactions in a 4x4 Dirac Hamiltonian without breaking time-reversal symmetry. That way is the Dirac oscillator Hamiltonian H = M (k)β + α · (p − imωrβ) [24,26], which in essence incorporates a magnetic field B = 2mω/e with opposite signs on each one of the two time-reversal symmetry-related Hamiltonians given by Eq. (2) and its time-reversal counterpart H =T H(k)T −1 , beingT the time-reversal symmetry operator [9]. The Dirac oscillator is a powerful tool to examine relativistic interactions between electrons and chiral photons or thermal excitations in TIs [25][26][27]. Besides the possibility to study higher-order effects, we have shown that these processes are compatible with the preservation of the topology and time-reversal symmetry, implying for the transport that at low fields the electric σ = e 2 /h (C − C ) and electronic thermal conductivities κ e = πk 2 B /(6 ) (C − C ) can remain quantized, being C and C the Chern number of H and H respectively [35]. Maintaining and combining these values with a good Seebeck coefficient and a low lattice thermal conductivity is determinant to obtain higher efficient thermoelectric devices [33,34,36].
In summary, we provide a relativistic quantum derivation for two-dimensional topological systems with non-zero Berry curvature in presence of a perpendicular magnetic field. We have found that the change in the velocity of the electrons due to the coupling of the magnetic field and the Berry curvature involves new corrections in their energy and magnetic moment which is associated with their relativistic nature. This is accompanied by a modulation of the Berry curvature that keeps the Chern number of the system invariant opening the door to study higher-order non-trivial magnetic and thermoelectric effects in Chern and topological insulators. | 4,996.6 | 2021-04-11T00:00:00.000 | [
"Physics"
] |
Design Study for a Quasisynchronous CDMA Sensor Data Collection System: An LEO Satellite Uplink Access Technique Based on GPS
With the development of the LEO satellite communication technology, highly dependable wireless communication and sensor data collection using LEO satellites have been getting much attention for emergency, marine research, and forest fire disaster in the remote region. The satellite system is expected to have the following features: rapid production, low cost, and fast construction of the satellite network. In this paper, a QS-CDMA uplink access technique in the LEO satellite is presented and discussed, which is focused on the local clocks using GPS 1PPS timing signals and the Doppler compensation for terminal uplink. The spreading code with length of 1023, which is used for the uplink preamble, selects the shift-m-sequence that can greatly reduce the MAI and increase the number of simultaneous access users. A novel analysis method for the accuracy of clock synchronization and a novel method for the estimation of Doppler shift and propagation delay are presented. These methods are used to guide the specific hardware implementation of the QS-CDMA LEO satellite sensor data collection system. Through simulations and experiments, it results in that this system structure can drastically reduce the complexity in implementing the acquisition in the satellite and increase the adaptability of the satellite system in different environments.
Introduction
When great disaster occurs, such as earthquake, many terrestrial infrastructures are seriously damaged.We had to take several days to get disaster situation and confirm safety of victims.So we expect that a satellite system provides a minimum reliable connection.The satellite system should have some disaster response features such as safety confirmation and position report.In marine research, oceanographic buoy can transmit information from the submerged nodes, which consist of sensors, to the remote ground station.When forest fire disaster happened in the remote region, the fire sensor transmits alert to the satellite and the satellite forwards the information to the nearest monitor station which maybe a hundred kilometers away.Meanwhile, many different kinds of sensors can collect the information of the forest such as temperature, humidity, and trespass.The satellite system should have some data collection features such as data store and forward.Nowadays the further development of satellite communication has been assisting a very high competition for the discovery of advanced technologies, which have demanded service to support more users and low complexity for satellite payload.In order to collect information of the disaster region in time, the modern trend in Low Earth Orbit (LEO) satellite communications system has to provide reliable short message communication to a large number of user terminals and sensors.An access technique for band-limited quasisynchronous CDMA (BLQS-CDMA) has been proposed in [1], and the network reference clock and frequency are transmitted embedded in the CDMA signal structure using a dedicated code, which is called master code.In [1], the preferentially phased Gold sequences are optimal for BLQS-CDMA with maximum timing jitter of ±0.5 ⋅ , where is the code duration.The possibility of keeping the timing error below 0.3 chips in the worst dynamic case for a chip rate of about 1 Mchip/s has been demonstrated.However, the network control station is hard to construct for marine research in the middle of ocean.Meanwhile, with the increasing of user requirements for data rate and the number of simultaneous access users, the Gold sequences cannot satisfy these requirements, because the higher date rate is, the more stringently the requirements for timing jitter are.The more simultaneous access users are, the worse the performance of BER is, a situation caused by the cross-correlation of the Gold sequence.The satellite wide-band CDMA consists of synchronous downlink and quasisynchronous uplink [2].The system also requires the Base Station to synchronize system clock.A slotted quasisynchronous CDMA access system has been proposed in [3], and the prime application of the system is short message services.The slotted QS-CDMA system requires the control earth station to provide accurate slot synchronization reference.In [1][2][3], previous research had not provided analysis method for the accuracy of clock synchronization and just made a request for system synchronization.Previous research had not provided estimation and analysis method for Doppler shift and propagation delay either.
The modern trend in digital communications is to synchronize with the local time, whose synchronous errors arise from different allowed uncertainties in communication systems.Global Positioning System (GPS) receivers are used by conveying the reference time to the locked-clock loop via the one-pulse-per-second (1PPS) output.It was noticed that the average time error produced by the receivers varied over a range of about 150 nanoseconds (ns) in 2002 [4].The current production as published showed that jumps are at the 10 ns level [5].An optimal synchronization of local clocks by GPS one-pulse-per-second (1PPS) timing signals is specified in [6], which use predictive FIR filter.The application of Kalman filter for clock synchronization is proposed in [7].Nowadays the clock synchronization technique based on GPS has reached a high degree of accuracy.
Generally, in severe Doppler environment, such as the LEO satellite communication, the pseudorandom (PN) code acquisition for the direct-sequence spread spectrum (DSSS) communication is hard to accomplish.The existence of carrier and code Doppler results in a prolonged acquisition process, and it also increased hardware complexity due to the need for a two-dimensional (chip delay and frequency) search structure of code and carrier synchronization.The Doppler characterization for LEO satellites is analyzed in [8].The direct-sequence spread spectrum code acquisition in the presence of Doppler shift was investigated in [9].In [10], Doppler compensation loop structure was proposed.In [9,10], some algorithms have been used to compensate for the Doppler shift by satellites.Due to low-power consumption, which is characteristic of LEO satellites, the acquisition and synchronization structure should meet the requirements of decreasing hardware complexity.At the same time, the satellites need to serve as many users as possible, but the complexity of hardware implementation will limit the number of users.
In this paper, we propose a novel quasisynchronous CDMA (QS-CDMA) transmission scheme based on GPS to increase system capacity, decrease hardware complexity of satellites, provide reliable short message service, and collect data from sensors.The starting point is to analyze the feasibility of implementing local clocks using GPS 1PPS for LEO satellites and terminals.The results will be used to specify the accuracy of clock synchronization.Due to the extremely high Doppler that is an important characteristic of LEO satellites, the acquisition of satellites is significantly simplified by using a continuous wave downlink pilot for uplink carrier Doppler estimation and compensation.The results are shown with the acquisition time performance of satellites that is considerably improved, the number of users is significantly increased and the anti-interception ability is improved.The following sections of this paper are organized as follows: Section 2 describes the overall system architecture and requirements, Section 3 depicts a novel analysis method for accuracy of the clock synchronization technique based on GPS, a novel method of carrier Doppler compensation, propagation delay estimation, and a receiver scheme of satellite, Section 4 introduces the simulation and experiment results, and Section 5 introduces the implementation results and gives a brief conclusion. 1.The main differences among QS-CDMA proposed in this paper, BLQS-CDMA in [1], and slotted QS-CDMA in [3] are shown in Table 2.
System Structure and Requirements
From Table 2, we can know that, the synchronization reference provided by the control station is complex in the middle of ocean.Therefore, synchronization reference provided by GPS receiver is wide applicability.
In Figure 1, the system of interest includes an LEO satellite, a large number of user terminals, sensors, and the GPS system.The LEO satellite broadcasts a continuous pilot carrier for downlink acquisition, tracking, uplink Doppler estimation, and compensation.A high-precision single GPS receiver is required by the LEO satellite.User terminal consists of a GPS receiver chip that offers 1PPS output, a local oven-controlled crystal oscillator (OCXO), or temperature compensated crystal oscillator (TCXO) which is used to form the local time scale with a high-resolution divider, baseband processing module, and so on.
System Synchronization Reference.
We expect to reduce the complexity and the expense of the QS-CDMA system and increase the adaptability of the system.With the technology development, GPS receiver chip is cheaper and consumes less power.In this paper, GPS receiver should provide accurate synchronization reference.Nowadays the clock synchronization technique based on GPS has reached a high degree of accuracy.So 1PPS signal can meet the requirements.The local clock of the LEO satellite and all user terminals should be aligned with 1PPS as reference.The analysis of the system time synchronization error will be discussed in Section 3.
Doppler Shift, Propagation Delay Compensation, and
Access Procedure.For QS-CDMA access, some main parameters are defined in Table 3.The flow diagram with the proposed access technique is shown in Figure 2. In Figure 2 (g) QS-CDMA access: At the beginning of next satellite 1PPS, the satellite receives all the uplink signals which achieve QS-CDMA access.
In Figure 3, Δ consists of the time error of the 1PPS produced by GPS receivers of satellite and terminal .Firstly through downlink continuous pilot carrier, 1PPS of the terminal, and down , the terminal should easily compute downlink propagation delay down .Secondly, it utilizes the pilot to measure the downlink carrier Doppler shift and code Doppler shift at this point.Thirdly, the uplink carrier Doppler shift will be estimated through downlink Doppler shift and the frequency ratio between downlink carrier frequency and uplink carrier frequency.Then up and uplink carrier Doppler shift will be used to compensate uplink propagation delay and Doppler shift.Finally, the terminals transmit signals at up before next 1PPS, and at the beginning of 1PPS, and the satellite will receive all the uplink signals which achieve QS-CDMA access.The QS-CDMA access process of sensors is similar to user terminals.The user terminals and sensors can use the same communication module.
Spreading Code for QS-CDMA.
Through QS-CDMA access, multiple-access interference (MAI) will be obviously decreased.Selecting the appropriate spreading codes is also important.We proposed that the uplink preamble of the system selects shift-m-sequence whose code length is 1023.The m-sequences possess the following three properties: the balance property, the run property, and the correlation property [11].If a complete sequence is compared bit-by-bit with any shift of the same sequence, the number of agreements minus the number of disagreements is always −1; that is, there is one more disagreement position than the number of agreement positions.Exploitation of the correlation property of PN sequences makes it possible to design direct sequence spread-spectrum (DSSS) systems.We compare the cross-correlation performance of different m-sequences, whose primitive polynomials are shown in Table 4.We also compare the cross-correlation performance of different Gold sequences whose code length is 1023.We assume that the code phase difference of shift-m-sequence, m-sequences, and Gold sequences is an integer.Normalized cross-correlation is shown in Figure 4.
From Figure 4(a), we can see that the normalized crosscorrelation of shift-m-sequences, whose primitive polynomials are 1033, is 9.8 × 10 −4 .From Figure 4(b), we can see that the average normalized cross-correlation of the m-sequences, whose primitive polynomials are shown in Table 3, is about 0.04.From Figure 4(c), we can see that the average normalized cross-correlation of the Gold sequences, which is a total of ten sequences, is about 0.3.That is the value of m-sequences about 10 times.The crosscorrelation performance of shift-m-sequence is much better than the Gold sequence.Thus the number of simultaneous access users that use shift-m-sequence is much more than the number of simultaneous access users that use Gold sequence.
Due to the correlation property of m-sequence, the crosscorrelation performance of shift-m-sequence is superior.Because any shift-m-sequence is shifted by the same msequence, it cannot be acquired in A-CDMA system.However, shift-m-sequence can be used in QS-CDMA system.Every user selects a shift-m-sequence that is different from initial code phase and the code phase interval between one user and the other is greater than or equal to 1 chip.Therefore, through QS-CDMA access with shift-m-sequence, MAI will be obviously decreased.
Theoretically, the QS-CDMA system uses a group of msequences whose code length is 1023 and can only provide service to 60 users at one time.The reason is that there are only 60 primitive polynomials for m-sequences with length of 1023.The QS-CDMA system uses a group of shift-msequences whose code length is 1023 and can provide service to 1023 users at one time.However, if the code offset of shiftm-sequence is within ±1 code epoch, in order to avoid the self-interference of shift-m-sequences, the number of users is only 341.It means that the smaller code offset is, the more users will be got.Thus, Section 3 will depict a novel method for accuracy of the clock synchronization technique and a novel method of Doppler compensation.
System Requirements.
In order to reduce the LEO satellite implementation complexity and the multiple-access interference (MAI), the system requires limiting the carrier Doppler shift to be within ±0. 5 Rb, where Rb is the bit rate of data, The requirements for the code offset in different code rate are shown in Table 5.
Pilot frame header PN code indication Contents
From Table 5, it is shown that the higher code rate is, the more stringently the requirement for code offset is.
Implementation Architecture and Performance Analysis
In this section, the key features of the QS-CDMA access technique will be studied in depth.Through the 1PPS, all users that use random spread spectrum codes employ slotted ALOHA (S-ALOHA) random access protocol.The pilot broadcasts the codes which collided with each other, and then the users repeat to transmit with spread spectrum random codes at next 1PPS or next slot.
Downlink Pilot and Uplink Preamble Frame Structure.
Downlink pilot structure consists of pilot frame header, PN code indication, and contents.The pilot frame header is aligned with 1PPS of satellite and used for all user acquisition.The PN code indication denotes the codes which collided with each other (see Figure 5).Uplink structure consists of preamble, frame header, and contents.The preamble is also aligned with 1PPS of terminal and is used for satellite acquisition.The frame header indicates the beginning of the contents.
All user terminals select a shift-m-sequence from a group of sequences, whose code length is 1023, for the uplink preamble of the system.Because of QS-CDMA access technique, the code phase of preamble should be predefined, so the acquisition of satellite will be easy to capture the signals from terminal, and the time of preamble should be shortened.
The short preamble which is spread by shift-m-sequence will increase ability to anti-intercept.Meanwhile, the shorter the preamble is, the more system capacity we will obtain.
Analysis of Clock Synchronization Time Error Based on GPS.
In this paper, we assume that the average time error of the 1PPS produced by GPS receivers of satellite varied over a range of about 10 ns and 100 ns by terminal receivers.Nowadays, these errors are common errors and the ranges can be easy to be achieved [5].The local clock synchronization block diagram is shown in Figure 6.
In Figure 6, we can see that the lead-lag comparator compares the 1PPS from GPS receiver and the local 1PPS.Through finite impulse response (FIR), the time error drives the direct digital synthesizer (DDS) to generate frequency control word.Finally, the local 1PPS generator provides the local 1PPS at a 40 MHz work clock.
Some main analysis parameters are defined in Table 6.
For propagation delay compensation, in Figure 3, the delay down is expressed as follows: where Δ consists of the time error of the 1PPS produced by GPS receivers of satellite and terminal, as well as the synchronization errors of local 1PPS generators.The speed of electromagnetic radiation varies, depending on temperature, pressure, and relative humidity, as it passes through the troposphere.Then the tropospheric time-delay results, also known as tropospheric errors.Due to tropospheric errors being independent of carrier frequency, the errors can be counteracted between downlink and uplink.The ionospheric uplink time-delay The velocity of electromagnetic wave in vacuum The time that the pilot travels for the varied distance between satellite and terminal when terminal estimates the propagation delay and waits to transmit The measurement accuracy of the down is decided by the tracking loop bandwidth (Hz) of phase lock loops (PLL), carrier to noise power expressed as a ratio (Hz), and period of the PN code (seconds).The standard deviation (1-sigma) for down is computed as follows [12]: where is the code duration, is the tracking loop bandwidth, and / 0 is carrier to noise power expressed as a ratio (Hz).Normally, ( down
𝑘
)/ < 0.05 [12], so the code rate is 5 Mchip/s, and then the measurement accuracy of the down will be less than 10 ns.The measurement accuracy of the terminals is similar to the satellite.
The ionospheric time-delay is computed as follows [12]: where down is the downlink carrier frequency of the signal, is the elevation angle at the ionospheric pierce point, is the velocity of electromagnetic wave in vacuum, and TEC is the total electron content.The GPS navigation message will provide ion down .To achieve QS-CDMA access, the terminals estimate the uplink propagation delay through down and transmit signals before next 1PPS in Figure 3.The estimation of the uplink propagation delay is computed as follows: where In the above equations, (Δ)/ is the time that the pilot travels for the varied distance between satellite and terminal when terminal estimates the propagation delay and waits to transmit.
Substituting (1) and ( 5) into (4), up is given by where − is the delay time difference between transmitter and receiver of terminal, which should be measured and be easy to eliminate in advance, − is the delay time difference between transmitter and receiver of satellite, and it is also easy to eliminate in advance, and ion up − ion down is the ionospheric time-delay difference between uplink and downlink.
In above equation, the parameters are decided for the accuracy of up .Hence, we analyze the precision of the parameters.
Time Error Δ𝑡 𝑘 .
The local clock synchronization is similar to PLL.One metric that is normally used to determine if loss of lock has occurred in a PLL is the total phase jitter, which is defined as [12] where 0 represents the standard deviation (1-sigma) thermal noise in degrees, V represents the 1-sigma vibrationinduced oscillator jitter in degrees, represents Allan variance-induced oscillator jitter in degrees, and represents dynamic stress error in the PLL tracking loop.
For the local clock synchronization, oscillator jitter is the prime jitter.The phase jitter V caused by the receiver clock depends on the quality of the clock.A close-form expression for phase jitter due to clock error in a third-order PLL can be given by [13] where is one-sided PLL loop bandwidth.ℎ −4 , ℎ −3 , and ℎ −2 are clock's coefficients, which can be determined experimentally in [13].Because their effect on phase jitter is minimal, ℎ −1 and ℎ 0 are neglected.The coefficients are shown in Table 7.
The phase jitter values as a function of computed using this model are shown in Figure 7.
The loop order is sensitive to the same order of dynamics, and the loop bandwidth must be wide enough to accommodate these higher-order dynamics.The first order is sensitive to velocity stress, second order to acceleration stress, and third order to jerk stress.For the local clock synchronization, the oscillator jitter is the prime jitter.The thermal noise and dynamic stress error have less effect on the time jitter of the local clock synchronization, in Figure 7, and increasing the one sided PLL loop bandwidth reduces the phase jitter; then the oscillator jitter can be neglected.So Δ is decided by the The FPGA implementation based on the local clock synchronization block in Figure 6 operated at a 40 MHz clock speed.TCXO was as a master clock and then the results of experiment are that Δ varied between 75 ns and 125 ns in a short time.
The Delay Time Difference between Transmitter and Receiver of Terminal
The delay time difference is the parameters of device design and can generally be controlled below 50 ns.
The Delay Time Difference between Transmitter and Receiver of Satellite 𝜏 𝑠
− .The delay time difference can generally be controlled below 30 ns.
The Ionospheric Time-Delay Difference between Uplink and Downlink 𝜏 𝑖𝑜𝑛
− .At the carrier center frequency, ion down is approximately equal to 30 ns and computed by (3).At the same time, ion up is decided by the uplink carrier frequency.In general, the ionospheric time-delay of the maximum Thus, the ionospheric time-delay difference is less than 15 ns.
The Time Light Travels for the Varied Distance between
Satellite and Terminal (Δ)/.The value is the time that electromagnetic wave travels for the varied distance between satellite and terminal when terminal estimates the propagation delay and waits to transmit.The accuracy of varied distance delay estimation can be achieved within 100 ns, so (Δ)/ can be precise to compensate.The analysis will be specifically discussed in Section 3.3.
In short, the estimation error of the uplink propagation delay is computed as follows: √ 10 2 + 100 2 + 10 2 + 30 2 + 50 2 + 15 2 + 100 2 = 154 ns.(11) The prime estimation error is the average time error of the 1PPS produced by terminal receivers, and the current production showed that jumps are much less than 100 ns [4].Thus, the novel system structure based on GPS 1PPS is shown to code Doppler shift which is less than 1 chip at 5 Mchip/s.
Doppler Shift and Propagation Delay Compensation.
In this paper, we assume that orbit altitude is 1000 km and maximum elevation angle is 90 degrees, so the visibility time is approximately 9 minutes.Some parameters are defined in Table 8.
Carrier Doppler Shift and Propagation Delay.
When the elevation angle is 90 degrees, we define that is 0 seconds.The carrier Doppler shift is computed as follows [8]: where Δ is the angular distance measured along the ground trace, () and ( 0 ) are different measured points on the surface of earth along the ground trace, is the velocity of electromagnetic wave in vacuum, is carrier frequency, is earth radius, and is the distance between geocenter and satellite and is equal to the sum of earth radius and circular orbit altitude. max is a maximum elevation angle and () is the angular velocity of the satellite in the ECF frame.We assume that the orbit is a circular orbit, the maximum elevation angle is 90 degrees, and a simplified expression for Doppler shift can be given by where is the velocity of the satellite for a circular orbit.
Then cos() is the radial velocity. is the velocity of electromagnetic wave in vacuum. is the acceleration of gravity. is the angle between the direction of incoming signal and the direction of the velocity ; is equal to the sum of earth radius and circular orbit altitude.The distance, carrier Doppler shift, and Doppler shift rate as a function of computed using this model are shown in Figure 8.
International Journal of Distributed Sensor Networks
In Figure 8(a), we can see the relationship between propagation delay and time.In Figure 8(b), we can see the relationship between propagation time-delay and time.In Figure 8(c), we can see the relationship between carrier Doppler shift and time.In Figure 8(d), we can see the relationship between carrier Doppler shift rate and time.We assume that satellite begins to be in vision when is −450 s.At this point, the value for the distance , the time-delay, and the Doppler shift are all the maximum, and the Doppler shift rate is the minimum.At the same time, the (Δ)/ will be achieved in 10 microseconds (s) level, and the chip error will be more than 50 chips.When is 0 s, the (Δ)/ will be achieved in 100 ns level, and the chip error will be less than one chip.
The Analysis and Estimation Method to Carrier Doppler
Shift and (Δ)/.We suggest using the following method to estimate carrier Doppler shift and (Δ)/.
Through the estimation of downlink carrier and chip frequency offered by receiver's tracking loop, the uplink carrier and code Doppler shift can be accurately computed.The cos() can be computed by the estimation of uplink frequency and updated every signal period whose rate is 5 kHz.The accuracy of estimation can be achieved to 100 ns.
Firstly, we have to analyze the terminal receiver's FLL, PLL, and DLL tracking loop measurement errors that directly affect the accuracy of uplink Doppler shift and propagation delay compensation.
We assume that the received signal power is −120 dBmW; noise power spectral density 0 is −175 dBmW.The tracking loop measurement errors can be computed from the formulas in [12] and be shown in Figure 9.
In Figure 9(a), we can see the relationship between total frequency lock loop (FLL) jitter and time.In Figure 9(b), we can see the relationship between FLL dynamic stress and time.In Figure 9(c), we can see the relationship between total PLL jitter and time.In Figure 9(d), we can see the relationship between phase lock loop (PLL) dynamic stress and time.In Figure 9(e), we can see the relationship between total code tracking loop (DLL) jitter and time.In Figure 9(f), we can see the relationship between DLL dynamic stress and time.From Figure 9, we can see that the terminal receiver's FLL, PLL, and DLL tracking loop measurement errors have less effect on Doppler shift compensation at high / 0 .Therefore, as long as the carrier loop remains stable, the code loop experiences negligible dynamic stress.
Secondly, we will analyze the frequency deviation caused by the TCXO with frequency stability of ±0.5 ppm or OCXO with frequency stability of ±0.05 ppm.The signal conditioned RF signals are down-converted to an intermediate frequency (IF) using signal mixing frequencies from local oscillators.The local oscillators are derived from the reference oscillator by the frequency synthesizer, based on the TCXO or OCXO.At downlink carrier frequency which is 1.5 GHz, the most frequency deviation of the frequency synthesizer, caused by TCXO, is ±750 Hz, and the most frequency deviation caused by OCXO is ±75 Hz.After the mixing process, at the IF, this frequency deviation is a fixed bias that will be additional carrier Doppler shift.From Figure 8, we can see that the maximum carrier Doppler shift rate is far less than 1/2 data rate in the time when signal is transmitted from the transmitter of satellite to the receiver of terminal.The tracking loop measurement error is less than 1 Hz.We assume that the satellite and terminal use the same TCXO or OCXO.The estimation error of uplink carrier Doppler shift can be given as follows: TCXO: √ 750 2 + 750 2 + 1 2 = 1061 Hz, OCXO: √ 75 2 + 75 2 + 1 2 = 106 Hz.
(17) Therefore, this frequency deviation is less than 1/2 data rate, and it will be easy to be acquired.Thus, it has less effect on increasing the complexity of satellite's receiver.
Finally, through the estimation of downlink carrier and chip frequency offered by receiver's tracking loop, we can compute the cos() by ( 16) and estimate the varied distance (Δ).The estimation of the varied distance (Δ) updates every signal period whose rate is 5 kHz.
We compute the cos() by ( 16) and estimate the varied distance (Δ).The estimation error of the varied distance (Δ) using this model is shown in Figures 10 and 11.It consists of theoretic estimation error, estimation error with TCXO and estimation error with OCXO.The theoretic estimation means that the frequency deviation is 0Hz.Because the terminals in the great disaster region or sensors in remote region are stationary or low velocity moving, it results that the carrier Doppler shift caused by motion is far less than the frequency deviation caused by the oscillator.Thus we will mainly analyze the frequency deviation caused by the oscillator.The estimation of the varied distance (Δ) updates every signal period whose time is 200 s.
In Figure 10(a), we can see the relationship between theoretic estimation error and time.Because estimation of the varied distance (Δ) updates every signal period, the theoretic errors can fluctuate caused by quantization error.In Figure 10(b), we can see the relationship between estimation error with TCXO and time.In Figure 10(c), we can see the relationship between estimation error with OCXO and time.The time is between −450 s and −449 s.
In Figure 11(a), we can see the relationship between theoretic estimation error and time, where theoretic estimation means that the frequency deviation is 0 Hz.In Figure 11(b), we can see the relationship between estimation error with TCXO and time.In Figure 11(c), we can see the relationship between estimation error with OCXO and time.The time is between −1 s and 0 s.
From Figure 10(a), when is −450 s, we can get the sum of varied distance estimation error in one second, and the accuracy of compensation for (Δ)/ will be achieved in 1 femtosecond (fs) level.From Figure 11(a), when is 0 s, then the accuracy of compensation will be achieved in 10 fs level.From Figures 10(b) and 11(b), the accumulative estimation error with TCXO is 240 meters (m) in one second, and the error of compensation is 800 ns.From Figures 10(c 100 ns, which has been required in Section 3.2.Therefore, this frequency deviation has significant effect on the estimation error of the varied distance (Δ).
In the visibility time, which is approximately 9 minutes, estimation errors through simulations are shown in Figure 12.
In Figure 12(a), we can see the relationship between theoretic accumulative estimation error in one second and time.In Figure 12(b), we can see the relationship between accumulative estimation error in one second with TCXO and time when estimation error of uplink carrier Doppler shift is 1200 Hz.In Figure 12(c), we can see the relationship between accumulative estimation error in one second with OCXO and time when estimation error of uplink carrier Doppler shift is 110 Hz.The time is between −450 s and 450 s.In Figure 12(d), we can see the relationship between accumulative estimation error and estimation error of uplink carrier Doppler shift.
From Figures 12(a), 12(b), and 12(c), we can see that the carrier Doppler shift rate has effect on the estimation error of the varied distance (Δ), but the error is only 4.7 millimetres (mm) when carrier Doppler shift rate is the maximum.
From Figure 12(d), we can see that the more estimation error of uplink carrier Doppler shift is, the more estimation error of the varied distance (Δ) we will endure.Therefore, the frequency stability of oscillator has significant effect on the estimation error of the varied distance (Δ).
From the above analysis, carrier Doppler shift and propagation delay compensation of terminal, based on the OCXO with frequency stability of ±0.05 ppm, can match the requirements of the QS-CDMA system.Because the prime estimation error is the average time error of the 1PPS produced by terminal receivers, the current production showed that jumps are much less than 100 ns [4].Through (11), it results that the OCXO with frequency stability of ±0.1 ppm can also meet the requirements for the clock synchronization time error in practice.
Analysis of Error Probability.
The QS-CDMA sensor data collection system proposed in this paper mainly focuses on the following applications: emergency, marine research, and forest fire disaster.For emergency, such as earthquake, people use terminals to transmit safety confirmation in the safety and open area.For marine research, the oceanographic buoys are scattered distribution in the vast ocean.For forest fire disaster, we recommend that the sinks placed in high or open place collect information from sensors, and the sinks transmit information of forest to the LEO satellite.Therefore, the satellite channel can be considered that there is a line-of-sight (LOS), which is a dominant stationary signal component.
BER performance in the presence of additive white Gaussian noise (AWGN) and cochannel interference is derived.
Through the BPSK modulation, the th user transmitted signal can be represented as where is theth user transmitter power, is the th chip of the code sequence with length for the th user, is the transmitted symbols of the th user, is the th user carrier angular frequency, and is the initial phase of the th user.
The received signal at the demodulator input can be represented as where () is the AWGN.The received signal after down-converting is filtered with a chip matched filter.When the carrier frequency offset is not concerned, the signal after being sampled at the chip rate can be simplified as where In [1], the probability of error for QPSK has been derived.We can use the same method to derive the BER of BPSK.It can be shown that, supposing that all the 2 −1 interference data patterns are equally distributed, the probability of error for the th user in QS-CDMA system, when 2 / 0 ≤ 2 /[ ⋅ ( − 1)], can be given as follows: where / 0 is the energy per bit to thermal noise density ratio. is the number of users. is the length of msequence. , is the power ratio between the th user and th user. , , is the cross-correlation factors of the In-Phase (I) branch. is the th chip of PN code for the th user.Δ is the residual carrier frequency offset.Δ is the PN code offset.Δ is the phase offset of carrier. is the code duration.
According to the analysis of Section 3, we assume that Δ is varied over a range of about 2 kHz; Δ is varied within a range of ±1 chip.Thus every user selects a shift-m-sequence, whose code phase interval between one user and the other is greater than or equal to 3 chips.
13 shows the theory BER curves of three systems.The Asynchronous Code Division Multiple Access (ACDMA dots) approaches a constant for different number of users.When the number of users is much more, the BER performance of ACDMA is so bad that the data of th user cannot be demodulated.The QSCDMA-I (dashed line) uses Gold sequence to spread spectrum.We can see that the BER performance of the QSCDMA-I is much better than that of the ACDMA.Unfortunately, with the increase of the number of users, the Gold sequences lose a lot of system is also a little better than the A-CDMA system.The prime reason of this phenomenon, which is different from the results in Figure 14, is that the power of jamming users is far more than main user.Thus the power control is important in QS-CDMA system, too.
Conclusions
In the paper, a quasisynchronous CDMA uplink access technique in the LEO satellite has been presented and discussed.
From the analysis of clock synchronization time error based on GPS, the novel system structure based on GPS 1PPS is shown to code offset which is less than 1 chip at 5 Mchip/s, and the effect of the multiple-access interference can be greatly reduced.The effect on Doppler compensation, caused by the frequency stability of terminal's oscillator, is analyzed emphatically.It results that, by Doppler compensation, we can reduce the time of acquisition and the complexity of implementation in satellite.These methods are used to guide the specific hardware implementation of the QS-CDMA.The FPGA implementation can be proved that Doppler compensation can achieve the requirements of QS-CDMA system, the probability of error is drastically reduced compared to A-CDMA system, and the number of users is drastically increased.The QS-CDMA sensor data collection system proposed in this paper mainly focuses on the following applications: emergency, marine research, and forest fire disaster.The QS-CDMA system is easy to implement, use in remote, and collect data from more sensors.Meanwhile, the system can respond quickly to emergencies.
Figure 3 :
Figure 3: QS-CDMA delay compensation based on GPS timing diagram.
Figure 8 :
Figure 8: (a) Distance versus time, (b) time-delay versus time, (c) Doppler shift versus time, and (d) Doppler shift rate versus time.
) is the th output sample of the chip matched filter, () is the th sample of the th user transmitted signal, is the th chip of PN code for the th user, and () = () * .
Figure 12 :
Figure 12: (a) Theoretic estimation error, (b) estimation error with TCXO, (c) estimation error with OCXO, and (d) estimation error versus estimation error of uplink Doppler shift.
Table 3 :
Main parameters of access procedure.
Table 5 :
Requirements for the code offset.
and the code offset to be within ±1 code epoch at 5 million chips per second (Mchip/s).By assuming that the proposed Doppler compensation meets the requirements, acquisition structure is demonstrated to be feasible with acceptable acquisition time by a 1-dimensional serial search instead of the considerably longer 2-dimensional search that will be required in the uncompensated case.
Table 6 :
Main parameters of clock synchronization analysis.
Table 7 :
Coefficients in TCXO and OCXO clock error models.
Table 8 :
Main parameters of compensation analysis. | 8,505 | 2015-09-01T00:00:00.000 | [
"Computer Science",
"Engineering",
"Environmental Science"
] |
MetaNetX/MNXref: unified namespace for metabolites and biochemical reactions in the context of metabolic models
Abstract MetaNetX/MNXref is a reconciliation of metabolites and biochemical reactions providing cross-links between major public biochemistry and Genome-Scale Metabolic Network (GSMN) databases. The new release brings several improvements with respect to the quality of the reconciliation, with particular attention dedicated to preserving the intrinsic properties of GSMN models. The MetaNetX website (https://www.metanetx.org/) provides access to the full database and online services. A major improvement is for mapping of user-provided GSMNs to MXNref, which now provides diagnostic messages about model content. In addition to the website and flat files, the resource can now be accessed through a SPARQL endpoint (https://rdf.metanetx.org).
INTRODUCTION
MetaNetX/MNXref provides computed cross-references between metabolites as well as biochemical reactions, to reconcile major public biochemical databases and a selection of public genome-scale metabolic networks (GSMN) from a few dedicated resources (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12). The previous releases of the MetaNetX/MNXref resource and website have already been presented (13,14) as well as the main challenges of the reconciliation (15)(16)(17). This paper focuses on the current status of the resource and the recent improvements accomplished through the complete redesign and rewriting of its production pipeline.
GSMN reconstruction is one of the foundations of Systems Biology. The development of such reconstruction involves the integration of knowledge about reactions and metabolites from the scientific literature, public databases and previously published GSMNs. Historically, many GSMNs were formulated using metabolites represented as 'symbols', i.e. without explicit reference to a molecular structure. The initial motivation for creating this resource ten years ago was to add molecular structures to existing GSMNs. More generally, the goal was to establish cross-links between symbols in GSMNs published by different groups and the molecules found in the major biochemical databases. This problem is trivial as long as oneto-one mappings can be established between the different resources, but this is not always the case. Merging metabolites in a metabolic network may lead to the merging of reactions, possibly altering the model properties, and hence the predictions that could be made using it.
Principles
For MetaNetX/MNXref, a metabolite identifier (e.g. MNXM123) first refers to a set of metabolites in external databases, which are merged together because they are assumed to be the same biochemical entity, i.e. distinctions in protonation states, tautomeric forms or isotopes are typically ignored. Secondly, for every set of metabolites, a single external database identifier is selected as the (best) reference, from which a molecular structure is possibly retrieved. ChEBI identifiers that appear in Rhea reactions are preferentially selected as reference. A consequence of the merging of metabolites is the merging of reactions involving these metabolites ( Figure 1). A reaction identifier (e.g. MNXR456) designates a set of reactions in external databases that are assumed to be the same biochemical entity, because they were merged together. A single external identifier is selected as the reference for this set, preferably a reaction from Rhea when feasible. However, a reaction rewritten with MNXref identifiers may differ from the original equation, for example, with respect to proton balancing. In addition, since release 2.0, a distinction was introduced between transported protons that account for the proton motive force (MNXM01) and those introduced to balance chemical equations (MNXM1). Such a distinction is also made in some recently published models (22).
Reconciling metabolites and reactions
Molecular structures are systematically exploited to reconcile metabolites. The proportion of chemicals in external databases endowed with a molecular structure has steadily increased over the last 10 years. However, many difficulties remain, such as incomplete information on cis/trans-and stereo-isomerisms. The interpretation of partially defined structures, especially those involving R-groups and polymers, also remains a challenge.
The availability of cross-references between reactions often enables the reconciliation of pairs of metabolites if supported by additional evidence, for example the compound name. This reconciliation of metabolites from the reaction context evidence was the key idea that allowed the first computation of MetaNetX/MNXref (15). It is to be noted that imported cross-references between metabolites are ignored during the reconciliation, to avoid propagating existing errors present in external databases.
Manual curation
Although we aimed to make the reconciliation procedure fully automated, errors are occasionally imported from external resources and these can affect the computed reconciliation. Automated detection of conflicting evidence and ambiguities has been central to our effort to rewrite the pipeline. Thereafter, manual case-by-case study enables fixing of flagged issues, for example by correcting the reference of a metabolite to a molecular structure. An archetypal example of such difficulties are the two stereo-isomers of a compound--according to the textual description--where the structure of the L-form is fully specified and the structure of the R-form misses the stereochemistry.
Two metabolites to be merged that appear in the same reaction, in the left and right terms for example, also deserve scrutiny. Pairs of tautomers or acid-bases can be validly merged, possibly yielding an empty reaction that will disappear from the mapped GSMN. Changes in reaction status (see below) have also been used as a trigger for the manual inspection of a particular reconciliation.
The errors we have detected have been systematically reported to the resource from which they originated. Most of them have since been corrected, thanks to the diligence of their curators.
Impact of reconciliation on model properties
One of the main challenges of the MNXref reconciliation is to ease comparison of GSMNs while preserving their intrinsic properties. We have attempted to summarize the latter by attributing a status to every reaction in a GSMN ( Figure 2): A, the reaction can carry a non-zero flux in the unaltered GSMN; a, the reaction can carry a flux after all boundary (exchange) reactions were set to bi-directional; b, the reaction can carry a flux after all reactions in the GSMN were set to bi-directional; B, the reaction cannot carry any flux because of the network topology, for example because of a dead-end metabolite. Computation is performed using a variant of the flux variability algorithm (23).
For example, the iAF1260 model for E. coli (24) contains a total of 2376 reactions. After mapping to MNXref, 2368 reactions are retrieved with a one-to-one mapping to an original reaction. The status of these reactions is distributed as follows: A, 1518; a, 627, b, 87; B, 136. The reaction status is perfectly conserved in this example, despite the merging of two metabolites namely 1agpg140 (1-acylsn-glycero-3-phosphoglycerol (n-C14:0)) and 1tdecg3p (1tetradecanoyl-sn-glycerol 3-phosphate). In other GSMNs, the merging of metabolites may cause the status of a few reactions to change, the latter not necessarily involving the merged metabolites and possibly augmenting the number of reactions that can carry a non-zero flux. Taking control of such indirect effects has been crucial for testing and improving the reconciliation. More public GSMNs will be added in the future to further challenge and improve the quality of the reconciliation.
Database content
Tables 1 and 2 list the different resources that were included in the latest release. The ratio of the numbers of entries before and after reconciliation is a measure of its efficiency. Indeed, this ratio is most optimal for the metabolites and reactions found in a hundred GSMNs hosted at MetaNetX.
Service
The MetaNetX website (https://www.metanetx.org) provides access to the full database and online services. Most notably, the service that permits a user to upload his or her own GSMN and map it to MNXref has been greatly improved to produce diagnostic messages about the model content. The database can be queried through the website user interface, as well as through a SPARQL endpoint (https://rdf.metanetx.org).
DISCUSSION
By design a GSMN is a model of the metabolism of low molecular weight compounds, where mass conservation and thermodynamics apply (25,26). GSMN models play a crucial role in the toolbox of synthetic biology (27,28). Beyond popular applications, such as metabolic flux prediction with flux balance analysis and prediction of the gene essentiality, GSMNs have been used in numerous applications (29), e.g. chemicals and materials production (30)(31)(32)(33), drug targeting (34,35), human metabolism, disease understanding (36,37) and, multi-organism interaction modeling (38,39). MNXref is now used within tools for testing GSMNs such as MEMOTE (40), and has been proposed as a reference for minimal standard content for metabolic network reconstruction (41). Finally, the ability to accurately reconcile metabolites and reactions within GSMNs paves the way for applications such as multi-omics data interpretation (42,43), and white-box AI models (44). Moving forward, MetaNetX/MNXref efforts to not only unify metabolites, reactions and subcellular compartments but also genes and proteins (45) into a single comprehensive namespace will continue to provide a strong basis for such key systems biology endeavors in the future.
DATA AVAILABILITY
Data is distributed under a Creative Commons Attribution 4.0 International License (CC BY 4.0). The MNXref reconciliation is available in TAB-delimited and RDF/Turtle formats. The mapped GSMNs are available in SBML level 2 and 3 formats from the web site and as part of the RDF graph. | 2,065 | 2020-11-06T00:00:00.000 | [
"Computer Science",
"Biology"
] |
Characterization of Timed Changes in Hepatic Copper Concentrations, Methionine Metabolism, Gene Expression, and Global DNA Methylation in the Jackson Toxic Milk Mouse Model of Wilson Disease
Background Wilson disease (WD) is characterized by hepatic copper accumulation with progressive liver damage to cirrhosis. This study aimed to characterize the toxic milk mouse from The Jackson Laboratory (Bar Harbor, ME, USA) (tx-j) mouse model of WD according to changes over time in hepatic copper concentrations, methionine metabolism, global DNA methylation, and gene expression from gestational day 17 (fetal) to adulthood (28 weeks). Methods Included liver histology and relevant biochemical analyses including hepatic copper quantification, S-adenosylmethionine (SAM) and S-adenosylhomocysteine (SAH) liver levels, qPCR for transcript levels of genes relevant to methionine metabolism and liver damage, and DNA dot blot for global DNA methylation. Results Hepatic copper was lower in tx-j fetuses but higher in weanling (three weeks) and adult tx-j mice compared to controls. S-adenosylhomocysteinase transcript levels were significantly lower at all time points, except at three weeks, correlating negatively with copper levels and with consequent changes in the SAM:SAH methylation ratio and global DNA methylation. Conclusion Compared to controls, methionine metabolism including S-adenosylhomocysteinase gene expression is persistently different in the tx-j mice with consequent alterations in global DNA methylation in more advanced stages of liver disease. The inhibitory effect of copper accumulation on S-adenosylhomocysteinase expression is associated with progressively abnormal methionine metabolism and decreased methylation capacity and DNA global methylation.
Introduction
Wilson disease (WD) is an autosomal recessive disorder characterized by mutations in the ATP7B gene which is responsible for copper (Cu) metabolism and excretion [1], with Cu accumulation in liver [2], and brain [3], that leads to progressive liver damage, as well as neurological and psychiatric manifestations [4,5]. The toxic milk mouse model of WD from The Jackson Laboratory (tx-j) has a G712D missense mutation in the second transmembrane region of ATP7B, which leads to hepatic Cu accumulation similar to the disease described in humans [6]. This Cu accumulation in hepatocytes results in microvesicular lipid droplets in association with damage to mitochondria [5], nuclei [7], and endoplasmic reticulum (ER) [8]. In addition, hepatic Cu accumulation correlates with down-regulation of gene transcripts related to lipid metabolism [9] including cholesterol synthesis [10].
Previous studies with the tx-j mouse model of WD have shown a progressive accumulation of liver Cu over 12 months, along with increases in hepatic apoptotic cells and hepatocyte metallothionein levels [11]. Apoptotic cell damage in the first six months of life was associated with increased levels of Commd1, a Cu binding protein, while decreased levels of proteins associated with inhibition of apoptosis were observed by eight months [4]. Reductions in liver Cu can be achieved in tx-j mice using the chelator tetrathiomolybdate [12].
We have previously demonstrated a close relationship between Cu accumulation and methionine metabolism in tx-j mice [9], as others have shown in other animal models of WD [13].
As shown in Figure 1, methionine metabolism is essential for the production of methyl groups used in transmethylation reactions. S-adenosylmethionine (SAM) is the principal methyl donor for DNA and histone methylation reactions, whereas S-adenosylhomocysteine (SAH) inhibits all SAM-dependent methylation reactions. S-adenosylhomocysteinase (AHCY) is the bi-directional enzyme that hydrolyzes SAH to generate homocysteine. Methionine synthase (MTR or MS) remethylates homocysteine to form methionine that is in turn converted to SAM via the enzyme methionine adenosyltransferase (isoenzymes MATI/II/III). Homocysteine can also be remethylated to methionine via the betaine homocysteine methyltransferase (BHMT) catalyzed reaction that utilizes betaine. Dimethylglycine (DMG) is a byproduct of the BHMT catalyzed reaction and is also a potent inhibitor of BHMT. Tetrahydrofolate (THF); DNA methyltransferase (DNMT); histone methyltransferase (HMT); glycine N-methyltransferase (GNMT); phosphatidylethanolamine N-methyltransferase (PEMT); DNMTs, GNMT, and PEMT are major consumers of SAM in the liver [14].
Methionine is an essential amino acid that must be ingested to ensure adequate provisions. In addition, methionine is generated from homocysteine via methionine synthase (MS or methionine transferase reductase (MTR) and BHMT-catalyzed reactions and is converted into S-adenosylmethionine (SAM), the main methyl donor for transmethylation reactions. DNA methyltransferases (DNMTs) catalyze DNA methylation reactions with production of S-adenosylhomocysteine (SAH). The maintenance of stable and balanced levels of SAM and SAH is crucial for cell physiology, as SAM is the main substrate for methylation reactions [15], whereas SAH is the major inhibitor for the same reactions. The ratio of SAM:SAH may be considered a relative index of methylation capacity [16], which in normal mouse liver tissue has been previously described to be in the range of 3 to 4 [14]. SAH regenerates homocysteine through S-adenosylhomocysteinase (AHCY), a bidirectional enzyme that favors the generation of SAH if the products homocysteine and adenosine are not removed. AHCY can be inhibited by Cu accumulation that results in elevated levels of SAH [9,17,18]. We recently associated hepatic Cu accumulation with reduced Ahcy gene expression and activity, subsequent elevations of SAH levels, reductions in the SAM: SAH ratio, and reduced DNA methylation. The above were associated with altered expression of genes relevant to liver injury [9]. This study also demonstrated that transcript levels of select genes related to methionine metabolism are down-regulated in tx-j mice and respond to choline supplementation with restoration of gene transcripts to control levels in fetal livers [19]. Others have shown that methionine metabolism and the need for methyl groups change over time, with the requirement for methyl groups being highest during gestational life [20].
In order to study the progression of WD, the present study examined the development of liver histology, methionine metabolism, transcript levels of selected genes central to lipid and methionine metabolism and global DNA methylation levels in tx-j mice from gestational day 17 (fetal) to postnatal week 28 (28 weeks). The study provides new temporal insights into relationships between hepatic Cu accumulation and liver damage, altered methionine metabolism, hepatic global DNA methylation, and regulation of gene expression.
Body and Liver Weights, Copper and Iron Status, SAM and SAH Levels, and Liver Histology
As shown in Table 1, body weights of the tx-j mice were significantly lower at three through 28 weeks of age than those of controls. Liver weights in the tx-j mice at three and 12 weeks of age were lower than those of controls. There was a significant increase in the liver/body weight ratio in the tx-j group at 20 and 28 weeks of age that coincided with a worsening of liver histology.
Liver Cu concentrations in fetal tx-j mice were significantly lower than in controls but by three weeks postnatal and thereafter, values were 2-50 times higher than in controls. Liver Cu concentration peaked at 20 weeks of age with significant age and genotype interaction (both p < 0.0001) indicating that liver Cu concentrations differed significantly over time between the tx-j and control mice. Liver iron concentrations in tx-j mice were similar to control levels at most time points, although values in the tx-j mice were 1.2 times higher than in controls at 28 weeks.
Postnatal hepatic SAM levels were higher in tx-j mice than in controls at three weeks with a significant interaction of age with genotype (p = 0.01) when examined over all time points. Liver SAH levels were similar in both groups at all time points except at three and 12 weeks with an overall significant interaction between age and genotype (p < 0.05) over time. The ratio of SAM to SAH (SAM:SAH ratio) was significantly lower at 12 weeks in the tx-j mice compared to ratios in the controls. When data from all time points were pooled, hepatic Cu concentrations were positively correlated with SAH levels (r = 0.44; p = 0.0002) and negatively correlated with SAM:SAH methylation ratio (r = −0.43; p = 0.0002) ( Figure 2). These findings are compatible with the known inhibitory effect of Cu on Ahcy expression and enzymatic activity [9] with a predictive decrease in methylation capacity. Table 1. Developmental changes (fetal-28 weeks) in body and liver weights, hepatic copper and iron, and SAM and SAH concentrations. Values are expressed as mean ± SD. Values with * are significantly different (p < 0.05) between tx-j vs. control at each time point; ** Copper and iron concentrations at the three weeks time points are from livers of 8 controls and 5 tx-j mice; Values with are significantly different (p < 0.05) within the same genotype between 20 and 28 weeks. ND = not determined. Fetal and three weeks data were previously published [19].
Analysis
Fetal 3 weeks 12 weeks 20 weeks 28 weeks Body weight (g) ND ND 9 Although there were no changes at 12 weeks, we observed an increase in lymphocyte and PMN infiltration and in hepatocyte size in the tx-j group at 20 weeks. At 28 weeks, all the tx-j mice had increased hepatocyte sizes with giant nuclei, necrosis, increased lymphocytes, and PMNs. There were no histological changes in the control mice at all time points ( Figure 3).
Figure 3.
Histology images of tx-j and control livers from three to 28 weeks of age. All hematoxylin and eosin stained, 436×. Whereas liver histology was normal in tx-j mice at both three and 12 weeks of age (1B and 2B), there was an increase in inflammatory infiltrates at 20 and 28 weeks (3B and 4B, thin arrows), in association with giant nuclei and markedly increased cell size of the hepatocytes (3B and 4B, thick arrows). Note that in tx-j mice hepatocyte cell diameters are 2.5 times and nuclear diameters are about two times larger than control mice [19]. Control mice had normal liver histology at all time points (1A, 2A, 3A and 4A).
Transcript Levels of Selected Genes Related to Methionine and Lipid Metabolism
Transcript levels of 11 different genes were quantified including genes central to lipogenesis, fatty acid oxidation, methionine metabolism, and DNA methylation ( Figure 4).
As previously reported [19], most of the fetal liver genes that were studied were down-regulated in the tx-j in comparison to control mice, with the exceptions of Dnmt3a and Mat1a. Subsequently, when comparing differences between gene transcript levels in control and tx-j mice at different time points, Ahcy was persistently down-regulated in tx-j mice except at three weeks, while Srebf1 and Dnmt3a were down-regulated in tx-j mice at 12 weeks. Dnmt1 was up-regulated at 20 weeks and Dnmt3b was down-regulated at three and 12 weeks. Both Dnmt3a and Dnmt3b were up-regulated in tx-j mice at 28 weeks. Mat1a was down-regulated at three weeks but was up-regulated at 12 weeks, and Mat2a was up-regulated in tx-j mice at 28 weeks. Mtr was up-regulated in tx-j mice at 12, 20, and 28 weeks. When comparing transcript levels in tx-j mice at different ages, transcript levels of almost all genes (except for Dnmt3b and Mat1a) were up-regulated at three weeks compared to fetal livers, whereas Dnmt3a and Dnmt3b levels were up-regulated at 28 weeks compared to 20 weeks. Consistent with our proposed interaction of Cu with methionine metabolism while considering all time points, Ahcy transcript levels were negatively correlated with hepatic Cu concentration (r = −0.58; p < 0.0001), and hepatic Cu was positively correlated with the expressions of Dnmt1 and Dnmt3a (r = 0.68, p < 0.0001 and r = 0.28, p = 0.01, respectively).
Hepatic Global DNA Methylation
DNA dot blots for global DNA methylation showed that there were no group differences in DNA methylation in fetal, three weeks, or 12 weeks old livers between tx-j and control mice. Starting at 20 weeks of age, tx-j mice DNA showed global hypomethylation compared to control mice with a significant interaction with age (p < 0.001), and this pattern persisted at 28 weeks ( [19]. In addition, when using data only from 20 and 28 weeks old tx-j and control mice, global DNA methylation was negatively correlated with Cu concentrations (r = −0.38; p = 0.049) and SAH levels (r = −0.69; p ≤ 0.0001) and positively correlated with SAM:SAH ratio (r = 0.54; p = 0.003) ( Figure 6). The tx-j mice represent a valid model of WD and offer the opportunity to study the relations between Cu accumulation and methionine metabolism and their consequences on DNA methylation and gene expression. The rationale underlying our study was to describe the temporal relations between changes in methionine metabolism, DNA methylation, and gene expression, given that epigenetic marks are very dynamic, subject to influences that start during the early development and continue throughout life as a consequence of continuous environmental changes. The major findings of our study include the following: first that hepatic Cu was significantly lower in fetal livers of tx-j than in controls but postnatal values increased significantly over time with a plateau starting at 20 weeks of age; in contrast there were only minor differences in liver Fe concentrations. The finding that liver Cu concentrations were lower in fetal tx-j than controls may be attributed to the fact that adult tx-j dams are characterized by low circulating ceruloplasmin levels, with a putative Cu transport protein [19]. The observation that liver Cu concentrations reached a plateau around five months of age has been described before in other murine models of hepatic Cu accumulation [21] and may be attributed to adaptation mechanisms to hepatic Cu accumulation [4]. Hepatic Fe accumulation, as shown at 28 weeks, has been described previously in the LEC rat model of WD [22] and it can be speculated that this Fe accumulation plays a role in liver damage progression. Kato et al. [22] demonstrated that Fe-deficient diet could even prevent the development of fulminant hepatitis in LEC rats. While the mechanisms of hepatic Fe accumulation have yet to be elucidated, it is reasonable to speculate that since ceruloplasmin can contribute to Fe transport through hepatocyte basolateral membranes, low levels of this protein in WD may contribute to hepatic Fe accumulation [23]. Second, whereas almost all measured gene transcript levels were down-regulated in the tx-j fetal livers relative to control values, low levels of Ahcy persisted throughout all other time points. As a consequence of Ahcy down-regulation, the SAM:SAH methylation ratio was lower at 12 weeks of age although not consistently at all time points. Similarly, both SAM and SAH did not change consistently over time as expected since SAM was increased only at three weeks and SAH was increased only at three and 12 weeks which may be related to increased Mtr and Mat transcript and activity levels at this time points. A previous study reported transcript levels of enzymes related to methionine metabolism and mean SAM levels of 112.8 ± 12.4 nmol/g, SAH levels of 25.5 ± 3.9 nmol/g and their ratio of 4.4 ± 0.8 in mouse liver tissue [14]. Even though it is difficult to compare different mouse strains and animal ages, our SAM and SAH data in fetal livers are comparable with a previous report indicating very low SAH levels in fetal livers [24]. However, our present postnatal data are similar to the previous report in tx-j and control mice only at three weeks of age, whereas at later time points our SAM:SAH ratio is lower (range 1.8-2) due to progressive reduction of SAM levels relative to progressive increase of SAH levels. In an unrelated study, untreated C57BL/6J mice had similar SAM:SAH ratio of 2 ± 0.6 at five months of age [25]. The effects of Cu levels on methionine metabolism are also emphasized by the positive correlation between Cu and SAH levels, and negative correlation between Cu with Ahcy transcript levels and the SAM:SAH ratio. Two previous studies in toxic milk mice showed that Ahcy has Cu binding properties and its hepatic transcript levels can be reduced up to 42% in association with Cu accumulation [17,26]. Interestingly, Bethin et al. showed that Cu deficiency was also associated with 45% reduction of Ahcy hepatic levels [26], a finding that is similar to our results in fetal tx-j livers and that indicates that Cu metabolism must be strictly regulated to ensure stable Ahcy levels. Others showed that Ahcy deficiency in a 26-year-old man was associated with myopathy and developmental delay. Electron microscopy of the liver biopsy demonstrated extensive cytoplasmic lipid droplets [27]. Mutation of Ahcy in zebrafish was associated with SAH accumulation, increased levels of TNFα, and hepatic steatosis [28]. Third, although gene transcript levels were all down-regulated in fetal livers of tx-j mice, their improvement to control values after cross-fostering with control dams in all but Dnmt3b, Ahcy, and Mat1a at three weeks [19] suggests that maternal milk components may regulate hepatic gene expression to control levels. Of note, Ahcy transcript levels were reduced as well in fetal livers, similarly to all the other studied genes, despite the fact there was no Cu accumulation. We previously hypothesized that fetal hepatocytes in tx-j mice present dysregulation of cell cycle that has consequences on gene transcript levels, including Ahcy, and is corrected by methyl groups provision [19]. Delgado et al. [13] previously conducted a study on nine-week-old LEC rat models of WD, and showed down-regulation of Ahcy transcript levels. Interestingly, their finding of down-regulation of Mtr is opposite to present data and they failed to demonstrate any difference in SAM or SAH levels compared to wild type rats. These data suggest that various other factors may affect methionine metabolites levels.
Although the gene transcript levels were quite variable over time, global DNA hypomethylation was observed at 20 weeks of age and DNA methylation levels correlated negatively with Dnmt3a and Dnmt3b and positively with Mat1a transcript levels over all time points. The positive correlation between SAM:SAH and global DNA methylation supports the concept that Cu concentrations, methionine metabolism, and global DNA methylation can be tightly interrelated with gene expression regulation. We confirmed that Ahcy transcript levels were the most affected with consequences on SAM:SAH ratio and global DNA hypomethylation at 20 and 28 weeks. In addition, noteworthy, hepatic global DNA hypomethylation observed at the later time points was associated with more advanced inflammatory infiltrate. The finding of an association of decreased global DNA methylation at later time points with inflammatory infiltrates supports our previous results that chronic inflammation in WD is associated with an increased demand for methyl groups and consequent global DNA hypomethylation [9]. Previous reports suggested that progressive liver disease with early indication of fibrosis can be associated with changes in Dnmt levels and global DNA methylation in a mouse model of fibrosis induced by carbon tetrachloride [29]. Another study on human liver biopsies from patients with various degrees of severity of liver disease from chronic hepatitis to cirrhosis and hepatocellular carcinoma showed a progressive increase transcript levels of Dnmts in association with more advanced liver disease [30], an observation that is similar to our current study. In addition, previous reports described increased Dnmts transcript levels correlating with reduced global DNA methylation likely as a result of a compensatory mechanism [31,32]. The design of our present study that is based on timed changes in methionine metabolism and DNA methylation does not allow us to determine if DNA methylation is the cause of worsening liver pathology or if it is epiphenomenon or a consequence of it. However, it is possible that both hypotheses may be true. As shown by our data, the changes in methionine metabolism including down-regulation of Ahcy expression in the fetal liver preceded Cu accumulation and inflammation and amplified liver damage, which in turn could increase a requirement for methyl groups. Global DNA hypomethylation has consequences on the regulation of gene expression as shown in a recent study of progressive liver fibrosis [29]. In addition, improvement of global DNA methylation after folate supplementation was associated with decreased inflammation in gastric mucosa infected by Helicobacter Pylori [33]. To summarize, our results indicate that the tx-j mouse model of WD is characterized by changes in methionine metabolism that are evident from the gestational phase of development onwards. Ahcy down-regulation is persistent over time and is negatively correlated with increasing hepatic Cu concentration, a finding that is consistent with the known inhibitory effects of Cu on its expression [9,26]. As a consequence of Ahcy down-regulation, there is a reduction in liver SAM:SAH levels which correlated with global DNA methylation observed at the later time points.
Animals and Care
The study was conducted using C3HeB/FeJ-Atp7b tx-J/J (tx-j) mice and C3HeB/FeJ (control) mice. All mice were bred in-house on the UC Davis campus (Davis, CA, USA). All animals had access to Purina LabDiet 5001 stock (13 µg Cu, 270 µg Fe, 70 µg Zn per g diet, 28% Kcal protein, 12% Kcal fat, and 60% Kcal carbohydrate) and deionized water ad libitum. Animals were group-housed in polycarbonate cages and maintained according to guidelines set forth by the American Association for Accreditation of Laboratory Animal Care IACUC (Institutional Animal Care and Use Committee, UC Davis, Davis, CA, USA). The animal room was maintained at 20-23 °C and 45%-65% relative humidity with a 14 h light/10 h dark light cycle.
Dams were anesthetized at gestational day 17 (GD17) via CO 2 anesthesia followed by cervical dislocation, and fetal livers were pooled and flash-frozen in liquid nitrogen (n = 8 pools of control fetal livers; n = 5 pools of tx-j fetal livers). All postnatal tx-j pups were cross-fostered to a lactating control dam between post-partum day 0 and 6 due to an insufficient amount of Cu to sustain neonatal development and growth in the milk of a tx-j mouse. Mice at 3 (control n = 11; tx-j n = 10), 12 (control n = 8; tx-j n = 7), 20 (control n = 9; tx-j n = 6), and 28 (control n = 7; tx-j n = 7) weeks of age were euthanized via isoflurane anesthetic followed by exsanguination and cervical dislocation. Sections of postnatal livers were placed in formalin or stored in the −80 °C freezer until analysis. Fetal livers and 3 weeks livers have been previously published [19]. The protocol was approved by UC Davis IACUC (protocol#16172, approved on 21 October 2010).
Hepatic SAM and SAH
Liver levels of SAM and SAH were measured through high-performance liquid chromatography. Liver tissue was homogenized in cold 0.5 N perchloric acid at a ratio of 50 mg tissue: 400 µL perchloric acid and subsequently centrifuged at 14,000 rpm for 10 min. The supernatant was then filtered through a 0.2 µm syringe filter, aliquoted, and stored in the −80 °C freezer until HPLC analysis could be performed to quantify SAM and SAH [34]. HPLC analysis was done within 4 weeks of tissue collection to ensure sample stability. This method has been confirmed independently in another laboratory [35].
Hepatic Copper and Iron
Approximately 100 mg of liver tissue was digested with concentrated nitric acid and then wet-ashed for analysis using flame atomic absorption spectroscopy [36].
Liver Histology
Liver tissue from both control and tx-j mice were prepared by staining sections with hematoxylin and eosin. Images were blind-evaluated for mitosis, nuclei, lymphocytes, PMNs, hepatocyte size, and fibrosis.
Transcript Levels of Selected Genes by qPCR
RNeasy Mini Kit (QIAGEN, Valencia, CA, USA) was used to isolate total RNA from liver tissue. Purity and concentration of extracted RNA was determined by NanoDrop spectrophotometry (Cole-Parmer, IL, USA) and RNA integrity determined by gel electrophoresis. Samples were stored at −80 °C until analysis. cDNA was synthesized using the SuperScript III First-Strand cDNA synthesis kit (Invitrogen, Carlsbad, CA, USA). SYBR green was used to detect transcript levels of 11 selected genes ( Table 2); all samples were run in triplicate. Primers for cDNA sequences were designed using AB Tm calculator (http://www6.appliedbiosystems.com/support/techtools/calc/index.cfm), NCBI Primer-BLAST (http://www.ncbi.nlm.nih.gov/tools/primer-blast/), and Premier Biosoft International Beacon Designer (http://www.premierbiosoft.com/qOligo/Oligo.jsp?PID=1). Efficiency of all primers was >95% and specificity checked via melt curve and gel electrophoresis. All primers were used at a concentration of 300 nM except for Mtr primers which were used at a concentration of 900 nM. qPCR was done on the AB ViiA 7 Real-Time PCR System (Applied Biosystem, Foster City, CA, USA).
Reactions were run at 50 °C for 2 min and 95 °C for 10 min, then 40 cycles at 95 °C for 15 s and 60 °C for 1 min. All Cq expression values were normalized to Gapdh and relative expression was calculated using the equation 2 −ΔΔCq , where ΔΔCq = ΔCq (sample) − Cq (calibrator). Table 2. qPCR primer sequences of selected genes.
Statistical Analysis
Statistical analysis was performed using a two-way ANOVA with an interaction term. Where the overall ANOVA was significant, we identified genotypes (tx-j vs. control) and cross-sectional time points (fetal and 3, 12, 20, or 28 weeks of age) that differed significantly using Tukey's multiple comparison procedure and maintained the family-wise error rate at 0.05. Pearson correlation coefficient and its p-value for significance of correlation were calculated to assess the magnitude and direction of an association between two given variables. For data that were highly skewed, we applied a natural log transformation to achieve normality prior to statistical analysis and significance testing was done on a log-transformed scale. All reported p-values are based on two-sided tests. A p-value <0.05 was considered significant. All statistical analyses were performed using SAS, Version 9.4 (SAS Institute, Cary, NC, USA).
Conclusions
In the present study, we observed that transcript levels of genes related to methionine metabolism are aberrant in the liver of the tx-j mouse model of WD from late gestation to adult life in parallel with increasing levels of hepatic Cu and abnormal histopathology. The accumulation of hepatic Cu correlated with decreasing expression of Ahcy, with consequent increases in SAH levels and reduction in SAM:SAH methylation ratios at several time points. In more advanced phases of liver disease, tx-j mice presented global DNA hypomethylation which in turn correlated with the SAM:SAH ratio. The interaction between Cu accumulation and methionine metabolism is a crucial mechanism of disease onset and progression in WD indicating that there is a close connection between genetic and epigenetic mechanisms that ultimately determinates the phenotypic expression of this condition. | 6,014.4 | 0001-01-01T00:00:00.000 | [
"Biology"
] |
Strength Characteristics of Concrete Beams Reinforced with Steel Bars of Equivalent Area but Different Diameters
Contractors occasionally substitute reinforcement bars during construction works, perhaps as a result of unavailability of the design-specified bars. As a result, this study have explored the basis, extent and the conditions for the mutual substitution of reinforcing bar groups of equivalent area but different bar diameters in reinforced concrete beams. A total of (20) concrete beams including the control beams were cast. These comprise (2) each of 100 mm×100 mm×500 mm and 150 mm×150 mm×750 mm beams as plain concrete (control beams) and (2) each of 100 mm×100 mm×500 mm and 150 mm×150 mm×750 mm beams were reinforced in turn with 20 mm, 16 mm, 12 mm and 10 mm bar diameters. The beams were subjected to centre-point loading using bending testing machine, in accordance with BS 1881-118 and with the load and compressive strain recorded to the point of failure. The results of the test beams showed that the greatest difference in the area of reinforcement between beams reinforced with 9Y12 bars (bar area = 1020 mm 2 ) and 3Y20 bars (bar area = 943 mm 2 ) is 7.5%. The results also showed that given the same area of steel in a cross section, the section with the greater number of bars has higher bending strength. It was also deduced that an increase in the area of reinforcement would cause a disproportionate increase in the strength of the beam.
INTRODUCTION
Concrete remains the most valuable construction material widely used for different construction purposes.Poor resistance of plain concrete to tensile loads constitute a major limitation to its usage, however, reinforcement bars are systematically embedded in concrete thus, forming a matrix, in order to enhance its resistance to forces.The reinforcing steel such as bars, mesh or even fiber absorbs the tensile, shear and sometimes the compressive stresses in a concrete structure (Boulekbache et al., 2012;Reinforced Concrete, 2015).It is widely known that plain concrete does not easily withstand tensile and shear stresses caused by wind, earthquakes, vibrations and other forces and are therefore unsuitable in most structural applications (Reinforced Concrete, 2015).In reinforced concrete, the tensile strength of steel and the compressive strength of concrete work together to allow the member sustain these stresses over considerable spans.
Non-availability of a particular reinforcement bar size which has been recommended by the structural engineer delays construction works and tend to alter work schedule.For these reasons, during construction some contractors and engineers occasionally adopt the available reinforcement bars of equivalent area to that provided from design.
Conversely, it is noteworthy that different bar diameters in reinforced concrete beams behave differently when subjected to bending (Taylor, 1974).Unfortunately, there is no available published material on the condition (s) for mutual substitution of reinforcement bars even if of equivalent areas.Hence, this research was set to use experimental method to ascertain the permissibility, extent and what conditions for which specified bars can be substituted with other bars of equivalent area, in structural concrete beams.
Consequently, good alternatives of choice of reinforcement bar could be ascertained via flexural testing of beams.Flexure test method measures behavior of materials subjected to simple beam loading.It is also called a transverse beam test.
When a beam undergoes bending, according to (Carino and Clifton, 1995;Fantilli et al., 1998), it experiences a range of stresses across its depth.At the edge of the object on the inside of the bend (concave face), the stress will be at its maximum compressive stress value.At the outside of the bend (convex face), the stress will be at its maximum tensile value (Mattew et al., 2014).These inner and outer edges of the beam are known as the extreme fibers.Jakubovskis et al. (2014) articulated that most materials fail under tensile stress before they fail under compressive stress, so the maximum tensile stress value sustained before failure is its flexural strength.
Designers of reinforced concrete use a theory based on flexural strength in determining concrete beam strengths (ACI Commitee 544, 1988).However, agencies not using flexural strength generally find the use of compressive strength convenient and reliable to judge the quality of reinforced concrete beams (Ritchard and Norman, 1991).
Flexural tests have been conducted on beams with different diameters of reinforcement bars.Teo et al. (2006), investigated the flexural strength behaviour of reinforced concrete beams with different bar diameters.They tested (4) reinforced concrete beams under centrepoint loading.The beam dimensions are as follows: 102 mm×203 mm, 102 mm×406 mm, 127 mm×610 mm and 152 mm×610 mm; but all the beams were equally spanned at 4500 mm and reinforced with Y12, Y14, Y16 and Y20, respectively.The beam flexural strengths obtained were 95, 71, 80 and 60 N/mm 2 , respectively.In another related study, Rashid and Mansur (2005) studied the flexural behaviour of High Strength Concrete (HSC) beams.Sixteen reinforced concrete beams were evaluated.Their findings showed that stresses generated by shrinkage of concrete and the creep associated with it significantly affect the cracking moment and service load deflection of reinforced HSC beams.
On the other hand, Mangat and Elgarf (1999) investigated one hundred and eleven (111) underreinforced concrete beams which underwent different degrees of reinforcement corrosion to determine their residual flexural capacity.In their results, there were marked reductions in flexural strength due to reinforcement corrosion, which was caused primarily by the breakdown of bond at the steel/concrete interface.Hence, to ascertain the limits was to mutual substitution of reinforcement bars in concrete, this study aims to evaluate the bending behaviour of beams reinforced with reinforcement bars of equivalent area but different bar diameters.
MATERIALS AND METHODS
The study focused on determination of the bending strength of reinforced concrete beams samples, whereas preliminary tests such as Aggregate Crushing Value (ACV), Aggregate Impact Value (AIV) and particle size distribution of aggregates were obtained prior to concrete making.
Both ACV and AIV tests were conducted in accordance with the requirements of British Standards Institution (1990aInstitution ( , 1990b) ) respectively, the tests were required in order to ascertain the resistance of aggregate to crushing under a gradually applied Moreover, sieve analysis was also conducted on the fine aggregates, in order to identify the gradation of the aggregate and more so, to see if it is suitable for various civil engineering purposes.The result of the particle size distribution curve for the fine aggregate is presented in Fig. 1.
Study has shown that the material passing the BS No. 200 sieve (aperture: 75 µm) is clay or silt, or combination of the two.The percentage of these in the fine aggregate is a factor that must be considered in the strength of concrete produced from sand.As described in BS 812-2, the total quantity of clay and silt in natural sand shall not exceed 4% by weight when determined by the field settling test decantation method.However, the percentage passing of clay and silt from the particle size distribution test carried out on the sand used for the concrete beams is 3.89%.This shows that the fine aggregate has the required strength and also meets the specification for the tested concrete beams.Results obtained from ACV and AIV tests on the coarse aggregate were 27 and 20% respectively.These values fall within limits (23 to 30%) for ACV and (17 to 21%) for AIV respectively, for BS standards test results for aggregates; thus the material is granite.
The bending strength test conducted on concrete beams satisfied the requirements of British Standards Institution (1983), using the centre-point loading method.A total of (20) concrete beams were produced.For unreinforced beams (control sample), (2) each of 100 mm×100 mm× 500 mm and 150 mm×150 mm×750 mm beams and (2) each of 100 mm×100 mm×500 mm and 150 mm×150 mm×750 mm beams reinforced in turns with 20 mm, 16 mm, 12 mm and 10 mm bar, were subjected to bending.Thus, about 943 mm 2 area of reinforcement was considered for all beams.The test samples have nominal depth d, for both the 100 mm×100 mm and 150 mm×150 mm cross sections and spans of 500 mm and 750 mm, respectively.The bottom bars include 3Y20, 5Y16, 9Y12, 12Y10 for the beams reinforced with 20 mm, 16 mm, 12 mm and The formwork for the concrete beams was made from dry Iroko wood, sawn and smoothened to the required dimensions for 100 mm×100 mm×500 mm and 150 mm×150 mm×750 mm beams, respectively.The concrete cover to reinforcement was limited to 20 mm in alignment with the importance of concrete cover highlighted by Awoyera et al. (2014).
A mix proportion of 1:2:4 by volume of cement, sand and granite aggregates with water-cement ratio of 0.45 were considered for casting the beams.Reinforcement bars were placed in the lubricated formwork and filled with concrete in three layers, each layer compacted with 25 blows using tamping rod.After the setting of the concrete beams had taken place, the formwork was carefully detached and the beams were placed in a water tank and cured for 28 days.
After the curing period, beams removed from the water tank were subjected to bending strength tests.During testing, each of the samples were placed in position in the flexural testing machine, correctly centered with the longitudinal axis of the beam at right angle to the supporting and load-applying rollers.This ensured that the top and bottom surfaces of the beam are parallel so that the loading was uniform across the width of the beam.The load was then applied steadily and without shock and increased continuously at 200 N/s for 100 mm×100 mm×500 mm and 450 N/s for 150 mm×150 mm×750 mm beams, in accordance with British Standards Institution (1983).The concrete beams were subjected to centre-point loading which was done simultaneously with concrete surface mounted strain gauge, used in measuring strain in the reinforced concrete beams.The strain gauge started to read immediately when the loading of the beams commenced until the breaking load was achieved.The loading rate was maintained without change until failure occurred.The maximum load read on the scale was recorded as the breaking load.
RESULTS AND DISCUSSION
Figure 5 and 6 present the results of bending tests obtained for 100 mm×100 mm×500 mm and 150 mm×150 mm×750 mm beams, respectively.The figures revealed the stresses and strains attained on each beam which showcased their bending capacity.However, the summary of the bending strengths at failure for the two sizes of beams is presented in Fig. 7.
The result obtained showed that beams reinforced with 9Y12 main bars have greater bending strengths than the other beams reinforced with 3Y20, 5Y16 and 12Y10.The percentage relative difference in the bending strength as well as their corresponding percentage relative difference in area of reinforcement can be deduced.Specifically, as the area of reinforcement increased from 943 mm 2 (for 3Y20 bars) to 1010 mm 2 (for 5Y16 bars), representing a 6.6% increase in bar area, the increase in the bending strength increased by 16.6 and 12.9%, for both the 100 mm×100 mm×500 mm and the 150 mm×150 mm×750 mm beams, respectively.In addition, as the area of reinforcement increased from 1010 mm 2 (for 5Y16 bars) to 1020 mm 2 (for 9Y12 bars), representing a 1% increase in bar area, the bending strength increased by 11.9%, for the 100 mm×100 mm×500 mm beams; whereas for the 150 mm×150 mm×750 mm beams the bending strength increased by 10.1%.Also, as the area of reinforcement decreased from 1020 mm 2 (for 9Y12 bars) to 943 mm 2 (for 12Y10 bars), representing a 8.2% decrease in bar area, the bending strength decreased by 19.2%, for the 100 mm×100 mm×500 mm beams; whereas for the 150 mm×150 mm×750 mm beams the bending strength decreased by 14.2%.Hence, it can be deduced that as the area of reinforcement increases, the bending strength of the reinforced concrete beams increase as well.
Fig. 1 :
Fig. 1: Particle size distribution curve for the fine aggregate Fig. 2: Reinforcement details for the test beams 10 mm bars respectively whereas the top bars comprise 3Y10 for all the beams except the beams reinforced with 12Y10 for which the top bars were 4Y10.However, 4 mm and 6 mm diameter bars were used as space bars and links for all beam samples reinforced with 3Y20, 5Y16, 9Y12 and 12Y10.The arrangement of reinforcement and beam details are presented from Figs. 2 to 4.The formwork for the concrete beams was made from dry Iroko wood, sawn and smoothened to the
Fig. 3 :Fig. 4 :
Fig. 3: Details of the reinforced concrete beams showing top and bottom bars for 100 mm×100 mm cross section | 2,893.8 | 2015-01-01T00:00:00.000 | [
"Engineering",
"Materials Science"
] |
Anti-Cancer Activity of Verteporfin in Cholangiocarcinoma
Simple Summary Cholangiocarcinoma (CCA) is a highly lethal malignancy, and its prognosis is poor. There are unmet needs to develop effective therapies. The overexpression of Hippo/YAP pathway and the association of Hippo/YAP pathway with an immunosuppressive microenvironment is indicated with bulk RNA sequencing data. In this study, we investigated the antitumoral effect of verteporfin in CCA YAP/AKT murine models. We found that verteporfin reduced liver weight and tumor formation in CCA YAP/AKT mice. Our results also showed the change in immune cell composition in liver/tumors with the treatment of verteporfin as well as the inhibition of cancer stemness. Our data suggest the potential application of verteporfin in patients with an overexpression of Hippo/YAP pathway. Abstract Cholangiocarcinoma (CCA) is a heterogenous malignancy that arises from the biliary epithelium and has a poor clinical prognosis. The Hippo/yes-associated protein (YAP) pathway has been reported to affect various aspects of tumorigenesis, with high expression of YAP1 being negatively associated with survival in CCA patients. Thus, we investigated the antitumoral effect of verteporfin, a YAP1 pathway inhibitor, in YAP1/AKT hydrodynamic tail vein injected murine models. We also used flow cytometry and single-cell RNA sequencing (scRNA-seq) to analyze the change in the immune cell profile and malignant cell stemness following verteporfin treatment. Our results demonstrated reduced liver weight and tumor formation in verteporfin-treated groups compared to that of a vehicle-treated group. Immune cell profiling through flow cytometry showed that relative to the vehicle, verteporfin induced a higher ratio of tumor-associated macrophage (TAM) M1/M2 and increased the percentage of activated CD8 T cell population (CD8+CD25+ and CD8+CD69+). scRNA-seq analysis showed significantly increased TAM M1 populations following verteporfin treatment and decreased proportions of stem-like cells within the malignant cell population. In summary, this study indicates that in CCA YAP/AKT murine models, verteporfin reduces tumorigenesis by polarizing anti-tumoral TAM and activating CD8 T cells and decreasing stem-like malignant cell proportions in the tumor microenvironment.
Background
Cholangiocarcinoma (CCA) is a heterogeneous malignancy originating from the biliary epithelium in the biliary tree system that has become one of the leading causes of liver cancer-related deaths worldwide. The occurrence of CCA has consistently increased
YAP/AKT CCA Mice Model and Tissue Process
Six-to eight-week-old C57BL/6 mice were purchased from Charles River Laboratory (Wilmington, MA, USA). The mice underwent hydrodynamic tail vein injections with the plasmid mixture as previously described [22], consisting of 30 µg of YAP1, 20 µg of AKT, and 2 µg of HSB2 plasmids. The mixture was dissolved in a total volume of 1600 µL of PBS. The plasmids were prepared by growing in E. coli cultures and isolated using a Plasmid DNA Maxiprep Kit (MACHEREY-NAGEL, Düren, Germany). Plasmid concentrations were measured using a NanoDrop Spectrophotometer TM (Thermo Fisher Scientific, Frederick, MD, USA). Mice were euthanized at 8 weeks after the plasmid injection and 5 weeks after the treatment. Sections of the mouse liver samples were collected and fixed in a formaldehyde solution. The fixed liver samples were trimmed, paraffin blocks and slides were made, and hematoxylin and eosin stain (H&E) staining was performed by Histoserv (Germantown, MD, USA). Quantification of the stained area was observed under Halo software in the Molecular Histopathology Laboratory (MHL) of the National Cancer Institute (NCI) (Frederick, MD, USA). Hematoxylin and eosin-stained sections were scanned at 20× objective magnification (0.5 µm/pixel) using an Aperio AT2 digital whole-slide scanner (Leica Biosystems, Deer Park, IL, USA). The presence of CCA and extent of tissue infiltration were confirmed by an experienced murine histopathologist. The remaining liver samples were processed for flow cytometry and scRNA-seq analysis as mentioned below. All experiments were conducted according to the local institution guidelines and approved by the Animal Care and Use Committee of the National Institutes of Health (Bethesda, MD, USA).
Verteporfin In Vivo Treatment
Three weeks after the tail vein injection, mice were randomly split into two groups treated with either vehicle (DMSO, containing PBS solution) or verteporfin (in PBS, 100 mg/kg) (Millipore Sigma, St. Louis, MO, USA) every three days for 5 weeks, respectively (Supplemental Figure S1). Eight weeks after the plasmid injection and 5 weeks after the initial treatment, all mice were euthanized using carbon dioxide asphyxiation. Mouse livers were removed and washed. The weight of the livers was measured and compared between the groups as the indication of tumorigenesis.
Library Preparation and Sequencing for Mouse Sample
Single-cell sequencing was performed using 10x Genomics scRNA-Seq 3 v3.1 according to the manufacturer's instructions. Cell suspensions were assessed and counted with acridine orange and propidium iodine fluorescence dye on an automated cell counter (LunaFL, Logos Biosystems) (Annandale, VA, USA) and adjusted for single-cell partitioning to target approximately 6000 datapoints per sample when possible. For single-cell library preparation, as defined in the 10x Genomics user guide, following cell partitioning with barcoded gel beads, the cells are lysed, and poly-adenylated transcripts are reverse-transcribed with the inclusion of a cell-specific barcode and a unique molecular identifier. Partitioning droplets are broken, and barcoded cDNA is amplified for 14 cycles before Illumina-based sequencing libraries are prepared by fragmenting cDNA and adding necessary sequencing adapters along with a sample-specific index barcode. For sample preparation on the 10x Genomics platform, the Chromium Next GEM Single Cell 3 Kit v3.1 (PN-1000268), Chromium Next GEM Chip G (PN-1000120) and Dual Index Kit TT Set A (PN-1000215) were used. The molarity of each library was calculated based on the concentration and library size measured using a Bioanalyzer (Agilent Technologies, Santa Clara, CA, USA). Libraries were pooled and normalized to a final loading concentration. The sequencing run was set up as recommended with 28 cycles + 10 cycles + 10 cycles + 90 cycles. Demultiplexing was performed using the cellranger mkfastq pipeline, which allows for one mismatch in the sample index barcodes. Raw reads were aligned to the mm10 reference genome (refdatagex-mm10-2020A) to generate a per-cell gene expression count matrix with cellranger count (cellranger v6.1.2, 10x Genomics). A per-cell mean sequencing depth of 50,000 reads/cell was targeted for each sample. Libraries were sequenced on an Illumina NextSeq 2000.
Murine CCA scRNA-Seq Data Analysis
Filtered feature-barcode matrix.h5 files from cellranger output for all samples were merged into a Seurat Object using the Seurat workflow [23]. Cells were preprocessed using Unique Molecular Identifier (UMI) counts, the number of expressed genes, and mitochondrial content; cells with low UMI counts (>500) or low complexity (<0.5 genes/UMI) were filtered from the data, along with cells whose gene or mitochondrial content exceeded 3 absolute deviations above the respective medians. The gene expression data were then normalized using the Seurat SCTransform function [23]. Downstream analyses involving differential gene expression (DEG) and gene set enrichment analyses (GSEA) were performed within the NIH Integrated Analysis Portal (NIDAP) using R programs developed on the Palantir Foundry platform (Palantir Technologies, Washington, DC, USA). All scRNA-seq data were submitted to the Gene Expression Omnibus (GEO) public database at the NCBI. The code used for the analysis was deposited in GitHub (https://github.com/ NIDAP-Community/Anti-cancer-activity-of-verteporfin-in-cholangiocarcinoma, accessed on 20 February 2023). Raw data were deposited in GEO (GSE229855).
Highly variable genes were outlined by principal component analysis (PCA) and the first 15 principal components were further projected as Uniform Manifold Approximation and Projection (UMAP) plots [24]. The number of principal components to be used was calculated using the Elbow method. Unsupervised clustering was achieved using the Seurat FindClusters function [23]. Cell clusters were illustrated according to the DEG and canonical marker genes. Sub-clustering analysis was conducted by re-running FindClusters on filtered subsets.
Cell Identification
For each individual cell, the average expression of immune cell markers in previously published literature [25] was calculated using the Seurat AddModuleScore function. Cells were then defined based on the marker set with the highest average. The copy number variation (CNV) across epithelial cells was calculated using inferCNV [26]. A cutoff of 0.1 was used to screen cells possessing low gene counts and an sd_amplifier value of 2 was applied to account for background noise. A copy number score (CNS) was arranged for each cell as the formula below: Epithelial cells with a CNV in the top 25 percentile were further classified as malignant cells. The remaining epithelial cells were defined as cholangiocytes.
Differential Expression Analysis and Gene Set Variation Analysis (GSVA)
Differential gene expression analysis was performed on log-normalized data using the limma function and according to the pseudobulk approach outlined in [23]. GSEA using the fgsea (version 1.8.0) R package was then run on the ranked list of differentially expressed genes. Pathways coinciding with important gene sets were referred from the H:Hallmark, CP:KEGG, and CP:Reactome collections within the Molecular Signature Database (MSigDB) (v2022.1.Mm). Pathways characterizing similar biological functions were eliminated from the visualization.
Human Bulk Transcriptomic Analysis of CCA Samples
TIMER2.0 was used to compare the expression level of the YAP signaling gene signature between non-tumor and tumor tissues and analyze the correlation between YAP1 signaling expression and stemness marker gene expression and infiltrating immune cells (http://timer.comp-genomics.org/, accessed on 20 February 2023) [27].
Statistical Analysis
Statistical analysis was performed with GraphPad Prism 8 (GraphPad Software). The significance of the difference between groups was calculated by Student's unpaired t test. p < 0.05 was considered statistically significant.
YAP1 Pathway Correlated with Cancer Stemness and Stromal Cells in CCA
To compare the expression levels of YAP1 signaling pathway genes between tumor and normal tissue samples, we used the TIMER2.0 platform to evaluate the expression profiles based on the cholangiocarcinoma cohort (CHOL) obtained from TCGA (The Cancer Genome Atlas) database [27]. As shown in Figure 1A and Supplemental Figure S2A, we found that the expression levels of YAP1, Transcriptional enhanced the associated domain (TEAD) family and YAP signaling signature in tumor tissues of CCA and were significantly higher than the corresponding normal tissues. There is a positive correlation of the expression level between the YAP1 pathway gene signature and key stemness transcription factor SOX9 ( Figure 1B and Supplemental Figure S2B). Moreover, the expression of the YAP1 pathway gene signature was significantly and positively associated with the infiltrating levels of immunosuppressive stromal cells, including cancer-associated fibroblasts, macrophage and Tregs, but negatively associated with antitumoral CD4 Th1 ( Figure 1C and Supplemental Figure S2C). These results indicate that the YAP1 pathway plays profound roles related with CCA stemness and immunosuppressive tumor microenvironment (TME).
Antitumoral Efficacy of Verteporfin in YAP/AKT Mouse Model
Since the liver weight represents the overall tumor growth or formation in this model, the liver weight was measured and compared between DMSO (vehicle-treated group) and verteporfin-treated groups (Figure 2A,B). As a result, the liver weights of verteporfin-treated mice were significantly reduced (21%) compared to the liver weights of vehicle-treated mice (Figure 2A, p = 0.0375). The tumor area was quantified using H&E staining ( Figure 2C). The stained tumor area was calculated based on the whole liver area as a percentage (%). The tumor areas of verteporfin-treated mice were significantly lower in comparison to the vehicle-treated group ( Figure 2D, p = 0.0097). Therefore, verteporfin reduced tumorigenesis in the YAP/AKT mouse model.
Antitumoral Efficacy of Verteporfin in YAP/AKT Mouse Model
Since the liver weight represents the overall tumor growth or formation in this model, the liver weight was measured and compared between DMSO (vehicle-treated group) and verteporfin-treated groups (Figure 2A,B). As a result, the liver weights of verteporfintreated mice were significantly reduced (21%) compared to the liver weights of vehicletreated mice (Figure 2A, p = 0.0375). The tumor area was quantified using H&E staining ( Figure 2C). The stained tumor area was calculated based on the whole liver area as a percentage (%). The tumor areas of verteporfin-treated mice were significantly lower in comparison to the vehicle-treated group ( Figure 2D, p = 0.0097). Therefore, verteporfin reduced tumorigenesis in the YAP/AKT mouse model.
Verteporfin Treatment Modulates Immune Cell Landscape of CCA in YAP/AKT Mouse Model
To investigate whether verteporfin modulates the TME that leads to the control of CCA growth in the YAP/AKT mouse CCA model, immune cells from whole liver tissues
Verteporfin Treatment Modulates Immune Cell Landscape of CCA in YAP/AKT Mouse Model
To investigate whether verteporfin modulates the TME that leads to the control of CCA growth in the YAP/AKT mouse CCA model, immune cells from whole liver tissues were isolated and analyzed using flow cytometry as described in the Materials and Methods section. B cells, CD4 and CD8 T cells, CD11b+ myeloid cells, macrophages and dendritic cells were identified (Supplementary Figure S3A,B). Gating strategies were shown in Supplemental Figure S4. Although there was no significant change in the percentage of CD8 T cells between the vehicle and verteporfin treatment groups (Supplementary Figure S3A), the proportion of activated CD8 T cells (CD25+CD8+) were significantly increased along with a decreased proportion of memory CD8 T cells (CD69+CD8+) ( Figure 3A). While the proportion of individual exhausted CD8 T cells [CD39+CD8+ and programmed cell death protein-1 (PD-1)+CD8+] showed no change, PD-1+CD39+ cells from CD8 T cells were significantly reduced in verteporfin treated group ( Figure 3B), which suggests that verteporfin may inhibit complete/terminal exhaustion of CD8 T cells. In addition, verteporfin increased the percentage of activated CD4 T cells (CD25+CD4+) and decreased the percentage of memory CD4 T cells (CD69+CD4+) ( Figure 3C) but had no effect on the overall percentages of the CD4 T cell population and exhausted CD4 T cells ( Figure 3D).
Macrophages play a critical role in tumorigenesis.
To study this, we tested the changes in TAM-M1 and TAM-M2 macrophages (CD80 and CD86 for TAM-M1 and CD163 and CD206 for TAM-M2, respectively). The proportion of CD163+ macrophages was significantly reduced in the verteporfin-treated group (p < 0.0001), whereas there was a decrease in the proportions of CD86-and CD80-positive cell populations ( Figure 4A). However, when looking at the relative proportions of TAM-M1 and TAM-M2 macrophages as measured by CD80/CD163 or CD86/CD163 ratios, verteporfin treatment was noted to significantly increase the TAM M1/M2 ratio ( Figure 4B). Although there was an increased trend of proportions of B cells and dendritic cells observed (Supplemental Figure S3A,B) in the verteporfin-treated group, the changes were not significant.
To further illustrate how verteporfin affects TME dynamics in the YAP/AKT CCA mouse model, a total of 33,769 isolated single cells was obtained from mouse normal livers or tumors, which covered various tumorigenic stages of CCA. In addition, we performed scRNA-seq on livers or tumors from a YAP/AKT mouse model treated either with a vehicle or verteporfin. A total of 14 clearly separated cell clusters were identified ( Figure 5A,B, Supplemental Figure S5). Based on the expression of known markers, we identified endothelial cells, hepatocytes, epithelial cells, immune cells, and fibroblasts ( Figure 5A, Supplemental Table S1). The immune cells were comprised of CD4, CD8 and Treg, NK cells, B cells and myeloid cells including dendritic cells, TAM-M1 and TAM-M2 ( Figure 5A,B, Supplemental Figure S5A,B).
Remarkably, the proportion of TAM-M1 cells, which function as pro-inflammatory/antitumorigenic immune cells, was greatly induced (fivefold) by verteporfin treatment, while TAM-M2 did not show a significant difference ( Figure 5B and Supplemental Figure S5C). The proportions of B cells and CD8 T cells decreased in the verteporfin-treated group, though these were insignificant changes (Supplemental Figure S5D,E). We further analyzed the subset of CD8, CD4 and TAMs (TAM-M1+TAM-M2) cell population based on the results from flow cytometry (Figures 3-5). As shown in Supplemental Figure S6A-C, only the change in the percentage of CD80+ TAMs (TAM-M1) among TAMs significantly increased after verteporfin treatment. Other changes showed a similar, although not significant, tendency to the flow results, for example, CD25+CD8+ and PD1+CD39+CD8+ cell populations. was significantly reduced in the verteporfin-treated group (p < 0.0001), whereas there was a decrease in the proportions of CD86-and CD80-positive cell populations ( Figure 4A). However, when looking at the relative proportions of TAM-M1 and TAM-M2 macrophages as measured by CD80/CD163 or CD86/CD163 ratios, verteporfin treatment was noted to significantly increase the TAM M1/M2 ratio ( Figure 4B). Although there was an increased trend of proportions of B cells and dendritic cells observed (Supplemental Figure S3A,B) in the verteporfin-treated group, the changes were not significant. To further illustrate how verteporfin affects TME dynamics in the YAP/AKT CCA mouse model, a total of 33,769 isolated single cells was obtained from mouse normal livers or tumors, which covered various tumorigenic stages of CCA. In addition, we performed scRNA-seq on livers or tumors from a YAP/AKT mouse model treated either with a vehicle or verteporfin. A total of 14 clearly separated cell clusters were identified ( Figure 5A,B, Supplemental Figure S5). Based on the expression of known markers, we identified endothelial cells, hepatocytes, epithelial cells, immune cells, and fibroblasts ( Figure 5A, Supplemental Table S1). The immune cells were comprised of CD4, CD8 and Treg, NK cells, B cells and myeloid cells including dendritic cells, TAM-M1 and TAM-M2 ( Figure 5A,B, Supplemental Figure S5A,B).
Remarkably, the proportion of TAM-M1 cells, which function as pro-inflammatory/anti-tumorigenic immune cells, was greatly induced (fivefold) by verteporfin treatment, while TAM-M2 did not show a significant difference ( Figure 5B and Supplemental Figure S5C). The proportions of B cells and CD8 T cells decreased in the verteporfintreated group, though these were insignificant changes (Supplemental Figure S5D,E). We
Verteporfin Reduced Expression of Cancer Stemness Genes in Malignant Cells
Overall, verteporfin significantly suppressed the Hippo/Yap1 pathway as determined through GSEA ( Figure 6A and Supplemental Table S2), indicating the effectiveness of treatment. To further investigate how verteporfin affects malignant cells, we compared the transcriptomic changes in the malignant cell population between the verteporfin treatment and vehicle control groups. We found many significant changes in this population treated with verteporfin (Supplemental Figure S7, Supplemental Table S3, Supplemental Figure S6). GSEA analysis indicated upregulated interferon α and γ signaling pathways, inflammatory response, and adaptive/innate immune process with the treatment of verteporfin ( Figure 6B, Supplemental Figure S8), which were consistent with the antitumoral
Verteporfin Reduced Expression of Cancer Stemness Genes in Malignant Cells
Overall, verteporfin significantly suppressed the Hippo/Yap1 pathway as determined through GSEA ( Figure 6A and Supplemental Table S2), indicating the effectiveness of treatment. To further investigate how verteporfin affects malignant cells, we compared the transcriptomic changes in the malignant cell population between the verteporfin treatment and vehicle control groups. We found many significant changes in this population treated with verteporfin (Supplemental Figure S7, Supplemental Table S3, Supplemental Figure S6). GSEA analysis indicated upregulated interferon α and γ signaling pathways, inflammatory response, and adaptive/innate immune process with the treatment of verteporfin ( Figure 6B, Supplemental Figure S8), which were consistent with the antitumoral outcome of verteporfin. Verteporfin treatment downregulated biosynthesis of steroids, lipoproteins, and cholesterol ( Figure 6C). These results indicated that verteporfin treatment induced an immune response within tumors as well as altering the liver function. We further questioned whether the proportion of cells with positive cancer stem cell markers was affected by verteporfin treatment ( Figure 6D). Overall, most of the proportions of stemness gene-expressing cells were reduced by verteporfin treatment ( Figure 6E). Based on the results, verteporfin might inhibit tumorigenesis in CCA via down-regulation of cancer stemness.
Discussion
In this study, we investigated the anti-tumoral effect of verteporfin in the YAP/AKT mouse CCA model and changes in malignant cells and immune cell compartment. Consistent with the results in a previous study [21], verteporfin treatment reduced the liver weight and tumor area while modulating immune cell profiles and suppressing cancer stemness.
To the best of our knowledge, the effect of YAP inhibition on immune cell modulation has not been widely reported. T cell activation is a pivotal event in the adaptive immune response, which leads to the production and release of proinflammatory cytokines. Eventually, activated T cells interact with the antigens on their target cells and then results in cytotoxicity, apoptosis and cell destruction [28]. Here, we showed that verteporfin treatment induced activation markers of CD25 in CD4 and CD8+ T cells according to our flow cytometry result, supporting that modulation of the immune response mediated by T cell activation might be one of factors in verteporfin causing tumor suppression in the YAP/AKT CCA mouse model.
Early and late dysfunctional tumor-specific T cells can be characterized by surface marker expression. PD1 and lymphocyte-activation gene 3 (LAG3) is expressed during both early and late stages of dysfunctional T cells, but late dysfunctional T cells express additional inhibitory receptors, such as CD38, CD39, CD101 and TIM3 (T-cell immunoglobulin and mucin-domain containing 3) [29]. Our results show that verteporfin treatment reduced the proportions of double-positive PD1+CD39+CD8+ T cells. At an early stage of tumor development, T cells undergo an anergy-like early dysfunctional state that allows cancer cells to grow. Constant stimulation by tumor antigens with cancer progression triggers a late dysfunctional state. T cell exhaustion mechanisms may regulate the loss of cytotoxic effector function, including cytokines and/or cytotoxic molecules, such as interferon-γ [30]. Therefore, reduced PD1+CD39+ in CD8+ T cell populations mean that the anti-tumor effect of verteporfin might result from the inhibition of terminal exhaustion/dysfunctional CD8+ T cells.
Differentiation of macrophages in the microenvironment is remarkably dynamic since macrophages can quickly transition from one phenotype to the other based on the microenvironment or stimulation [31]. M1/M2 macrophage balance polarization determines the inflammatory status and homeostasis; M1 is considered to be pro-inflammatory, while M2 macrophages suppress inflammation by secreting high amounts of interleukin 10 (IL-10) and transforming growth factor-beta (TGF-β) [32].
In our study, another major change in immune cells by verteporfin treatment is TAM-M1 and M2. Our flow cytometry data showed an increased M1/M2 ratio (CD80/CD163 and CD86/CD163), which was different from scRNA-seq data that showed a significantly increased TAM-M1 population with verteporfin treatment. Although there is a discrepancy between these two sets of data in terms of cell composition, our data showed an overall decrease in the tumor volume with verteporfin treatment, which matched either the increased overall ratio of M1/M2 by flow cytometry or increased the TAM-M1 population by scRNA-seq.
Verteporfin was reported previously to decrease the stem cell marker Oct4, protein expression of epithelial-mesenchymal transition marker N-cadherin and spheroid formation [18]. YAP upregulates cancer stemness properties and phenotypes via Sox9, and verteporfin inhibits those characteristics [33]. We tested verteporfin using the animal model derived by YAP/Akt transduction and investigated if verteporfin affects cancer stemness. Our single-cell analysis showed that malignant cells with the expression of cancer stemness genes were reduced in the verteporfin-treated group. This result suggests that verteporfin reduced tumorigenesis partially derived by the inhibition of cancer stemness.
Recent transcriptomics analysis of human CCA suggested that human iCCA can be classified into four different groups based on the stroma, immune and tumor microenvironment [34]. One of the groups, characterized as a hepatic stem-like group, presented with high TAM-M2 infiltration, enrichment of Hippo/YAP pathway and Notch pathways, indicating potential therapeutic targets of CCA. Our study suggests that targeting the YAP pathway may be a potential candidate for drug development in CCA with a stemness feature.
Conclusions
Our data suggested the anti-tumoral activity of verteporfin in a YAP/AKT CCA animal model. We demonstrated that verteporfin remodels the immune environment, which might mediate the antitumoral effect of verteporfin through the immune response. In addition, our single-cell analysis data showed that verteporfin reduced the cancer stemness gene expressing malignant cells, suggesting that the inhibition of cancer stemness might also mediate tumor suppressive effect of verteporfin.
Supplementary Materials: The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/cancers15092454/s1, Figure S1. Schema of treatment experiment plan. Figure S2. (A) The expression levels of YAP1 signaling downstream targets in cholangiocarcinoma cohort in TCGA cancers and the corresponding normal tissues. (B) correlation between representative genes of YAP1 signaling downstream targets with SOX9. (C) Correlation between the expression of representative individual of YAP1 signaling downstream targets with immune suppressive cell infiltration. Figure S3. Immune cell populations of YAP/AKT model. Figure S4. Flow cytometry gating strategy for (A) immune profiling, (B) T cell activation/exhaustion and (C) myeloids panels. Figure S5. Single-cell analysis of liver and CCA from YAP/AKT mice treated with vehicle and verteporfin, respectively. Figure S6. Single-cell analysis and comparison of subset of CD8 T cells (A), CD4 T cells (B), and TAMs (C) from YAP/AKT mice treated with verteporfin and vehicle. Figure S7. Volcano plot showed the differential expressed genes of malignant cells from YAP/AKT mice treated with verteporfin in comparison to vehicle. Figure S8. GSEA analysis of upregulated pathway in malignant cells with verteporfin treatment. Table S1. Cell counts from single cell RNA sequencing. Table S2. GSEA analysis of all differential expressed genes in all cells between treated with verteporfin and vehicle. Table S3. GSEA analysis of all differential expressed genes in malignant cells between treated with verteporfin and vehicle.
Author Contributions: C.X. conceived and designed the study. J.L.G., X.W. and J.B. conducted the experiments. J.L.G., X.W., J.B., B.R., B.O.K. and C.X. analyzed the data. J.L.G. and C.X. wrote the manuscript with input from all authors. M.K., B.O.K. and M.C.C. provided comments and feedback on the data and manuscript. All authors edited and revised the manuscript, provided comments, and coordinated the collaboration. All authors have read and agreed to the published version of the manuscript.
Funding: This research was funded by the Physician-Scientist Early Investigator Program at CCR of NIH/NCI to CX (ZIA BC 011888).
Institutional Review Board Statement:
All animal experiments were conducted according to local institutional guidelines and approved by the Animal Care and Use Committee of the National Institutes of Health (TGOB-014) (Bethesda, MD, USA).
Informed Consent Statement: Not applicable.
Data Availability Statement: The processed scRNA-seq dataset was deposited at the NCBI's Gene expression omnibus (GEO) data repository. The remaining data are present in the article, Supplementary Materials, or available from the authors upon reasonable request.
Conflicts of Interest:
The authors declare no competing interests. | 5,964 | 2023-04-25T00:00:00.000 | [
"Biology",
"Medicine"
] |
An Ensemble Learning Algorithm for Machinery Fault Diagnosis Based on Convolutional Neural Network and Gradient Boosting Decision Tree
In the massive mechanical fault data, the value density of fault information is low, and the data quality is uneven. What’s more, the multi-source signals collected by different sampling methods are different. At present, the expert system or shallow neural network model with weak self-learning ability cannot meet the requirements. Therefore, aiming at the characteristics of coupling, uncertainty and concurrency of mechanical faults, this paper constructs two kinds of 2D-CNN fault feature data sets, and uses Convolutional Neural Network (CNN) with strong self-learning ability to build two kinds of fault diagnosis models: CNN-Z and CNN-F. With CNN-Z and CNN-F models as base learners, this paper utilizes the ensemble algorithm Gradient Boosting Decision Tree (GBDT) to combine multiple bases. Compared with the results of the single base learner, the outcomes have higher accuracy and lower generalization error. Through the analysis and comparison of the performance indicators of the algorithm, this paper concludes that the diagnosis error of the fault diagnosis algorithm based on CNN and GBDT is the lowest with 1.79%, and the effectiveness, reliability and accuracy of the proposed algorithm in mining hidden fault state information are verified.
Introduction
Mechanical equipment is an important carrier of national economy and national defence construction.
With the advancement of the information age, its degree of automation, real-time, intelligence is higher than before. A lot of equipment works in harsh environment like high temperature, high pressure and enemy threat. All these factors put forward higher requirements for its operation quality and performance. In the process of mechanical equipment operation, mechanical failure is the "potential killer" of the whole safety service of mechanical equipment [1]. Once a failure occurs, it will affect the function of mechanical equipment, leading to safety accidents in serious cases. Therefore, fault diagnosis research, mining hidden fault state information in multi-source signals, timely positioning and confirming fault location and degree, provide accurate information for maintenance of mechanical equipment and fault prediction, and play a key role in ensuring the normal working performance of equipment.
Mechanical equipment has a long service time and many data acquisition points, so we can obtain massive data, which is suitable for using artificial intelligence methods such as machine learning and IOP Publishing doi: 10.1088/1742-6596/2025/1/012041 2 deep learning for fault diagnosis and diagnosis [2]. Traditional machine learning algorithms such as Support Vector Machines (SVM) [3], Probabilistic Neural Networks (PNN) [4], Back Propagation Neural Networks (BP Neural Networks) [5], Radial Basis Function Networks (RBF) and so on, RBF Networks [6] and other algorithms are suitable for processing small-scale data samples. Due to the influence of input data dimension, traditional algorithms have limited learning ability and are sensitive to samples, which easily leads to over fitting. Therefore, researchers gradually introduce deep learning, such as RBM, CNN and RNN [7][8][9][10]. In view of the randomness, discreteness, periodicity and structure of fault data, RBM is not suitable for supervised learning and has no scale invariance. RNN is used to process continuous data and cannot identify faults with high accuracy. There are many researches on using CNN algorithm to realize fault diagnosis. Chen and others use deep neural network model to identify the fault state of rolling bearing, which shows that the method has high accuracy and reliability [11]. Chen et al. propose a deep learning method based on convolutional neural network, which introduces the advantages of image recognition and visual perception into bearing, and has achieved high accuracy by simulating the cognitive process of cerebral cortex [12]. Zhang et al. propose a CNN model with kernel in input layer [13]. There are many forms of data input for CNN algorithm: O. Janssens et al. process the original signal by EEMD, and then put one-dimensional signal into CNN model [14]. The diagnosis accuracy is higher than that in reference [15]. However, this method not only takes a long time, but also does not consider the internal correlation of bearing vibration signal, resulting in low fault diagnosis accuracy. In order to improve the accuracy, M. Zhang et al. use CNN algorithm based on two-dimensional samples [16]. Hoang et al. also use CNN algorithm based on two-dimensional data, which obtains better accuracy and consumes longer time [17]. In addition, in order to improve the diagnosis accuracy, it is necessary to deepen the network layers of a single classifier, which will lead to the increase of parameters and make the model fall into the local optimal value, which is prone to over fitting. In order to improve the generalization performance of the algorithm, the ensemble algorithm synthesizes the results of each base classifier, thus reducing the dependence on a single classifier. For example, J. Wang et al. use ensemble learning for Autism Spectrum Disorder (ASD) Diagnosis [18]. Lango et al. use ensemble algorithm for unbalanced data processing [19], and obtain a system with low generalization performance. To conclude, we may find that ensemble algorithms can solve this kind of problems very well.
Therefore, aiming at the sample data of mechanical fault feature information, feature similarity and difference mixed together, this paper constructs 2D-CNN data set, establishes CNN based classifier, and finally proposes an ensemble learning algorithm for mechanical fault diagnosis based on CNN and GBDT. This model trains multi-classifier to replace single classifier, improves the accuracy of fault diagnosis and narrows the generalization gap of the model. The implementation flow chart of the proposed algorithm is shown in figure 1.
Intercepting The Tested Data Samples
This paper, targeting the general unbalanced fault data from sampling counter examples and over sampling positive example, assumes that there are k ( 1 k ) fault types of the tested object, then . Time series transformation is performed for each sample in the tested sample set , in which the data characteristic period T is the width of time series image
Obtaining Time-Frequency Image
As for the non-stationary and nonlinear mechanical fault signals, we perform Continuous Wavelet Transform (CWT) on the data set , so as to produce the time-frequency image. Assumption: a is a scale and ,0 a R a , indicating the frequency-related scaling; means translational value and is the wavelet basis function, which is obtained by the stretch and translation of wavelets. The transforming process of CWT is as follows: We get time-frequency image
CNN
In order to reduce the requirements of memory consumption and computation, the classical LetNet5 Convolutional Neural Network (LetNet5 CNN) model is used as the base classification model. The LetNet5 CNN model consists of the input layer, the convolutional layer C1, the sampling layer S1, the fully connected layer and the output layer. The framework of the classic LetNet5 CNN model is shown figure 3. As is shown in figure 3, the input image 11 WH is input through the input layer. After that, S W H is obtained by stretching and expansion, and finally output layer transmits after the fully connected layer.
In figure 3, the CNN output layer uses the softmax function to calculate the maximum value of various output results of the fully connected layer, which is the output prediction. The expression is as follows: In which, P is Pooling Feature Matrix; is the weight matrix of fully connected layer; b is the bias. Remark for figure 3. There are two kinds of convolution: strict convolution and convolution after padding. Dimensions remain unchanged after strict convolution, while the dimensionality decreases after convolution are padded. In order to avoid the reduction of the dimensionality of the input data during the convolution process, this paper adopts the method of convolution after padding.
Setting up CNN Based Classifier Model Based on Time Series Image (CNN-Z)
The time series image is divided into groups, and the balance data is input into the LeNet5 CNN model as the first training data set 1
Setting up CNN Based Classifier Model Based on Time-Frequency Image (CNN-F)
In the same way, the time-frequency image is divided into groups, and the balance data is input into the LeNet5 CNN model as the second training data set 1
Setting up Fault Diagnosis Model Based on CNN and GBDT
In this paper, the CNN-Z model and CNN-F model are serially integrated by GBDT algorithm. The first base classification model In this paper, GBDT algorithm is used to deal with multi classification problem. Therefore, its Loglikelihood Loss Function is: 6 We initial the classification tree by adopting log-likelihood loss function, which is: The best residual fitting value of each leaf node is calculated: After updating the tree: The formula of feasibility index F1 is: where P is the precision rate and R is the recall rate.
Model Validation
In order to verify the proposed CNN and GBDT based fault diagnosis algorithm, this paper uses the rolling bearing fault data of Western Reserve University, which is the signal with the motor drive terminal DE and the sampling frequency of 12KHZ. Bearing failure occurs in these position of inner race, bar and outer race, so the (10) and (11). The results are shown in table 1. Table 1 shows that the diagnosis accuracy of GBDT model based on CNN is high, with the lowest 97.98% and the highest 99.44%, and the metric F1 can reach 0.976, which proves the feasibility of the invention.
In order to prove the effectiveness and high-precision performance of the model, this paper compares Figure 8 shows the comparison results of diagnosis error among CNN model based on time series image (CNN-Z), CNN model based on time-frequency image (CNN-F) and GBDT model based on CNN. As can be seen from figure 8, when the number of training periods is 50, the average diagnostic errors of CNN-Z, CNN-F and GBDT model based on CNN reach relaxation, and when the number of training periods is 55, the diagnostic errors of the three models are 8.83%, 2.89% and 1.79% respectively. In addition, the diagnosis error of the integrated model GBDT model based on CNN is smaller, which improves the fault diagnosis accuracy.
Conclusion
In this paper, the fault data of bearings is transformed into different data feature sets to improve the value density of fault data and increase the fault database. And GBDT algorithm is used to integrate the results of multiple base learners. The fault diagnosis algorithm based on CNN and GBDT has the highest accuracy. The related research of this paper has transformed into invention patents. In addition, the research results of this paper provide the data and fault diagnosis model for the follow-up research of data fusion, intelligent fault diagnosis and fault-tolerant control. | 2,478 | 2021-09-01T00:00:00.000 | [
"Engineering",
"Computer Science"
] |
Dynamics and Phases of Nonunitary Floquet Transverse-Field Ising Model
Inspired by current research on measurement-induced quantum phase transitions, we analyze the nonunitary Floquet transverse-field Ising model with complex nearest-neighbor couplings and complex transverse fields. Unlike its unitary counterpart, the model shows a number of steady phases, stable to integrability breaking perturbations. Some phases have robust edge modes and/or spatiotemporal long-range orders in the bulk. The transitions between the phases have extensive entanglement entropy, whose scaling with the system size depends on the number of the real quasiparticle modes in the spectrum at the transition. In particular, the volume law scaling appears on some critical lines, protected by pseudo-Hermiticity. Both the scaling of entanglement entropy in steady states and the evolution after a quench are compatible with the non-Hermitian generalization of the quasiparticle picture of Calabrese and Cardy at least qualitatively.
I. INTRODUCTION
Non-equilibrium quantum dynamics in many-body systems is an active area of research cutting across many different subfields of physics.While nontrivial dynamics can be generated in many different ways, there are two generic routes that are particularly attractive.The first is to induce dynamics by a periodic drive, the socalled Floquet approach.A wealth of recent work shows that many-body Floquet systems can exhibit novel phase transitions [1][2][3][4][5].Realizing nontrivial quantum dynamics in interacting Floquet systems, however, requires extra ingredients that help suppress or completely avoid heating to an uninteresting infinite-temperature state [6][7][8].
Another, seemingly distinct route to novel nonequilibrium dynamics is to consider the evolution of a monitored many-body quantum system.By tuning the measurement rate, and considering an ensemble of quantum trajectories (each corresponding to a particular set of measurement outcomes), one can induce a novel class of phase transitions [12][13][14].Instead of traditional phase transitions due to symmetry breaking, these measurement-induced phase transitions (MIPT) do not have conventional order parameters, but instead are witnessed by entanglement properties and other quantum information-theoretical quantities [15,16].First experimental evidence of such transitions has recently been reported [17,18].
In this work, we analyze a potentially even richer class of non-equilibrium many-body dynamics realized by combining time-periodic Floquet driving with effective nonunitary evolution (which can be associated with monitoring of the quantum system).Our starting point is the archetypal Floquet transverse-field Ising model (TFIM), where a one-dimensional (1D) lattice of spins (described by Pauli operators X j , Y j , Z j ) evolves in each drive pe-riod according to the operator: U F = e iJ j Xj Xj+1 e ih j Zj . (1) In the well-studied measurement-free case, J and h are real, and correspond respectively to uniform nearestneighbor Ising interactions and transverse fields.For uniform J and h, if the initial state |Ψ 0 ⟩ (Fig. 1(a)) is not a Floquet eigenstate, the system, in the long time limit, may locally approach a periodic version of a generalized Gibbs ensemble [19].On the other hand, if disorder is included, the model exhibits a number of unique nonequilibrium phases [1,4,20].Instead of the unitary case specified above, here we consider what happens when the evolution operator U F is made non-unitary by allowing both J and h to be complex.This is equivalent to adding measurement and postselection to our Floquet dynamics.To be concrete, suppose that each Z j and each bond variable X j X j+1 are continuously monitored using a click style measurement [21].For each site j in the lattice there are two click detectors A i and B i , with the probability of detector A generating a click in some time interval dt being controlled by the operator Âi = (1 ± Z i )/2, and the probability of detector B clicking being controlled by the operator Bi = (1 ± X j X j+1 )/2.We specifically consider postselected evolution on experimental runs where no clicks in any of the detectors are recorded.Using the standard theory of continuously monitored systems (see e.g.Ref. [22]), one can show that the resulting evolution is controlled by a non-Hermitian Hamiltonian.The anti-Hermitian part is generated by the imaginary parts of J and h, which we denote β J and β h ; they correspond respectively to the strengths of the A j and B j measurements.We note that special cases and particular aspects have been discussed in, e.g., Refs.[23][24][25].
The Floquet non-unitary TFIM allows us to study the interplay of Floquet driving and measurement-induced dynamics in the simpler setting where the evolution is deterministic (the specific post-selection that we use eliminates the stochasticity inherent in quantum measure- • The entanglement entropies of the steady states can be understood in terms of the non-Hermitian quasiparticle picture, at least at the spectral level.In particular, non-area-law steady states appear when there are real modes in the spectrum.For example, this occurs on the boundaries between distinct phases, where there is an extensive growth in the steady-state entanglement entropy, with the growth being logarithmic or in some cases volume law.While some of the volume law behaviors were previously noticed (when the non-uniatry model is a spacetime-dual to a unitary model [26][27][28][29][30][31]), we find new volume law regimes that cannot be understood from the duality.Instead, we tie this new volume-law regime to the pseudo-Hermiticity of the non-Hermitian Floquet Hamiltonian.We show that the topological entanglement entropy that was employed to detect measurement-induced transitions in random quantum circuits [32] can also be used to locate some of these boundaries.This may provide an alternative angle to study Floquet non-Hermitian topological phases (see, e.g., Refs. [33,34]).
• The postselected measurement-induced dynamics we study allows one to directly stabilize dynamical phases, without the need for disorder, MBL, or additional engineered dissipation.Importantly, this dynamics is robust against (at least) some integrability breaking perturbations.
• Simple conformal field theory (CFT) with complex time can provide qualitative description of the entanglement entropy evolution, and the "central charge" of the Floquet criticality is parameter dependent.
In the rest of the paper, we substantiate and expand on these results as follows.In Sec.II, we describe the spin model and its fermionization as well as formulate the qualitative quasiparticle picture.Furthermore, we analyze the spectrum of the effective Hamiltonian with both periodic boundary conditions (PBCs) and open boundary conditions (OBCs) and study the evolution of entanglement entropy after a quantum quench.We then present the general phase diagram of steady states.In Sec.III, we report the detailed numerical analysis of entanglement entropy evolution and scaling, as well as topological entanglement entropy (TEE).We show that the entanglement entropy growth is consistent with the quasiparticle picture at least on the spectral level.Then, in Sec.IV, we discuss different quench dynamics of an open chain of spins in different phases.The effect of breaking the integrability is also briefly discussed.In Sec.V, we focus on the J = h case (both complex), and compare the numerical results and the CFT results in both the continuous time limit and the Floquet case.Finally, in Sec.VI, we summarize and mention some future directions.Some details are relegated to the Appendix.
II. MODEL
In our work, we consider a 1D chain of 1/2-spins undergoing a time-periodic non-unitary evolution U F described in Eq. ( 1).We start with an initial state |Ψ 0 ⟩, e.g. a product state and study the quench dynamics [see Fig. 1(a)].We take J ≡ α J + iβ J and h ≡ α h + iβ h to be complex.Then U F induces a nonunitary Floquet evolution under non-Hermitian Hamiltonians H 1 = J j X j X j+1 and H 2 = h j Z j .Since U F = e −β J j Xj Xj+1 e iα J j Xj Xj+1 e −β h j Zj e iα h j Zj , (2) U F can be regarded as a unitary evolution interspersed with imaginary-time evolution.The imaginary time evolution may be achieved by introducing couplings to ancillary spins (external to the circuit) that are being measured projectively.[35].As discussed in the Introduction, the imaginary-time evolution can also be associated with post-selected measurement-induced dynamics.
Our study interpolates between and extends beyond several special cases that have been considered previously in the literature.If J and h are real, U F gives a unitary evolution, and it corresponds to the noninteracting case of the kicked Ising model.Upon making a spacetime duality transformation, i.e. exchanging space and time, J and h become generally complex and satisfy α J = α h = ±π/4.There are self dual points at |J| = |h| = π/4 [26][27][28][29].At these points, the dual of the original unitary circuit is also unitary, and such a circuit is called dual unitary.Many exact results can be derived using this defining property [26-29, 36, 37].Away from self dual points, however, the spacetime dual is no longer unitary, and corresponds to a non-Hermitian evolution.Naturally, the "evolution" along the spatial direction is not independent of the temporal evolution [30,31,38].For instance, it has been shown that the entanglement entropy scaling (volume vs. area law) of the output of the dual nonunitary circuit is directly related to the entanglement growth starting from an unentangled initial state in the original time direction (up to some boundary conditions) [31,39].It was argued in Ref. [30] that the impediment to the entaglement growth in the presence of projective measurements is directly related to localization (area law) in the dual circuit.
When J and h are purely imaginary and small (β J > 0 and β h < 0), we recover continuum limit, which was discussed in Ref. [40].Our phase diagram includes an arealaw-to-area-law phase transition via a logarithmic critical point, similar to the results in Ref. [41] (which were for a non-Floquet system).It was also found there that the phase diagram under the non-Hermitian evolution is smoothly connected to the phase diagram of a continuously monitored free fermion system.Related ideas have been explored also in Ref. [42], where MIPT was studied in a special model with an effective PT-symmetric non-Hermitian Hamiltonian.
Although our model has a large parameter space [spanned by complex (J, h)], we will primarily focus here on the interesting case where α J = α h (but β J and β h are general).Physically this corresponds to continuous monitoring of a critical unitary system [red line in the inset of Fig. 1(b)].As we show, the continuous monitoring can drive the system into several distinct steady states as shown in the main panel of Fig. 1(b).We also note that while we focus on a particular set of post-selected trajectories (the "no-click" trajectories), recent work on a related system suggests that the qualitative features here may also be characteristic of all trajectories [40].
A. The Jordan-Wigner transformation
To facilitate the analysis, we write the TFIM in terms of complex fermions by using the Jordan-Wigner transformation, (3) Furthermore, we define the real Majorana modes which lead to further simplification, Here we have imposed the antiperiodic (periodic) boundary condition on fermions for the even(odd) fermion parity sector.In later discussions, we will also consider the case when OBCs are used.We can write and where W ′ and W ′′ are 2L × 2L matrices.Upon application of the Baker-Campbell-Hausdorff (BCH) formula, the bilinear structure of H 1 and H 2 leads to an effective bilinear Floquet Hamiltonian with B. The quasiparticle picture The simple bilinear form of Hamiltonian (8) implies the existence of non-interacting quasiparticle modes.The quasiparticle picture can be very useful for expressing the time dependence of wavefunctions as well as for interpreting the entanglement evolution after a quench [43,44].Since the effective H is non-Hermitian, the quasiparticles are not canonical fermions [45,46].
If the non-Hermitian quadratic Hamiltonian H is diagonalizable, then H = ADA −1 with diagonal D. The matrix A relates the canonical fermion modes a j and the quasiparticles γ k , and Here ϵ k is in general complex and γ † Depending on the sign of Im(ϵ k ), ⟨N k ⟩ will evolve in time to either 0 or 1.In the long time limit, only the real modes with Im(ϵ k ) = 0 play a nontrivial role, similar to the purely real modes in a unitary systems.Such (propagating) modes are expected to play an important role in distributing entanglement through a system starting from unentangled states [43].In the thermodynamic limit, qualitatively, we expect that in the absence of real modes, the final entanglement scaling satisfies an area law.In contrast, for a finite density of real modes, the entanglement scaling will satisfy a volume law [43], whereas if we only have a finite number of real modes the entanglement scaling satisfies the logarithmic law.
There are few points to be noted here.First, the system can be protected by the pseudo-Hermiticity [47] in some parameter regimes.Namely, there exists a Hermitian matrix η such that ηHη −1 = H † .If a pseudo-Hermitian Hamiltonian H is diagonalizable, then it has an antilinear symmetry such as a PT-symmetry.The spectrum of H can be real if the antilinear symmetry is not spontaneously broken.Second, the real eigenmodes and the complex eigenmodes are not necessarily orthogonal, which could affect the quasiparticle picture of entanglement spreading.Nevertheless, we find that the heuristic non-Hermitian quasiparticle picture described above properly accounts for our numerical results.Similar discussion of the Su-Schrieffer-Heeger model can be found in Ref. [48] where it was found that the spectrum is dictated by the PT-symmetry and that the entanglement scaling also depends on the (partial) reality of the spectrum (see also Refs.[49][50][51][52][53]).
C. The spectrum
To obtain basic insights into our model, we first consider the spectrum of the problem.For PBCs, we identify regimes where the system has pseudo-Hermiticity symmetry, which has profound implications for the phase diagram.For PBCs, we find different localized edge Majorana mode configurations that correspond to different phases.
Periodic boundary condition: continuous time limit
Let us first consider the case |J| = |h| → 0; then Diagonalizing the Hamiltonian in k space gives us the eigenvalues Importantly, it is possible for λ 1,2 to be real even for complex J and h.In those cases, the real modes behave similarly to the Hermitian case and may contribute to a non-area-law behavior in the steady-state entanglement entropy [43].We now consider these special cases.If J = h, then λ 1,2 = ±4J| sin(k/2)|.Therefore, for complex J = h with small absolute values, at k = 0 we have λ 1,2 = 0.The quasiparticle picture suggests that the steady state will have a logarithmic law behavior in entanglement entropy.This is not surprising because all modes but the zero mode will either decay or grow and will not contribute to the entanglement entropy. If For a given k, the modes are either complex conjugates of one another or purely real.The condition cos k = (α 2 − β 2 )/(β 2 + α 2 ) determines the exceptional points in the k space where the eigenvectors coalesce to (−1, 1)/ √ 2. The existence of real modes and/or complex conjugate pairs is not a coincidence: for these parameters, it is protected by the pseudo-Hermiticity.In fact, if we write the Hamiltonian in Eq. ( 12) in the k space, for each 2×2 H k , η is explicitly given by η = 1 Note that for generic complex J and h, there is no PT or pseudo-Hermiticity symmetry to protect the reality of the spectrum, unlike in Refs.[42,48].The pseudo-Hermiticity is important because it allows for the partially real spectrum, with the real modes generating a steady state with a volume law in entanglement entropy.
Periodic boundary conditions: general case
Now let us consider the Floquet unitary U F of Eq. 1 for general parameter values.The spectrum is given by [30] where ).Similar to the continuous-time limit, a real zero mode exists at k = 0 for J = h.It is also easy to check that there are two cases that can lead to an extensive number of real modes: (1) α J = α h = π/4 mod π/2 (dual to the unitary case) and ( 2) The spacetime duality is implemented by exchanging time and space coordinates [26,27,30].In particular, for U F , the spacetime dual has the form up to some boundary terms.Here . It is easy to check that real modes exist between [0, 2πλ] because cos −1 ( cosh(4β)−1 cosh(4β)+3 ) = 2πλ.This case is protected by the pseudo-Hermiticity of the effective Hamiltonian (expressed in terms of complex fermions in the k space) with the η matrix given by η = σ x .The second case is a natural extension of the continuous-time case we discussed in the previous section.It is still protected by pseudo-Hermiticity but the η matrix is more complicated.This extensive number of real modes will produce a volume law in the entanglement entropy in the steady state.
The cases with real modes define the position of the phase boundaries as shown in Fig. 1(b).Indeed, the quasiparticle picture implies that these real modes will not decay or grow and produce a non-area law steady state.We will verify this numerically in the next section.
Open boundary condition
If we use OBCs, it is easy to calculate the spectrum numerically in real space directly.The bulk of the spectrum is not very sensitive to the boundary conditions, but there can also be special edge modes: zero modes and π modes.In Fig. 2, we show the absolute value of the spectrum as we tune α = α J = α h .We can check that these edge-mode energies are real.Because of the reflection symmetry, let us focus on the 0 ≤ α ≤ π/2 regime.In the upper panel, β J < −β h .When α ≲ π/4, the spectrum has zero edge modes, while for α ≳ π/4, the spectrum has π edge modes.In the lower panel, β J > −β h .When α ≲ π/4, the spectrum has no edge modes, while when α ≳ π/4, the spectrum has both zero and π modes.The presence or absence of the edge modes distinguishes different regimes in Fig. 1(b) and thus can be used to label the phases.Note that there is a strong finite size effect when α is close to π/4.As the phase boundaries are approached, the edge modes become non-normalizable for finite L. These edge modes are close relatives of those in the clean unitary case [54,55] as well as the Floquet-MBL unitary case [1].They are the topological edge modes associated with Floquet symmetry-protected phases [56][57][58].They retain real energies even when J and h become complex.We will see later in Sec.IV that these modes are good indicators of different dynamical behaviors after a quantum quench.
D. Evolution and steady states
Having established basic spectral features of our model, we now turn to the dynamics in a quench protocol where we start the system in a fermionic Gaussian state and let it evolve under U F .The Floquet Hamiltonian H [Eq. 8] has the following form in terms of complex fermions: In general, ∆ + ij ̸ = (∆ − ij ) * .In terms of real Majorana fermions: and hence We want to study the evolution of the states under this generally non-Hermitian Hamiltonian.
Note that since we used the effective Floquet Hamiltonian, only the correlation functions at multiples of the periods correspond to those in the original system.The time evolution of C can be obtained by solving this equation numerically.If it is a continuous time evolution, the steady state is approached when dC/dt → 0. In the Floquet setting, the definition of a steady state can be weakened: where n is a positive integer and T is a period also yields a steady state, even if C(t + T ) ̸ = C(t).This case corresponds to discrete time crystals that spontaneously break the discrete time translation symmetry.
If we have a density matrix ρ of a total system comprised of subsystem A and subsystem B, we can obtain the reduced density matrix ρ A by tracing out subsystem B: ρ A = tr B ρ. Then the von Neumann entanglement entropy is defined as S A = −tr[ρ A ln ρ A ].For the free fermion system, it can be evaluated directly using [43]: where A are denoted as {±ν i }, we have In the case of OBCs, we will also be interested in a generalized TEE, which can be obtained from partitioning the one-dimensional system into four segments as follows: Then TEE is defined as [32,40,59,60] This TEE was designed to detect ground-state topological transitions.As we will see in the next section, it can also be used to identify certain transitions in the steady state of our non-unitary Floquet system.
E. Phase diagram
We now briefly summarize the main features in the phase diagram of steady states shown in Fig. 1.The phase diagram can be determined easily by studying the spectra of the Hamiltonian H in Eq. 8.It depends on the relative magnitude of β J and β h .The phases are demarcated by the lines |β J | = |β h |, and α = π/4.When β J = −β h , the steady-state entanglement entropy satisfies the volume law; when β J = β h the steady state entanglement entropy satisfies the logarithmic law (see next section).The volume-law phase at α = π/4 exists because the nonunitary circuit is dual to a unitary circuit, as was already remarked in Ref. [30], but also because it is protected by the pseudo-Hermiticity, just as in the case β J = −β h .The rest of the phase diagram has an area law.If OBCs are imposed, the non-Hermitian spectrum may contain different real-energy edge modes (zero or π Majorana modes).Different phases are labeled by the modes present within them: (⊘) region (no edge modes), (0) region (zero modes), (π) region (π modes), and (0π) region (both zero and π modes).
In this work, we focused on the α J = α h plane on the entire complex manifold where volume law critical lines can be found.While we have not exhaustively studied parameter regimes α J ̸ = α h , a few general comments can be made on differences that emerge in this more general case.If α J ̸ = α h , the area-law phases can become logarithmic-law phases depending on β J and β h .The transitions between area-law phases become transitions between area-law phases and logarithmic-law phases.These scaling laws are still compatible with the quasiparticle picture at least at the spectral level: if the spectrum of the effective Floquet Hamiltonian contains no real modes, then it has an area-law scaling; on the other hand, if the spectrum contains a few real modes, the scaling is logarithmic.The volume laws we discussed on critical lines are replaced with logarithmic laws (see, e.g., [25]).There is a critical line for α J ̸ = α h that corresponds to the critical line for α J = α h = π/4 while the boundaries at β J = ±β h remain where they were.Within phases, the edge modes persist, and different quench dynamics with OBC (discussed in Sec.IV) only weakly depend on the condition α J = α h .We leave this detailed discussion to future work.
III. ENTANGLEMENT ENTROPY EVOLUTION AND SCALING
In this section, we present the numerical results on the temporal evolution of entanglement entropy and its scaling in the steady states.For simplicity, we take L to be even and focus on the case in the initial state with odd (even) sites occupied and even (odd) sites empty.We will see the entanglement scaling is compatible with the quasiparticle picture for a quench problem.Namely, the steady state can have an area law, a logarithmic law, and a volume law, depending on whether the spectrum of the non-Hermitian Hamiltonian contains no real modes, a few real modes, or an extensive number of real modes, respectively.We also compute the TEE defined in Eq. 24 and use it to detect the phase transitions at β J = ±β h .
The phase diagram for this case can be seen in Fig. 1(b).We sample three representative points from the phase diagram: β J = −0.2,−0.1, 0.1 while fixing α = 0.2 and β h = 0.1 (in units of π/4).The evolution of the entanglement entropy of subsystem A is shown in Fig. 3.The entanglement scaling in different phases is presented in Fig. 4 both on the linear scale and logarithmic scale.
If the system is in the area-law phase, the entanglement entropy first increases, and possibly drops before it saturates at long times.When β J = β h , the qualitative behavior of the evolution curve is similar and the system flows to a steady state with a logarithmic law.This pattern is general and shared by the CFT calculation to be discussed in Sec.V. When β J = −β h , the FIG.4: Dependence of S A on the subsystem size L A .Linear (left) and logarithmic (right).α = 0.2, β h = 0.1 (in units of π/4).L A /L = 1/10.system approaches a volume law in the long time limit.The evolution curve of S A is similar to that of a unitary quench: it increases almost linearly at first and then saturates gradually after a time roughly proportional to L A .The wiggly features are due to the finite size effects: increasing the total system size reduces the entanglement revivals and thus smooths the curve.
In the above discussion, we imposed PBCs.If different boundary conditions are imposed, e.g., OBCs, the dynamical behavior can be slightly different.With OBCs, the entanglement entropy also depends on the location of subsystem A. If A is located deep in the bulk, then the entanglement entropy S A becomes insensitive to the choice of boundary conditions and the curves approach those with PBCs (see the inset in Fig. 3).However, if A sits by the boundary, say, [1, L A ], even though the qualitative features are the same, the saturated values of S A are slightly different. .By resorting to the spacetime duality, it is easy to see that the steady state under the evolution of U F has a volume-law scaling [dotted magenta line in Fig. 1(b)].The volume law is compatible with the observation in Ref. [31] that an area-law steady state is ruled out (up to boundary conditions and fine tuning) for a nonunitary circuit that is dual to a unitary circuit which produces a non-area-law steady state.Previous works found that volume-law entanglement in a free-fermion chain is destroyed in the presence of arbitrarily weak measurements [61,62], and it was suggested in Ref. [30] that the volume law is symmetry protected by the unitarity of the unrotated circuit.However, as we have already mentioned, more generally, the volume law phase is protected by the pseudo-Hermiticity of the effective Hamiltonian.
We also mentioned in Sec.II C that if J = h = α in the unitary circuit, then 2 log(tan(α)) and the real modes exist in the interval [0, 8α].In fact, we checked numerically that the entanglement entropy density S A /L A is almost linear in α if α is not too small (Fig. 5).Plotted together is the initial entanglement entropy growth rate.We see indeed that these two quantities are almost the same, which is not surprising because they are related by the spacetime duality [31,39] (up to boundary conditions and finite-size and finite-time effects).
We also present the time evolution of S A of the nonunitary case with different β = β J ′ = β h ′ in Fig. 6.We see that S A increases almost linearly for small T and then saturates.As we increase β, since more modes become complex, S A of the steady state decreases.Since S A /L A is almost linear in α, the dependence of S A /L A on β can be easily obtained by inverting the relation between β and α.In particular, if α is close to π/4, β ≈ α − π/4, and thus S A /L A is also linear in β for small β.
C. Topological entanglement entropy
We also compute the TEE [Eq.( 24)] of different phases and show that it can always be used to detect the transition between (0) phase and the trivial (⊘) phases.In Fig. 7, TEE is shown for fixed α and β h , and varying β J .The TEE approaches zero for small |β J | and ln 2 when |β J | is large.The curves associated with different sizes cross at a point where β J0 ≈ β h .The contribution to ln 2 comes from a pair of Majorana modes (2 ln √ 2).The finite size scaling is presented in the lower panel by plotting S top against (β J − β J0 )L ν .All data collapse almost perfectly onto a single curve.The critical exponent ν is determined to be approximately 1.
The TEE is also quantized to ln 2 in the (π) phase as long as it stays away from the special line α = π/4 where a phase transition occurs.We can interpret the (π) phase as alternation between two states in the (0) phase with opposite polarization.Then the TEE in the (π) phase at one instant is the same as that in the (0) phase.The topological information in the (0π)-phase is more subtle, and we may need to construct a new quantity to extract it, which we leave for future work.
IV. QUANTUM QUENCH IN THE SPIN LANGUAGE
We have shown that zero modes and/or π modes exist in the fermionic language if OBCs are imposed (see Fig. 2), the same as in the unitary case [54,55].Different combinations of edge modes are expected to be associated with different evolutions of many-body states.In this section we summarize the results on the time evolution obtained directly in the spin language, starting from some random initial states (not close to Floquet eigenstates).We find four types of evolution corresponding to different phases in Fig. 1(b): • In the trivial phase (⊘), both ⟨S i x ⟩ → 0 for all sites and ⟨S 1 x S N x ⟩ → 0, where N is the total size, after a few drive periods [Fig.8
(a1)].
• There are two regions in the phase diagram with zero modes (0).If β J < −β h , for a small system, ⟨S i x ⟩ of the state rapidly drops to zero while ⟨S 1 x S N x ⟩ stays finite.For a small system, the final state has a large overlap with the Green- x ⟩ of different sizes is shown in Fig. 9(a).We expect that in the thermodynamic limit, the steady state is in a Floquet (discrete time-crystal) phase.Moreover, if β J > β h , the steady state also FIG. 10: Effect of the integrability breaking term K j X j for a special initial (antiferromagnetic) state.breaks the Z 2 translational symmetry, corresponding to an antiferromagnet as opposed to the case β J < −β h when it is a ferromagnet [Fig.8(c1)].
• In the phase with both zero modes and π modes (0π), the spins in the bulk ⟨S i x ⟩ and the spins near the edges behave differently as illustrated in Fig. 8(d1).We take the initial state as a product state of polarized spins.Bulk spin correlations lim |i−j|≫1 ⟨S i x S j x ⟩ drop to zero, in contrast to the phases with only zero or π modes.The steady states depend on β J and β h .Thus, the initial behavior of different initial states can be different.In general, the oscillating pattern can be observed but edge spins have larger amplitudes.We expect that the bulk spin amplitudes approach zero in the thermodynamic limit, while the edge oscillations persist.
In the above discussion, OBCs were used.The main features in the (0) phase and the (π) phase are basically unaffected if PBCs are used.This implies emergence of the long-range order in the bulk.However, the (0π)-phase depends crucially on the boundary conditions: Since this phase is evidenced solely by the edge spin oscillations, this signature disappears if we use PBCs.
We next compare these different dynamics with those in the unitary case.To this end, we plot quench dynamics with different real parameters in Figs.8(a2)-8(d2).The four panels correspond to the same combinations of edge modes as in the non-unitary case.In a clean system, we can see that the edge states are robust.These features can be attributed to the presence of (almost) strong edge modes [55,63,64].However, the bulk flows to the "infinite-temperature" state very quickly (up to revivals due to the finite system size).In the magnetically ordered phases, (0) and (π), physically this can be understood in terms of domain-wall dynamics: domain walls can move freely in the absence of disorder, quickly destroying the bulk order; however, they cannot flip the edge spins, since that would lead to a change in the number of domain walls, and thus significantly change the quasienergy.The situation is very different from the system with disorder (MBL regime) [1], where there are four different Floquet-MBL phases, each characterized by a unique eigenstate order.Apparently, comparing the figures on the left and on the right in Fig. 8, we find that the impact of imaginary parts of J and h is significant.In particular, the long-range bulk orders cannot be stabilized without the imaginary parts, i.e. measurements.
Since the TFIM is integrable, the steady states may depend on the initial states.Indeed, we see that if we start with some special initial states, say, with i ⟨S i x ⟩ = 0, the quench dynamics can have a different behavior.One example in the (π) phase is given in Fig. 10(a) where the initial state is the antiferromagnetic state.This state has no overlap with the ferromagnetic (π) steady state [see Fig. 8(b1)] and as a result becomes featureless very quickly.However, if we add a small longitudinal field K j X j to break the integrability, the steady state reminiscent of Fig. 8(b1) above reemerges [Fig.10(b)].
We also studied the effect of the same integrabilitybreaking term K j X j on dynamics.The dependence of the evolution on the system size in the (π) phase when K ̸ = 0 is shown in Fig. 9(b).As we can see, when we increase the system size, the decay rate drops rapidly to zero.A similar pattern in the (0) phase is observed.Thus we expect these phases to be stable in the thermodynamic limit under the small perturbation (0 < K ≪ 1).As can be seen from Fig. 11, in the (0π) phase, a small K can polarize the spins, but the edge-bulk distinction survives for a long time.This observation suggests that the influence of almost strong edge modes remains beyond the unitary case discussed in Ref. [55].It is interesting to compare this behavior with the observation in the Google simulation in Ref. [65], where they observed that the edge spins under the unitary U F evolution, in contrast to bulk spins, are resilient to integrability-and symmetry-breaking effects and dephasing effects such as low-frequency noise.
Finally, note that α J = α h is not necessary to obtain different dynamics regimes in the nonunitary case that we identified above.We also expect that the main features are robust against other non-Hermitian deformations.
V. CONFORMAL FIELD THEORY AT J = h
So far, our focus has been on the area-law phases as well as volume-law critical lines in the phase diagram shown in Fig. 1(b).Now let us shift attention to the critical line with a logarithmic law at J = h.In the unitary case, i.e., J and h are real, if |J| = |h| → 0, U F approaches that of the TFIM in the continuous time limit.The critical point is the celebrated Ising critical point described by the Ising CFT and the quench problem is well studied [43,66].It is interpretable using the quasiparticle picture [43].In the general case, the critical line (stabilized by disorder or interactions) may be called Floquet quantum criticality [67].In this section, we extend J and h to complex values and study the quench problem.
A. Continuous-time limit
When J = h and |J| = |h| → 0, the qualitative behavior of the system is captured by the continuous time limit where the dispersion is given by ±4J| sin(k/2)| [Eq.( 13)].For complex J and h, the dispersion is rotated to the complex plane in general.If we assume that the formalism developed by Calabrese and Cardy [43] can be generalized to this case, the quench problem can equivalently be described by exp(−i(1 − iη)tH CFT ), where η ≥ 0 quantifies the rotation.For more information, see the Appendix.Since exp(−i(1 − iη)tH CFT ) = exp(−itH CFT ) exp(−ηtH CFT ), the initial state first evolves by exp(−ηtH CFT ) then by the unitary operator exp(−itH CFT ).Since exp(−ηtH CFT ) evolves the initial state to the ground state of H CFT asymptotically, the long-time evolution approaches that of the ground state.
As discussed in the Appendix, the von Neumann entanglement entropy is Typical evolutions of (normalized) von Neumann entanglement entropy S A are depicted in Fig. 12. ϵ = 0.185 is chosen such that if η = 0, S A for l = L A saturates at the same value S A ∼ πcl/12ϵ of the Ising CFT (c = 1/2).When η becomes finite, S A keeps increasing until t ∼ l/2, then it starts to drop.In a closed system, the regularization ϵ affects both the initial growth rate and the saturation value of entanglement entropy.With dissipation η, ϵ becomes less important after some time: t > ϵ/η.However, ϵ determines not only the initial maximum of S A but also the ground state entanglement entropy.The long time limit depends on ϵ but not η because as we mentioned the state approaches the ground state.The larger η is, the faster the decaying rate is.In general, S A can have a volume law before gradually approaching a logarithmic law at long times.The evolutions of S A of the TFIM with continuous time and different η [Eq.( 12)] are compared with those predicted by Eq. ( 25) in Fig. 13.We see that they match qualitatively.
Note that even thought H CFT is the critical Ising Hamiltonian in our main discussion, the formalism of Calabrese and Cardy [43] applies to general critical H CFT .Thus, we expect the simple qualitative prediction from the CFT to be much more general.Also, as mentioned in Sec.III A, the pattern of the evolution of S A i.e., increasing first then decaying, is shared by the area law phases.Similar features were observed in dissipative systems (see e.g., Refs.[68,69]).
B. Floquet criticality
Since there is no phase transition until α J = α h = π/4, even though the preceding discussion was focused on the continuous time limit, the evolution of entanglement entropy in Fig. 12 should qualitatively apply more broadly (i.e., for finite J = h).Once we move away from the continuous time limit, the Floquet criticality [67] is no longer the canonical c = 1/2 Ising CFT.In Fig. 14(a), we fix the total system size L = 100 and plot S A against FIG.14: (a) Subsystem dependence of S A in a total system with L = 100 with fit in Eq. ( 27 to extract the central charge [32,66].In the continuous time limit, a = 1/6 = c/3 since c = 1/2.In the Floquet setting, both a and b depend on J = h.The fitting in Eq. ( 27) applies as long as α = α J = α h is away from π/4, the critical line where the quench resembles that in the unitary case with an extensive number of real modes.For example, if J = h = 0.2 − 0.1i (in units of π/4), we find a ≈ 0.165 and b ≈ 0.54.In general, the fit a depends on imaginary part β but not the real part α.Larger β leads to smaller a.In Fig. 14(b), we set α = 0 and β = η, i.e.J = h = ηi, and plot a for several values of η.We see that it decreases as a function of η.
VI. DISCUSSION
In this work, we have studied the nonunitary Floquet TFIM (kicked Ising model) with complex couplings and transverse fields.We analyzed the spectrum of the Floquet Hamiltonian in the fermionic language using the Jordan-Wigner transformation with both PBCs and OBCs, and used it to map out the phase diagram.For PBCs, we found that the spectrum may contain no real modes, a few real modes, or a finite density of real modes, the latter enabled by pseudo-Hermiticity of the Hamiltonian for special values of parameters.For OBCs, we found that real zero-and/or π edge modes can exist in different phases.We presented the numerical result for the evolution of subsystem entanglement entropy after a quantum quench.In general, the entanglement entropy increases initially, then begins to drop, and eventually saturates to some steady-state value.The three just mentioned spectral cases lead to an area law, a logarithmic law, and a volume law of entanglement entropy in the steady state, respectively.The scaling behavior can be interpreted in terms of real-energy non-Hermitian quasiparticles being responsible for establishing entanglement (the initial entanglement peak can be attributed to complex-energy quasiparticles, which can lead to enhanced entanglement on the time scales of their lifetime).A quantized TEE exists if a zero mode or π mode exists.We also studied the quench dynamics of an open spin chain from a typical initial state and identified four types of dynamical behaviors corresponding to different edge mode configurations.Compared to the clean unitary case, which generally lacks bulk long range order, bulk order is stabilized by nonzero imaginary parts of J and h, i.e. measurements.Finally, we considered the case when J = h and compared the numerical results in the continuous time limit with the analytical result of a CFT by extending Calabrese and Cardy's formalism to complex time.They match qualitatively.Also, the effective central charge of the Floquet criticality was found to depend on J = h.
There are many promising future directions.First, there are many observables that can be used to study the nonunitary Floquet TFIM.In this work, we only computed entanglement entropy.As a matter of fact, we found mutual information has a similar behavior.It is also possible to compute other quantities such as entanglement negativity [70].In particular, the general CFT formalism can also be generalized properly to give us some insights into the evolution and the scaling of these quantities.In our work, we only discussed the non-Hermitian generalization of the quasiparticle picture at the spectral level; a quantitative check on the entanglement entropy growth as in Ref. [44,68,69] should be done.It is also interesting to see if more general topological quantities can be constructed to distinguish all four cases [so far we found that the (0, π) phase is not clearly detected by TEE, in contrast to (0) and (π) phases].In addition, the relation to the skin effects in the context of Floquet non-Hermitian topological phases [33,34] should be explored [71].Also, we have focused on 1D spin chains.Some of our discussion for the 1D case can be easily generalized to higher dimensions.
Second, we have used non-Hermitian Hamiltonians as our starting point to study the effect of measurements by complexifying the coefficients.Complex J and h correspond to post-selecting no-jump trajectories, with the jump operators L i = (1±X i X i+1 )/2 and L i = (1±Z i )/2, respectively.There are many other types of measurements.We hope that the results of the simplified system can at least yield some insights into dynamical systems described by the stochastic Schrodinger equation where there are few or no post-selections [40].How more general continuously monitored systems behave deserves to be studied more closely, see, e.g., Ref. [41,61,69].Whether different spin dynamics of a dissipative Floquet TFIM survive under a quench without post-selection should be explored [10,40,65,72].
Third, there are many ways to extend the non-Hermitian Hamiltonian.Other physical effective Hamiltonians can be studied in a similar way.In this work we only briefly discussed the effect of the integrabilitybreaking term h ′ i X i in the Hamiltonian.We can also include terms like J z Z i Z i+1 which after the Jordan-Wigner transformation is mapped to a density-density interaction [1].Introducing long range interactions is another direction with possible experimental relevance [10].We know that introducing spatial disorder in the unitary case into such a system with a small J z leads to MBL and stabilizes the Floquet phases [1,4].How these systems respond to complexification of the coefficients is an interesting open question.
Lastly, several more general ideas discussed in this work deserve further investigations.For example, the partially real spectrum on some critical lines implies a spontaneous breaking of the antilinear symmetry associated with a diagonalizable pseudo-Hermitian Hamiltonian [47] as a function of momentum k (rather than some external control parameter).The effect of the existence of such an exceptional point in the k space on entanglement and purification transition should be further explored [42].As another example, we noticed that positive or negative decay rates effectively lead to projective measurements in the momentum space.A general question is whether engineered dissipation can be used to construct interesting phases like topological phases [73][74][75].
integrals: the first one starts with ψ ′ (x ′ , τ ) at τ = −τ 1 and ends with ψ 0 (x) at τ = 0, and the second one starts with ψ 0 (x) at τ = 0 and terminates with ψ(x, τ ) at τ = τ 2 .Divide the system (at τ = 0) into region A and its complement B, then the reduced density matrix ρ A can be obtained by gluing ψ 0 (x) of the first integral with that of the second one at τ = 0 for x inside region B. trρ n
FIG. 1 :
FIG. 1: (a) Floquet evolution in Eq. 1 of |Ψ 0 ⟩.(b) Phase diagram of steady states for α J = α h ≡ α. β h > 0 is fixed and β J is varied.It contains four different phases that satisfy an area law in entanglement entropy.The magenta boundaries (solid line, α J = α h = π/4, and dotted line, β J = −β h ) represent a volume law while the blue solid line represents a logarithmic law.The critical points for α J = α h = 0 have a logarithmic law.The four phases are distinguished by the presence or absence of real 0-or π-edge modes in the spectrum with open boundary conditions.In particular, ⊘ means no edge modes.Inset: The phase diagram of the unitary Floquet model [1]; the real parts of the parameters used in the main panel sweep the red diagonal (α h = α J ).
FIG. 3 :
FIG. 3: Temporal evolution of entanglement entropy S A with the PBCs.α = 0.2, β h = 0.1 (in units of π/4).L A = 8 and L A /L = 1/20.Inset: Evolution of S A with OBCs.The subsystem A is chosen to be [1, L A ].If the subsystem A is moved away from the boundary, the curves approach those with PBCs shown in the main panel.
FIG. 14: (a) Subsystem dependence of S A in a total system with L = 100 with fit in Eq. (27) using J = h = 0.2 − 0.1i (in units of π/4).a ≈ 0.165 and b ≈ 0.54.(b) Fitting values of a as a function of η.J = h = ηi (in units of π/4). | 10,990 | 2023-06-12T00:00:00.000 | [
"Physics"
] |
Time-resolved high harmonic spectroscopy of dynamical symmetry breaking in bi-circular laser fields
The bi-circular scheme for high harmonic generation, which combines two counter-rotating circular fields with frequency ratio 2:1, has recently permitted to generate high harmonics with essentially circular polarization, opening the way for ultrafast chiral studies. This scheme produces harmonic lines at 3N + 1 and 3N + 2 multiples of the fundamental driving frequency, while the 3N lines are forbidden owing to the three-fold symmetry of the field. It is generally established that the routinely observed signals at these forbidden harmonic lines come from a slight ellipticity in the driving fields, which breaks the three-fold symmetry. We find that this is neither the only nor it is the dominant mechanism responsible. The forbidden lines can be observed even for perfectly circular, long driving pulses. We show that they encode rich information on the sub-cycle electronic dynamics that occur during the generation process. By varying the time delay and relative intensity between the two drivers, we demonstrate that when the second harmonic either precedes or is more intense than the fundamental field, the dynamical symmetry of the system is broken by electrons trapped in Rydberg orbits (i.e., Freeman resonances), and that the forbidden harmonic lines are a witness of this.
While the potential of high harmonic generation in bi-circular fields as a light source is actively explored, the complementary spectroscopic potential of this scheme for studying the underlying electronic dynamics and dynamical symmetries is far less known.Pertinent recent papers include Refs.[19,34,36,38].This situation stands in stark contrast to the two-dimensional high harmonic spectroscopy which uses the combination of linearly polarized fundamental and its second harmonic [11,[13][14][15][16][17][18][47][48][49][50][51][52][53], allowing one to track electronic and vibronic [13] dynamics with temporal resolution from tens of femtoseconds down to tens of attoseconds.
Here we demonstrate the spectroscopic potential of high harmonic generation in bi-circular laser fields to track light-driven dynamical symmetry breaking in a quantum system.In general, the emergence of strong, symmetry forbidden, lines in high harmonic spectra is a tell-tale sign of symmetry breaking induced by the underlying attosecond electronic [54,55] or vibronic dynamics [56][57][58].Specifically, we show that symmetry forbidden lines in high harmonic spectra generated in bi-circular fields are sensitive to frustrated tunnel ionization [59][60][61][62][63][64] and the presence of strongly laser-driven Rydberg states, the so-called 'bound states of the free electron' [65], which are able to survive intense laser fields [60][61][62][63][64][66][67][68][69] even when the ground state of the neutral is completely depleted [61,70].
In contrast to single-color high harmonic spectroscopy of the dynamical symmetry breaking [54,[56][57][58], the two-color laser field offers clear advantages: it allows one to tune the time-delay between the two colors and their relative intensities.We rely on this ability in the present work.It allows us to make first steps towards adressing an extremely exciting but equally challenging problem of time-resolving the frustrated tunneling process [60,61,63,71,72] during the driving laser pulse.
The ability to control the shape of the driving field by changing the relative intensities of the two colors and their delay also brings up the complementary aspect of attosecond electron dynamics in multi-color fields -the ability to control these dynamics and the properties of the emitted radiation [14,[47][48][49]52].We explore this ability in the present work.
When a circularly polarized driver with frequency ω is used in combination with its counterrotating second harmonic, the resulting field has the three-fold symmetry shown in Fig. 1.As a consequence, high harmonic spectra generated in centrally symmetric media present peaks at the 3N + 1 and 3N + 2 harmonic lines, but not at 3N.The 3N + 1 and 3N + 2 harmonics are circularly polarized and rotate in the directions of the ω and 2ω fields, respectively.The 3N harmonic lines are symmetry forbidden, their lack reflecting the conservation of the angular momentum.Indeed, these lines correspond to the absorption of the net amount N of the fundamental ω photons and the net amount N of the second harmonic 2 ω photons, i.e. the net total of 2N photons, preserving the partity of the initial state and thus precluding one-photon radiative recombination to it.
In spite of this clear symmetry argument, non-negligible signals at 3N harmonic lines have been routinely observed in experiments, starting with the pioneering work [28].Their presence has been systematically ascribed to slight ellipticity of the drivers.While this is certainly an important experimental reason, it is not the only one, as has been recently highlighted by Baykusheva [34].The emergence of strong forbidden lines can manifest the lack of symmetry of the quantum system, in particular the destruction of the dynamical symmetry within the laser cycle (Fig. 1).This makes the analysis of the forbidden lines, ideally in a time-resolved fashion, very interesting, opening a route to time-resolving the changing symmetries of the quantum system.
Turning from the spectroscopic aspect of high harmonic generation to the light-source aspect, it is also important to understand the origin of the forbidden lines, the mechanisms controlling their strengths and polarization.Indeed, these lines will play crucial role in determining the polarization properties of attosecond pulses or pulse trains produced by the combination of circularly polarized high harmonics generated in a bi-circular field.
Addressing these issues is the focus of this paper.In particular, we find theoretically that small deviations from perfectly circular light = 1.0, e.g.= 0.95, which would be typical for realistic experiments, is hardly the main reason for their prominence.Thus, the emergence of strong forbidden lines in standard experiments with nearly circular pulses is rather unexpected and cannot be blamed entirely on small deviations from perfect circularity.
To uncover the physics responsible for the 3N lines, we study the case when the two pulses constituting the bicircular field, ω and 2ω, are time-delayed but still overlap.This allows us to track the emergence of the 3N lines as a function of the ω − 2ω delay.Using Helium as a target gas and the combination of 800 nm and 400 nm driving fields, we find experimentally and theoretically that the 3N lines become stronger as the delay between the two pulses increases and their overlap decreases, especially when the 2ω (400 nm) pulse comes first.
It is well known that, in contrast to 800 nm, the 400 nm pump leads to efficient accumulation of population in Rydberg states via frustrated tunnelling (see e.g.[64] for detailed expermental and theoretical analysis), and that these states survive strong dressing fields [60,61,63,71,72].Thus, our results suggest that in the pump-probe type setup, when the 800 nm pulse is delayed, the 400 nm field excites the bound states and breaks the dynamical symmetry due to sub-cycle accumulation of population in these states.Since frustrated tunnelling in the 800 nm field is less efficient than for 400 nm field [64], the dynamical symmetry breaking should be weaker when the 800 nm pulse comes first.This expectation is confirmed by our observations: the forbidden 3N lines are more prominent when the 400 nm pulse precedes the 800 nm pulse.
The importance of Rydberg excitation is further tested experimentally by changing the intensity of the 400 nm pulse.In agreement with the above physical picture, we find that the forbidden lines become more prominent with higher intensity of the 400 nm light.Theoretically, even for perfectly circular pulses, the forbidden harmonic lines appear in a dramatic way if the intensity of the 400 nm field is increased substantially above the fundamental.In contrast, raising the 800 nm intensity does not have the same effect.
We further confirm this physical picture by showing how the gradual build up of the forbidden lines in the spectrum.Thus, from the high harmonic spectroscopy perspective, analyzing the appearance of the forbidden harmonics as a function of the ω-2ω delay and intensities, we make first steps towards seeing how the frustrated tunneling process [60,61,63,71,72] unfolds in time.
From the light source perspective, we analyze the unusual polarization properties of the 3N lines and show the ways of controlling their strength and ellipticity: by varying the two-color delay or the relative intensities of the two driving fields.The intensities and the polarization properties of these lines are important in determining the polarization properties of the attosecond pulse trains produced via high harmonic generation in bi-circular fields.
Dynamical symmetry and the selection rules
Consider high harmonics generated by the two counter-rotating circular pulses with frequencies ω and 2ω.We write the total electric field as The three components of the field correspond to the counter-clockwise (ê + = −(ê x + iê y )/ √ 2) and clockwise (ê − = (ê x − iê y )/ √ 2) rotations in the x-y plane, and a linear component (ê 0 = êz ) along the z axis.For collinear driving fields, which we assume in this work, the latter is always zero.The fundamental field rotates in the counter-clockwise, positive direction (polarization ê+ ), while the second harmonic rotates clockwise (polarization ê− ).
The inset in Fig 1d shows the total field, which has characteristic three-leaf structure.The total field rotates counter-clockwise, from the leaf k = 1 aligned horizontally, along the x-axis, to the leaf k = 2 turned 120 degrees counter-clockwise, to the leaf k = 3 turned 240 degrees counterclockwise.Each leaf generates a burst of emission.To simplify the discussion and notations, Fig. 1.Typical harmonic spectra in bi-circular fields.Strong field approximation solutions for the bicircular scheme using a short-range potential with an ionization potential of I p = 24.6 eV (as helium).In the top row, the amplitude distribution of the different bursts, temporally ordered, that contribute to an arbitrary high harmonic (H60).In the bottom row, the HHG spectra.The fields are Gaussian-shaped, with a peak intensity of I = 3.5 × 10 14 W/cm 2 , and duration of: (a,d) 38 fs, (b,e) 38 fs with an ellipticity of 0.9, and (c,f) 6 fs.The Lissajous figures of the corresponding fields are shown in the top right corners of the bottom panels.
but without the loss of generality, we consider emission associated with the so-called short trajectories [73].In bicircular fields, their contribution on the single-atom level is dominant [29].
Within each cycle of the fundamental field, the emission contains three bursts, each associated with one of the three leafs of the total field and labelled by the index k = 1, 2, 3.The corresponding induced dipoles are Each dipole has components with both polarizations, ê± , and each component is carrying its own amplitude and phase.As always in strong-field driven high harmonic generation, the phase is dominated by the action accumulated during the motion of the electron in the continuum, while the amplitude is dominated by strong-field ionization conditioned on the electron return to the vicinity of the parent ion.Note that the two-color driving field curves the electron trajectory.This curved continuum motion imposed by the field means that the recombination dipole matrix elements will be different for the emission of photons co-rotating and counter-rotating with the fundamental laser field.
If the circular pulses at the frequencies ω and 2ω are long and overlap perfectly, then a rotation of 2πk/3 (with k integer) leaves the field invariant (see Fig. 1).This three-fold symmetry of the field, together with the symmetry of the medium, imply that the phases and the amplitudes for k = 2, 3 are the same as for k = 1, up to the 2π/3 and 4π/3 rotations of the associated vectors ê± for k = 2 and k = 3, and the time-delay of the emission bursts by 1/3 and 2/3 of the laser cycle correspondingly.Under rotation by an angle α, the ê± vectors transform as Upon the Fourier transform into the frequency domain, the contributions from each leaf will gain additional phases exp(iM k2π/3) from the exp(iMωt) factor in the Fourier integral, due to the corresponding time-delays in emission by ωt = k2π/3.Hence, the total contribution of the three bursts to the emission dipole at the frequency Mω is, for the component co-rotating with the fundamental field, Similarly, for the component of the harmonics which co-rotates with the second harmonic, we have For the intensities I ê± ∝ |d ± (Mω)| 2 we obtain The expressions Eqs.(4,5,6) show the symmetry-imposed selection rules for the harmonics of different polarization.We stress again that these rules assume that three emission bursts associated with the three leaves of the driving field are identical, up to rotation and time-delay.
The counter-clockwise component, co-rotating with the red field, will be enhanced for the M = 3N + 1 harmonics and cancelled by the interference of the three terms for the M = 3N + 2 harmonics.The clockwise component, co-rotating with the blue field, will be enhanced the M = 3N + 2 harmonics and cancelled by the interference of the three terms for M = 3N + 1 harmonic.Finally, the M = 3N harmonics will be always suppressed (provided the fields are propagating collinearly), giving rise to the characteristic HHG spectrum of the ω + 2ω scheme [28,29](Fig.1d).Fig. 1(a) shows the calculated amplitudes | A| of the different emission bursts for a given harmonic (we have used M = 60 in this Figure) using an ellipticity of 1.0 in both fields, in the case when the two driving fields have identical pulse durations and overlap perfectly.The calculations are based on using the saddle point method and the standard strong field approximation (SFA), following Milosevic and Becker [29] and considering the contribution of the saddle points associated with the short trajectories in the bicircular field.The ionization potential was set to I p = 24.6 eV (Helium), with the ground s-state being the initial state.The driving pulses are both Gaussian-shaped, with a peak field strength of F ω = F 2ω = 0.1 a.u., and duration of (a,d) 38 fs.The harmonic spectrum, shown in Fig. 1(d), demonstrates the lack of M=60 and all harmonics with orders M = 3N.Interestingly, the lines M = 3N + 1 and 3N + 2, with opposite helicity, have different heights, even though we used the ground s-state.This propensity reflects the curvature of the motion imposed on the electron between ionization and recombination.Here, the curvature is dominated by the fundamental field.
Physical origin of the forbidden harmonics
Several factors can alter the simple selection rules associated with the three-fold dynamical symmetry of the driving field.Two possibilities lie on the surface and are illustrated in Fig. 1(b,c,e,f).
First, if the pulses are elliptical rather than perfectly circular, the field will not be invariant under a 2π/3 rotation anymore.Fig. 1b shows the amplitudes | A| for a given harmonic (we have used M = 60 in this Figure ) the different emission bursts, but now for the ellipticity of 0.9 (for both fields).To eliminate other possible mechanisms responsible for the 3N lines and focus on the role of ellipticity, the calculations used the strong field approximation (SFA) approach for the bi-circular fields [29].One of the bursts inside the cycle is stronger than the other two, leading to the appearance of the forbidden harmonics in the spectrum (see Fig. 1(e) This assymmetry in the driving field is hardly visible in Fig. 1(e) inset, but becomes noticeable in the harmonic amplitudes due to exponential sensitivity of tunnel ionization to the field.Nevertheless, the forbidden lines are quite weak, even for these rather substantial deviations from the perfectly circular driving fields.
Second, for short pulses, many of the bursts will be strongly suppressed by a rapidly changing envelope.Their amplitudes and phases, for a specific harmonic, will depend on the rapidly changing fields at the times of ionization and recombination.In particular, this leads to a heavily non-symmetric amplitude distribution with respect to the central (more intense) burst, as can be seen in Fig. 1(c), again for H60.This loss of symmetry can be observed in the HHG as a signal at the forbidden harmonic lines.These indeed arise prominently for H60 and higher orders (Fig. 1
(f).
There are, however, two additional, more subtle, possibilities of breaking the dynamical symmetry that are crucial in this work.First, a memory present in the quantum system would make the contributions from successive peaks of the field different.This is in analogy to XUVassisted high harmonic generation in linear fields [74], where an XUV pulse pumps the system to a superposition of Rydberg states, from which ionization occurs easier.In this case, the 400 nm pulse acts as a multi-photon pump which excites the system into a superposition of Rydberg states.Ionization in the subsequent bursts is therefore enhanced and hence A (1) +/− , which breaks the dynamical symmetry.Second, one can vary the time delay between the two driving pulses, the fundamental and the second harmonic, breaking the symmetry of the total field in a well controlled way.For the two circular driving fields, high harmonic signal will only be produced in the region of their overlap.Time delaying one of the two pulses leads to the asymmetric behaviour of the successive emission bursts, similar to a short two-color pulse.We use the interplay of these two possibilities in our analysis below.
The physical idea is as follows: the system memory is linked to the excitations generated by the driving pulse.The efficiency of the excitations by the second harmonic field is higher than by the fundamental.Hence, memory effects and the strengths of the forbidden harmonics should be more prominent when the second harmonic arrives first, compared to the case when the second harmonic arrives second.Thus, systematically varying the two-color delay and recording the relative strength of the forbidden lines allows us to gauge the role of the dynamical symmetry breaking associated with the memory of the quantum system.
Experimental setup
We have performed experiments in helium using a Ti:sapphire-based laser system with a single stage regenerative amplifier producing 38 fs pulses with up to 4 mJ energy and a central wavelength of ∼ 795 nm at 1 kHz repetition rate.The carrier-envelope phase (CEP) of the pulses was not locked.The laser beam was directed into the optical setup shown in Fig. 2.
The original beam was split into two beams, with the possibility to use the splitting ratios of 50/50, 70/30 and 80/20.The first beam was directed into a BBO crystal to generate the second harmonic (at ∼ 400 nm) with the pulse energy up to 0.8 mJ.The second beam, remaining at fundamental wavelength 795 nm, had the pulse energy up to 1.0 mJ.We could also smoothly tune the energies of the pulses and ratio between the ''red" and the ''blue" beams by changing the pump pulse energy in the amplifier.
Both beams passed through the corresponding achromatic broadband λ/2 and λ/4 waveplates, where their polarization was converted into nearly circular, with the ellipticity as high as ε 0.95.The optical path of the fundamental beam was controlled using a rooftop mirror mounted on a translation stage.The fundamental and the second harmonic beams were combined together in the collinear geometry and focused with a single Ag-mirror at f/100 into a 5-mm-long gas cell containing helium.
The waists of the fundamental and the second harmonic (red and blue) beams were measured to be w 0 (ω) 33 µm and w 0 (2ω) 27 µm respectively, so that the maximum intensity could reach as high as I ω ∼ 9.0 × 10 14 W/cm 2 and I 2ω ∼ 7.2 × 10 14 W/cm 2 .The pulses were focused approximately 2 mm before the target, minimizing the contribution of the Gouy phase to macroscopic effects and selecting short electron trajectories.The gas cell, placed inside the vacuum chamber, was initially sealed with a metal foil.The foil was burned through by the laser beam at the start of the experiment.The resulting cell opening had the size d = 40 µm similar to the spot size on the cell position, allowing us to keep the gas pressure inside the cell constant at 40 mbar at the appropriate level of vacuum (typically P rest ≈ 10 −4 mbar) inside the interaction chamber.
After passing the 5 mm gas cell, the driving 'red' and 'blue' beams were blocked by an 300 nm thick aluminum foil.The transmitted XUV radiation was directed towards the XUV spectrometer placed insight the vacuum chamber differentially separated from the interaction chamber.The XUV-spectromenter was based on the silicon nitride transmission nanograting operating in the wavelength range of 10 to 80 nm [75] with a resolution of 0, 25 − 0, 13 nm across the whole spectral range.The generated and spectrally resolved XUV radiation was detected by a double-microchannel plate (MCP) with a phosphor screen and recorded by a fast CMOS camera (PointGrey).Radiation up to harmonic orders ∼ 50 was observed.
Experimental results
Fig. 3 shows the observed XUV-spectra, for the bi-circular driving field and different red-blue time-delays.When the two driving pulses overlap (see Fig. 3 (b)), the harmonics with order 3N are suppressed.
We have measured and analysed the XUV spectra as a function of the time delay between the 800 nm and the 400 nm pulses.The time zero of the perfect overlap between the two pulses was determined via the cross-correlation between the two beams in the BBO crystal, with the measured cross-correlation length 40 fs.The positive time delay means that the second harmonics arrives after the fundamental.
While the experimentally observed spectra are likely affected by the macroscopic propagation effects, we focus on the features that must originate in the single-atom response: the dependence of the forbidden harmonic lines on the delay and the relative intensities of the two driving fields.Obviously, macroscopic propagation cannot lead to the appearance of forbidden harmonics if they are not generated at the single-atom level.
From this perspective, the main features in the experimental spectra in Fig. 3 are as follows.First, we see the appearance of the forbidden 3N harmonics when we increase the time-delay between the two pulses, while at τ=0 these harmonics are very strongly suppressed.Second, the 3N harmonics are a lot more prominent for the negative time delay, i.e. when the blue pulse arrives first.This experimentally observed feature was found to be robust with respect to varying the intensities of the two-color laser field.Fig. 4 shows how changing the light intensity, especially the ratio between the fundamental and the second harmonic, affects the high harmonic spectrum.Apart from the clear effect of absorption in the lower energy region and the expected trend that higher intensities leads to higher harmonic cut-offs, we again bring the reader's attention to the forbidden 3N orders.We observe, that the forbidden 3N harmonics are effectively suppressed when the fundamental field is stronger than the second harmonic (Fig. 4a), or when the two intensities are close to each other (Fig. 3b).When the intensity of the 400 nm pulse is higher than that of the 800 nm pulse, however, the forbidden harmonics become prominent (Fig. 4b).These observations again seem to confirm the idea that frustrated tunneling is playing a prominent role.
Numerical Results
We now turn to numerical simulations to reinforce this physical idea and rule out propagation effects.The strong field approximation, which neglects the excited states, is not adequate for the analysis, and we solve the time-dependent Schrödinger equation for the Helium atom.We used the code described in [76].To simulate the helium atom, we used the 3D single-active electron pseudo-potential given in [77].We have used a radial box of 600 a.u., with a total number of points nr = 1535.We use a uniform grid, with 33 points (grid spacing of 0.14 a.u.) at the origin, followed by 34 points on a logarithmic grid, with a scaling parameter of 1.03, starting at 5 a.u., and finally 1468 points on a uniform grid with a spacing of 0.4 a.u.We placed a complex boundary absorber at the border of the radial box (starting at 470 a.u.), in order to avoid reflections.However, the box is sufficiently large to contain the full wave-function at the end of the pulse (we check that the total norm in the simulation volume is 1.0 at the end of the pulse).Therefore we can apply the iSURFC method [78].The maximum angular momenta included in the spherical harmonics expansion was max = 70.The time grid had a spacing of dt = 0.04 a.u.All the discretization parameters have been checked for convergence.
Fig. 5 shows our results obtained for 20 fs Gaussian pulses with intensities I th ω = I th 2ω = 0.12 PW/cm 2 , corresponding to the peak fields of F th ω = F th 2ω = 0.058 a.u., with variable time delay of τ = −16, 0, 16 fsec.The center of the fundamental pulse is fixed at t 0,ω = 0, and τ = t 0,2ω markes the center of the second harmonic pulse.Positive τ means that the second harmonic pulse comes later, negative τ means that it comes earlier.The top row shows the x-component of the total field, while the other rows show the harmonic spectra and the ratio between the forbidden and permitted lines.The spectra are presented for both perfectly circular (panels d-f) and elliptic = 0.9 (panels j-l) fields, and the intensities of the two fields are equal.
As expected, the 3N lines are suppressed for τ = 0 but become stronger as we increase time delays between the two pulses.Crucially, the ratio R(τ) = S 3N (τ)/S 3N +1 (τ) (panels g-i in Fig. 5) is asymmetric as a function of τ, strongly suggesting that the memory of the quantum system is playing a role, i.e. the blue pulse excites the system and the delayed red pulse probes the excitation.The effect is common for both perfectly circular and elliptic fields, with the pulse ellipticity playing a secondary role in the effect.
We now focus on perfectly circular and perfectly overlapping pulses and show how the forbidden harmonics arise even in these cases, thanks to the role of strongly driven Rydberg states trapping population during strong field ionization.To this end, we have performed theoretical simulations with perfectly circular, overlapping pulses of 12 fs FWHM duration for three different ratios of the field strengths, see Fig. 6.The ratio F 2ω /F ω is varied from . The total intensity and, hence, the peak of the total electric field are kept constant for (a) and (c), I max = I 2ω + I ω = 3.7 × 10 14 W/cm 2 , and is lowered for (b), Substantial 3N lines such as H24, H27, H30 and especially H33 appear when the second harmonic is stronger than the fundamental (F 2ω = (3/2)F ω = 0.085 a.u.) and dominates ionization, see panel (a).When the strength of the fundamental field field strengths are equal (F 2ω = F ω = 0.057 a.u.,), panel (a), or when the fundamental is stronger (F 2ω = (2/3)F ω = 0.038 a.u.) the 3N harmonics are essentially absent.
To understand the reason behind this breaking of the symmetry, we projected the wavefunction at the end of the pulse onto the bound states of the atom.In Fig. 6d we show the bound population of the first seven excited states (excluding the ground state), sorted by total angular momentum, at the end of the pulse.When the blue field is stronger than the red field, irrespective of the maximum peak intensity, the bound state population is dramatically higher.In the energy domain (multiphoton) picture, this is the consequence of fewer high energy photons needed to resonantly populate the higher lying states.In the time-domain (tunneling) picture, when the blue field dominates ionization, the electron orbit is more likely to be trapped -the frustrated tunnelling is more efficient at 400 nm than at 800 nm.
This picture is confirmed in Fig. 7, where we show six snapshots of how the spectrum in Fig. 6a and 6c builds with time.To do this, we apply a gradually increasing window function to the time-dependent induced dipole D(t) = Ψ(t)| d|Ψ(t) .The upper panel shows the length of x-component of the bicircular field; second row: spectra for perfectly circular driving pulses; third row: ratio of the forbidden 3N harmonic to its 3N+1 neighbor; fourth row: spectra for elliptical pulses, = 0.9.Left column: the 400 nm pulse comes first; middle column: perfect overlap; right column: the 400 nm pulse is delayed.
this temporal window as the shaded area, along with the total intensity F 2 x + F 2 y of the ω + 2ω laser field (red line).The central and bottom panels show the corresponding spectrum for that energy window for the cases when the 400 nm field is stronger or weaker than the 800 nm field, respectively.
Early on, Fig. 7(a), the lower harmonics show only symmetry-allowed harmonics.For the higher harmonics, there is not yet enough time to provide a sequence of consecutive bursts with sufficient energy, which would interfere to yield clear harmonic lines.The forbidden harmonics are absent or very low in both spectra, indicating that the excited states are not sufficiently populated to play any significant role.As we increase the temporal window (Fig. 7b), the excited states start to get populated when the blue field is stronger, and the electrons begin to get trapped in trajectories orbiting around the ionic core.The forbidden harmonics start to emerge when the blue field is stronger, but not when the red is stronger.The prohibited lines appear first at higher harmonics.As we keep increasing the temporal window (Fig. 7c), lower harmonics start to show the forbidden lines.
More importantly, with increased time resolution the forbidden lines such as H30, H33 or H36 in Fig. 6c start to show a doublet structure.This is a characteristic feature of symmetry-forbidden lines, known for single-color fields [54] and demonstrating the population of more than one Floquet state during the laser pulse.As time keeps increasing and the field becomes stronger, the doublet lines start to appear also for lower harmonics (see H18 and H21 in Fig. 7d and H6 and H9 in Fig. 7e).Higher harmonics now start to show a more complex structure, suggesting that multiple Floquet states are being populated by the rapidly changing field.While similar arguments are applicable for the case in which the red field is stronger, and indeed the forbidden harmonic lines are observable, the strengths of the signal is orders of magnitudes smaller due to the very small population of the excited states in the first place.This information can be partially accessed experimentally by time-delaying the driving pulses.When the overlap between the two pulses is small, the spectrum should be similar to that in the case of the the short Fourier transform window, Fig. 7a.As the overlap of the pulses increases, the spectrum features will build up as in Fig. 7.With the blue pulse coming first, the excited population will be higher, leading to more prominent forbidden lines as discussed in the previous section.
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In conclusion of the theoretical analysis, we also point out that varying the time delay between the two driving pulses allows us to control not only the strength of the forbidden harmonics, but also their ellipticity.Here we define the ellipticity as In Fig. 8 we show how this value changes as a function of the time delay for the four most visible forbidden harmonics in the spectrum: 30, 33, 36 and 39.A clear trend is observed.The forbidden harmonics rotate preferentially with the field that comes first, thus providing a mechanism to coherently control their ellipticity.Finally, we also observe strong blue-shift for higher harmonics when the blue light comes first.As we can see from the field profile in the top panel of Fig. 5, in this case the more intense bursts are happen during the rising part of the field, leading to the blue shift of the harmonic lines just like in the case of linearly polarized few-cycle drivers.The opposite is true when red comes last.Indeed, a high harmonic H37 experiences a strong blue-shift of E H37 (τ = −16 f s) − E H37 (τ = 16 f s) = 0.34 eV.The situation seems to reverse for lower harmonics.A lower harmonic H25 slightly red-shifts its position by E H25 (τ = −16 f s) − E H25 (τ = 16 f s) = −0.12eV.This provides a mechanism to fine tune the relative energy distance between harmonics.
Conclusion
In conclusion, we have shown the different mechanisms by which the forbidden harmonic lines may appear in the high harmonic spectrum generated by bicircular fields.In contrast to the commonly accepted wisdom that strong forbidden harmonics originate from slight ellipticity of the driving fields, we show that this is not the case.For ellipticities ≈ 0.95 dynamical symmetry breaking is too weak to be fully responsible for the strong forbidden lines.We have demonstrated that population of Rydberg states breaks the dynamical symmetry and leads to prominent signals at the forbidden harmonics.The population of laser-driven Rydberg states is revealed by tracking the strength of the forbidden harmonic lines via the time delay between the two driving pulses.Increasing the intensity of the second harmonic field leads to stronger trapping of the electrons in high Rydberg orbits.In time domain, this is the consequence of the frustrated tunneling mechanism.In the frequency domain, they can be seen as the Freeman resonances [79,80].We have demonstrated that such dynamics are mapped on the forbidden harmonic lines that appear even for perfectly circular, long driving pulses.
We have temporally resolved these dynamics by applying a gradually increasing window function to the Fourier transform of the induced dipole, demonstrating the build-up of the forbidden harmonic lines as the excited states are populated on the rising edge of the laser pulse.Finally, in analogy with the blue-shift observed in the high harmonic generation triggered by short linearly polarized drivers, we have predicted and experimentally confirmed a substantial blue-shift of higher harmonics when the blue driver precedes the red driver.
Fig. 5 .
Fig. 5. Theoretical HHG spectra as a function of the blue-red time delay.Top row:x-component of the bicircular field; second row: spectra for perfectly circular driving pulses; third row: ratio of the forbidden 3N harmonic to its 3N+1 neighbor; fourth row: spectra for elliptical pulses, = 0.9.Left column: the 400 nm pulse comes first; middle column: perfect overlap; right column: the 400 nm pulse is delayed.
Fig. 6 .
Fig. 6.Influence of bound state population.High harmonic spectrum of helium generated by two counter-rotating 12 fs long fields of frequencies 1.55 eV and 3.1 eV, for three different ratios of the field strengths: (a) F 2ω = 3/2F ω = 0.085, (b) F 2ω = F ω = 0.057, and (c) F 2ω = 2/3F ω = 0.038.Peak intensities are the same for (a) and (c) and it is lower for (b), see text for details.Panel (d) shows the population of the bound states of the atom (in logarithmic scale) after the interaction with the field, for the three intensity ratios.
Fig. 7 .Fig. 8 .
Fig. 7. Build up of the spectrum.Snapshots of the spectra in Fig. 6a (central panel) and Fig. 6c (bottom panel), at different times in the presence of the 12 fs long laser field: (a) 6 fs before the peak of the field, (b) 2.42 fs before the peak of the field, (c) 0.6 fs after the peak of the field, (d) 3 fs after the peak of the field, (e) 6.65 fs after the peak of the field, and (f) 12.7 fs after the peak of the field.The upper panel shows the maximum intensity of the field, I max = F 2x + F 2 y , which is always the same for the upper and lower spectra, as the red line, and the shaded area indicates the temporal window applied to the dipole to obtain the corresponding spectrum. | 8,236.2 | 2017-07-18T00:00:00.000 | [
"Physics"
] |
Mutations in the AF-2/Hormone-binding Domain of the Chimeric Activator GAL4 z Estrogen Receptor z VP16 Inhibit Hormone-dependent Transcriptional Activation and Chromatin Remodeling in Yeast*
GAL4 z estrogen receptor z VP16 (GAL4 z ER z VP16), which contains the GAL4 DNA-binding domain, the human ER hormone binding (AF-2) domain, and the VP16 activation domain, functions as a hormone-dependent transcriptional activator in yeast (Louvion, J.-F., Havaux-Copf, B., and Picard, D. (1993) Gene ( Amst .) 131, 129–134). Previously, we showed that this activator can remodel chromatin in yeast in a hormone-dependent manner. In this work, we show that a weakened VP16 activation domain in GAL4 z ER z VP16 still allows hormone-depend-ent chromatin remodeling, but mutations in the AF-2 domain that abolish activity in the native ER also eliminate the ability of GAL4 z ER z VP16 to activate transcription and to remodel chromatin. These findings suggest that an important role of the AF-2 domain in the native ER is to mask the activation potential of the AF-1 activation domain in the unliganded state; upon ligand activation, a conformational change releases AF-2-medi-ated repression and transcriptional activation ensues. We also show that the AF-2 domain, although inactive at simple promoters on its own in yeast, can enhance transcription by the MCM1 activator in hormone-dependent manner, consistent with its having a role in activation as well as repression in the native ER.
The estrogen receptor (ER) 1 is a member of a superfamily of nuclear receptors, which are ligand-activated transcription factors. These proteins have independent modular domains capable of DNA binding, ligand binding (LBD), and transcriptional activation (1). Two distinct domains have transactivation capacity: a hormone-independent transactivation function (AF-1) resides in the N terminus, while the hormone-dependent AF-2 lies within the hormone-binding domain (2,3). These domains appear to interact functionally and probably physically. For example, when expressed as separate peptides in mammalian cells, the two domains synergize to activate a reporter plasmid only in the presence of hormone (4). The AF-1 domain displays constitutive activity in some cells (3) and is active in yeast cells, and both the AF-1 and the AF-2 domains can behave as transcriptional activators when fused to a heterologous DNA-binding domain (5,6). Additionally, coactivators for nuclear receptors interact with AF-2 in mammalian cells (7).
With the determination of the partial crystal structure (LBD) of four nuclear receptors, including the liganded estrogen receptor (8 -11), the mechanism of action of this superfamily is coming into focus. The ligand-binding domain of nuclear receptors appears to act as a switch or a "mouse-trap." The ligand binds to a pocket in the receptor, tripping a conformational change that rearranges helix 12 to form a "lid" over the agonist. Helix 12 contains the AF-2 core, and Wurtz et al. (12) suggest that realignment may create a new surface for interactions with co-activators and/or break connections with repressors. Brzozowski et al. (8) have shown that an estrogen antagonist prevents the alignment of helix 12, providing further evidence that activation requires this new surface.
However, it is still not clear how tripping the mouse-trap of the LBD leads to activation of the receptor. It is certain that the AF-2 core is vital for productive interaction with agonist. Danielian et al. (13) demonstrated that mutations in this core significantly reduce ligand-dependent transcription, without affecting steroid or DNA binding. The co-activators RIP 140 and TIF2 likewise require AF-2 core activity to interact with nuclear receptors (14,15), while SRC-1 also requires a lysine residue in helix 3 (16).
Experiments utilizing the modular domains of nuclear receptors are instructional in elucidating the mechanisms of receptor activation and transcription. Previously, using a chimeric transcription factor, GAL4⅐ER⅐VP16, we demonstrated that disruption of chromatin structure required an unmasked activation domain (17). GAL4⅐ER⅐VP16 is composed of the yeast GAL4 DNA-binding domain, the human estrogen receptor hormone binding/AF-2 domain, and the viral VP16 activation domain (18). This hormone-dependent transcriptional activator perturbed chromatin in a yeast episome, outside of the context of a bona fide promoter, only when both hormone and the VP16 activation domain were present. Likewise, the yeast GAL4 protein significantly disrupted chromatin structure only when in an active form.
Here, we further show that a weakened VP16 domain in GAL4⅐ER⅐VP16 does not abrogate its ability to disrupt chromatin. Conversely, mutations that abolish AF-2 activity without compromising hormone binding or binding to DNA in the intact estrogen receptor (13) also eliminate the ability of GAL4⅐ER⅐VP16 to activate a lacZ reporter and disrupt chromatin structure without interfering with the ability of the chimeric receptor to bind hormone or to bind to DNA. These results suggest that the AF-2 domain has a repressive function in the unliganded ER, which can act even on a heterologous activation domain, and that mutations in the AF-2 domain can prevent ligand from "unlocking" this configuration. Additionally, these results support the tight correlation between an intact activation domain and chromatin remodeling observed previously (17, 19 -21). We also show that, while eliminating the VP16 moiety results in a factor incapable of independently activating transcription or remodeling our chromatin reporter, GAL4⅐ER can still synergize with a proximal activator.
Analysis of Plasmid Chromatin-Yeast cells (1 liter) were grown at 30°C to A 600 between 0.6 and 1.6. Yeast nuclei were prepared as described previously (17,30) and digested with varying concentrations of micrococcal nuclease (MNase) (Worthington) for 10 min at 37°C. Cleavage patterns were consistent over a range of 0 -50 units/ml. Naked DNA controls were purified from nuclei preparations prior to digestion with MNase. Cleavage patterns were visualized by indirect end labeling (31,32). Following clean-up with phenol and chloroform, aliquots were treated with RNase and digested with EcoRV. The samples were electrophoresed along with HaeIII-digested ⌽X markers in a 1.2% agarose gel at 4 V/cm for 5-5.5 h. The DNA was transferred to nylon membranes (Duralon UV, Stratagene) and Southern analysis performed. Probes were EcoRV to XbaI fragments from TALS prepared by polymerase chain reaction. Indirect end label analysis was done in two independent experiments for each of the AF-2 mutants examined here, as well as for the parent F442P receptor.
Topoisomer Analysis-DNA was prepared by pelleting 10 ml of cell cultures grown to A 600 ϭ 0.6 -1.2, resuspending in 500 l of 10 mM Tris, 1 mM EDTA, and rapidly lysing with glass beads in the presence of 100 l of 5% SDS, 5 mg/ml proteinase K. Purified DNA was separated on 1.5% agarose gels with 40 g/ml chloroquine diphosphate (Sigma) in both gel and buffer at 2.5 V/cm for 18 -20 h. The gel was blotted and probed as above. Quantitation of topoisomers was performed by Phos-phorImager analysis (Molecular Dynamics) and the Gaussian centers of distribution calculated.
RESULTS
A Slight Reduction in the Activating Potential of GAL4⅐ER⅐VP16 Does Not Affect Its Ability to Remodel Chromatin-We previously used the chimeric transcription factor GAL4⅐ER⅐VP16 to demonstrate activation domain-dependent chromatin disruption in the yeast episome TALS, which contains a strong binding site for GAL4 within a positioned nucleosome (17). Since it has been reported that the DNA binding activity of the intact estrogen receptor is affected by hormone addition (33-35), we wished to separate possible effects of the hormone-binding domain of GAL4⅐ER⅐VP16 on its DNA-binding domain from those due to unmasking of the activation domain. We first examined the effect of reducing the activation potential of GAL4⅐ER⅐VP16 by introducing a point mutation into the VP16 activation domain, F442P, which reduces activity of GAL4-VP16 at a CYC1-lacZ reporter driven by the GAL1-10 UAS by two-thirds (36). Transcription was monitored using a lacZ construct containing a single strong GAL4 binding site (UAS 17 ) in the presence and absence of hormone. Transcription by the mutant GAL4⅐ER⅐VP16(F442P) showed a modest reduction, to about 60% of the activity induced by GAL4⅐ER⅐VP16 (Fig. 1). (Although the standard errors for these measurements were fairly large, we consistently observed lower activity of the mutant than of the parental GAL4⅐ER⅐VP16 when the two were measured simultaneously. Furthermore, Student's t test yields p Ͻ 0.001 for the null hypothesis that the two activators are equally active.) We next assessed the ability of GAL4⅐ER⅐VP16(F442P) to remodel chromatin structure in the TALS reporter plasmid. The TALS minichromosome is packaged into strongly positioned nucleosomes in yeast ␣ cells by the ␣2⅐MCM1 protein complex in conjunction with Ssn6p and Tup1p (37). We assayed chromatin remodeling in TALS by following hormone-dependent changes in MNase cleavage patterns in the presence of GAL4⅐ER⅐VP16(F442P). Isolated nuclei were subjected to different concentrations of MNase for 10 min, followed by indirect 2 S. Hanes, unpublished results.
FIG. 1. Transcriptional activation by GAL4⅐ER⅐VP16 derivatives.
Activation of pRS314 -17⌬80lacZ, a CYC1-lacZ reporter gene with a single strong GAL4 binding site (UAS 17 ), by derivatives of GAL4⅐ER⅐VP16 was monitored in the absence or presence of -estradiol (Ϯ E2). The VP16 activation domain was either absent or present as wild type or with the F442P mutation, as indicated, and the AF-2 domain was either present as wild type or mutant, or absent, as indicated. The first two columns show measurements done in the absence of GAL4⅐ER⅐VP16. All measurements were performed with cells grown in glucose medium, and are averages of at least five independent determinations; standard errors are indicated or else are too small to be visible. end label analysis (31,32). The pattern of MNase cleavages in TALS chromatin induced by GAL4⅐ER⅐VP16(F442P) changed upon the addition of -estradiol (Fig. 2, left panel). The lowest arrowhead marks a site of enhanced cleavage seen when cells are grown with hormone. The upper two arrowheads mark cleavage sites seen only in the presence of hormone. These hormone-dependent alterations in TALS chromatin demonstrate perturbation of nucleosome IV, which contains the GAL4 binding site, and the adjacent nucleosome III, and are indistinguishable from those seen previously with GAL4⅐ER⅐VP16 (17).
Perturbation of chromatin structure in a closed circular minichromosome can result in a change in the distribution of supercoiled topoisomers, since each nucleosome in the plasmid constrains one negative supercoil (38). To investigate the effect of GAL4⅐ER⅐VP16(F442P) on TALS topology, DNA from cells expressing the chimeric factor was rapidly harvested and treated to inactivate topoisomerases (so that the distribution of supercoiled plasmids reflected the in vivo distribution). We previously demonstrated that GAL4⅐ER⅐VP16 in the absence of -estradiol did not alter plasmid topology as compared with DNA from cells lacking GAL4⅐ER⅐VP16. Cells harboring GAL4⅐ER⅐VP16 and grown in the presence of hormone exhibited a shift in the center of distribution of the topoisomers equivalent to the loss of almost one negative turn (17). Hormone induction of GAL4⅐ER⅐VP16(F442P) likewise resulted in the loss of negative supercoiling in TALS (Fig. 3, lanes 1 and 2). These topoisomer distributions conform to Gaussian distributions, which allows their centers to be measured precisely from the relative intensities of individual topoisomers (39). Consequently, differences in topology can also be measured with precision. Quantitation yielded a value for the loss of negative supercoiling in TALS in the presence of hormone-activated GAL4⅐ER⅐VP16(F442P) of 0.6 Ϯ 0.2 (Table I), similar to the value seen with GAL4⅐ER⅐VP16 (0.7 Ϯ 0.1) (17). Thus, the modest reduction in activation potential caused by the F442P mutation did not detectably diminish the ability of GAL4⅐ ER⅐VP16 to remodel TALS chromatin.
A Functional AF-2 Core Is Required for Both Transcriptional Activation and Chromatin Disruption by GAL4⅐ER⅐VP16 -The hormone-binding domain of the estrogen receptor also contains an activation domain (AF-2). The AF-2 domain can activate transcription in the absence of the AF-1 or any other transcriptional activation domain in mammalian cells (2). In yeast, the AF-2 domain apparently lacks a universal ability to activate transcription on its own; although it can activate transcription from a complex promoter, it does not activate trancription from a simple promoter lacking binding site(s) for other activators (6,17,18).
Either of two pairs of mutations within AF-2 (L539A/L540A and M543A/L544A of the human ER) almost totally abolishes transcriptional activation by the estrogen receptor in mammalian cells, without affecting DNA or ligand binding (13). In order to assess the requirements for AF-2 activity in the context of the chimeric activator, we introduced these mutations into GAL4⅐ER⅐VP16(F442P) and expressed the resulting mutant proteins in yeast.
To demonstrate that the mutant GAL4⅐ER⅐VP16 receptors still effectively bound hormone, we first attempted binding assays using radiolabeled -estradiol with both intact yeast cells (40) or yeast cellular extracts (41). Unfortunately, although binding was easily measured and could be competed with unlabeled -estradiol, identical results were obtained whether or not the yeast cells expressed GAL4⅐ER⅐VP16. As an alternative, we therefore performed an in vivo competition assay. YJ0 cells harboring an expression vector for LexA⅐ER⅐ VP16 and a -galactosidase reporter containing eight LexA binding sites were transformed with expression plasmids for mutant and wild type GAL4⅐ER⅐VP16(F442P) or an empty vector control. LexA⅐ER⅐VP16 is identical to GAL4⅐ER⅐VP16, except it contains the LexA DNA-binding domain in place of that for GAL4, and functions as a hormone-dependent transcriptional activator via LexA binding sites. 3 At limiting hormone concentrations, we expected that the GAL4⅐ER⅐VP16 chimeras might compete with LexA⅐ER⅐VP16 for the available -estradiol and hence decrease transcription of the -galactosidase reporter gene. As shown in Table II, -galactosidase activity induced by LexA⅐ER⅐VP16 in the presence of 2.5 nM -estradiol was indeed reduced by about 40% in cells harboring pRS414GAL4⅐ER⅐VP16(F442P) compared with cells harboring the empty vector pRS414. Similarly, the chimeric GAL4⅐ER⅐ VP16(F442P) receptors containing mutated AF-2 domains also reduced -galactosidase activity induced by LexA⅐ER⅐VP16 by about 50% (Table II). In contrast, -galactosidase activity induced by LexA⅐ER⅐VP16 was reduced only slightly by either the wild type or mutant GAL4⅐ER⅐VP16(F442P) receptors at 250 nM -estradiol (Table II), supporting the interpretation of the results at 2.5 nM -estradiol as being due to competition for limiting hormone. Thus, these results indicate that, as for the intact ER (13), the L539A/L540A and M543A/L544A mutations in the AF-2 domain do not affect hormone binding in the GAL4⅐ER⅐VP16 chimeras.
When GAL4⅐ER⅐VP16(F442P) harboring either the L539A/ L540A or M543A/L544A mutation were assayed for transcriptional activity using the UAS 17 -lacZ reporter, both were found to be completely inactive (Fig. 1). The L539A/L540A and M543A/L544A mutations also result in nearly complete inactivation of GAL4⅐ER⅐VP16 (i.e. with completely active VP16) ( Fig. 1 and data not shown). The data of Table II suggest that the mutated proteins were expressed at levels comparable to the parent GAL4⅐ER⅐VP16(F442P). To provide further evidence for their expression and to show that the AF-2 mutants were capable of binding to a GAL4 binding site, we examined the ability of unliganded GAL4⅐ER⅐VP16, GAL4⅐ER⅐VP16(F442P), and the AF-2 mutants derived from the latter to interfere with transcriptional activation by native GAL4 in cells grown in galactose-containing media (Fig. 4). Both unliganded mutant and wild-type receptors interfered with activation by GAL4, indicating that they occupy the UAS 17 to similar extents. As a control, we examined transcription of a LexA-lacZ reporter by a fusion protein containing the LexA DNA-binding domain and the GAL4 activation domain and found that transcription was unaffected by the presence of unliganded GAL4⅐ER⅐VP16 (data not shown). Thus, even in the context of a heterologous activation domain [VP16 or VP16(F442P)], the chimeric receptor requires an active AF-2 function to activate transcription.
We next assessed the effect of the AF-2 mutation on the ability of the chimeric activator to remodel chromatin. In contrast to GAL4⅐ER⅐VP16(F442P), GAL4⅐ER(L539A;L540A)⅐VP16 (F442P) does not alter the MNase cleavage pattern of TALS chromatin upon addition of -estradiol (Fig. 2). Consistent with this result, the distribution of supercoiled TALS topoisomers is not affected by hormone induction in the presence of the AF-2 mutants (Fig. 3, lanes 3 and 4; Table I). We conclude that the AF-2 mutations, which do not affect DNA binding or hormone binding (13), abolish the ability of GAL4⅐ER⅐VP16(F442P) both to activate transcription and to remodel chromatin.
Hormone-dependent Synergy between the AF-2 Domain and the Yeast Activator MCM1-To investigate the effect of a nonactivating GAL4⅐ER⅐VP16 derivative with an intact regulatory (ER) domain, we excised the VP16 moiety to recover GAL4⅐ER. GAL4⅐ER is unable to activate transcription from the UAS 17 -lacZ reporter in our assay ( Fig. 1 and Ref. 17). It does, however, measurably inhibit transcription by endogenous GAL4, showing that it is expressed and capable of DNA binding (17). GAL4⅐ER binding slightly affects TALS chromatin, but addition of hormone does not induce any further changes, as assayed by MNase digestion, restriction enzyme accessibility, or plasmid topology (17).
To discern whether the presence of hormone could increase DNA binding of GAL4⅐ER, we utilized a different lacZ reporter, pRS314␣2GAL4lacZ⌬Nco. In addition to a single GAL4 binding site in the promoter, this reporter has a binding site for the ␣2 and MCM1 proteins further upstream. In yeast a cells, which lack ␣2 protein, MCM1 binds to this site and activates transcription ( Fig. 5; Ref. 42). Non-activating proteins binding at the GAL4 site are expected to interfere sterically with activation by MCM1 (43). Indeed, GAL4⅐ER measurably reduced lacZ activity (Fig. 5) in the absence of hormone, as did GAL4⅐ER(L539A;L540A) and GAL4⅐ER(M543A;L544A). However, the addition of hormone did not result in a greater reduction of lacZ activity by GAL4⅐ER, as would be expected if 3
AF-2 Mutations in GAL4⅐ER⅐VP16
DNA-binding of transcriptionally inert GAL4⅐ER were increased by hormone binding. Instead, lacZ activity was increased nearly 2-fold (Fig. 5). This level is higher than that seen in the absence of any GAL4⅐ER, indicating that it cannot be attributed to loss of GAL4⅐ER binding, but rather must reflect enhanced transcription from the combined effects of MCM1 and ligand-bound GAL4⅐ER. We observed a similar effect in a different yeast strain, YJ0 (data not shown). This increase in activity required a functional AF-2 core, as neither GAL4⅐ER(L539A;L540A) nor GAL4⅐ER(M543A;L544A) increased MCM1-activated transcription in the presence of -estradiol (Fig. 5).
DISCUSSION
The results presented here support the view of the hormone binding/AF-2 domain of the human estrogen receptor as a modular entity that is capable of regulating the activity of a heterologous activation domain, in agreement with previous results (Ref. 18 and references therein). We further show that the hormone-dependent release of the heterologous VP16 activation domain from ER-mediated repression is abolished by mutations in the AF-2 domain (Fig. 1), which do not affect DNA binding or ligand binding (Figs. 4 and 5; Table II; Ref. 13), suggesting that these mutations lock the AF-2 domain in a repressive configuration. These findings suggest that an important role of the AF-2 domain in the native ER is to mask the activation potential of AF-1 in the unliganded state; upon ligand activation, a conformational change releases AF-2-mediated repression and transcriptional activation ensues. Transcriptional activation by the native ER and other nuclear hormone receptors in their native, physiological contexts is clearly more complicated than this, with ligand binding result-ing in release of co-repressors and recruitment of co-activators (7). These additional complexities are absent in the heterologous system studied here, and their relative importance therefore cannot be assessed; nevertheless, the work reported here indicates a role for the unliganded AF-2 domain in directly preventing activation by a linked activation domain that is likely to be relevant to its normal function in the intact ER.
We also show that the AF-2 domain, although inactive at simple promoters on its own in yeast (Refs. 17 and 18; Fig. 1), can increase transcription by the MCM1 activator in a hormonedependent fashion (Fig. 5). This would be consistent with the AF-2 domain contributing to activation as well as repression in the native ER, as suggested by previous work (2)(3)(4). Finally, we demonstrate that the AF-2 mutations which abolish transcriptional activation by GAL4⅐ER⅐VP16 also abolish chromatin remodeling ( Figs. 2 and 3), supporting our previous conclusion that chromatin remodeling by GAL4⅐ER⅐VP16 and by GAL4 requires an unmasked transcription activation domain (17).
Considerable progress has been made toward understanding the mechanism whereby the binding of a ligand to the estrogen receptor promotes transcription. Structural studies have shown that ligand binding causes a conformational change within the ligand-binding domain, repositioning several helices, most importantly helix 12 (8 -11). It has been proposed that the proper placement of helix 12 creates a surface that interacts with coactivators (12). Although the evidence for coactivators in mammalian cells is overwhelming (7), any mechanism for ER activation must also include AF-1, which can function alone (3,5) and which synergizes with AF-2, even when expressed as a separate protein (4). The activation potential of AF-1 must therefore somehow be nullified in the absence of hormone in the intact ER. Furthermore, GAL4⅐ ER⅐VP16 is virtually inactive in the absence of hormone (17,18), indicating that AF-2 can prevent even a heterologous activation domain from functioning in the absence of ligand. 17 ) and an ␣2/MCM1 operator and expression vectors for the indicated GAL4⅐ER derivatives were grown in glucose medium, in the presence or absence of hormone, and -galactosidase activity was measured. Values are averages of at least three independent measurements, and standard errors are indicated. Note that GAL4⅐ER does not activate transcription with or without hormone in the absence of an MCM1 binding site (Fig. 1).
The unliganded AF-2 domain could act as a modular repressor domain by interacting with another protein(s) that could prevent the receptor from binding to its cognate site. Steroid hormone receptors can complex with many proteins, including hsp90, which could prevent the estrogen receptor from binding to promoter sites (1). However, Lee et al. (44) have demonstrated that this mechanism cannot provide a complete explanation by designing chimeric receptors that do not bind hsp90, yet still display hormone dependence. They fused a VP16 activation domain N-terminal to the GAL4 DNA-binding domain and several truncations of the ER ligand-binding domain. These chimeras displayed 15-35% of the activity of VP16⅐GAL4 in the absence of hormone, but activity was enhanced 4-fold by estradiol. These results indicate that at least part of the hormone dependence of the AF-2 domain is independent of sequestration by hsp90, consistent with previous suggestions (45,46). Even more directly, we have found that GAL4⅐ER⅐VP16 and GAL4⅐ER bind DNA in the absence of -estradiol, as inferred from their ability to inhibit activation by GAL4 ( Fig. 4; Ref. 17) and by MCM1 via steric interference (Fig. 5), as well as the ability of unliganded GAL4⅐ER⅐VP16 to perturb chromatin structure, albeit weakly (17).
The AF-2 domain of the unliganded receptor could interact with a repressor. For example, the thyroid hormone receptor binds the repressor SMRT, although its exact mechanism of action is unknown (47). However, the presence of a repressor in yeast that would act on the AF-2 of the mammalian receptor seems unlikely, although certainly not impossible (48,49). More tellingly, we do not see evidence of trans-repression (e.g. of MCM1), as we would expect from a repressor that contacts general transcription factors or modifies chromatin (as expected for a histone deacetylase; Ref. 50).
We propose that the unliganded AF-2 domain presents a surface that binds nearby activation domains (AF-1 or VP16), preventing them from contacting normal targets. If the unliganded AF-2 surface resembled such a target, it would explain why AF-2 inhibits a heterologous activator. This is also consistent with the differences between GAL4⅐ER⅐VP16, which is essentially inactive in the absence of hormone, and VP16⅐ GAL4⅐ER, which retains 15-35% of its hormone-stimulated activity even in the absence of hormone (44); the conformation of the activation domain with respect to AF-2 determines the extent of inhibition. We suggest that, in yeast, the ligandbinding domain principally regulates the linked activation domain, which, when unmasked, recruits general transcription factors and/or chromatin remodeling complex(es). When the core AF-2 is mutated, the second activation domain cannot be released from its repression by AF-2, and no remodeling or transcription is seen. This hypothesis does not dismiss the role of co-activators like SRC-1 and RIP-140 in the native context (7,14). Rather, it adds another level of control over the estrogen receptor.
The chromatin remodeling activity tightly correlates with the transcriptional potential of the receptor, consistent with findings with the thyroid hormone receptor and the yeast transcriptional activators Gal4p and Pho4p, as well as with our previous work (17, 19 -21). GAL4⅐ER was not able to activate transcription or cause chromatin remodeling (17), and the AF-2 mutants used in this paper cause simultaneous extinction of transcriptional activation and chromatin remodeling by GAL4⅐ER⅐VP16(F442P). Thus, chromatin remodeling appears generally to be intimately linked to transcriptional activation. Uncoupling these functions, other than by the trivial routes of disabling transcription by crippling critical promoter elements or downstream components of transcription (as with ␣-amanitin), is likely to require considerable ingenuity (51,52).
The increase in MCM1-activated transcription caused by ligand-bound GAL4⅐ER was unexpected, and suggests that there can exist a threshold below which an "activator" cannot function on its own, although it can still synergize with another (weak) activator. Similar results have been reported using the vitellogenin A1 io promoter (53). This promoter contains estrogen response elements which cannot activate the promoter on their own, but which contribute to transcription by Sp1. One mechanism suggested to account for this synergy was that Sp1 could interact with the same transcriptional machinery as the liganded estrogen receptor at the downstream estrogen response elements. In our system, it may be that the AF-2 domain alone does not interact strongly enough with the transcriptional machinery in yeast to activate transcription in isolation, but does interact sufficiently to stabilize interactions created by another activator (e.g. MCM1) and thus to increase levels of transcription. This mechanism does not differ in principle from mechanisms proposed to account for synergy between activators, but adds the proviso that one activator can be so weak that it cannot activate transcription by itself and yet still can enhance transcription if another, stronger activator acts at the same promoter. | 5,952.8 | 1998-12-18T00:00:00.000 | [
"Biology"
] |
Surface guided radiotherapy practice in paediatric oncology: a survey on behalf of the SIOPE Radiation Oncology Working Group
Abstract Introduction Surface guided radiotherapy (SGRT) is increasingly being implemented to track patient’s surface movement and position during radiation therapy. However, limited information is available on the SGRT use in paediatrics. The aim of this double survey was to map SIOPE (European Society for Paediatric Oncology)-affiliated centres using SGRT and to gain information on potential indications, observed, or expected benefits. Methods A double online survey was distributed to 246 SIOPE-affiliated radiotherapy (RT) centres. Multiple choices, yes/no, and open answers were included. The first survey (41 questions) was active from February to March 2021. A shortened version (13 questions) was repeated in March 2023 to detect trends in SGRT use within the same community. Results Respectively, 76/142 (54%) and 28/142 (20%) responding centres used and planned to use SGRT clinically, including 4/34 (12%) new centres since 2021. Among the SGRT users, 33/76 (43%) already applied this technology to paediatric treatments. The main benefits of improved patient comfort, better monitoring of intrafraction motion, and more accurate initial patient set-up expected by future users did not differ from current SGRT-users (P = .893). Among non-SGRT users, the main hurdles to implement SGRT were costs and time for installation. In paediatrics, SGRT is applied to all anatomical sites. Conclusion This work provides information on the practice of SGRT in paediatrics across SIOPE-affiliated RT centres which can serve as a basis for departments when considering the purchase of SGRT systems. Advances in knowledge Since little information is available in the literature on the use of SGRT in paediatrics, the results of this double survey can serve as a basis for departments treating children when considering the purchase of an SGRT system.
Introduction
Surface guided radiotherapy (SGRT) uses optical imaging technology to track the patient's surface movement and position during radiation therapy without additional radiation dose. 1,2A reference surface is used to calculate the correction of the actual patient position in translations and rotations.When the patient's surface deviates from the reference position above a user-defined tolerance, the treatment beam can be interrupted.SGRT offers imaging with sub-millimetre detectability, real-time performance, availability at all couch angles, and the largest field of view among all clinical imaging modalities. 2,3 recent years, the clinical use of SGRT has increased, demonstrating utility for initial patient positioning 4,5 and real-time patient motion monitoring in a variety of anatomical sites.Examples of SGRT applications are breathing motion monitoring in breast deep inspiration breath hold treatment 3,6,7 and locally advanced lung cancer, 8 or monitoring the patient's head during non-coplanar treatments. 9For targets located in the extremities, SGRT can lead to an improved treatment posture thanks to the extended field-ofview, thereby reducing the need for repositioning, or reentering the room to adjust the patient, and so reducing the overall time per session. 10,11Moreover, it has been shown that SGRT can improve the efficiency of the radiotherapy (RT) workflow, by reducing the time required to set-up the patient, 12,13 and patient safety. 146][17][18] Two surveys reporting on the practice, mainly with adult patients, of this technology in the United States 16 and Europe 19 have been published.Information on the SGRT use in paediatrics (patients up to 18 years old) is limited, although SGRT could improve monitoring of the possible intrafraction motion of young patients during treatment.In a case report, the palliative radiation treatment of an 18-month old boy with a relapsed Wilms tumour using SGRT was described. 20The patient had a large anterior mediastinal mass which critically obstructed his airway.SGRT treatment could be delivered in a sufficiently short time slot without the need of anaesthesia.
Taylor et al investigated the potential role of SGRT for the management of interfractional gastrointestinal gas volume variation in paediatric abdominal RT. 21The key idea is that while SGRT would not replace cone beam CT (CBCT) imaging, it could enable a fully personalized Image Guided Radiotherapy (IGRT) schedule for each patient and reduce CBCT imaging to only required fractions.Also, SGRT systems have been recommended as a safety feature in paediatric treatments to assist in patient set-up and provide additional error detection. 14,22he purpose of this study was to map the SGRT practice in paediatric patients across SIOPE (European Society for Paediatric Oncology)-affiliated centres and so to gain more insight into its implementation.An electronic survey was conducted in 2021 and 2023 to identify actual and future SGRT users, any change over time in potential users, the advantages of this technology in clinical practice, the hurdles to implement it and finally to which anatomical sites SGRT is applied.
Methods
Two online open voluntary questionnaire were designed using Survey Monkey (SVMK Inc., CA, United States) to assess the use and implementation of SGRT across 246 SIOPEaffiliated paediatric RT departments in 35 countries 23 (https://SIOP-E.eu/about-SIOP-E/members/).
The first survey (41 questions) was active from February to March 2021 (Supplementary Data S1).A shorter version of the first survey (13 questions) was repeated in March 2023, aiming to detect changes in the use of SGRT over time (Supplementary Data S2).The survey length was intended to be brief: 10 min for participants who had surface imaging and less than 5 min for those who did not.Only one responder per institution was asked to fill in and return the survey.
The link to the survey was sent by e-mail and allowed for web-based data entry.The questionnaire announcement can be found in the Supplementary material.No incentives were offered for the participation to the questionnaire.
The survey was developed by a medical physicist expert and radiation oncologist both with vast experience in paediatrics.Survey questions were organized into two parts: the first part focussed on the participant institutional setting, the availability of SGRT and the time since implementation, the potential advantages in clinical practice for actual and future users and the reasons for not implementing this technology among non-users.The second part addressed the clinical use of SGRT, including applications (eg, initial positioning, intrafraction monitoring) and types of treatment (eg, anatomical site).The survey included multiple-choice questions with room for remarks, as well as yes/no and open-ended questions.Depending on the answers given, certain questions were skipped if not applicable.A maximum of two questions per page were included; the first survey had 31 pages, the second had 13.The selection of one response option was enforced.The respondents were able to review and change their answers through a back button.The usability and technical functionality of the electronic questionnaire had been tested before fielding the questionnaire.A unique site visitor was based on the IP address.No cookies were used to assign a unique user identifier to each client computer.The identification of potential duplicate entries was not based on the IP address of the client computer but on the name of the person, and department, filling the questionnaire.
The responses were reviewed to improve data quality, that is, to avoid duplicate, inconsistent, or contradictory answers within the same institution.Questionnaires which terminated early (where, eg, users did not go through all questionnaire pages) were also analysed.Multiple answers from the same institution were concatenated.Answers from non-existent names/cities/facilities were excluded.The answers of the responders that completed both surveys were counted once.If the answers differed between the two surveys, the answers of the most recent survey were considered.Open-ended questions were individually evaluated; similar answers/comments were grouped together.
Data were processed in Excel.The view rate and participation rate were computed.The former is the ratio of unique survey and unique site visitors, while the latter the ratio of unique visitors who agreed to participate and unique first survey page visitors. 24The differences in expected and observed SGRT benefits were assessed by the two-sided Wilcoxon signed-rank test using paired comparison in SPSS version 25 (IBM corporation) and statistical significance was defined as P < .05.
Results
The view rate was 99% and 100% for the 1st and 2nd survey, while the participation rate was 63% and 96%, respectively.An overview of the survey's responses, completed by radiation oncologists, is given in Figure 1.In the following sections, the results are based on the respondents who completed the first and second survey, unless stated otherwise.
In Figure 2, the geographical distribution of the responding centres is depicted: 76/142 (54%) of the responders used SGRT clinically, 28/142 (20%) were considering purchasing the technology in the near future, while 38/142 (27%) did not have SGRT and were not considering investing in this technology.Based on the information provided by the 34 responders who completed both questionnaires, 4/34 (12%) additional RT departments implemented SGRT in the clinic between 2021 and 2023.
Among the SGRT users, only 33/76 (43%) apply this technology to paediatric treatments.However, 55% of the other centres are planning to expand the use of SGRT to children soon.The majority (55%) of the SGRT users not applying this technology to paediatrics (43/76) is planning to expand BJR, 2024, Volume 97, Issue 1157 its use for this patient category, while 27% and 18% of these departments do not apply it to paediatrics because of no (expected) benefit of SGRT above the IGRT technology already used for paediatrics and the limited patient numbers.
Expected benefits in paediatrics among the responders who are considering the purchase of surface imaging technology (28/142) are improved patient comfort (25%), better monitoring of the intrafraction motion (23%) and more accurate initial patient set-up (22%) (Figure 3).Similar results were found when asking current SGRT users (76/142) for the observed benefits in children of this technology in daily practice (P ¼ .893).
Among the non-SGRT users, 22% do not expect a benefit of this technology above the IGRT technology already available in the clinic.The main hurdles to implement this technology were costs (37%) and time for installation (24%), as shown in Figure 4.
For 94/104 (90%) of the users and the potential users, SGRT can significantly improve the daily workflow of paediatric RT.
Relevant remarks in the free text box, made by the SGRT users, concerned the inability to use blankets and towels during treatment potentially resulting in patient discomfort and temperature drop for those requiring anaesthesia.In contrast to adults, children can consciously interact with the SGRT system, for example by moving on purpose, interrupting the treatment delivery.This issue should be taken into account when instructing the patient on the treatment.Several responders expressed the need for a guideline dedicated to paediatrics for this technology.
Discussion
This report, based on a survey performed in 2021 and repeated in 2023, aimed to assess the practice of SGRT in paediatrics across RT departments located in SIOPE-affiliated countries; 76 departments use SGRT while only 33 of the respondent centres apply this technique in paediatrics.Between 2021 and 2023, four additional departments implemented SGRT showing the growing interest in the clinical use of this technology.The main benefits in paediatrics reported by SGRT users are improved patient comfort, better monitoring of intrafraction motion, and more accurate initial patient setup.Among non-users, the biggest hurdles to implement SGRT in the clinic are time and costs.SGRT is used for all anatomical sites.The percentage of SIOPE-affiliated centres using SGRT in daily practice is around 54% and is comparable with the percentage reported by similar surveys in adults. 16,19owever, the majority of SGRT users are not (yet) applying this technology for paediatric indications although half of current SGRT users are planning to start with children soon.This indicates that the starting group is adult patients probably due to the larger number of cases. 23It is expected that a modification of the existing guidelines 1,18 including recommendations for paediatrics could accelerate its implementation for this group.
This survey has demonstrated that the benefits expected by future SGRT-users are in line with the experiences of current users.Current SGRT-users observe in paediatrics improved patient comfort due to open face mask treatments and the omission of (permanent) skin markers.Tattoo-less RT is really an advantage for paediatrics as the process of getting these tattoos or permanent set-up marks can be traumatizing for a young cohort. 257][28] Other benefits are a more accurate initial patient set-up, as well as better monitoring of intrafraction motion.These benefits correspond to the advantages seen during applications in adult treatments. 11,19The improved initial patient set-up has the potential to decrease the frequency of verification images, which could reduce set-up time and minimize imaging dose exposure (for CBCT, the dose per image ranges from 1 up to 3 mGy depending on the anatomical region that needs to be imaged 29 ).For internal treatment sites, the target position is not always well represented by a surface image, 30 therefore SGRT is often considered a complement to radiographic image guidance.However, a recent study showed that SGRT may also be able to detect gastrointestinal variations triggering adaptive RT pathways. 21For deep-seated target volumes, especially those moving independently of bony anatomy, other imaging techniques using CBCT or MRI are generally more accurate for localization. 6However, SGRT can reduce target localization uncertainty due to intrafraction motion by the real-time monitoring of the patient surface.
Users are little convinced of a reduction in the use of general anaesthesia using SGRT.This benefit may be difficult to assess outside of a study context since logistics do not allow an anaesthesia team to be available ad-hoc just and only in case of poor compliance.
Nonetheless, based on the survey results, it appears that the field of experts involved in irradiating paediatric patients is not convinced about the benefits provided by SGRT.In addition to modify the current guidelines, 1,18 there is an urgent need to advocate for greater adoption and use of this technology for childhood radiation therapy.
Some limitations in the survey are recognized.(1) Although the participation rate of both rounds was in line with other similar questionnaires, 16,19 fewer centres responded to the second survey compared to the first survey.(2) The geographical distribution of the responders was not uniform across countries, so results may not reflect the situation within all SIOPE-affiliated countries.(3) While the analysis of the results was based on the CHERRIES checklist, the creation of the survey was not. 24(4) The answers may be biased by the vision of the professional who returned the survey and therefore it possibly not represents the vision of the whole RT team involved in paediatrics.(5) The nuances of patient comfort, e.g.physical, mental, were not differentiated in the questions of the two surveys.As a consequence from the results it cannot be extracted for which aspect of patient comfort SGRT has the most added value.(6) Considering the fast adoption of this technology in recent years, SGRT practice in paediatrics may change quickly in the near future.Nevertheless, this survey has provided valuable insights into the availability, indications and hurdles in the use of SGRT across the SIOPE-affiliated RT departments at the moment of writing.
Conclusions
This work provides an overview of the status of SGRT in paediatrics across SIOPE-affiliated centres in 2023.The presented results focusing on paediatric treatments can serve as a basis for departments considering investing in SGRT systems.
Figure 1 .
Figure 1.Overview of the survey's responders.Radiation oncologists working in the 246 SIOPE-affiliated paediatric RT departments were invited to participate and returned the survey.
Figure 2 .
Figure 2. Geographical distribution of the 35 SIOPE-affiliated countries (grey-blue colour) with the 246 invited radiotherapy departments and the different responses (user, no user considering purchase, no user) regarding the status of SGRT in 2021/2023.The map was created with https://www.mapchart.net/.
Figure 3 .
Figure 3. Expected and observed benefits of SGRT in paediatrics among the SIOPE responders who are considering the acquisition of an SGRT system (28/142) and the SGRT users (76/142), respectively. | 3,596.6 | 2024-03-05T00:00:00.000 | [
"Medicine",
"Engineering"
] |
UHF Partial Discharge Location in Power Transformers via Solution of the Maxwell Equations in a Computational Environment
This paper presents an algorithm for the localisation of partial discharge (PD) sources in power transformers based on the electromagnetic waves radiated by a PD pulse. The proposed algorithm is more accurate than existing methods, since it considers the effects of the reflection, refractions and diffractions undergone by the ultra-high frequency (UHF) signal within the equipment tank. The proposed method uses computational simulations of the electromagnetic waves generated by PD, and obtains the time delay of the signal between each point in the 3D space and the UHF sensors. The calculated signals can be compared with the signals measured in the field, so that the position of the PD source can be located based on the best correlation between the simulated propagation delay and the measured data. The equations used in the proposed method are defined as a 3D optimisation problem, so that the binary particle swarm optimisation algorithm can be used. To test and demonstrate the proposed algorithm, computational simulations were performed. The solutions were sufficient to identify not only the occurrence of defects, but also the winding and the region (top, centre or base) in which the defect occurred. In all cases, an accuracy of greater than 15 cm was obtained for the location, in a 180 MVA three-phase transformer.
Introduction
Power transformers are among the most important components of an electrical power system, due to their high cost and functionality within the system. Monitoring of the levels of partial discharge (PD) activity inside transformers is an important step in the predictive maintenance process, as it can indicate internal faults that must be corrected before the system is compromised.
Several techniques have been used to detect PD within a transformer, such as the standard method defined by IEC 60270 [1], dissolved gas analysis (DGA) [2][3][4], the acoustic method [5][6][7] and the ultra-high frequency (UHF) method [8][9][10][11][12]. In addition to PD detection, studies have been carried out to determine the location of the PD based on the acoustic wave generated by the PD or the electromagnetic radiation in the UHF band. However, the acoustic method has less sensitivity to low-intensity PD and to those occurring within the winding, so the UHF method is therefore preferable [5,[13][14][15].
UHF location of PD in power transformers has been traditionally performed using the time difference of arrival (TDOA) between signals that are captured from a set of UHF sensors. From these, the PD location can be found by geometric triangulation, which involves solving a set of nonlinear equations. Two approaches have been used. The first is the traditional method, which presupposes a line-of-sight propagation from the source to the sensors, so that the location of the PD source can be performed based on the solution of simple distance equations [16][17][18]. However, this assumption induces errors in the PD location by neglecting the obstacles in the propagation path. The second approach involves the calculation of the signal propagation time based on geometric modelling of the power transformer, followed by an algorithm that correlates the calculated values with the measured data [19,20]. Although the use of geometric modelling results in a better PD location estimation than the straight line-of-sight method, the geometric method gives a very simplified model of the transformer and is not able to represent all of the effects along the propagation path, such as reflections, refractions and diffractions in different materials, and this causes errors in the TDOA estimation.
In order to optimise the PD location, a third approach can be used that corresponds to estimation of the TDOA from the solution of the Maxwell equations in a computational environment. As shown in [21], the estimated propagation times for the signals based on computational simulations are closer to the experimental results than when using simple distance equations or geometric modelling. In addition, computational simulation of the UHF PD propagation using the Maxwell equations shows reasonable agreement with PD phenomena measured in the laboratory [21].
The objective of this paper is to propose a PD localisation algorithm for power transformers that uses the solution of Maxwell equations in a computational environment to estimate the TDOA between signals captured from a set of UHF sensors. Using the proposed algorithm, it is possible to include the reflection, refraction and diffraction effects that occur during the propagation path in the localisation method.
The rest of this paper is organised as follows: Section 2 explains the localisation algorithm. Detailed simulations and the 3D modelling technique for testing and demonstrating the localisation algorithm are described in Section 3. In Section 4, the results of the computational procedures are presented and discussed. Section 5 presents the conclusions.
PD Localisation Method
This work proposes a method for the location of PD in power transformers, based on the solution of the Maxwell equations in a computational environment. Four procedures are used, as described below.
Sensor Positioning
Initially, at least four UHF sensors must be installed in the equipment tank through dielectric windows, as previously described in [8]. The sensors must be installed with the maximum spatial distance between them on the surface of the transformer tank and not geometrically placed on the same plane [10], as illustrated in Figure 1.
Transformer Modelling
The second procedure corresponds to the modelling of the power transformer. For this, the power transformer must first be modelled in software that allows 3D electromagnetic simulation. A 3D matrix composed of cells of size ∆x × ∆y × ∆z is then created in order to represent the various positions in the transformer model, where each point in the 3D space is represented by the x = i∆x, y = j∆y and z = k∆z coordinates [19], as illustrated in Figure 2.
Calculation of the Propagation Matrix
Once the discrete transformer model has been created, as represented by the matrix C(i, j, k), the third step is the calculation of the propagation time for a UHF signal from each cell in the 3D space to the UHF sensors on the equipment tank. Figure 3 shows a flowchart of the proposed methodology for obtaining the propagation times, generalized to N sensors. Initially, a calibration pulse is injected from one of the sensors n = {1, 2, ..., N} into the simulator, and the signal propagation time ∆t C n is recorded for each model cell C(i, j, k). The procedure is then repeated by changing the origin of the calibration pulse to each of the other sensors. The equivalent of N computational simulations are performed and N matrices C(i, j, k){n} are obtained with the propagation times. The calculation of the propagation time is based on the Fermat principle. According to this principle, in an isotropic environment, the signal time for propagation from point A to point B is the same as for propagation from point B to point A. Thus, instead of simulating the signal propagation from all points of the mesh C(i, j, k) to the N sensors, which would demand a large computational effort, the signal propagation is simulated from the sensors to all points of the mesh. The procedure is performed only once for each transformer geometry, and this is an advantage of the proposed method. The model can then be used for continuous, online and permanent monitoring of the transformer by means of the fourth procedure described below.
Binary Particle Swarm Optimisation (BPSO) Algorithm for 3D Optimisation
Once the propagation matrix C(i, j, k){n} has been obtained for each sensor n, the location of PD can be carried out for the modelled transformer. The TDOA of the signals to sensors 1 to N are measured and the PD location is then performed by determining the cell that minimises the following objective function, as proposed in [20]: where the superscripts m and C refer to the measured and calculated times for cell C i,j,k , respectively. In other words, the location method consists of a search by the cell in space (or set of cells) where the time delays correspond to the measured data within a specified tolerance. In order to obtain the minimum value of Equation (1), it is proposed to use the binary particle swarm optimisation (BPSO) algorithm, instead of the conventional particle swarm pptimisation (PSO) proposed in [20], since the binary version of the method is more appropriate for discrete optimisation.
Evaluation of the Localisation Algorithm
In order to test the proposed algorithm, computational simulations were used to represent the PD phenomenon in power transformers. The following procedures were adopted: (i) A real power transformer was modelled using electromagnetic simulation software, (ii) PD were simulated in the transformer windings and the signals were received from four simulated UHF sensors located on the equipment tank, and (iii) a demonstration test of the proposed localisation algorithm was performed.
Construction Characteristics of the Modelled Transformer
To test the algorithm, 3D modelling of a 230/69 kV, 180 MVA three-phase transformer was performed. Table 1 shows the characteristics of each element of the modelled transformer. As can be seen, the number of turns and the gaps between the winding discs for radial oil ventilating were considered.
Modelling in CST Microwave
The propagation of PD-related EM waves was simulated using the finite integration technique (FIT) through the application of CST Microwave Studio software. The FIT is a discrete method that solves Maxwell's equations in an integral form rather than the differential form used in the finite-difference time-domain (FDTD) method [22]. However, other software that can give a solution to the Maxwell equations could also have been used.
A Gaussian pulse of width of 1.5 ns, current 1 A, and radiated UHF frequency in the range 0 to 1.5 GHz was used to represent the PD phenomenon [20,[23][24][25]. Figure 4 shows the Gaussian pulse used to represent the PD pulse. In order to reduce the computational effort, certain simplifications were adopted in the power transformer model based on recommendations found in the literature. All of the metallic structures were modelled as perfect electric conductors (PEC) [23], and the insulating paper present in the conductors and windings was neglected [20,26]. With these simplifications, the computational effort was markedly reduced, with negligible effect on the PD propagation. The propagation was simulated in transformer oil with a relative permittivity of 2.33.
Simulation of Defects
Six 3D simulations were created to evaluate the proposed localisation algorithm, and in each case, the defect was simulated in a different position inside the equipment. Priority was given to locating defects in various positions, including the three phases and positions at the top, centre and base of the windings. Figure 5 shows a graphical representation of the transform with the positions of the simulated defects. Once the positions of the defects were chosen, the sensors were located in the simulation. The sensors were modelled as an electric field probe, and were arranged in four distinct positions as shown in Figure 6. The coordinates of both the defects and the sensors for each case simulated here are given in Table 2, for a coordinate system centred on the lower left corner of the transformer. To apply the localisation algorithm, we first obtained the propagation matrix C(i, j, k) for the transformer under analysis, according to the procedure set out in Section 2. The localisation algorithm was then applied in the six situations described above, using the BPSO algorithm to minimize Equation (1). Since the BPSO algorithm is a probabilistic method, it was applied twenty times, and the centroid of the solutions obtained at each iteration was taken as the global solution of the proposed method.
The simulations using the CST Microwave were performed in approximately 12 h each, using a 64,473,750 meshcell on an Intel Xeon E5-2620 computer with 12 processing cores of 2 GHz and 128 GB of DDR3 memory. The BPSO algorithm parameters were an inertia weight of 1.1 and learning coefficients of 1.49. One hundred particles were used, and were distributed randomly within the equipment. A common personal computer was used for the BPSO application.
Results
The results obtained in this work are presented below.
Transformer Propagation Model
The construction of the transformer propagation model is the first step of the localisation algorithm. As explained in Section 2, this model needs to be obtained only once, and can be used as many times as necessary in the localization algorithm. In order to graphically represent the obtained matrix C(i, j, k) from the transformer under analysis, a longitudinal and horizontal cross-section along the central axis of the transformer is used, as shown in Figure 7. The colours represent the propagation time of the signal from the various points in matrix C(i, j, k) to sensor 1, located on the left side of the equipment tank. The blank silhouette represents the metal structure of the transformer, where there is no signal propagation. Figure 7 shows the possibility of obtaining the propagation times from all coordinates of the transformer to the UHF sensor. Thus, it is demonstrated that the transformer propagation model was successfully acquired by the presented methodology. It can be observed from the Figure 7 that there are regions closer to the UHF sensor that have a longer propagation time than more distant regions. This difference is explained by the fact that in some propagation paths, the signal encounters obstacles that delay it. Thus, the signal propagation time is defined not by the spatial distance between two points, but by the real propagation path that the signal takes as it circumvents the obstacles.
Signals Obtained from the UHF Sensors
To exemplify the signals obtained from the simulations, Figure 8 shows the magnitude of the signals obtained from the sensors for the defect 6. The obtained result is similar to the acquisition of signals in a field test through the use of an oscilloscope, and can therefore be used for testing of the localisation algorithm. As observed, the signals show different intensities and propagation times for each sensor; this is as expected, since the signals travel along different paths to the installed UHF sensors. Calculating the propagation time for the case presented below gives times of 14.25 ns, 10.21 ns, 1.4 ns and 14.37 ns for sensors 1 to 4, respectively.
Localisation of PD Source
From the signals obtained by the UHF sensors and the propagation matrix C(i, j, k) obtained for the transformer under analysis, the PD source was located for the six simulated cases. The solutions from the localisation method and the errors obtained are presented in Table 3 for each case, and Figure 9 illustrates these results. The blue circles indicate the 3D location obtained for each iteration of the location algorithm, the black circle indicates the geometric centre of the solutions, and the red circle indicates the position of the defect. Table 3. Results obtained from the localisation algorithm. For the six simulated cases, we verified that the method achieved a high level of accuracy, thus meeting the demands of practical engineering scenarios. In the best case, the method had an accuracy of 4 cm in the location (defect 2), while in the worst case, the accuracy obtained was 15 cm, which is a good result considering the size of the simulated transformer. This precision was sufficient to identify not only the occurrence of defects, but also the winding in which they occurred and the region (top, centre or base) in which they were located. This information is useful for diagnosis of the equipment, since it allows us to evaluate the location and severity of the problem and facilitates a more detailed investigation of the equipment. Moreover, the convergence time of the localisation algorithm was approximately 50 s (i.e., when the stop criteria were met). Thus, the computational speed of the method is sufficiently high for all practical purposes, including online monitoring.
Conclusions
This paper has presented a new UHF PD localisation algorithm for power transformers by solving the Maxwell equations in a computational environment. The propagation delay of the signal from each point in the 3D space to the UHF sensors was first obtained, and the simulated propagation delays were then compared with the measured signals, meaning that the PD location corresponds to the position where the simulated propagation time best approaches the measured data. The equations used in the method were defined as a three-dimensional optimisation problem, so that the BPSO algorithm could be used to minimise the objective function of the algorithm.
The effectiveness of the localisation algorithm was demonstrated using six 3D simulations (with four other simulations that obtained the propagation times used in the method). The proposed algorithm was able to include the effects of the reflections, refractions and diffractions undergone by the UHF signal in the equipment tank. Thus, a methodological progress was obtained in PD location methods. In the simulated cases used for testing the algorithm, the solution was able to identify not only the occurrence of defects, but also the winding and the region (top, centre or base) in which the defect occurred. In most cases, an accuracy of greater than 15 cm was obtained for the location of the simulated defect.
Our localisation method therefore proved to be useful for diagnosis of the equipment, since it allows us to evaluate not only the severity of the problem, but also the location, and facilitates a more detailed investigation of the equipment. | 4,048.8 | 2019-08-01T00:00:00.000 | [
"Physics"
] |
Foundations of optical diagnostics in low-temperature plasmas
Over the past few decades many diagnostics have been developed to study the non-equilibrium nature of plasma. These developments have given experimentalists the possibility to measure in situ molecular and atomic densities, electron and ion densities, temperatures and velocities of species in the plasma, to just name a few. Many of the diagnostic techniques are based on the ‘photon-in, photon-out’ principle and were at first developed to perform spectroscopy on atoms and molecules. Much later they were introduced in the research of plasmas. In this foundation paper we will focus on optical-based diagnostics that are now for quite some time common use in the field of low-temperature plasma physics research. The basic principles of the diagnostics will be outlined and references will be given to papers where these techniques were successfully applied. For a more comprehensive understanding of the techniques the reader will be referred to textbooks.
Introduction
The diagnostic toolbox for the experimental low-temperature plasma physicist has been expanded enormously over the past decades. At first the toolbox consisted of a spectrometer to measure the emission lines of plasma excited species and a Langmuir probe to measure electron densities. But nowadays also mass spectrometers, to determine the composition of the plasma, and even advanced laser-based diagnostics are being used to determine e.g. time and spatially-resolved temperatures, densities and velocities of the plasma species, or even electric field strengths. Every diagnostic in the toolbox has its pros and cons, and all should be considered complimentary to each other. E.g. Langmuir probes are cheap, however, cannot always be applied, due to its intrusive character [1]. In fact, a probe is measuring the disturbance by the probe on the charged species and a model is necessary to extract the electron density and temperature from the measurement. Mass spectrometry can give detailed information on both neutrals and ions but requires to sample part of the gas, which is a delicate procedure in case of quantitative measurements and perturbative especially at atmospheric-pressure [2]. Nevertheless, these non-optical techniques, which have been improved and further developed to overcome many of their limitations, are very successfully applied in the study of plasma [3]. Optical techniques, which can be divided into passive and active techniques, have also shown their merits in low-temperature plasma physics. In Plasma Spectroscopy by Griem [4] the working principle of several passive optical techniques is discussed. Demtröder [5] discusses many laserbased active spectroscopic techniques and their applications. Most of the laser-based diagnostics were first applied under clean and well-determined conditions, and used to measure e.g. absorption cross-sections or lifetimes. But, while lasers were becoming more and more available to non laser-specialists, these techniques are now also shown to be applicable in harsher circumstances, like plasmas and flames. With active spectroscopic gas phase diagnostics like absorption spectroscopy and laser-scattering techniques, quantities like atomic and molecular densities, ion and electron densities, temperature of electrons and heavy particles, and their velocities, can be determined. Several review papers have been published over the years that show the applicability of optical diagnostic techniques for the study of different types of plasma [6][7][8][9][10]. A collection of papers has been published very recently in a special issue of the 'Journal of Applied Physics D: Applied Physics' on plasma diagnostics using spectroscopic methods highlighting some of the recent developments in optical diagnostics for measuring physical parameters in low-temperature plasmas, with a focus on atmospheric-pressure plasmas [11]. A review devoted to the spectroscopic detection of molecular radicals in atmosphericpressure plasma has also recently been published [12].
It is clear from the above that many diagnostic techniques are available to the experimental (plasma) researcher and it is up to the researcher to find the right diagnostic that will deliver the information one is looking for. In this paper we will focus on a selection of optical-based diagnostics that have shown to be applicable to the study of low-temperature plasma. All of the techniques that will be described in more detail are already being used for many years in plasma physics, and are generally being regarded as a standard diagnostic. The experimental schemes of some of the basic diagnostic techniques have been extended to e.g. increase their sensitivity or applicability for dedicated plasma studies. These schemes will only be mentioned and appropriate references will be given.
General concepts
Generally speaking, optical diagnostic techniques can be separated into two categories: passive (see section 3) and active optical techniques (see section 4). In plasma studies, emission spectroscopy is one of the most commonly used passive optical diagnostic techniques. This technique is based on the recording of radiation emitted by excited species in the plasma that send out this radiation when spontaneously relaxing to a lower energetic state. From the recorded radiation the densities of excited species present in the plasma can be obtained. Information about the basic plasma parameters, i.e. the electron density and temperature, can be obtained from the measured densities of the excited species. However, a model is needed and assumptions have to be made on the (non-)equilibrium state in which the densities over the energy levels are distributed (see section 3). Information about e.g. the electron density or the translational temperature can under certain circumstances also be obtained from an accurate recording of the line shape of the emitted radiation (see section 3.2.1).
In a passive spectroscopic technique one relies on the excitation of species by the plasma. In case of active spectroscopic techniques one introduces light into the plasma, and determines the effect of the plasma on this light. In very general terms, the light can be absorbed, resulting in an excitation of species or the light can be scattered from species in the plasma. After absorption of the light by the plasma, the information can be extracted in two ways. One is to measure the intensity of the light before and after passing through the plasma. The information on the absorbing species in the plasma is directly obtained from the ratio of the two signals. This technique is called absorption spectroscopy (see section 4.1). And two is to record the light that might be emitted by the excited species when decaying to a lower energy state after absorption of the incoming light. This technique is called laser induced fluorescence (LIF) spectroscopy (see section 4.2). During a LIF experiment one extracts the information about the plasma from the spectral distribution of the emission or from the (total) emission intensity as function of the laser wavelength. In light-scattering techniques three processes are distinguished: Thomson, Rayleigh and Raman scattering. Thomson scattering is elastic scattering from free electrons, Rayleigh scattering is the elastic scattering from heavy particles, and Raman scattering is inelastic scattering from molecules. Although the crosssection for Thomson scattering is much smaller than for the other scattering processes, progress in lasers and spectrograph-detector combinations has allowed researchers to successfully apply Thomson scattering in many different plasmas, like low-pressure technological plasmas, high-pressure thermal plasmas and fusion plasmas, to just name a few. In general, the information on the electron temperature and density is extracted from the spectrally resolved scattered radiation: the width of the spectral profile is a measure of the average electron temperature, and the area under the profile can be related to the electron density (see section 4.3). Rayleigh scattering can be used to determine the total density and temperature of the heavy particles, while Raman scattering can e.g. give information about the density and temperature of a particular molecule (every molecule has at least one active Raman mode) in the plasma. In table 1 a non-exhaustive summary is given of the different parameters that can be obtained with optical diagnostics in non thermal plasma. In the table we use n T , e e for resp. electron density and temperature, E field for electric field strength, and T rot , T g and T vib for resp. rotational, gas and vibrational temperature. Only examples of the more commonly-used optical diagnostic techniques are given. It illustrates how versatile these techniques are and how crucial for understanding plasmas. In this paper a selection of some of these optical diagnostic techniques will be discussed in more detail. For the other optical techniques mentioned in the table the reader is referred to the references given in the last column.
Passive optical diagnostic techniques
Passive optical diagnostic techniques are based on the recording of radiation spontaneously emitted by the plasma. This spectroscopic technique is experimentally the most simple variant of the optical diagnostics that is discussed in this paper. The intensity, I pq , of radiation emitted when species in an excited state, p, spontaneously decay to a lower state q can be expressed as follows: Here, A pq is the Einstein transition probability of spontaneous emission from initial state p to final state q (vide infra), h is Planck's constant, ν pq is the frequency of the emitted radiation, V the volume from which the radiation is emitted, and N p is the number density of emitting species in the initial state. In practice, the radiation emitted by the plasma is typically dispersed and recorded by a spectrograph-detector combination. For a given light emission intensity emitted by the plasma, the intensity actually detected will depend on the solid angle of the light collection and the spectral response of the optical setup. The choice of the dispersive element and detector type in terms of sensitivity and/or time response is crucial and discussed for instance in [41,42]. However, equation (1) clearly shows that the recorded intensity of the emitted radiation is proportional to the density of species in the excited state p. In case the excited state is predominantly populated through excitations from the ground state, a situation that is called the Corona balance, the measured intensity is to a good approximation also proportional to the density in the groundstate. However, very often other plasma processes, like electron de-excitation processes, three-particle recombination, radiative recombination and electron impact ionisation, can play a role as well. In that case, collisional radiative models need to be used to extract information about the plasma from absolute plasma emission measurements [41,43]. In general, the radiation emitted by a body at temperature T can be described with Planck's radiation law: r n n p n n n = - where the radiation density per unit of frequency (Hz), r n n n T , d ( ) is expressed in J m −3 s −1 . In this equation c is the speed of light (in m s −1 ), k B Boltzmann's constant (in J K −1 ), h Planck's constant (in Js), T the equilibrium temperature (in K) and ν the frequency of the radiation (in Hz). If a plasma would be in thermodynamic equilibrium (TE), it could be treated as a black-body radiator. Consequently, the equilibrium temperature deduced from Planck's radiation law is then the parameter that can be used to describe excited state densities using the Boltzmann distribution, ion densities (and electron densities because of charge neutrality) using the Saha equation, and energy distributions of the particles, since these follow a Maxwellian distribution. The Boltzmann distribution gives the relation between the populations, n p and n q , in energy states, E p and E q , of atoms and molecules at an equilibrium temperature, T: Here, g p and g q are the statistical weights of the energy states p and q, resp. For high electron densities the excited levels are in equilibrium with the continuum. The population of an in which g e , n e and g i , n i are the statistical weights and densities of resp. the electron and the ion and is proportional to n e 2 (assuming quasi-neutrality). The dependence on T e is however different; the line to continuum ratio can be used as a measurement of T e . E p ion is the ionisation energy of state p. However, non-thermal plasmas are not in thermodynamic equilibrium, i.e. they have to be maintained by supplying energy and are therefore characterised by temperature and density gradients. Dense plasmas with a high electron density, locally follow Boltzmann, Saha and Maxwell (Local TE (LTE)). However, since plasma emits light, i.e. the amount of emission and absorption in the system is not equal, the radiation is not in equilibrium, and thus Planck's radiation law does not apply for the spectral distribution and the intensity of the emitted light (i.e. equation (2) cannot be used to extract a temperature). At lower densities the Saha and Boltzmann relations are no longer valid and the temperature of the electrons, ions, atoms and molecules are different. At even lower densities the energy distribution of the electrons starts to deviate from a Maxwellian distribution. For the understanding of the electron dynamics in RF driven discharges, discharges that are frequently used in technological applications, it is of importance to measure these deviations in the electron energy distribution function (EEDF) with high temporal resolution (nanosecond range). Phase resolved optical emission spectroscopy (PROES) has successfully been employed to determine with high spatial and temporal resolution electron density and temperature, drift velocities and EEDFs in both inductively coupled plasmas (ICP) and capacitively coupled plasmas (CCP) [44][45][46].
Recently a lot of work has been performed on atmospheric-pressure plasmas. Analysing emission spectra from this kind of plasma brings additional difficulties, because of e.g. strong gradients, being optically thick, i.e. radiation is emitted and reabsorbed while passing through the plasma, or many-body collisional processes [32]. Still, Liu et al [47] have reported studies on the excitation dynamics and plasma generation mechanisms in an atmospheric-pressure diffuse dielectric barrier discharge (DBD) using PROES. As a result the authors have shown that a DBD, typically operating in a filamentary mode, can also be operated in a diffuse mode, which expands the application of this kind of discharges to the field of plasma-assisted surface treatment.
In the next sections the different types of emitted radiation will be treated, and the plasma parameters that can be determined from the (absolute) intensity of that radiation will be discussed. Depending on the plasma conditions and gas composition, the radiation can consist of continuum and line radiation. In plasmas that contain molecules, the plasma emission can also show molecular bands.
Continuum radiation
Within this type of radiation we distinguish free-free emission, also called Bremsstrahlung, and free-bound emission, also called recombination radiation.
Bremsstrahlung originates from Coulomb collisions. In those collisions the charged particles are accelerated and thereby emit radiation. In low-temperature plasmas the radiation arises almost solely from the electrons in the electron-ion interaction. The electron undergoes a transition between two free states, which is the reason why we call this radiation also 'free-free' radiation. It should be mentioned that electron-electron scattering does not lead to free-free radiation due to momentum conservation, and that the contribution of ion scattering from neutrals can be neglected due to the heavy mass of the ions. Also, electron-atom contributions to the free-free radiation is usually less important (it might be important in parts of the spectrum of plasma of low-ionisation degree (typically below 10 −3 )). As there are no bound states involved in the transition, the Bremsstrahlung is continuous in wavelength. For 10 eV electrons the maximum intensity of the radiation emitted in a Coulomb collision with ions is around 100 nm. It can be shown that for plasma at temperatures below a few 100 eV, Bremsstrahlung can be neglected [48].
Recombination radiation is generated when an electron recombines with an ion to form the excited state or ground state of the corresponding atom (or the Z + charged ion forms the (Z − 1) + charged ion). This component is called 'freebound' continuous emission. It has been observed that the chance of radiative recombination decreases fast with increasing quantum number, i.e. decreasing ionisation energy, of the resulting atom. This means that the most energetic photons are produced with highest probability. Since the photon has to take care of both energy and momentum conservation, the cross-section for radiative recombination is very small.
Line radiation ('bound-bound')
Line radiation arises from transitions in atoms or molecules between two bound states. For an atomic plasma, the spectral distribution of the radiation, in short the spectrum, consists of individual lines at well-defined frequencies. The transitions occur between different electronic states. For molecules the same is true. However, since molecules, in contrast to atoms, can vibrate and rotate, they have a much denser energy level scheme. As a consequence the molecular emissions show up in the form of bands, which (in the visible part of the spectrum) are in fact congestions of ro-vibronic transitions in the molecule. In figure 1 an optical emission spectrum is shown that has been recorded during etching of an amorphous hydrogenated carbon layer by means of an Ar/H 2 plasma expansion. The low-pressure recombining Ar/H 2 plasma expansion impinges in the subsonic part of the expansion on a carbon surface. The emission of atoms and molecules is recorded just in front of the carbon surface that is exposed to the plasma. Ro-vibronic emissions of CH (electronic transitions A X and B X ) and C 2 (denoted with the change in vibrational quantum number, Δν, in the electronic transition d a) radicals are clearly observed. These species are formed in the plasma etching process of the carbon layer. For more information on the plasma expansion and the plasma chemistry in this system the reader is referred to the PhD thesis of T. Hansen [49].
3.2.1. Line shapes. None of the spectral lines in a spectrum is Dirac delta function. Without any interaction with other particles, the population in an excited state will decrease because of spontaneous emission to a lower energy state. The probability of this transition process is described by the Einstein coefficient A pq (see also equation (1)), p depicting the upper state and q the lower state. The sum of the transition probabilities for radiative decay to all levels q<p determines the natural lifetime τ of state p in the following way: Through the Heisenberg uncertainty relation this life time is related to the natural line width, n D nat , of the transition: The line profile, f(ν), i.e. the spectral intensity distribution of the radiation, is Lorentzian: with ν 0 the centre frequency of the transition and n D nat the full width at half-maximum (FWHM) of the distribution.
There are several processes that lead to a change in width of the natural line profile, but can also show their effect in a change in shape of the line profile. E.g. collisions with other particles will lead to a shortening of the life time of the excited state, and thus (Heisenberg uncertainty relation) a broadening of the line profile. To a very good approximation this collision-induced line broadening (also called pressure broadening) can be expressed as follows: with p cp the partial pressure of the collision partner and T the temperature of the gas. Another process that leads to broadening is the interaction of the excited state with the charged particles in the plasma: this is called Stark broadening. Looking at an spectrally-isolated single transition, all the previously described processes lead to Lorentzian spectral intensity distributions. The total line broadening for the single transition will be again Lorentzian, with a width equal to the sum of the individual line widths. In figure 2 an example of a Lorentzian line profile is plotted. Here, the x-axis is plotted in wavenumbers (cm −1 ), as this is the most commonly used unit in spectroscopy, i.e. the true frequency, ν, divided by the speed of light. The FWHM of the Lorentzian line profile in figure 2 is 30 GHz, which is equal to 1 cm −1 .
When the radiating particles are isotropically moving in all directions, e.g. due to temperature, the spectral intensity distribution of the emission will appear as a Gaussian line shape: the FWHM of the distribution, is the socalled Doppler width. For a particle with molar mass M (in amu), in a gas with temperature T (in Kelvin), and a transition at a frequency ν 0 , the Doppler width can be shown to be [5]: , is plotted. As the spectral distribution of the emission reflects the process(es) that play a role in the broadening of the distribution, an accurate recording of the profile can be used diagnostically to obtain plasma parameters like heavy particle temperature, velocity, and electron density. Critically depending on the relative importance of the different processes that are responsible for the line broadening, the line shape in general can be described with a Voigt profile (see figure 2), i.e. a convolution of a Lorentzian and Gaussian profile. In figure 2 it is clear from the comparison of the three line profiles, all plotted with the same FWHM and normalised to 1, that the differences are most pronounced in the wings of the profiles.
3.2.2. Line distributions. Among the parameters measured with optical emission spectroscopy, the rotational temperature (T rot ) of molecular bands is one of the most commonly studied. The reason is that it is a very simple way to measure the gas temperature (T g ) when equilibrium between T rot and T g can be assumed. This equilibrium is likely to occur because the energy difference between rotational levels is in the order of the gas temperature (few tens of mK). In order to be able to define T rot as a 'temperature', the population densities of the rotational energy levels of the excited state considered have to be in equilibrium and thus follow a Boltzman distribution shown in equation (10) = Here, N 0 and N u denote resp. the number density of molecules in the ground state and in level u with statistical weight g u and energy E u , and Q T rot ( ) is the partition function. By measuring the relative density of several levels with known Einstein coefficient and energy, T rot can be deduced. However, in a non-thermal plasma the assumption T rot equals T g is not always valid, either because of the mechanisms populating the excited state or because of the depopulating processes. The short lifetime of the excited states observed through optical emission sometimes prevents the thermalization to happen before the excited state has decayed. For this reason, it can be more interesting to measure the rotational distribution of ground state molecules that usually have much longer life times and thus enough time to reach equilibrium with the surrounding gas. This, however, requires active optical diagnostic techniques such as Raman scattering or absorption spectroscopy (see section 4). Even if the rotational distribution measured by emission spectroscopy is a Boltzmann distribution, this does not always mean that it is in equilibrium with T g . It is always important to compare the effective life time of the radiative level (including collisional de-excitation) with the characteristic time of rotational energy transfer. The conditions under which the rotational structure of a molecular emission band can be used to estimate the gas temperature are discussed in detail in [32,33].
As shown above, spontaneous emission spectroscopy is a powerful diagnostic tool to study plasma. And in combination with collisional radiative models, which use absolute densities of excited species, plasma parameters such as the electron density, the electron temperature and the density of atomic ground state species can be determined. However, to determine the absolute density of excited species, an absolute measurement of the emission between two levels is necessary. To perform absolute emission measurements quite some experimental efforts are required. E.g. one needs to determine the collection angle, the spectral transmission of the system, the response of the detection system, etc.... Still, when this calibration is carefully performed, the absolute density of the excited levels can be compared with a collisional radiative model, and plasma quantities like e.g. heavy particle and electron temperature and ground state densities can be determined [50].
3.2.3. Actinometry. A classical technique to retrieve plasma parameters from intensity ratios from emission lines is called actinometry. Actinometry is a widely used passive optical diagnostic technique that has been successfully applied to plasmas in which the population in excited states of atomic species can be described with the so called Corona model, i.e. excitation is solely by electron impact and de-excitation by radiative decay (and not through collisions). Typically, a known amount of a rare gas is added to the plasma under study. The density of this 'actinometer' (a) in the gas mixture being known, its emission intensity is used as a tracer of variation of electron density and energy responsible for the population of the excited levels of the specie (s) being studied. The relative line intensities I of the excited states of s * and a * allow, under certain plasma conditions, to infer the density of the emitting species. If the light collection angle is the same for both s and a, and the spectral transmission of the optical system is well calibrated, the density of s, [s], is obtained using a simple equation of the type: where C x are constants that depend on the detection system and that must be calibrated at the wavelengths of the lines used for s and a, A ij is the Einstein coefficient for the observed transition and åAij is the sum of all Einstein coefficients of the radiative transition from the ith level. The density of s, which is determined from the line intensity ratio, depends on the electron excitation rate coefficients k e of both the actinometer and the atom being measured. k e x can be calculated from the integration of the collision cross section σ(ò) with threshold energy ò th and the electron energy distribution function f (ò) (EEDF) with the expression [51]: The final density obtained for the specie s is therefore depending on the accuracy of the EEDF which depends on the Boltzmann solver and the set of cross sections used for this calculation. It is also preferable to choose an excited state of the actinometer having a threshold energy ò th for its excitation cross section σ(ò) close to the one of the excited state of s in order to prevent possible artefacts induced by complex EEDFs. Equation (11) can be adapted in case the emitting level is also depopulated by non-radiative quenching but then quenching coefficients and densities of the quenchers need to be known [25]. In plasmas with molecular fragments atomic emission can result from dissociative recombination of molecular ions. In that case classical actinometry cannot be applied. In a topical review of Donnelly [52] the possibilities of this technique are extensively discussed, showing that under certain conditions electron temperature and energy distributions can be determined for non-equilibrium plasmas. For instance, by using several lines of both s and a and using the variation of the excitation coefficient k e , one can infer the electron energy [16]. In a paper of Lopaev et al [53] the applicability of actinometry for measuring absolute concentrations of atomic oxygen, nitrogen and fluorine in an ICP plasma is reported.
Absorption spectroscopy
Absorption techniques are based on the measurement of the intensity decrease of a light beam that passes through a medium. If only linear effects are considered, one can show that the intensity decrease as function of path length through the medium can be written as: This is the so-called Lambert-Beer law. I(ν) is the intensity after passing through the medium, I 0 (ν) the intensity before passing through the medium, n j is the density of the absorbing species j, σ j (ν) the absorption cross section of a transition of species j and L the length over which the medium absorbs (assuming homogeneous density distributions for the species). The absorption cross section of a transition around center frequency ν 0 can be expressed as: One of the great advantages of this technique over the other diagnostic techniques is: when the cross section of the absorbing medium is known, the density can be directly determined from the ratio of I(ν) and I 0 (ν), and no calibration is necessary (vide infra). However, the absorption measurement is not a zero-background measurement, in contrast to e.g. laser induced fluorescence (see section 4.2). One has to record small changes, i.e. ΔI(ν)=I 0 (ν)−I(ν) on a large signal I 0 (ν). The absorption measurement is also a so-called line-of-sight measurement, which means that spatial resolution cannot be obtained from one measurement.
There are many different absorption detection schemes reported in literature, all having their advantages and disadvantages. One can make a rough distinction between schemes in which a broad band light source is used or a narrow band light source.
Absorption spectroscopy with a broad band light
source. When a broadband light source is used in an absorption experiment the light can be analysed by means of a monochromator, which disperses the light [57][58][59], or with a Fourier transform spectrometer, in which the intensity of the light after passing a Michelson interferometer is measured [60,61]. When a photo multiplier is used as the detector behind a monochromator, every wavelength has to be recorded one after the other. However, nowadays very often a CCD camera is used, which allows recording a range of wavelengths at the same time. In a Fourier transform spectrometer a collimated beam from a light source is divided into two by a beamsplitter and sent to two mirrors. These mirrors reflect the beams back along the same paths to the beamsplitter, where they interfere. If the optical path difference between the two beams is zero or a multiple of the wavelength of the light then the light beams will constructively interfere and the output will be bright, but if the optical path difference is an odd multiple of half the wavelength of the light then the light beams will destructively interfere and the output will be dark. In one arm the light is reflected to the beam splitter after travelling a fixed distance, while in the other arm the light is reflected to the beam splitter from a mirror of which the position is changed during the experiment. After interference of both beams on the beam splitter the beam is directed through the sample and the intensity of the light is recorded as function of the optical path length difference introduced by the moving mirror, i.e. a socalled interferogram is recorded. The Fourier transform of this interferogram shows the intensity of the light at every wavelength, as in the case of the monochromator. During an experiment two interferograms are recorded, i.e. one with and one without sample in the beam. The ratio of the Fourier transforms of the interferograms shows the absorption spectrum (see also equation (13)). The advantage of the FT spectrometer is the fact that during the experiment the detector is measuring all wavelengths at the same time, and thus the total intensity of the light source (this is called multiplexing), while in the monochromator the detector only measures the intensity at a certain wavelength. Certainly in the infra-red part of the spectrum, where detectors are less sensitive, this is an important advantage. This is why in the early days FT spectrometers were mainly used to record spectra in the (far-)infra-red. Due to the fact that it is easier to record spectra with a resolution of about -0.1 cm 1 with a FT spectrometer than with a monochromator, FT spectrometers are nowadays also used to record spectra in the visible and even UV-part of the spectrum.
Absorption spectroscopy with a narrow band light
source. In case narrow band tunable lasers are used in absorption spectrometers, the laser itself acts as the frequency selective element. In the visible part of the spectrum typical line widths of tunable pulsed dye lasers are in the order of 0.2 cm −1 , while in the infrared tunable diode and quantum cascade lasers can easily have line widths two orders of magnitude smaller. An absorption spectrum is recorded by tuning the laser over the absorption feature. The intensity is recorded in front and behind the sample and with equation (13) the absorption can be deduced. If the cross section of the transition is known, the density can directly be determined. This is in sharp contrast to the LIF technique that always needs calibration (see section 4.2).
In figure 3 the transmission spectrum is shown of the exhaust of a DBD reactor with CO 2 as input gas. A detailed description of the DBD setup can be found in [62]. The laser that was used to record the spectrum was a single-mode pulsed quantum cascade laser. Recent developments of laser diodes both in the visible and infrared range has allowed experimentalists to apply absorption spectroscopy under many different conditions. These laser sources offer the advantage of high spectral resolution with high sensitivity (typically -10 cm 12 3 in single path) and high time resolution (few μs). They make acquisitions possible at relatively short optical paths without the need for signal accumulation. A laser diode can emit radiation at a well-defined wavelength for a certain current and temperature applied to it. It is then possible to scan over a rather narrow wavenumber range (typically a few wavenumbers) by simply changing either the temperature or the current. The radiation emitted by the laser is detected simply with a photodiode (for visible range lasers) or a Mercury-Cadmium-Telluride (MCT) detector (in the infrared). The wavelength range scanned by the laser has to be calibrated using an interferometric element such as a Fabry-Perot. Laser diodes can have a stronger intensity at a given wavelength than broadband sources. This is an advantage to use them as source for cavity based techniques, but this can also induce artefacts in absorption measurements. E.g. if the absorbing level is too much depopulated by the laser, then the absorption coefficient k j (ν) from equation (15) is not proportional anymore to the density of n j because the upper level of the absorption transition is now significantly populated. The spectral resolution of laser diodes (in the order of 300 MHz (10 −2 cm −1 ) and less) offer also the possibility to resolve the Doppler profile of an absorption line. From the Doppler width the gas temperature, T g , can be inferred [34,63].
Absorption spectroscopy has been successfully applied both with continuous wave (cw) as well as pulsed lasers. Tunable cw diode lasers in the 3-30 μm wavelength range, and recently quantum cascade lasers [6], have shown their merits in detecting molecular species in reactive plasmas. Over the years also many different detection techniques have been reported, all aimed at increasing the sensitivity of the absorption technique [64]. One is particularly interesting to mention, since it is very often easy to implement. In that case the intensity of the cw laser is modulated, e.g. by means of a chopper, and the signal is recorded with a lock-in amplifier at the modulation frequency. In this way any background light from the sample (which is not modulated) or electronic signals at other frequencies than the modulation frequency is suppressed, which can lead to a sensitivity increase of an order of magnitude (see e.g. chapter 6 of [5]). Another detection technique uses a tunable pulsed dye laser. And even though pulsed lasers very often suffer from large pulse-topulse intensity fluctuations, they can still be used for ultrasensitive absorption measurements in the range between 200 and 800 nm. The basic principle for this ultra-sensitive absorption technique, called cavity ring down(CRD) spectroscopy, was reported in 1988 by O'Keefe and Deacon [65]. This technique is based upon the measurement of the rate of absorption rather than the magnitude of absorption of a light pulse confined in a closed optical cavity with a high Qfactor. The advantage over normal absorption spectroscopy results from (i) the intrinsic insensitivity of the CRD technique to light source intensity fluctuations, and (ii) the extremely long effective path lengths (many kilometers) that can be realized in stable optical cavities [66]. In Chapter 3 of
Laser induced fluorescence spectroscopy
During a LIF experiment a light source, very often a laser, is used to excite species to an excited state and the fluorescence emitted by the excited state is detected. The number of photons, N fl , emitted at a wavelength λ jk from a volume V after excitation of atoms or molecules from an initial state i to a final state f with a laser with intensity I L , is given by (see figure 4): Here, s I n ij l i is the amount of photons absorbed per unit volume and time, with s ij the cross section for absorption from state i to state j. A jk is the Einstein coefficient for the transition from state j to k, which is responsible for the emitted fluorescence at λ jk . A j is determined by the fluorescence lifetime τ j of state j, i.e. A j =1/τ j . R is the total loss rate due to other processes than fluorescence. At low pressures this loss process can usually be neglected. During any experiment only part of the total emitted fluorescence can be collected. The measured LIF signal, S fl , is then written as: with Ω the solid angle over which the fluorescence is detected. Q incorporates all losses due to the optics between the imaged LIF volume and the detector used to measure the LIF signal and the quantum efficiency of the detector [67].
Equations (17) and (18) show that the LIF signal is proportional to the density of the atoms or molecules in the lower state i. The sensitivity of the technique stems from the fact that the detector recording the LIF signal is not detecting any LIF signal when the laser is not on resonance with a transition of the species under investigation; this is a so-called zerobackground measurement technique. Also, the detection can be performed on a different wavelength as the excitation wavelength, i.e. off-resonant detection. In this way spurious scatter from optics in the beam path can be blocked by means of optical filters. Like in Thomson-Rayleigh scattering experiments (vide infra), also here the emission of the plasma detected during the experiment can be reduced by gated detection, i.e. the detector only looks at the plasma when species, which were excited by the light source, fluoresce. For an absolute density measurement a calibration is necessary to determine e.g. V, Q and Ω [68]. This is one of the main drawbacks of this technique. Next to that, also the total loss rate R should be determined (see equation (17)). However, if one is working in an environment in which the composition of the sampled gas changes during the experiment, R is changing during the experiment. Only when the time dependence of the LIF signal can be recorded accurately enough and with enough time resolution, R can be determined, and subsequently an absolute determination of the excited species is possible [69,70]. This very often means that the excitation source should deliver pulses with sub-nanosecond duration.
In order to be able to detect a molecule by means of laser induced fluorescence, the molecule should possess at least an excited state that is preferably single-photon accessible and is at an energy that corresponds to a wavelength that can be produced with the help of a dye laser. Roughly speaking, this means between 200 and 800 nm. Nd:YAG pumped tunable dye lasers readily deliver light at wavelengths with which ground state densities of molecular radicals can be determined. Also, the fluorescence lifetime of the upper state should not be too long, since otherwise the excited particle might have moved out of the detection volume or de-excited via collisions. For the detection of the ground state of several atoms and small molecules the first prerequisite is not fulfilled e.g. in case atomic ground state densities have to be determined, the wavelength for excitation is very often in the vacuum ultra-violet (VUV) region of the spectrum, and other excitation schemes have to be used. One of the schemes that have been successfully applied in determining ground state densities of atomic hydrogen, nitrogen and oxygen is twophoton absorption laser induced fluorescence (TALIF) [51,[71][72][73][74][75]. Recently this has also been reported with femtosecond time resolution and 2D-imaging of the fluorescence signal of atomic oxygen on an iCCD-camera [76] and on a molecular species, i.e. carbon monoxide, produced in a glow discharge operating on CO 2 [77]. The excitation from the ground state is performed with two photons in the UV, and the fluorescence is detected in the (infra-)red. The detected fluorescence is proportional to the ground state density, like in the normal LIF detection scheme, but the dependence on laser intensity is quadratic. This makes calibration a tedious exercise. For the detection of molecular hydrogen in the different ro-vibrational states in its electronic ground state LIF in the VUV has been successfully applied [78]. Rotational density distributions in vibrational states with v>3 were recorded. Both excitation and fluorescence were in the VUV, which made a more elaborate experimental setup necessary [79].
Thomson, Rayleigh and Raman scattering
The most important parameter that characterizes the plasma is the electron density. It determines the conductivity of the plasma, the excitation and light emission, the production of radicals and thus the chemical reactivity. Another important parameter is the electron temperature.
As we already discussed in section 3, several optical techniques are available to determine both the electron density and temperature, i.e. Stark broadening, actinometry, and line and continuum emission [4,80], to just name a few. All have their advantages and disadvantages. Stark broadening, actinometry, and line and continuum emission measurements are all non-intrusive, but, as they are all line-of-sight measurements, a reconstruction technique, like e.g. Abel inversion, has to be applied to the line-of-sight integrated data to obtain spatial resolution. Thomson scattering is a non-intrusive optical diagnostic with which spatially resolved electron densities and temperatures can be readily obtained. Thomson scattering is based on the elastic scattering of light from free electrons [81,82]. The amount of scattered photons is linear proportional to the electron density and laser power. Due to the movement of the electrons, the scattered light is Doppler broadened with respect to the line width of the excitation source. As the electrons have a much higher velocity than the heavy particles, the light that scatters off the free electrons shows a much broader scattering feature than the scattering originating from the bound electrons of the heavy particles i.e. the Rayleigh scattering feature [83]. Although the electron scattering cross-section is much smaller than the heavy particle scattering cross-section and the density of the heavy particles is usually much higher than the electron density, the large difference between the Doppler broadening allows distinguishing between the electron and heavy particle scattered signal in frequency space. Interpolation of the Thomson scattering feature in the central part of the spectrum allows for the determination of the Rayleigh scattering signal. Next to the Thomson and Rayleigh scattering component, a third component is always present, i.e. the stray light component arising from windows and surfaces of the chamber. The width is determined by the laser line width. The basic components of a Thomson-Rayleigh setup are shown in figure 5(a).
The total Thomson scattered light intensity is directly proportional to the electron density. This means that if the sensitivity of the system is calibrated, the electron density can be determined from the area under the Thomson spectrum. The calibration can easily be performed by measuring the Rayleigh scattered signal from a known amount of gas in the plasma chamber [84]. The electron temperature can be determined from the Doppler width of the Thomson scattered spectrum. The width is determined by the velocity distribution function of the scattering electrons. It should be mentioned that the velocity distribution function that is actually measured, is the one-dimensional velocity distribution function in a direction determined by the relative directions of the incident laser and detection axes. When the distribution function is Maxwellian, the electron temperature, T e in eV, is determined by: Here, Δν Th is the full width at half maximum of the Thomson scattering spectrum, ν 0 the laser frequency, θ the angle between the incoming laser beam and scattered light, and m e c , and e are the electron mass, the electron charge and the speed of light, respectively. As the Thomson scattering signal is proportional to the laser power, high-power, and often pulsed, lasers are used in these experiments. The advantage of a pulsed laser in combination with gated detection of the scattered signal is that the measured emission of the plasma can be decreased relatively with respect to the measured scattered radiation. However, care has to be taken not to use too high powers for the radiation, since that can lead to excitation and/or dissociation of the gasses in the plasma, and thus disturbing the system under investigation, rendering it intrusive. The elastic scattering from the heavy particles in the plasma, i.e. the Rayleigh scattering, is almost always the most intense feature in the measured spectrum. The height of the signal is proportional to the total density of the heavy particles in the plasma [85]. From this scattering signal no direct information can be obtained about the kind of species present in the plasma. However, under some circumstances from the ratio of the polarized and depolarized Rayleigh scattering, one can get more information about the species in the scattering medium [86].
Thomson and Rayleigh scattering are elastic scattering processes. Inelastic scattering, that only occurs at molecular species (in contrast to Rayleigh scattering, which occurs at all heavy particles), is called Raman scattering [14,87]. In a Raman scattering process the molecule ends up after the scattering process in a different energy state than before the process. When the molecule is after the scattering process in a higher (lower) state, i.e. the scattered light has a longer (shorter) wavelength, the scattering is called (anti-)Stokes Raman scattering (see figure 5(a)). This technique has not often been employed in the study of plasma, because of the small cross section for Raman scattering. However, the advantage is that every molecule has a Raman spectrum, and can thus in principle be detected. This is especially interesting for homonuclear diatomic species like H 2 , N 2 and O 2 , which are very difficult to detect otherwise. As in the case of Thomson-Rayleigh scattering, a laser is used as a light source. As the Raman scattering cross-section becomes bigger at shorter wavelength, light in the blue part of the spectrum is preferably used. A laser that is very often used in these studies is the Ar-ion laser, which has strong emissions at 488 and 514 nm. As previously mentioned, pulsed Nd:YAG lasers are commonly used for Thomson scattering experiments. As a consequence, nowadays, also Raman scattering in plasmas is conducted with Nd:YAG lasers [31,88,89].
A main drawback of the spontaneous scattering processes on molecules, i.e. Raman scattering, discussed above, is the fact that the scattered light in the plane of the laser beam and perpendicular to the polarization of the laser, is homogeneously emitted in all directions, which makes it very often difficult to detect in environments that strongly radiate. A technique in which the signal is created in a laser-like beam is the so-called Coherent Anti-Stokes Raman Scattering (CARS) technique [90]. During a CARS experiment two collinear laser beams with frequencies ω 1 and ω 2 (ω 1 >ω 2 ) are focussed into the sample. The two waves are mixed via the nonlinear polarization of the sample. When ω 1 −ω 2 equals the frequency of a Raman active transition of the medium, an anti-Stokes(as) and Stokes(s) wave at the frequencies ω as =2ω 1 −ω 2 and ω s =2ω 2 −ω 1 is generated. Spatial filtering allows for very efficient reduction of the background radiation without loss of CARS signal. Already from this short description of the CARS technique it will be clear that this is an experimentally much more elaborate technique than spontaneous Raman scattering [91]. This technique is presently also being explored to measure electric fields in plasma [92,93].
In [88] the authors measure the scattering of Nd:YAG laser light from a microwave surfatron plasma jet with a triple grating spectrometer. Depending on the radial and axial position in the jet, the recorded scattering spectra show mainly Raman scattering (close to the exit of the source and away from the expansion axis), mainly Thomson scattering (close to the exit of the source and on the expansion axis) and a combination of both (a few millimeters downstream recording the Thomson and Raman scattering spectra). The spectrometer is equipped with a mask between the first and second grating, to block the much intenser Rayleigh signal and stray light (the green crosses in figure 19). A result of a measurement which only shows Thomson scattering is depicted in figure 6. This spectrum is recorded in the centre of the plasma jet and 1 mm downstream from the source exit. The center part is blocked by the mask to avoid spilling over of charge from the overexposed pixels by the strong Rayleigh scattering signal in the center of the CCDcamera, when no mask would be present. From these kind of measurements the authors derive electron density and temperature, rotational temperature, partial (N 2 +O 2 )-pressure and the N 2 /O 2 ratio. From the Thomson fit, i.e. the line in the graph, and using equation (19), the electron temperature can be deduced. To do this, it is convenient to rewrite equation (19) to: where we have used that the scattering was recorded with θ=90 o . Measuring the full width at half maximum of the dashed curve (Δλ Th ), taking the laser wavelength as the centre wavelength (λ 0 ) and using equation (20), an electron temperature of 1.5 eV is obtained (in accordance with what is reported in [88]). To absolutely calibrate the intensity axis, the authors used the rotational Raman scattering spectrum of one atmosphere of air [94]. This spectrum can be measured at a position on the CCD chip different from the simultaneously recorded Thomson scattering spectrum. An electron density of 4.6×10 20 m −3 is deduced from the Thomson scattered signal in figure 6. Recently, a similar technique has been applied in an atmospheric-pressure plasma jet [14]. Here, the Rayleigh signal was filtered out with a Bragg grating, which is experimentally less complicated than using a triple grating setup.
Conclusions
In this paper we have given an introduction in some of the optical diagnostic techniques that are nowadays commonly used in the study of low-temperature plasmas. The focus has been on optical diagnostics that can be used to study the plasma phase. Diagnostics like spectroscopic ellipsometry, sum frequency and second harmonic generation and attenuated total reflection spectroscopy, which are used to study plasma-surface interactions, have not been discussed. This paper is meant for scientists new in the field of plasma diagnostics and should serve as a starting point to explore further. It is not a review, but much more a description of the basic principles of some of the commonly used plasma diagnostics. Many references are given to books where the basic principles are further clarified and to papers in which these diagnostics are successfully applied in the study of plasma. | 11,993.8 | 2020-01-07T00:00:00.000 | [
"Physics"
] |
End-to-end simulations of photonic phase correctors for adaptive optics systems
Optical beams and starlight distorted by atmospheric turbulence can be corrected with adaptive optics systems to enable efficient coupling into single-mode fibers. Deformable mirrors, used to flatten the wavefront in astronomical telescopes, are costly, sensitive, and complex mechanical components that require careful calibration to enable high-quality imaging in astronomy, microscopy, and vision science. They are also impractical to deploy in large numbers for non-imaging applications like free-space optical communication. Here, we propose a photonic integrated c rcuit capable of spatially sampling the wavefront collected by the telescope and co-phasing the subapertures to maximize the flux delivered to an output single-mode fiber as the integrated photonic implementation of a deformable mirror. We present the results of end-to-end simulations to quantify the performance of the proposed photonic solution under varying atmospheric conditions toward realizing an adaptive optics system without a deformable mirror for free-space optical receivers.
Introduction
All-optical interfacing of free-space optical (FSO) satellite-to-ground communication with existing fiber networks requires the coupling of the optical beams from satellite transmitters into single-mode fibers (SMFs).This enables high bandwidth links, optical amplification, coherent and quantum communication schemes, and long propagation distances.However, light propagating through Earth's turbulent atmosphere suffers from distortions that destroy its spatial coherence, prohibiting efficient coupling into SMFs.The aberrations cause the focal pattern of a point source, i.e., the point spread function (PSF), to break into an extended speckle pattern that evolves rapidly, mainly driven by the wind, which has velocities < 50 m/s, in the case of astronomical telescopes.For applications in FSO communication, the temporal variations are dominated by the slewing rate of the orbiting satellite, which in the case of low Earth orbit (LEO)-to-ground links [1], can reach up to 1 deg/s, or 400 m/s effective speeds of the optical column.Furthermore, communication links need to be established soon after the satellite has risen above the horizon to maximize the link duration [2], leading to highly distorted beams propagating through a larger airmass during the low-elevation stages of the link.
Adaptive optics (AO) systems in astronomical telescopes use wavefront sensors (WFSs) to sample the wavefront and feed commands, through a controller, to deformable mirrors (DMs) that change shape to correct the distorted wavefronts.DMs are mechanical in nature and tend to be too costly for many applications outside of astronomy, like the large-scale deployment of optical 1©2024 Optica Publishing Group.Users may use, reuse, and build upon the article, or use the article for text or data mining, so long as such uses are for non-commercial purposes and appropriate attribution is maintained.All other rights are reserved.
ground stations (OGSs) to serve rural and remote communities.DMs are also mechanically limited in speed and stroke, inhibiting their use in situations that require higher correction bandwidths, like LEO-to-ground FSO links.Replacing bulk optics with integrated optics and photonic components has regularly been an alternative for overcoming such challenges in optical systems.
Photonic technologies for processing light in waveguides and optical fibers have been developed for several applications, mainly driven by the demands of the telecommunication industry in fiber-to-copper transceivers.The photonic approach offers a platform to realize devices that can overcome the limitations of bulk optics instruments, producing solutions that are compact, scalable, lower in cost, and easier to replicate.Photonic spectrographs [3], integrated beam combiners [4], fiber-based hydroxyl-suppression filters [5], and many other concepts have been developed for astronomical applications [6].However, the poor coupling of starlight and the low total throughput of these astrophotonic devices remains a challenge that needs to be addressed before they are adopted as facility instruments.In AO systems, several concepts for photonic wavefront sensors (WFSs) have been suggested as focal plane sensors that can detect non-common path aberrations (NCPAs) and petal modes in astronomical telescopes [7,8].Wavefront correctors based on multiplane light converters (MPLC) have also been developed for FSO links, which use phase plates to sequentially decompose the light into orthogonal modes [9], and integrated circuits for coherent combination [10].However, the strategy still involves bulk optic phase plates for spatial demultiplexing.
In this work, we propose a photonic integrated circuit (PIC) that spatially samples the light from the exit pupil of an optical ground station (OGS) and corrects the phase distortions in the incoming wavefront to boost the coupling efficiency into SMFs before amplification, transmission, demodulation, and eventual detection.The silicon-on-insulator (SOI) chip, shown in Fig. 1, incorporates an array of vertical incidence grating couplers that direct light focused by a microlens array (MLA) into the plane of the PIC single-mode waveguides.Light from each spatial channel is phase-shifted using thermo-optic microheaters to modulate the refractive index and thus change the optical path length (OPL).An external controller, fed by a wavefront sensor, drives the heaters to match the modes in phase.The co-phased beamlets are combined into one single-mode waveguide using a multimode interferometer (MMI) beam combiner.Finally, a sub-wavelength grating (SWG) [11] expands the propagating mode and couples the light out to an SMF.Using thermo-optic phase shifters (TOPSs) in combination with spiral [12] or serpentine waveguides provides up to 100 kHz control bandwidth and a phase shift > 10 m, exceeding what is possible with DMs based on voice coils or micro-electromechanical systems (MEMS).The size of the array, i.e., the number of controlled subapertures, also scales more gradually with cost in the case of the photonic corrector compared to DMs.Other advantages include a smaller footprint, lower power consumption, and a multiplexing advantage that could be applied in fiber-fed astrophotonic instruments [6,13] and multi-object spectroscopy (MOS) applications in astronomy [14].
We previously presented proof-of-concept simulations of a generic system with square arrays and assumed idealized models for the coupling and combination components in [15].In this work, we report on the results of end-to-end simulations for the expected performance of the proposed photonic solution.The models for the grating couplers and the waveguide-to-fiber couplers match the design of a fabricated chip that we plan to use in lab and field experiments.We also investigate various turbulence and link scenarios, accounting for scintillation and fill factor effects on a simulated system.In Sec. 2, we describe the numerical tools and methods used in the simulation pipeline.Section 3 details the geometry of the circuit components and presents a characterization of the tolerances and the spectral range of the elements.The simulation results are given in Sec. 4 for devices of different geometries and various turbulence conditions.A discussion of the results and their significance to the design process is also provided in that section.
Fig. 1.Schematic of the integrated chip, with a microlens array to sample and focus the distorted wavefront on the grating coupler array (a).Co-phased beams from the TOPSs (b) are coherently combined using an MMI beam combiner like the 7 × 1 combiner shown in (c).The combined beams are coupled out to a lensed SMF (d) using an SWG coupler (e) that matches the waveguide mode to the fiber mode.The cross-section of the single-mode waveguides is shown in (f).
Optical Simulation Pipeline
The simulation results we present in this work quantify the performance of the photonic wavefront corrector assuming an ideal WFS and controller.The results give the expected optical power collected at the output SMF for the scenarios encountered in a LEO-to-ground FSO link.To do so, the pipeline begins by propagating the optical wavefronts from the top of the atmosphere down to the output SMF.The simulation pipeline in Fig. 2 includes both the free space and guided wave parts of the system, and proceeds as follows: 1. Atmospheric phase generation, free space propagation, and scintillation As shown in Fig. 2, The simulation pipeline begins by generating an ensemble of phase screens representing wavefronts distorted by atmospheric layers at a given altitude.The screens have a von Kármán phase power spectral density [16] where the Fried parameter 0 is the atmosphere's coherence length, is the spatial frequency and 0 is the outer scale which is the maximum vortices size at which energy is supplied to the atmosphere.We take 0 = 22 m [17] for the results in Sec. 4. The metrics for the correction quality and the coupling efficiency of the PIC are calculated for a wide range of turbulence strength values to cover all the scenarios encountered in a LEO-to-ground link as the satellite passes from its lowest to highest elevations.When the link is first established, the Fried parameter 0 is the smallest, while at zenith the turbulence is weaker and the satellite slew rate is at its maximum.We assume Taylor's frozen flow hypothesis [18], which states that the temporal evolution of the phase distortions is driven by the transverse effective velocities of the wind and the source rather than the inherent dynamics from temperature fluctuations.The phase screens are propagated through free space along the line of sight to the aperture using the Fresnel diffraction integral.The generated phase screens are 3 times larger than the telescope aperture to reduce aliasing in Fresnel propagation.For a LEO satellite with a 422 km altitude (ISS-like orbit), the maximum link distance is ∼ 1500 km at a 10 deg elevation angle while the distance to the tropopause, the highest turbulence layer, is ∼ 50 km.The long propagation distance between the highest atmospheric layer and the OGS causes intensity fluctuations at the pupil, a scintillation effect that further complicates the wavefront sensing and correction process.
Given the pseudorandom nature of atmospheric turbulence, the numerical results in Sec. 4 are averages obtained from a Monte Carlo simulation that calculates the performance metrics for a large sample of random realizations of the atmospheric layer.The sample size of the Monte Carlo phase screens is 100 realizations, chosen since it is the sample size at which the standard deviations in our performance metrics converge to their true values as shown in Fig. 3.
Telescope optics, and relay optics
The diameter of the collecting telescope is assumed to be = 40 cm, a representative aperture size for OGSs.In our concept, the MLA feeding the PIC samples the pupil spatially which means that the channels that are to be co-phased and combined vary in intensity due to scintillation, degrading the efficiency of the coherent combination scheme.Therefore, we include the scintillation effect in the simulation pipeline to assess how it limits the device's performance.Subsequently, the aperture function that defines the size and arrangement of the secondary mirror and its spiders is applied to the propagated fields.However, the results given in Sec. 4 are for a clear aperture to maintain their generality.A ray trace of the relay optics is also performed to assess the effect of the aberrations of off-the-shelf optics on the quality of the focal spots at the grating couplers.The resulting complex field is demagnified and imaged at the exit pupil of the optical system where the MLA is ideally placed.
Microlens array focal plane
The MLA is used to spatially sample and focus subapertures from the telescope's exit pupil onto the 2D array of grating couplers in the PIC.Coupling with an MLA instead of directly intercepting the beam with the grating coupler array at the demagnified pupil adds an alignment step, but greatly enhances the system throughput.Furthermore, the configuration of the grating coupler array must match that of the MLA in size and format.
We take the MLA to have a 300 m pitch and a 1 mm focal length, which matches the specifications of commercially available arrays.Ideally, the pitch of the MLA should be ≤ 0 on the sky.We also consider two configurations for the MLA and the corresponding array of grating couplers, a square and a hexagonal arrangement of the subapertures.While the hexagonal configuration has a better fill factor on the circular aperture, the routing of the waveguides in the PIC is more straightforward for the orthogonal square array, especially as the size of the array grows larger.A 25% threshold is applied after masking with the aperture function to determine the partially illuminated subapertures that are not receiving enough optical power and therefore neglect them since their inclusion adversely affects the efficiency of the combination.
Photonic components design and simulations
The models for the photonic components are described here, together with simulation results of the spectral response of each component and their tolerance to fabrication inconsistencies.As shown in Fig. 1, the simulated PIC consists of four main components.The grating couplers inject the spots focused by the MLA into single-mode waveguides in the plane of the PIC.Afterward, the TOPSs and the MMI co-phase and combine the modes into one single-mode waveguide, respectively.The last component is the SWG mode expander that enlarges the mode in diameter to 3 m to efficiently couple the light out into a lensed SMF [11].We used a finite-difference time-domain (FDTD) solver and the beam propagation method (BPM) to model the photonic components.An operating central wavelength = 1550 nm is assumed for the optimization process since it is at the overlap of the wavelength range of SOI components, the astronomical H band which is an atmospheric transmission window, and the C band of fiber optic and FSO communication links [2].
The PIC is based on the 220 nm SOI photonics platform, with 500 nm wide Si waveguides.The buried oxide (BOX) layer is 2 m thick SiO 2 and the top oxide (TOX) cladding is 2.2 m thick.These specifications are in line with the SOI process of typical Si photonic foundry offerings.High-resistance metal layers, e.g., TiW, are assumed for the heaters and the electrical contacts, but they are not incorporated in the optical simulations in this work.
The complex fields at the MLA that pass the threshold test described above are propagated to the focal plane by performing a Fraunhofer diffraction integral.The 2D focal fields are line-scanned and the 1D profiles are used as launch fields in the 2D-FDTD solver to propagate the beamlets through to the grating couplers model in the array.Using a 2D-FDTD solver reduces the computation time significantly with negligible impact on the accuracy of the results [19].
Surface grating couplers
Grating couplers are a modulation in the refractive index that is etched onto the waveguide to couple the free-space wave to the guided wave [20].They are typically designed to interface PICs with tilted fibers, however, our concept requires the coupling of normally incident beams from free space.Therefore, the grating design adopted here couples vertically incident transverse electric (TE) polarized light into the waveguides [21].
The grating couplers on the PIC consist of fully etched double gratings with equal periods Λ = 648 nm and widths 1 = 363 nm and 2 = 86 nm, giving duty cycles of ∼ 56% and ∼ 13%, respectively.Figure 1a shows a schematic of the grating coupler model.
The grating coupler is optimized for coupling a vertically incident converging beam focused by an MLA with a focal length of 1 mm at = 1550 nm, which gives a spot size of ∼ 12.6 m.The spectral bandwidth dependence on the focal length is shown in Fig. 4a.The gratings extend to 35 m in length with the maximum efficiency obtained when the focal spot is incident ∼ 14 m off-center toward the waveguide as shown in Fig. 4b.The performance of the surface grating couplers is calculated using a 2D FDTD solver with a 2D model of the structure described.The duty cycles of the two gratings are scanned to estimate the penalty in coupling efficiency that we get as fabrication deviates from the design.Figure 4c shows the coupling efficiency tolerance to the changes in the duty cycles of the smaller and the bigger gratings in the − and −axes, respectively.
Beam combiner
The beam combiner is an MMI that combines the co-phased waveguides in its multimode region through the self-imaging principle.The interference between the eigenmodes of the wide waveguide produces a pattern that varies along the MMI, allowing for a design that couples all the light into one output single-mode waveguide [22].The design can only be optimized for one state of phase and amplitude distributions of the input waveguides.Therefore, optical losses would occur whenever the MMI is fed with any other state.The efficiency of the beam combiner is calculated using BPM.An × 1 MMI combines single-mode waveguides into one output beam.The design of the MMI combiners follows [23] and an example of the field propagation through a 7 × 1 combiner is shown in Fig. 5. Since the amplitudes of the modes to be combined are not always uniform due to scintillation and fill factor effects as discussed later, the impact these effects have on the combiner efficiency is also investigated.Figure 5 shows the light intensity along the beam combiner for uniform and non-uniform amplitude and phase distributions.The maximum combination efficiency (99.3%) is obtained for matched amplitudes and the following phases for the 7 inputs: 230.As seen in Fig. 5a and 5b, the combiner exhibits high efficiencies for co-phased beams with a weak dependence on amplitude distribution.For the large arrays, e.g., 8 × 8 subapertures, the simulation of the 64 × 1 MMI is computationally expensive.We therefore combine the beamlets for the larger arrays in multiple stages in a binary tree of smaller MMIs, e.g., two stages of 8 × 1 MMIs.Both combination schemes, i.e., all-in-one MMIs and MMI binary trees can be realized on SOI PICs.
Edge coupler
The core size of the Si waveguide in the PIC is an order of magnitude smaller than the mode of the output lensed SMF.A taper structure is therefore needed to expand the beam before interfacing with the fiber.A subwavelength-scale grating with a period smaller than the Bragg period expands the waveguide mode to match the fiber mode.The width of the SWG structure tapers down gradually towards the facet and the duty cycle smoothly decreases, reducing the effective refractive index and therefore expanding the mode [24].
The FDTD model of the SWG is shown in Fig. 1e.It adiabatically expands the mode diameter of the ∼ 500 nm wide single-mode waveguide in the PIC to the lensed SMF aligned at the output facet [25].The SWG model is required to estimate the coupling efficiency of the PIC-to-SMF segment and investigate its dependence on wavelength and air gap misalignment.Figure 4d shows the dependence of the SWG to the SMF power transfer on the air gap assuming an off-the-shelf lensed fiber with a mode field diameter (MFD) of 2.5 m and a working distance of 14 m.The air gap is necessary to allow the beam to evolve in free-space from its size at the facet to match the mode size of the lensed fiber at the working distance.
The total output intensity calculated from the output field coupled into the SMF is used in the next section to quantify the total efficiency of the photonic wavefront corrector.
Performance metrics results and discussion
The performance of any AO system is limited by instrumental errors contributed by the three main components of the system: the corrector, the WFS, and the controller.The WFS introduces errors resulting from the finite number of measurements it takes, the noise-limited detector, the angular separation between the reference and the target (i.e., anisoplanatism), and the cone effect in the case of laser guide stars.Only the first two are relevant to FSO links.The controller's limited bandwidth causes a delay between the time the measurements were acquired and the time the correction is applied, thus introducing temporal errors.The wavefront corrector also has a non-zero response time that adds to the temporal errors, but most importantly it adds a fitting error since its ability to match, and thus flatten, the distorted wavefront is limited by the finite number of degrees of freedom it has.Our interest here is in the ability of the PIC to correct atmospheric distortions and the losses inherent to SOI components.While TOPSs always have a smaller bandwidth than electro-optic modulators, the bandwidth required in LEO laser downlinks is < 10 kHz during the worst-case scenario stages of the link.Therefore the photonic corrector is only limited by its throughput and correction degrees of freedom.
The dependence of the coupling efficiency on focal length (see Fig. 4a) is a direct result of the focal spot increasing in size at the coupling plane with longer focal lengths.The weak dependence relaxes the design requirements of the grating couplers and means that off-the-shelf MLAs could be conveniently used.Figure 4a also shows the opportunity at shorter focal lengths for trading off maximum efficiency at the central wavelength for a wider spectral bandwidth.The short focal length also means that lateral motions of the spots across the grating couplers, due to tip/tilt errors in the incident wavefront, are minimal, ensuring that the focal spots always remain within the active coupling area of the gratings [see Patel et al. (submitted)].The tolerance of the grating coupler's efficiency to offsets in the duty cycles of the interleaved gratings is shown in Fig. 4c.The tolerance to the relative position of the focused beam to the grating is more relaxed with a ∼ 4% penalty in efficiency for a 1 m offset as shown in Fig. 4b.
The relatively low 32% coupling efficiency is a consequence of restricting the grating couplers' design to the common fabrication processes offered by most silicon photonics foundries.Adding Si overlays to the grating notches [26], switching to low-index core materials (e.g., Si 3 N 4 ) apodizing the grating in the coupling direction [27], and including Bragg reflectors [28] are all strategies that can help improve the free space-to-chip coupling efficiency up to 80%.
The other point of significant loss occurs at the off-chip coupling to the SMF.The narrow size of single-mode Si waveguides in SOI chips results in the mode size being significantly smaller than the ∼ 10 m MFD of a silica SMF at 1550 nm.Furthermore, the thin BOX layer prevents the use of direct tapers to expand the mode in the vertical dimension to match the fiber since the mode would overlap with the Si substrate.Therefore, the SWG mode expander is used to couple the light efficiently out of the PIC.The fiber used for coupling is aligned at a working distance from the output facet, allowing the beam to diverge in free space to the correct size at the coupling plane.The spectral range of the SWG coupler is > 100 nm [11] and Fig. 4d shows the tolerance of the coupling efficiency to the air gap between the output facet and the lensed fiber.The relatively low efficiency is a result of assuming a sub-optimal off-the-shelf lensed SMF for the simulations, in the interest of estimating the performance of future lab experiments that use them.However, either an optimized SWG or a matching SMF would produce a coupling efficiency better than 92%.Interfacing the fiber to the PIC with a grating coupler is possible but only with a coupling efficiency < 80% and with a complex grating.
The simulation pipeline in Fig. 2 includes all the components the beam propagates through in our device except the phase shifters.They are omitted since they are active components that can be precisely controlled, limited only by the resolution of the digital-to-analog conversion and the noise in the driving electronics.The propagation and bending losses in the PIC depend on the exact routing of the waveguides in the circuit and can be easily accumulated to estimate the total throughput for a given final design.
As a performance metric, we borrow the concept of the Strehl ratio (SR) used to quantify the quality of seeing-limited PSFs in astronomy.We define SR ph (where the subscript ph is short for photonic) as the total optical power in the output SMF under seeing-limited conditions relative to that at the diffraction-limited case.Strictly speaking, our photonic wavefront corrector does not flatten the wavefront propagating in free space or restore the quality of the image at the focal plane as is the case in imaging systems.Nevertheless, since the coupling efficiency in an SMF is directly related to the SR [13,29], the same metric can be used for both AO concepts.
The worst-case scintillation at / 0 = 8 results from propagating the phase screens 50 km in free space along the line-of-sight (see Fig. 7).This is the propagation distance during the lowest elevation stage of a typical LEO-to-ground downlink.At the diffraction limit (/ 0 = 0), the SR ph is unity by definition, and SI = 0.The drop in SR ph is steeper for the cases with fewer subapertures as expected.From Fig. 8 it can be seen that the hexagonal array always performs better under strong turbulence conditions while using fewer subapertures.This advantage is due to the higher fill factor that hexagonal arrays have on the telescope's circular aperture.An essential quality of wavefront correctors is their ability to fit and hence correct the aberrated wavefront.The fitting error of DMs was calculated by Hudgin [30].For segmented DMs, it depends on the number of actuators and the arrangement of the segments.The mean-square fitting error is where is the number of segments along one dimension and is a constant that depends on the influence function.For piston-only actuators = 1.26 rad 2 .The SR falls off exponentially with 2 according to Maréchal approximation (SR = − 2 ), providing a way to directly compare the photonic corrector to segmented DMs.The data points in Fig. 8 have / 0 = 8.Fitting an exponential function with one independent variable, , and three constant parameters, we write SR ph as We find out that our photonic wavefront corrector with a square array follows an adjusted law with = 0.86 rad 2 and = 0.85.The parameter , which we name the scintillation coefficient, accounts for scintillation effects.It is calculated by finding the multiplication factor between the with and without scintillation curves in Fig. 8.Its value is 1.28 when the corrector is operating under / 0 = 8 (SI ≈ 1).Otherwise, its value is unity for negligible scintillation.Table 1 lists the values for and for both configurations.A comparison between a toy model of our concept and circular DMs that perfectly remove the low-order Zernike modes as estimated by Noll [31] was given in [15].Notice that SR ph only quantifies the correction quality and is not sensitive to the coupling and propagation losses in the PIC.To characterize the total throughput of the corrector, the SR ph must be multiplied by the total throughput of the PIC to estimate the output optical power provided by the system.The expected total throughput of the device simulated in this paper is ∼ 0.1, but optimized grating couplers with an > 80% efficiency [32] and an SWG mode expander with a > 92% efficiency [11] could boost the total throughput up to > 0.5 at the cost of a more complex fabrication process.The propagation loss can be reduced by switching to a silicon nitride (SiN) platform.We chose to simulate sub-optimum devices to predict the performance of our first-generation PIC that we will use to prove the concept of photonic AO correction experimentally.
Conclusions and future work
We performed simulations to predict the total optical power delivered by silicon photonics wavefront correctors designed to efficiently couple light into SMFs in the presence of atmospheric turbulence.The simulations explored the parameter space of the design geometries and produced estimates for the quality of correction expected from devices with different sizes and under the various turbulence conditions expected in LEO-to-ground FSO links.
In terms of fitting errors, PICs with hexagonal arrays operating in the presence of scintillation effects are expected to provide an SR ph that is ∼ 1.4 times higher than that provided by segmented DMs.Moreover, the temporal errors of the photonic concept are much smaller thanks to the fast rise time of the phase shifters.Continuous facesheet mirrors perform better than both approaches; however, they are limited in stroke, along with lower control bandwidths and higher inter-actuator crosstalk [33,34].PICs are not immune to crosstalk, but the thermal crosstalk between the TOPSs in the PIC can be mitigated by adding trenches and suspended waveguides to thermally isolate them.Electro-and piezo-optic modulators could also be used to eliminate crosstalk, which additionally facilitates the placement of photonic wavefront correctors inside cryostats for infrared astronomical instrumentation.
As in a classical AO system, the photonic corrector requires a WFS and a controller to measure and reconstruct the wavefront before the commands for co-phasing the beams can be calculated.Two wavefront sensing schemes are proposed: an open-loop Shack-Hartmann WFS that samples and senses the incoming wavefront before coupling into the PIC, and an integrated binary tree of Mach-Zehnder interferometers (MZIs) [35] to measure and directly correct the relative phase errors on-chip.The results from simulations and experimental work that includes the WFS in the pipeline will be reported in a future publication.
Apart from the simulation work reported here, we ran lab experiments on smaller 2 × 2 square arrays using multiple phase plates to introduce atmospheric distortions in the beam and relay optics to image the wavefront on the MLA.The loop was closed on these arrays using a sensorless gradient descent algorithm that maximizes the power in the output SMF.We also designed and fabricated larger arrays that we plan to test in combination with an external SH-WFS and integrated MZI trees.The results from the experimental work will also be reported in future communications.Later, field-testing on ground-to-ground analog links should help raise the system's technological readiness level (TRL) and prepare the setup for establishing links with LEO satellites equipped with FSO laser terminals.
2 .
Telescope and relay optics 3. Microlens array focal plane 4. Surface grating coupler 5. Optical beam phasing and beam combiner simulation 6. SWG mode converter and edge coupler 2.1.Atmospheric phase generation, free space propagation, and scintillation
Fig. 2 .
Fig. 2. Optical simulations pipeline.A generator computes distorted phase screens with Kolmogorov statistics, followed by a wave optics propagator to calculate the fields at the telescope pupil.The spots at the focal plane of a lenslet array where the PIC is aligned are then computed.An FDTD calculator propagates the focal fields into a 2D model of the grating couplers.The output fields are co-phased and then combined by the MMI.The coupling efficiency into the output SMF is calculated by propagating the field through the SWG structure to the chip's facet and into the lensed SMF.
Fig. 3 .
Fig.3.The mean and the standard deviation of the performance metric (SR ph , described in Sec. 4) for an increasing number of randomly-sampled phase screens for devices with 61 hexagons arrangement and in the presence of scintillation.
Fig. 4 .
Fig. 4. Characterization and tolerances of the grating couplers and the SWG mode expander.(a) Spectral range of the grating couplers as a function of the MLA focal length.The isolines trace the FWHM points and indicate the spectral bandwidth.The design wavelength is = 1550 nm and the maximum efficiency is obtained at = 1.25 mm.(b) Dependence of the coupling efficiency of the grating couplers on the launch position of the focal spot.The center of the grating structure is at = 0 and coupling is in the negative -direction.(c) Tolerance of the grating coupler to the duty cycles of the two interleaved gratings.The widths 1 and 2 , and the period Λ are indicated in Fig. 1a.(d) Coupling efficiency as a function of the gap between the SWG and the lensed single-mode fiber.Maximum outcoupling of 30.05% is achieved at a working distance 14 m.
Fig. 5 .
Fig. 5. Intensity maps of the beams propagating through the 7 × 1 MMI combiner, with the respective phasor diagrams for the input fields.The phases of the input beamlets are indicated relative to the reference, i.e., the in-phase condition, that produces the maximum combination efficiency.(a) The beamlets are co-phased and matched in amplitude to give a combination efficiency of 99.3%.(b) The beamlets are co-phased but mismatched in amplitude giving a combination efficiency of 96.6%.(c) The out-of-phase condition results in very poor combining efficiency.
Fig. 6 .
Fig. 6.Strehl ratio of the hexagonal and square arrays as a function of the turbulence strength, / 0 .Left: devices performing free of scintillation.Right: devices performing under scintillation.The top abscissa indicates the scintillation index.
Fig. 7 .
Fig. 7. Distribution of the optical intensity at the telescope pupil with overlaid subapertures for a 61 hexagons array.The wavefront that produced the distribution in (a) has / 0 = 1, while for (b) / 0 = 8.The simulation results for the degradation of the SR ph , as the atmospheric turbulence gets stronger, are shown in Fig. 6.The comparison is made between the 3 × 3 subapertures square array and the 7 subapertures (1-ring) hexagonal array, and then between the 8 × 8 subapertures square array and the 61 subapertures (4-rings) hexagonal array.The results shown in Fig. 6b are for when scintillation effects are included in the pipeline where the scintillation index, SI, indicated on the top abscissa for each / 0 value, measures the normalized variance in the intensity :
Fig. 8 .
Fig. 8. Strehl ratio of hexagonal and square arrays as a function of subapertures at / 0 = 8.The aperture size is kept constant at = 0.4 m for both arrangements.The bottom abscissa is for the total number of subapertures in hexagonal arrays while the top abscissa shows the same for square arrays.
Table 1 .
Values of , , and for the fitting error in Eq. 4. | 7,691.6 | 2024-07-04T00:00:00.000 | [
"Engineering",
"Physics"
] |
A Review Toward Internet Crime Evaluation
The idea of guilty party profiling in computer related wrongdoing is in its earliest stages. Essentially no exploration exists that relates guilty party profiling unequivocally to digital violations or digital hoodlums. However it can't be denied that, given the expansiveness of potential suspects in a digital occasion, some strategy for diminishing that number to a reasonable level took after by the capacity to distinguish a modest number of trustworthy suspects is extremely alluring. Today, much digital wrongdoing is dealt with by the criminal equity framework as unique instances of physical wrongdoing. There is little contention, in any case, that there are parts of PC related wrongdoings and the offenders who execute them that are special to the virtual, as opposed to the physical world. The examination portrayed in this paper looks to set up criteria for dissecting digital wrongdoings and hoodlums in the clear, unambiguous setting of the virtual world. The creators have conjectured four general classes of PC related wrongdoing: 1) robbery, 2) framework assault, 3) individual and 4) psychological warfare. This paper talks about a particular part of the individual class of digital wrongdoing: digital stalking. The four sub-types talked about are the consequence of many years of observational application involving a large number of cases in the physical world. They have demonstrated dependable in examination of vicious violations, for example, assault and kill. A basic reason in the momentum look into is use of the sub-types in digital examination. This is a "Explore in-advance" paper, exhibiting a theory that will be tried exactly in the following period of the exploration. Nonetheless, we give a model case which we delineate the potential utilization of the profiling strategies introduced. Keywords— internet crime, power assertive,typology,subtypes,cyber stalking
I. INTRODUCTION
HE Web is a general empowering agent. It not just gives open doors for research and business to this point inaccessible to the vast majority, it likewise gives a way to criminal action conceivably unrivaled in the pre-Web age. Since the Web gives the dreamand, once in a while, the truthof namelessness, those wishing to seek after criminal action discover the Web a sheltered and prolific ground for their endeavors. One of those exercises, empowered by the Web and the current condition of the Internet (some of the time alluded to as "web 2.0"), is cyber stalking. There has been some discourse in the writing of cyber stalking as an expansion of physical stalking [2][6] [7], be that as it may, McFarlane and Bocij [8] oppose this idea. The separation of cyber stalking as a one of a kind demonstration, yet sharing a portion of the attributes of physical stalking, is an essential point for giving a typology of cyber stalkers that can be utilized solidly by agents. Our situation in such manner underpins McFarlane and Bocij, notwithstanding, we discover their typologies constrained with respect to their utilization as an investigative instrument. With minimal solid data on stalking in the physical world and even less in the virtual world [5], the thought of creating reasonable typologies for cyber stalkers has not been all around created. McFarlane and Bocij [8] have proposed a cyber stalker typologypernicious, formed, cozy and grouphowever this typology does little to separate individual cyber stalkers with the end goal that examiners can center around one of a kind speculates in view of their individual practices. It is that concentration with which this paper bargains.
II. RELATED WORK
There are a few hypotheses from the more natural wrongdoing of physical stalking that can be considered for incorporation in the domain of cyber stalking. One such hypothesis is standard action hypothesis (Rodent) [3] [4]. Basically, Rodent says that wrongdoing is unavoidable (inspired guilty parties) and that if an appropriate target is unprotected (nonattendance of a fit gatekeeper), he or she is a potential casualty. The simple in the virtual world says that if an objective frequents open locales and isn't secured, he or she may succumb to some type of digital evil. Rodent in the internet is most effectively outlined by the weakness of numerous PC clients to malware (malevolent programming, for example, infections) and hacking dangers. For instance, Web surfers who visit erotic entertainment locales will probably confront security dangers, for example, an infection or session capturing (34.2% of free smut destinations and 11.4% of for-pay destinations are influenced) than the individuals who don't visit those locales [9]. Likewise, one may estimate that people who visit long range interpersonal communication destinations, for example, Facebook or utilize items, for example, AOL Moment Detachment vigorously are putting themselves in an unsafe position in respect to cyber stalking. The way to maintaining a strategic distance from trade off under the Rodent is ensuring oneself. On account of malware security, this comprises of staying away from perilous sites and guaranteeing that hostile to malware assurance is introduced and forward. On account of cyber stalking, security may comprise of restricting the measure of individual data the individual makes accessible on the web. Holt and Bossler [10] report some achievement in applying Rodent to cyber harassment and cyber stalking. While Rodent offers a decent structure for helping potential focuses of cyber stalking abstain from getting to be casualties, it doesn't offer the examiner much help with recognizing a cyber stalker. McFarlane and Bocij's typology is constrained in that it centers around wide portrayals of cyber stalkers. These wide portrayals don't offer the granular differentiators that examiners require to lead a tenable, prosecutable cyber stalking examination. The four kinds portrayed by these creators put cyber stalkers in gatherings, however don't separate satisfactorily at the individual levelnor are they combined with an investigative approach that makes them valuable to examiners. As clinical portrayals they do, in any case, have justify if taken in the organization of other clinical analyses. Too, the exact research detailed in [8] and [14] are very valuable in understanding the wrongdoing of cyber stalking, in any event in the UK where a great part of the exploration was led. The most encouraging typology originates from Keppel and Walter [1]. This typology, the way things are, is centered around sexual related kill. Be that as it may, we have discovered that it can be stretched out neatly to give a helpful typology to surveying cybercrimes and profiling digital guilty parties, for this situation, cyber stalkers. An essential qualification must be made between a mental appraisal and a criminological evaluation. A mental evaluation centers upon the clinical viewpoints (e.g., analysis and treatment) of the person. A criminological appraisal centers upon wrongdoing and criminal acts. For the reasons for wrongdoing appraisal, we look at the criminologicaland for this situation, the digital criminologicalcontinuum. The examiner applies the subsorts to the wrongdoing and after that works outward towards the individual suspects. The Keppel/Walter Sub-Sorts Working off of early research by Groth and Birnbaum [11] and resulting work by Hazelwood and Burgess detailed in an early release of [12], Keppel and Walter stretched out the typology of attackers to incorporate assault/kill [1]. The extensibility of this typology, as appeared by Hazelwood, Walter, et al, proposes that it is a perfect possibility for looking at digital stalking. It is on these sub-types that we base our examination into profiling of digital wrongdoings and hoodlums. The profiling of cyber stalkers is an initial phase toward that path. The sub-types depicted in [1] incorporate Power Self-assured, Power Consolation, Outrage Retaliatory, and Outrage Excitation. Quickly, this paper portrays these subtypes in the accompanying segment in spite of the fact that we are intrigued fundamentally in Power Self-assured and Power Consolation when we examine cyber stalking
A. Power Confident
The power decisive (Dad) performing artist is engaged upon power and animosity and utilizations them to control the casualty. Mighty terrorizing and direct utilization of power are signs of the power decisive subtype. We expand this into the virtual world by including, for instance, the measurements of boasting about the on-screen character's stalking achievements in such mysterious settings as open gatherings, interpersonal interaction locales and unknown dialog gatherings, and capability in PC innovation. The Dad on-screen character has a tendency to be sorted out and in the digital world might be a software engineer or favor him or herself to be a super programmer. The power emphatic onscreen character must keep up his or her power and does it through expanding the level of haughtiness and terrorizing that can be seen in messages and different postings. The performer is egocentric and applies his or her sense of self to look after strength. In the Dad cyber stalker, the level of control accessible in the virtual world may not be sufficient for the stalker to trust that he or she is keeping up control over the casualty and, in this way, may rise to a physical gathering in reality. That gathering can bring about assault or assault kill.
B. Power Consolation
The power consolation (PR) performing artist is like the Dad on-screen character with some essential contrasts. The huge distinction is the effect of imagination on this performing artist. By dream, we mean the distinction amongst reality and what the performing artist needs as well as accepts to be genuine by means of supernatural thinking1. In the composed performer, this may play out as big name stalking, for instance, where the on-screen character trusts that the big name is enamored with him or her. Conversely, the confused on-screen character may focus on either side of his or her age gathering or, if inside a similar age range, he or she may center upon the tested physically, rationally, or credulous -for the investigation and abuse of energy. The PR performer needs to strengthen his or her perspective of him-or her-self and this occasionally displays as a basic absence of selfassurance and refinement. This may, however, be a piece of the PR performing artist's dream. The performer will endeavor to draw in the casualty in his or her dream and will build animosity more respectably than the Dad on-screen character. Nonetheless, when that does not work, the PR conduct may raise to Dad. The PR performer is less sorted out than the Dad and may leave more pieces of information that empower the following of the cyber trail all the more effectively. In the digital world, the PR on-screen character may utilize a doctored photograph and make a persona that he or she accepts will be appealing to the casualty. In spite of the fact that the on-screen character may present as being low on self-assurance, he or she will endeavor to seem certain and when the online association stops to fulfill the performing artist's dream, he or she may endeavor to heighten to a gathering in the
C. Outrage Retaliatory
The outrage retaliatory (AR) on-screen character is brimming with threatening vibe and will act that fierceness out against the particular source or, if the source is inaccessible, an emblematic focus on that speaks to the genuine reason for genuine or envisioned wrongs. While the objective of the wrath might be at least one people, the genuine reason might be at least one people or an association. AR performing artists in the internet don't as a rule raise to gatherings in the physical world and, truth be told, AR conduct is rarer than Dad or PR conduct in the online world. D. Outrage Excitation Outrage excitation (AE) performing artists are perverted and concentrate their exercises on threatening the casualty. The level of hostility increments until the point when the performing artist accomplishes the demolition of the objective. Since AE activities are hard to accomplish in the internet, the AE compose cyber stalker is extremely uncommon.
D. Utilizing THE SUB-Sorts IN The internet
The sub-types are connected particularly in criminal profiling and profiling stalkers in the internet is no exemption. Basically, the profiler starts by describing the wrongdoing in light of the confirmation accessible. The proof, for this situation, incorporates interviews with casualties, criminological examination of the casualty computer(s), Web access Supplier (ISP) logs, subpoena comes about because of ISPs, long range informal communication destinations and other online entrances that were associated with getting to the casualty. These outcomes in a profile of the wrongdoing that the agent can coordinate with the profiles of suspects. Since most stalkers in the physical world are known by their casualties, we may expect that the same is valid in the online world [13]. This ends up being the situation, yet the elements of that nature are fairly unique in the internet. In the online world, the adjust of previous huge others versus new "companions" met online in visit rooms, informal communication destinations, and so on is tilted towards those met on the web. Nonetheless, Bocij does not concur totally [14]. He reports that there is dependably [his emphasis] some sort of connection between the disconnected physical world stalker and his casualty." Bocij puts forth this expression as a differentiator between physical world and digital world stalkers. He battles that cyber stalkers don't generally know their casualties. This does not consider the broad utilization of informal communities in the internet where associations can turn out to be extremely individual despite the fact that the on-screen characters have never met face to face. For a PR cyber stalker, such restricted contact online can form into a dream that outcomes in forceful cyber stalking and once in a while, a heightening to a genuine physical gathering, frequently with genuine results. Factually most physical stalkers are men and most casualties are ladies [13]. There is little proof to question that adjust in the internet, albeit approving it is one of the objectives of the experimental segment of this exploration.
A.Examination Investigation of a cyber stalking occurrence should start with a reasonable comprehension of the occasions making up the episode. That incorporates point by point interviews with the casualty and a nitty gritty measurable investigation of the casualty's PC. Dad cyber stalkers are probably going to have a direct to abnormal state of PC ability and that will be obvious in anonymization of messages and different messages or direct access, assuming any, to the casualty's PC. Regularly the casualty will have erased hostile messages and different postings. Those should be recuperated forensically from the casualty's PC. Examination of the exercises of the cyber stalker through reproduction of correspondences with the casualty is the following stage. That imaginable will require subpoenas ISPs, entryway administrators, email administrations, and person to person communication locales. There is a high probability that some type of false name will have been utilized by the cyber stalker. Cross that false name to a genuine individual. That chain of proofadditionally called a cyber trailmight be a many-headed hydra driving in an assortment of bearings. A solitary cyber stalker may utilize numerous assumed names. Once the profile of the wrongdoing is finished it must be coordinated with that of the individual cyber stalker. The cyber stalker's moniker is then followed to a genuine individual and that individual is profiled utilizing a similar sub-types. That might be finished by performing broad inquiries on the Web to discover different cases of the speculates exercises or by examination of the known qualities of the recognized person. On the off chance that the speculates profile coordinates the profile of the occasion, the last advance is to break down the appropriate cyber trail to build up that there was, truth be told, contact with the casualty. While cyber stalking reaches out into this present reality, confirm assembled through this procedure can be of material help to examiners. Since one of the fundamental contrasts amongst physical and cyber stalking is the effect of topographyphysical stalkers must be in the geographic region of their casualties, while cyber stalkers don't should be [13] an imperative part of cyber stalking-turned-physical is geology. Note that a PR cyber stalker can heighten to Dad, yet going the other way is farfetched. The PR cyber stalker at first may adopt a to some degree gentler strategy towards satisfying his or her dream with the casualty than will a Dad cyber stalker. At the point when that does not create comes about, the cyber stalker may turn out to be more forceful and the attributes of the Dad go to the fore. On the off chance that a cyber stalker begins as Dad and progresses toward becoming PR, the specialist ought to be suspicious that he or she is being gamed by the subject. It is likely that the performing artist is Dad. One more essential point merits specifying. It is less regular for a performer to present as just a single kind than to exhibit some adjust of more than one. For instance, a Dad cyber stalker may have a touch of AR that tends to present as outrage towards the casualty. Be that as it may, the agent ought to be ready when creating intention to the overwhelming kind, which for this situation is Dad. The thought process is power and control over the casualty. The outrage may essentially be a appearance of the cyber stalker's have to control and is to a greater degree an instrument than a total typology.
IV. CASE EXAMPLE
In the mid 1990s, one of the creators took a shot at a stalking situation where the casualty was a lady in the HR bureau of a medium-measure organization. She had been utilized already by another association and had been compelled to flame a man who therefore stalked her physically for quite a while. Subsequently, she cleared out the association in light of the fact that there appeared to be nothing that the association would do to secure her and the performing artist was an exceptionally vicious man. Quite a while had passed when the cyber stalking and provocation (digital badgering is a superset of cyber stalking for the motivations behind this illustration) started, however the bugging messages demonstrated definite information of the prior occasions. She normally accepted that it was a similar individual. After finishing an examinationwhich did exclude profilingthe on-screen character was observed to be a co-representative of the casualty. The casualty had been enlisted, to a limited extent, to control the conduct of other HR representatives, particularly in their selecting practices, and this specific worker disdained that control. She, subsequently, utilized cyber stalking to restore her control and power inside the office. A. Examination This was a great Dad cyber stalking. The on-screen character utilized email with anonymization to stalk the casualty and expanded the level of animosity to the point where the casualty started to fear for her life and thought about leaving the organizations utilize. This, obviously, was the goal of the cyber stalker. In her every day work, the performing artist could be viewed as Dad. She was controlling, somewhat of an unstable presence and endeavored to threaten colleagues and chiefs into giving her a chance to have her direction and exercise her obligations as and when she wished. Coordinating the conspicuous Dad qualities with the Dad idea of the associate would have indicated the performing artist instantly, yet tragically, digital profiling systems were not grown at that point even as they are not presently. There is the conspicuous contention that there is no assurance, given the size and dispersal of the online world, that the cyber stalker would be anyplace close to the physical closeness to the casualty or that there would be an association that would help examiners in recognizing the suspect. In any case, there are various devices today that can help in that distinguishing proof. At the season of the occurrence, those apparatuses did not, obviously, exist. That being stated, the factual association amongst assailants and casualties in the physical world may have a tendency to be reproduced in the internet [13]. On the off chance that that is the situation, as it was for the situation case, distinguishing suspects is commonsense. Moreover, following the cyber trail of the stalker can enable examiners to distinguish the speculate paying little mind to where he or she may be geologically found with respect to the casualty. This case shows the potential advantages of creating digital profiling. Setting up parallels between the physical and online universes is a target of future periods of This exploration. Once the profiles of the occurrence and the potential suspects had been finished, following the cyber trail would have driven unavoidably to the performing artist. The performer was heightening her cyber stalking into the physical world by debilitating the casualty's young childraising the level hostilityand setting nails under the child's auto tires. Despite the fact that the cyber stalker herself did not have a sufficiently high ability level to play out the anonymizing of the stalking messages, her better half did and in evident Dad form, the performer got her significant other to make and send the messages for her. Including somebody with more prominent PC aptitudes through terrorizing isn't phenomenal with Dad cyber stalkers.
V. CONCLUSION AND FUTURE SCOPE
Future Exploration As this paper appears, stretching out the sub-sorts to the on-line world is doable. Following stages in this examination incorporate performing exact research utilizing genuine cases, analyzing parallels between the on the web and physical universes, and stretching out the subsorts to alternate classes of digital wrongdoing. Wrongdoing evaluation in the physical world incorporates inspecting exercises amid the wrongdoing and additionally prewrongdoing and post-wrongdoing exercises. These are lined up with the sub-sorts to comprehend the idea of the wrongdoing and afterward connected to suspects. Now, examiners create profiles of the presumes utilizing the subsorts and match them to the wrongdoing evaluation. Regularly this examination will point to at least one suitable suspect. Future research will test this approach in the advanced world.
The advancement of a solid technique for wrong doing appraisal and wrongdoer profiling for digital violations is both alluring and, in the present online condition, vital. Sadly, most endeavors at this so far have been clinically engaged inside the mental area instead of applying the criminological continuum and being expected for the specialist of digital episodes. Surveying cyber stalking episodes and profiling cyber stalkers utilizing the Keppel/Walter sub-types is a magnificent place to begin building up this investigative capacity in light of the fact that there is a nearby connection between's physical stalking and cyber stalking. The creators speculate, be that as it may, that the sub-sorts can be reached out to all types of digital wrongdoing: burglary, framework assault, individual, and psychological oppression. | 5,238.8 | 2018-06-30T00:00:00.000 | [
"Computer Science",
"Law"
] |
Better Unification for Physics in General Through Quantum Mechanics in Particular
Physics has always had several different domains of application in on-going development, and physicists have always striven for unification among its different domains. Unification is usually achieved through development of so-called ‘covering theories’. In the nineteenth century, the stunning example was Maxwell’s Electrodynamics (MED), which unified electricity and magnetism as one domain of theory. Another major domain of theory then present was Newton’s Mechanics (NM), which in the eighteenth century had really launched modern physics as a mathematical discipline. At the turn of the twentieth century, NM and MED were well in place, and were fulfilling many technologically important requirements. But there seemed to be an incompatibility between them. The problem concerned their invariance with respect to choice of reference frame: NM exhibited invariance if the allowed reference frames were all connected through Galilean transformations, whereas MED exhibited invariance if the allowed reference frames were all connected through Lorentz transformations. It looked as though one of these two theories must be more nearly correct than the other, but it was not clear which one was the better one. That problem seemed resolved with the advent of Einstein’s Special Relativity Theory (SRT). SRT was believed to capture the true meaning of MED concerning the behavior of light signals, and SRT was certainly an endorsement of Lorentz transformation, so SRT was believed to offer the one possible revision of NM that could make mechanics fully consistent with MED. But meanwhile, new phenomena were being discovered at the micro scale of physics, and they often seemed inexplicable with any known theory, whether NM, SRT, or MED. These were phenomena suggesting quantization of light, quantized atomic states, atomic, molecular and crystal structures, radioactivity, etc. So at almost the same time as one problem seemed to be resolved, other problems were emerging. Since the earlier situation between NM and MED had demanded that Physics allow two seemingly discordant theories to co-exist until some good argument could replace one of them, the situation then presented by the new phenomena being discovered naturally invited the development of another potentially discordant theory: Quantum Mechanics (QM). The discovery of the photoelectric effect, and the introduction of the idea of the photon, initiated QM. Almost immediately, QM was developed to handle the Hydrogen atom, and the ground state thereof, the stability of which was thought to be impossible with MED.
Cynthia Kolb Whitney
Galilean Electrodynamics USA
Introduction
Physics has always had several different domains of application in on-going development, and physicists have always striven for unification among its different domains.Unification is usually achieved through development of so-called 'covering theories'.In the nineteenth century, the stunning example was Maxwell's Electrodynamics (MED), which unified electricity and magnetism as one domain of theory.Another major domain of theory then present was Newton's Mechanics (NM), which in the eighteenth century had really launched modern physics as a mathematical discipline.At the turn of the twentieth century, NM and MED were well in place, and were fulfilling many technologically important requirements.But there seemed to be an incompatibility between them.The problem concerned their invariance with respect to choice of reference frame: NM exhibited invariance if the allowed reference frames were all connected through Galilean transformations, whereas MED exhibited invariance if the allowed reference frames were all connected through Lorentz transformations.It looked as though one of these two theories must be more nearly correct than the other, but it was not clear which one was the better one.
That problem seemed resolved with the advent of Einstein's Special Relativity Theory (SRT).SRT was believed to capture the true meaning of MED concerning the behavior of light signals, and SRT was certainly an endorsement of Lorentz transformation, so SRT was believed to offer the one possible revision of NM that could make mechanics fully consistent with MED.But meanwhile, new phenomena were being discovered at the micro scale of physics, and they often seemed inexplicable with any known theory, whether NM, SRT, or MED.These were phenomena suggesting quantization of light, quantized atomic states, atomic, molecular and crystal structures, radioactivity, etc.So at almost the same time as one problem seemed to be resolved, other problems were emerging.Since the earlier situation between NM and MED had demanded that Physics allow two seemingly discordant theories to co-exist until some good argument could replace one of them, the situation then presented by the new phenomena being discovered naturally invited the development of another potentially discordant theory: Quantum Mechanics (QM).The discovery of the photoelectric effect, and the introduction of the idea of the photon, initiated QM.Almost immediately, QM was developed to handle the Hydrogen atom, and the ground state thereof, the stability of which was thought to be impossible with MED.
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Theoretical Concepts of Quantum Mechanics 128 Accepting that apparent incompatibility with MED, and even embracing it, researchers moved on to excited states, to other atoms, then to molecules, and reactions, and to all the rest of the complexity that today makes up modern Quantum Chemistry (QC).Also, experimenters got into sub-atomic elementary particles, especially electrons and positrons, their annihilation and creation, along with creation and annihilation of photons.
All that led to Quantum Electrodynamics (QED).So today physics still has several different bodies of theory, aimed at several different domains of application.On the one hand, we have QM for atomic and other micro-system interactions.It has at least two identifiable parts: QC for interactions at the level of atoms and molecules, and QED for interactions at the level of elementary particles.And on the other hand, we have Einstein's relativity theory (RT) for physics at human scale and larger.
It too has two parts: SRT for electromagnetic interactions, and general relativity theory (GRT) for gravitational interactions.QM and RT are the major pillars of twentieth century physics.And they are not entirely compatible.QM features wave-like entities with seemingly instantaneous correlations between the states of even quite distant entities, whereas RT features point-like entities interacting via fields propagating at a finite speed.So are we defeated in the quest for unification in Physics?Apparently many people hope not, as they do vigorously pursue various forms of unification.The prominent one sought today is Quantum Gravity (QG).It would be the twenty-first century capstone for the two twentieth-century pillars of QM and RT.But it is not yet fully in sight.
In the pursuit of unification, one often sees phrases like 'Theory of Everything'.The objective of this Chapter is certainly modest by comparison!It just notes some observations about the status of available theories, and discusses the removal of some incompatibilities between the available theories that arose only because of unfortunate choices.
Because QM is relatively new, there are still lots of alternative approaches being developed in parallel.Putz (2009) gives us one very big and recent anthology about them, and this book will give another even more recent one.The QM atmosphere is clearly right for generating new illumination that can facilitate new observations about physics overall.
The first observation driving the present work is just this: QED is arguably the most successful theory that modern Physics possesses.The fact that QED now exists, and that is has the name that it has, naturally begs the question: How could there have been any real disconnect between MED1 and early QM?It is this author's belief that Nature is not so perverse.Connections between different domains of theory are still possible to find, even though the diligent search that was conducted a century ago did not find them.We have developed more tools now.Every new tool developed should invite us to revisit the old problems.
Section 2 talks about the photon from the point of view of MED.It explores the implications of the finite energy, which characterizes a photon.It finds a plausible model for the photon expressed in terms of MED.
The second observation is just this: If MED can connect better with QM, then shouldn't SRT also connect better with QM?After all, how much difference can there be between a photon in QM and a light signal in SRT?
Section 3 explores the implications of modeling the light signal in SRT in the same way as the photon in QM.The photon model suggests a slight alteration to Einstein's second postulate, and thereby produces a slightly altered version of SRT.The third observation is just this: If SRT is to be altered, however slightly, in response to the photon concept from QM, isn't it then possible that the revised SRT can be used to better explain some things about QM that presently seem mysterious?Section 4 talks about what the photon/signal model implies about atoms: the stability of atoms, the occurrence of Planck's constant.
The fourth observation is this: Much of science works on scaling laws.It is in that spirit that we should look for scaling laws about atoms, and thereby reduce the effort of looking at each element as a particular special-case problem for detailed calculations.
Section 5 talks about the inferences from to the story about all isotopes of Hydrogen, all elements beyond Hydrogen, and the ions of any element; the possible nature of 'excited' atomic states, and the character of the light spectrum that an element produces.
The fifth observation is this: If QM can be better connected to SRT, then where does that leave its relationship with NM? Early QM was basically NM, although not for particles possessing momentum and energy in the classical way, but rather for waves, with an amplitude factor and a phase factor, in the latter of which momentum and energy appeared as variables.Is that formulation now completely outdated on account of a rift between NM and MED? Section 6 establishes that there was no necessary disconnect even between NM and MED.It argues that, with an adequately extended notation to support an extended tensor calculus, Maxwell's equations can be seen to be invariant in form, even under Galilean transformation.
(It is useful here to distinguish two kinds of invariance: 'form invariance' for symbolic equations, and 'number invariance' for individual symbols that have numerical values.) The last observation is the 'meta' observation about the present work: Physics in general can become significantly more unified throughout because of some specific developments surrounding QM.Section 7 summarizes the several specific conclusions implied by the present work.Boiled down to one sentence, these conclusions come to this: the existence of apparent discord between theories that are addressed to different problem domains within Physics sometimes means that there exists a more productive way to pose one or more of the theories involved.
Maxwell's electrodynamics and QM's photons
It often seems that MED, a theory largely about spatially extended EM fields, has little in common with QM, a theory largely about discrete material systems and the discrete photons that they emit and absorb.Photons are imagined to be the opposite of spatially extended; i.e., localized, like the matter particles that emit and absorb them.So our mental picture for a photon in its interactions with matter is rather bullet-like: the photon is shot out of a source, travels through space, and hits a receiver that absorbs it.But the travel part of the story is unobservable.So we imagine that the photon in flight is possibly wavelike, in accord with Maxwell theory.Certainly the evidence for that is present, in the form of interference effects, even with small numbers of photons.So the photon is assigned a quality of 'duality'.This is a rather mysterious way of describing a photon.What seems missing here is an adequate model for the photon throughout its life history, expressed in terms of EM fields.The purpose of this Section is to develop one.
I like to begin the development of such a history with a waveform consisting of finite energy distributed in a three-dimensional Gaussian peak located very close to a source that has emitted it.This three-dimensional Gaussian peak is limited in all three spatial directions so as to integrate to a finite total energy.To allow subsequent propagation, the energy has to be divided between two orthogonal fields, electric and magnetic.To allow circular polarization, the energy has to be further divided between real and imaginary parts, real being alive now, and imaginary becoming alive a quarter of an oscillation cycle later.
Given such a start, the whole life history of a photon can then develop in the manner that Maxwell's equations allow.Describing that development is the objective of the following Sub-Sections.
Waveform development
The first step in the life history of a photon is its development from a spatially localized energy bundle that is emitted from a source into a spatially extended waveform that travels through space.To help think about this problem, it is useful to recall some phenomenology familiar from physics at a more macroscopic scale.1.One phenomenon very well known for light modeled as EM waves is the spreading transverse to the propagation direction known as of 'diffraction'.Diffraction is the result of some sort of limitation transverse to the propagation direction.Historically, the limitation has been due to a finite aperture through which the light propagates.The light spreads out from the aperture, more-so the smaller the aperture is.In the photon model discussed here, the limitation is softer than an aperture edge, but a limitation nevertheless: it is the finite spread of the Gaussian waveform in the two directions transverse to the propagation direction.The more narrow the Gaussian peak is, the more spread there will be.But sideways spreading is not the main requirement for a photon model; spreading in the longitudinal direction is what is most needed.Could longitudinal spreading be caused in a manner similar to diffraction, by the initial waveform limitation in the longitudinal direction?2. The closest familiar analog for longitudinal spreading is known as 'dispersion'.This word refers to the 'blurring' effect that any frequency dependence the propagation speed through the medium entails.For example, a signal pulse in a medium looses its sharp edges because those sharp edges imply superposition of many different wavelengths, and hence different frequencies, which the medium may affect differently.In Earth's atmosphere, or ocean, square waves can turn to blob waves because of dispersion.
But we don't have the traditional medium-induced frequency dispersion for a photon in free space.So 'dispersion' isn't a close analog for any effect that may be induced by longitudinal limitation due to the finite spread of the Gaussian waveform in the longitudinal direction.
For the photon model, we need to find and combine just the useful features from both the diffraction and dispersion ideas.Here is a workable approach.Diffraction comes out of optical system response in the spatial domain.Dispersion comes out of transmission system response in the temporal domain.Maxwell's equations link space and time variation together.So we look at pulse profiles in the longitudinal direction, and allow Maxwell's equations to work on them.
Let us begin a scenario with a single pulse in E .Let it have a Gaussian profile along the propagation direction, say x , with 2 exp( ) Ex . We can apply Maxwell's equations, and watch what happens.The Gaussian is the so-called 'generating function' for the infinite set of Hermite polynomials, all of which have very regularly spaced zero crossings.What happens is that the single pulse in E (an even function) generates a double pulse in B (an odd function), which in turn generates a triple pulse in E (another even function), and so on; that is, all the derivatives in play generate successively higher-order Hermite polynomials multiplying the Gaussian.Meanwhile, all the EB Poynting vectors in play support general spreading of the Gaussian.With each step, the emergent functions look more and more like wavelets, and the individual peaks in the wavelets stay about the same width as more of them accrue, so the wavelength for the emergent wavelet becomes more and more defined.Figure 1 illustrates this behavior at the stage where E has developed five peaks (four zero crossings).Series 1 is the original input Gaussian function, Series 2 is the Gaussian after the overall spreading has developed to this point, and Series 3 is the wavelet that has emerged in the process; i.e. the spread-out Gaussian times the fourth-order Hermit polynomial generated.What we have so far is only one eighth of the story needed to fully represent a photon: development from a pulse into a waveform.We have told the story for one pulse in E .If we would match that with another pulse in B , we would have overall propagation along with waveform development.That would bring us to one quarter of the whole story of the photon.If we would match that with two more pulses, E and B pointing at 90 in space from the first pair and coming 'alive' a quarter cycle out of phase with the first pair, we would have the circular polarization characteristic of photons, but we would still have just half the story.So let us move on, and seek the other half. 2 Wheeler and Feynman were looking to time symmetry as the basis for an electromagnetic generalization of instantaneous (Newtonian) gravitational interaction.There are important differences between the regressing waveforms introduced above and the Wheeler-Feynman advanced solutions: 1) Wheeler and Feynman were looking at interactions between essentially point sources and receivers, and so had to be looking at spherically expanding retarded solutions and spherically contracting advanced solutions, not at essentially one-dimensional expanding and contracting wavelets.2) The Wheeler-Feynman expansion or contraction is related to the spherical area of a wave front, not the waveform in the radial propagation direction.3) A lengthy discussion of the paradox of advanced actions is necessitated in the Wheeler-Feynman work, whereas the 'regressing' solutions introduced here are not in fact 'advanced' at all; they are just regressing, in real time, in the propagation direction.equations running backwards in time; there is just 'piling up' of a solution to differential equations in response to a boundary condition.
The photon model in terms of EM fields
Taken together, the waveform development followed by the waveform regression suggest a photon model in terms of EM fields that exhibits continuous evolution: it goes from a state of pulse-like localization near its source, to a state of wave-like extension in space during its travel, and then back to a state of pulse-like localization near its receiver.Observe that with this photon model, 'light in flight' develops its wavelength only during its flight.It doesn't have it to start with, and it gives it up at the end.So light at emission, or reception, has a position, but no wavelength, whereas light in flight has a wavelength, but no position.Thus the model expresses a 'wave-particle duality' for light.Observe too that this photon model exhibits a form of QM 'complementarity', or uncertainty relationship.Consider that, under Fourier transformation, Gaussians map into Gaussians, and that the product of the spreads of such Gaussians is a constant.In the process of wave train development, a Gaussian in position space x spreads out, while its corresponding Gaussian in wave number space k sharpens up.Inasmuch as the discovery of photons was the point of departure for the development of QM, having this photon model expressed in terms of Maxwell fields is a first step in reconciling MED with QM.But there is much more to do, because the bigger problem for MED was not the photon itself, but rather the atom that emitted or absorbed it.It looked as though MED could never explain an atom being stable in its ground state, much less anything about its excited states.To find any reconciliation there, we must move on.
EM signals as photons
Every neutral atom contains at least two particles, and generally a lot more.Prior to QM, electromagnetic forces were presumed to hold such a system together, but there was clearly a problem with that understanding.The simplest atom is the Hydrogen atom, with just one electron circulating about a nucleus consisting of just one proton.So consider the Hydrogen atom.The electron circulates and so accelerates, and that must generate radiation.It was assumed that this radiation would rob the atomic system of energy, and thereby cause the collapse of the atom.So it was assumed that Maxwell's EMT is simply incompatible with the stability of atoms.The solution then was to postulate the existence of a different regime of physics in which that wouldn't happen.But was that really necessary?The purpose of this Section is to argue that it was not.The underlying belief in inevitability of atomic collapse reflects a belief that the electrodynamic forces within the atom are essentially central, and therefore cannot affect the energy budget of the atom.This latter belief traces to the turn of the 20 th century, when A. Liénard (1898) and E. Wiechert (1901) developed models for the potentials and fields created by rapidly moving charges.Although Liénard and Wiechert worked independently, they made the same assumption, and they got the same results, and so confirmed each other.This Section looks at those results, and thereby develops a motivation to look back at their underlying assumption.One can feel moved to check this surprising result.Fortunately, one can look up the original sources, obtain translations if necessary, and verify the original algebra.There is no problem with the algebra.There are also numerous re-derivations that use more modern techniques involving the Dirac delta function and the Heaviside step function.These are 'generalized' functions of some parameter that, when driven to infinity, produces an infinite pulse or a unit step.One can study these re-derivations too.One finds various re-orderings of the mathematical operators 'differentiate', 'integrate', and 'go to parameter limit'.These reorderings are dodgy because the generalized functions lack the mathematical property of uniform convergence, so these operations don't necessarily commute; it is possible to change the result by changing operation order.But even so, such findings do not change the fact that the original LW derivations, although pedestrian, were correct.If a problem exists with this LW result, then there is really only one place where it can arise: in the initial assumption; namely, that electromagnetic fields propagate like bullets shot at speed c .But this is the very same assumption that Einstein later formalized as his Second Postulate (1905,1907).He just called them "signals" rather than "fields".The LW idea of bullets shot at speed c is the foundation for Special Relativity Theory (SRT).(Indeed, SRT offers one of the modern ways to re-derive the LW results.)But SRT is also the foundation for General Relativity Theory (GRT).SRT and GRT together make one of the two great pillars of 20 th century Physics: Relativity Theory (RT).So questioning the LW assumption is not just questioning the LW results; it is questioning the founding assumption of SRT, and so threatening this whole pillar of 20 th century theory.Many people have just accepted that this is just 'the way things are' with classical field theory, and with SRT, and with all of relativity theory as well.But what if one wanted to describe the same scenarios in a thoroughly modern way, with photons instead of radiation fields, and virtual photons instead of Coulomb-Ampère fields?Could anyone really accept the idea that the real photons and the virtual photons created by the same space-time event would arrive at a detector from different directions?But one needn't accept any such thing, given the photon model in terms of Maxwell fields developed in Sect. 2. In short, since we have a model for photons in terms of fields, we should be able to reverse engineer a model for fields in terms of photons.So what does the photon model developed in Sect. 2 imply?Observe that the developing wavelet can move at speed c relative to the source, and the regressing wavelet can move at speed c relative to the receiver.Applying this idea can help to modify the LW results appropriately.
Updated formulae for scalar and vector potentials
Recall that with the photon model developed in terms of Maxwell fields in Sect.2, the life history of the photon has a symmetry point in the middle.Before the mid point of the propagation scenario, the waveform is developing, and after the mid point of the propagation scenario the waveform is regressing.That makes the mid point very important.So far as the receiver is concerned, nothing that happened before the midpoint affects the signal he receives.The source position and velocity information he receives is determined, not by the specification 'retarded', but rather by the specification 'half retarded'.With this new specification, the scalar and vector potentials become: The fields become: The Poynting vector (,) t Pr becomes: And the gifts of photon model in terms of EM fields go well beyond this rather arcane problem about field direction.The photon model in terms of EM fields eliminates the central mystery of Einstein's SRT: having just one light speed relative to however many different observers there may be.This is complexity at the level of 'multiplicity', much more daunting than the complexity at the level of the mere 'duality' that is found in modern QM.
EM fields within atoms
An noted in Sect.2, atoms were the really big problem for Maxwell's EMT.Now armed with some new information about EMT, it is appropriate the revisit the problem about atoms.We turn again to Hydrogen.From Sect. 3 can infer that at least two processes go on inside the Hydrogen atom, and we shall discover shortly that there are actually three.Only one is familiar.The other two challenge familiar concepts of 'conservation' that originally grew out of Newtonian mechanics.But electromagnetism is not Newtonian mechanics.In electromagnetic problems, the concepts of momentum and energy 'conservation' have to include the momentum and energy of fields, as well as those of matter.Momentum and energy can both be exchanged between matter and fields.'Conservation' applies only to the system overall, not to matter alone (nor to fields alone either).
Energy loss due to far-field radiation
The first process that occurs with the Hydrogen atom is the familiar energy loss from the atom due to far-field radiation.There will be a far-field power radiated (energy loss per unit time) of magnitude where means 'solid angle'.Because the full 4 of solid angle captures opposing directions of n , contributions to the integral from the vector visible in the integrand cancel out.Contributions to the integral that come from the dot product that is hidden in the 6 factor may not be zero at every moment, but they time-average to zero.So let us simplify the expression for far-field power radiated by setting to zero.We have: It evaluates to the well-known Larmor result:
Energy gain due to internal torquing
The second process that occurs in the Hydrogen atom is a not previously noticed energy gain due to internal torquing.This process occurs because the Coulomb force within the atom is not central; it is along half retarded n , and not along T is the magnitude of the torque on the electron, given by eee TrF where e r is the electron orbit radius, and e F is the tangential force on the electron.But that is not all.The proton also orbits at frequency e , and experiences its own torque, given by ppp TrF , where p r is the proton orbit radius (tiny) and p F is the tangential force on the proton (huge), with the result that the magnitude p T is the same as e The existence of such a process is why the concept of 'balance' emerges: there can be a balance between gain of energy due to internal torquing and the inevitable loss of energy due to radiation.But we are not done with radiation yet.
Extra radiation due to Thomas rotation
The fact that the electron and the proton have such different masses, and orbit at such different radii, means that the EM forces within the atom are not only not central; they are not even balanced.This situation has another major implications: The system as a whole experiences a net force.That means the system center of mass (C of M) can move.This sort of effect does not occur in Newtonian mechanics due to the fact that Newtonian mechanics assumes infinite signal propagation speed.
Looking in more detail, the unbalanced forces in the Hydrogen atom must cause the C of M of the whole atom to traverse its own circular orbit, on top of the orbits of the electron and proton individually.This is an additional source of accelerations, and hence of radiation.It evidently makes even worse the original problem of putative energy loss by radiation that prompted the development of QM.But on the other hand, the torque on the system is a candidate mechanism to compensate the rate of energy loss due to radiation, even if there is a lot more radiation than originally thought..The details are worked out quantitatively as follows.First ask what the circulation can do to the radiation.Some 20 years after the advent of SRT, a relevant kinematic truth about systems traversing circular paths was uncovered by L.H. Thomas (1927), in connection with explaining the then anomalous magnetic moment of the electron: 1/2 its expected value.He showed that a coordinate frame attached to a particle driven around a circle naturally rotates at half the imposed circular revolution rate.Applied to the scenario of the electron orbiting the proton, the gradually rotating , xy coordinate frame of the electron means that the electron sees the proton moving only half as fast as an external observer would see it.That fact explained the electron's anomalous magnetic moment, and so was received with great interest in its day.But the fact of Thomas rotation has since slipped to the status of mere curiosity, because Dirac theory has replaced it as the favored explanation for the magnetic moment problem.Now, however, there is a new problem in which to consider Thomas rotation: the case of the C of M of a whole Hydrogen atom being driven in a circle by unbalanced forces.In this scenario, the gradually rotating local , xy coordinate frame of the C of M means that the atom system doing its internal orbiting at frequency e relative to the C of M will be judged by an external observer to be orbiting twice as fast, at frequency e 2 relative to inertial space.This perhaps surprising result can be established in at least three ways: 1) by analogy to the old electron-magnetic-moment problem; 2) by construction from e in the C of M system as the
Unification of physics via Planck's constant
In conventional QM, ep rr is expressed in terms of Planck's constant h , which is presumed to be a fundamental constant of Nature: Here is the so-called 'reduced mass', defined by Joule-sec.This reasonable degree of closeness suggests that Planck's constant may reasonably be considered a possible function of other fundamental constants of Nature, and so not itself an independent fundamental constant of Nature.Or the situation may reasonably be considered the other way around: that some other fundamental constant of Nature is really a function of Planck's constant.Either way, we would have one less independent fundamental constant of Nature, and that would mean one more degree of unification among the different branches of physics.But of course, the expression for h developed here can fulfill such aspirations only if the theory being developed can do a great deal more than just match the ground state of Hydrogen.Worthy targets for additional work include: anticipating the story for isotopes of Hydrogen, anticipating from there what happens with other elements, explaining the excited states of Hydrogen and their resulting spectral lines, anticipating from there the spectral features of some other elements, and characterizing the behavior of the full database on ionization potentials of all elements, and much more.It all constitutes a developing research area that I refer to as 'Algebraic Chemistry'.
Larger nuclear mass
The negative energy of the electron in the ground state of the Hydrogen is This is the energy that would have to be provided to liberate the electron, or ionize the atom: the 'ionization potential'.Eq. ( 16) provides the basis from which to build corresponding expressions for other entities.
For example, the extension to Deuterium and/or Tritium requires that the proton mass p m be replaced with a more generic nuclear mass M , and that p r be replaced by M r .Then we have for the ionization potential of this more massive system:
Arbitrary nuclear charge
The extension of the model to a neutral atom with nuclear charge number Z involves Z electrons as well.To develop the mathematical model, we must return to the expressions for torquing P and total radiated P , Eqs. (10) This scaled-up expression represents the magnitude of the total ionization potential of the system involving Z protons and Z electrons.What is then comparable to the ionization potential for removing a single electron is: Thus in the math we find a / ZM scaling law.What do we find in the actual data?Something much more complicated, and indeed so complicated that we would be unlikely ever to figure it out without the clue that / ZM is part of the story.The involvement of M means the involvement of isotopes, and unwanted complexity.So the clue tells us to look at ionization potentials, not in raw form, but scaled by / M Z , to remove the / ZM factor that the math anticipates.Figure 2 shows the pattern found.Seven orders of ionization are included.There is a fascinating, but lengthy, story about ionization orders 2 and up; see Whitney (2012).The part of it that will be most important for the present development is obvious from Fig. 2: the energy required to completely strip the atom scales with 2 Z . .The increment arises from interactions just between the electrons, quite apart from the nucleus.The electron-onelectron increments are very regular in their behavior.First of all, every period exhibits a general rise, and by the same factor of 7/2.Second, there is a general drop from one period to the next, for the first three periods, and all by the same factor of 7 / 8 .Then within periods, there is a very regular pattern.There are sub-period rises keyed to the traditional 'angular momentum' quantum number l , and to a non-traditional parameter N that goes 1,2,2,3,3,4,4 for periods 1 through 7 , and gives the number of elements in a period as 2 2N .For 0 l , we have: incremental rise total rise fraction , and The following The scaled ionization potentials are called IP 's.They are meant to be 'population generic'; that is, the information they contain concerning one element can be applied to a calculation about another element in a different state of ionization, or excitation, by applying the / ZM appropriate for the second element and its state.
Unequal counts for electrons and protons
Let us first consider ionization sates.These are important for applications in Chemistry, since chemical reactions involve ions.With all this regularity displayed in Fig. 1, it should be possible to use it to help predict the energy budget for all sorts of chemical reactions.We just need a rational way to extrapolate from all the formulae representing the regularities for single electrons being removed from neutral atoms to formulae for electrons being removed from, or added to, ions of all sorts.Generally, if an atom is in an ionized state, then in place of just Z we have an electron count e Z distinct from the proton count p Z .The electron-on-electron interaction does not involve the nucleus, and so always scales with e / ZM .But electron-nucleus interaction previously represented by 1,1 (/ ) ZM I P now has to involve both e Z and p Z .We have for the total system 22 2 5 pe e pe e () 32 What is then generally comparable to the nuclear-orbit part of the ionization potential for removing a single electron?To develop an answer to this question, we must return again to the expressions for torquing P and total radiated P , Eqs. ( 10 () 32 Thus for ions, we see in the math a pe p () ZZ MZ scaling law for that part of the ionization potential that reflects electron-nucleus interaction, 1,1 IP .So for computations we use: For the other part of the ionization potential, that reflecting just the electron-on-electron interactions, This basic information can help one to model the energy budget for any chemical reaction.
To assist readers who want to try this out, the necessary data displayed by Fig. 1 is tabulated in numerical form as Appendix 1 at the end of this Chapter.Here is one small example.Recall the comment about Fig. 1 that, for nuclear charge 2 Z and up, the energy required to completely strip the atom scales with 2 Z .The actual formula plotted on Fig. 1 eV's.We can now compare the total energy required to strip an atom one electron at a time with the energy required to strip it of its electrons all at once.The two elements Helium and Lithium are good examples because they represent the extremes of very high first-order ionization potential and very low first-order ionization potential.The data for them in numerical form comes from Appendix 1.Here is how the calculations go: Write Formulae: 22 He He : In these two examples, we see that removal of all the electrons, all at once, takes much more energy than removing the electrons one electron at a time.It is plain to see that total stripping all-at-once is a vigorous, even violent, event.It is the stuff of special-purpose laboratory or field investigation.By contrast, total stripping one-at-a-time is a gentle process.The one-at-atime process is an example of the stuff of ordinary production Chemistry.
Excited states -hydrogen
Now let us begin to consider excitation states.These are key for understanding emission or absorption spectra, a fabulously rich source of data about atoms.But atomic spectra are complicated.The standard way to begin to understand them is mathematically, from the family of solutions provided by the differential equation that Schrödinger postulated for the abstract wave function characterizing the electron in the Hydrogen atom.
The standard QM view is that the Hydrogen atom has multiple 'stable states', each with negative energy, E , determined largely by a principle quantum number 1, 2, 3...
. The idea is that the electron can reside in an upper state (1 n ), but only rather precariously, and when it teeters and falls back to the ground state (1 n ), a photon is emitted.But the Hydrogen atom has only two constituent particles, the electron and the proton, and thus very few classical degrees of freedom.That fact makes it difficult to imagine an infinite multiplicity of different 'states' that a Hydrogen atom could exhibit.We are left to ponder a mystery of mathematical QM.So it is tempting to try to develop an additional, more immediately physical, way of understanding the spectral complexity that we see.Consider the possibility that individual Hydrogen atoms may not, by themselves, actually have excited states.Instead, the term 'excited state' may be better applied to a system that involves several Hydrogen atoms.Key to this idea is that charges can form entities called 'charge clusters'.[Concerning charge clusters at the macro scale of laboratory experiments and field observations: see, for example, Beckmann (1990), Aspden (1990), Piestrup and Puthoff (1998).]Evidence concerning the probable existence of charge clusters at the micro scale of atoms is plainly visible in the data on IP 's (Fig. 1): some electron counts are very stable and hard to break apart (e.g.noble gasses), while some electron counts are very un-stable and hard to keep together (e.g.alkali metals).Why would electron counts matter so much if the electrons were not in deep relationships with each other?But how can electrons outwit electrostatic repulsion?Once given the clue that they evidently can do this, it becomes possible to imagine how they might do it.The key is that electrostatic repulsion dominates in a static situation.In a dynamic situation, electrons may move at speeds exceeding light speed (Remember, Sect. 3 cast doubt on the founding postulate of SRT, and SRT is all there is to forbid superluminal speeds.).If so, a repulsion signal from one electron may reach another electron only by the time the first electron has moved so much that the repulsion from its 'then' position has become the attraction to its 'now' position.In fact, multiple electrons can form circulating ring structures that are quite stable (for details, see Whitney 2012) i.e., the system orbital energy also scales with H n .This result is the same as if the atoms were isolated, instead of being organized into a big system with two charge clusters.This suggests that the energy available for generating photons by de-excitation isn't 'orbital' at all, but is instead the energy tied up in forming the charge clusters out of the multiple electrons and the multiple protons from the multiple Hydrogen atoms.What can we infer about such charge clusters?As in the modeling of IP 's for ions, we can again consider Fig. 1 as a source of information about electron clusters of sizes up to 118, quite apart from the particular element that the information is located with.From Fig. 1, It is clear that most of the IP 's are positive, meaning their electron clusters are hard to break.
So despite being made of same-sign charges, most of them exist in negative energy states.
The ones that are particularly hard to break are the ones associated with the noble gasses: 10, 18, 36, 54, 86, (118) .These elements are at the ends of periods on the periodic table, and the lengths of the periods themselves are: 2, 8, 8, 18, 18, 32, (32) .(Parentheses mean we haven't discovered, or created, that element yet.)The implication is that excited states of Hydrogen existing in the form of 'super Hydrogen' would most frequently exist with H 2, 8, 18, 32, ... n Can we anticipate what would happen when any such excited state de-excites?Suppose we started with H 32 n .It could, for example, decompose into 18, 8, 2, 2, and 1, 1; i.e. some less excited states and a couple of ground-state atoms; 6 daughter systems in all.Suppose that for every such daughter produced, there is a photon released.Exactly how might that work?Observe that four daughters are in states that are even more negative than the starting state, so those are no problem.But two daughters are in the ground states, which is not more negative than the starting state.So energy from the other daughters has to be enlisted to create any photons there.For any H n , there may be a de-excitation path, or paths, for which the energy budget is insufficient, in which case those paths won't be taken.There may also be de-excitation paths for which the energy budget is more than sufficient, in which case there will be, not only spectral radiation, but also a bit of heat radiation.Very rarely, there might be a de-excitation path for which the energy budget is just exactly right.The spectral lines that occur with Hydrogen (or any element) are typically characterized in part by differences in inverse square integers.The integers involved are traditionally understood in terms of the familiar radial quantum number n .Is it possible to understand them also in terms of the H n used here?Recall that if one then chooses to model the behavior of Hydrogen 'excitation' in terms of a single Hydrogen atom with discrete radial states identified with the radial quantum number n , then the orbit-radius scaling has to be the quadratic scaling 1 r .So H n actually does encode something that is quadratic, namely the 2 N , and is therefore similar to the quadratic 2 n .
Beyond both hydrogen and ground states: Spectroscopy
In spectroscopy, we observe light created when an atomic system relaxes in some way.For elements beyond Hydrogen, the spectral lines that occur are often characterized in part by the so-called Rydberg factor: The R is traditionally interpreted as the energy needed for total removal of one electron from the ground state to infinity, leaving an ion.The energy needed for an electron to get from a state labeled 1 n to a higher state labeled 21 nn , and conversely the energy released when it goes back to 1 n , is then modeled as Observe that R contains a factor of 2 Z , just like the IP 's for total ionization, , ZZ IP of Eq. ( 25) do.That means R is referring to the absolutely largest photon energy that the system could ever possibly be imagined deliver: starting from a state of total ionization, i.e. a naked nucleus, and having the entire electron population return in one fell swoop, with the emission of just one photon for the whole job.That scenario could never actually happen.One-at-a-time electron return is the only plausible return scenario.The inverse square integers in the square bracket bring E down to values appropriate for one-at-a-time scenarios.
Observe that the Rydberg model for spectral lines already conflicts with an older model for the atom developed from the PT; i.e., electron 'shells' enclosing the nucleus, inner shells filled, and at most one outer shell unfilled; partially filled for most elements, and completely filled for noble gasses.ZM , would be included.Now consider that spectral lines might not to arise from de-ionizing one ion of one atom, but rather from de-exciting a system involving multiple neutral atoms.In this description, the 1 n and 2 n are not identifiers of different states of one atom, but rather numbers of atoms organized into super atoms.Otherwise, nothing really changes.However we interpret their meaning, the predicted spectral lines remain the same.
Unification between Newton and Maxwell
This last technical Section of this Chapter returns to the first physics disunity mentioned in the Introduction: the seemingly different coordinate-transformation properties of Newton's Laws for mechanics and Maxwell's equations for electrodynamics.Newton's laws are form invariant under Galilean transformations.But Maxwell's equations are generally thought to be form invariant only under Lorentz transformations.Especially, they are thought to be not form invariant under Galilean transformations.So a curious situation exists within physics today.It is generally expected that the equations of physics should be tensor equations.By definition of the word 'tensor', a tensor equation is form invariant under arbitrary changes of reference frame, assuming no singularities or other cruel and unusual circumstances in the transformation or its inverse transformation.That means a tensor equation should be form invariant under arbitrary, though reasonably well-behaved, space-time transformations.So, are Maxwell's equations really tensor equations?Or not?Mathematicians have good reason to challenge the believed tensor status of Maxwell's equations, while physicists have good reason to challenge the believed requirement for invariance under anything other than Lorentz transformation.But the situation is not generally acknowledged.It is the proverbial 'elephant in the living room'.Clarifying this situation can assist physics in becoming more unified from its beginning to its present.And mathematics has lots of applicable tools; see Kiein (2009).The present work offers an approach that is also mathematical, but a lot more elementary.Maybe it will communicate to different readers.The problem, I believe, is of a type with which QM has some history.QM appears to be the first branch of physics that well and truly needed complex numbers.They may have been used in physics before QM, but they were only one of the tools available for the problems then at hand.Sines and cosines could generally handle any problem just as well as complex exponentials could handle it.But with QM, complex exponentials became truly essential for doing physics.The history of mathematics has been a tale of increasing range of objects included in the discussion.It began with real, positive integers; it grew with the inclusion of zero and negative integers, and grew again with the inclusion of all rational numbers, and again with the inclusion of all irrational numbers.Then it grew with the inclusion of imaginary numbers, thus creating complex numbers.This was the first of a number of 'doublings' of the number of dimensions attributed to mathematical objects.[See Rowlands (2007).]After complex numbers, we got quaternions, and bi-quaternions, or octonians, and there is no reason to suppose that further doublings will not continue to prove useful.Complex numbers make possible operations that are not possible without them.Consider, for example, the square root of 3 .It cannot be evaluated within the real number system, but in the complex number system, it is just 3 i .I believe 'doublings' are generally like this: they make possible operations that were not possible without them.There appears to be today an opportunity for a doubling in the realm of tensor calculus.There are presently exactly two tensor-transformation behaviors identified, called 'contravariant' and 'covariant'.It appears that tensor calculus can be usefully extended through a doubling of the number of transformation behaviors that can be described, from two to four.It appears that such a doubling can resolve the apparent conflict between Newtonian and Maxwellian physics: it can make possible a display showing how Maxwell's equations can actually be form invariant under arbitrary coordinate transformations.
The opportunity offered by tensor notation
The display of four transformation behaviors requires the use of four tensor index positions.So in addition to the usual contravariant (index up-right) and covariant (index down-right) positions on the right side of a tensor symbol, we need to us the positions available on the left side: index up-left and index down-left.Since left-side index positions have not been in used in this new way before, they need new names designed for the purpose.To recall the move from right to left, let us use the prefix 'trans'.So let the up-left index position be called 'transcontravariant', and let the down-left index position be called 'transcovariant').All the transformations are describing what happens to tensor merates when the frame of reference changes; i.e. when the basis unit vectors defining the frame of references are replaced with other basis unit vectors.The transformations discussed here are arbitrary within the specifications that make the connections between reference frames reasonably well behaved; the individual relationships are differentiable and reversible, the matrix representations of them are invertible and unimodular.I mention both tensors and matrices because they are equivalent notation schemes that can be used interchangeably for describing systems of linear equations.Tensor notation is useful for making a compact statement of a whole mathematical situation.Matrix notation is useful for separating a whole mathematical situation into constituent parts for calculations.Individual linear equations are useful for focusing on individual parts of the mathematical problem.Human beings do have strong personal preferences about which approach to use, but all of these approaches should agree on the basic facts of a given situation, so any of these approaches should be acceptable.In the present work, all approaches will be used.That way, everyone can find something to like, and everyone can find something to dislike!In the case of the matrix displays and the linear equations, the presentation does save a little space by ignoring two spatial dimensions and focusing on one spatial dimension (call it 1) and the temporal dimension (call it 0).
Transformation of a contravariant object
The most familiar transformation is the contravariant one.The prefix 'contra' means these tensor merates change opposite to the way the basis unit vectors of the reference frame change.For an arbitrary input vector X , the transformation reads where we see the transformation as partial derivatives of coordinates, new with respect to old.Equivalently XT X , where we see the transformation written as the tensor T .
Also equivalently, we have , where we see everything, the input and output vectors and the transformation, in matrix format.Or equivalently, we have
RR
Observe that the R matrix is transposed from what it would need to be to make the RT matrix product collapse to the identity.So the inner product XX is generally not preserved if we do not have space-time symmetry.
Transformations for objects of four types
In order to recover the general availability of preserved inner products, the two additional transformation behaviors are defined.The transcovariant transformation is defined as the transposed inverse of the contravariant one.The transcontravariant transformation is defined as the transposed inverse of the covariant one.
Recall that this discussion began with the contravariant transformation written in the tensor The covariant, Observe that this Table uses negative signs on the arbitrary A and B in the contravariant and transcontravariant cases, positive signs in the covariant and transcovariant cases.This sign choice is used to help recall the prefixes 'contra' and 'co'.Observe too that if BA , we have space-time symmetry, which is the case of Lorentz transformations.And observe finally that if 0 B , we have universal time, which is the case of Galilean transformations.But A and B are arbitrary, and so can also represent other transformations as yet unnamed.
Transformations for invariant objects
The underlying purpose of tensor calculus is to focus on mathematical objects that are 'coordinate free', or 'frame independent', or 'invariant' (whether in form or in numerical value), -all expressions meaning that coordinate transformation does not change anything fundamental about an object so-described: values of scalars, or relationships expressed as equations involving tensors.The user of tensor calculus expects certain behaviors.There should be number invariant inner products of vectors and of higher-order tensors.The 'unity', or 'Kronecker delta' is not presently regarded as a real tensor, but can be accepted as one if it can be demonstrated number invariant.Finally, the user will certainly expect a number invariant 'metric tensor', the essential tool for manipulating index positions to develop tensor equations.Displaying that all these expectations can be met in the case of arbitrary transformations, not just Lorentz transformations, is the objective of this Sub-Section.The matrix notation is useful in checking out the transformation of all these entities.For example, the preserved inner product of a vector X with itself looks like (note the transpositions for operating on row vectors): The more familiar inner product XX is preserved with Lorentz transformations, but not with arbitrary transformations.So it shouldn't be considered any kind of 'invariant'.The same is true of the unfamiliar ( )( ) With the extended tensor notation, we can identify the index positions that definitely make a number invariant Kronecker delta.It looks like (note the transpositions for operating on row vectors): The more familiar is preserved with Lorentz transformations, but not with arbitrary transformations.That is why it does not qualify as a tensor.The same is true of the unfamiliar .Some readers will be surprised to see the present argument using the Lorentz metric, 1 0 0 1
, without accepting a limitation to Loentz transformations.It is widely supposed that the Lorentz metric requires Lorentz transformations, and/or Lorentz transformations require the Lorentz metric.But such a connection is not in fact mandatory.
The generally preserved forms of the Lorentz metric tensor look like (note the transpositions for operating on row vectors): and The more familiar g and g are preserved with Lorentz transformations, but not with arbitrary transformations.They shouldn't be considered any kind of 'invariant'.The same is true of the unfamiliar g and g .
The number invariant g and g can function to raise and lower indices on objects.For example, () One can also write additional index assignments for g .Altogether, there are The bottom line is this: to be sure of invariance under arbitrary transformation, not just Lorentz transformation, always contract a regular index with a trans index.
General invariance for Maxwell's equations
Maxwell's equations in current tensor notation read: The two-index F and D tensors refer to the electromagnetic field and the 'dual' thereof.The electromagnetic field tensor F has merates that are components of the threedimensional electric and magnetic field vectors, E and B .The D is the dual to F , whose merates are components of B and E .The one-index tensors J and refer to the source charge-current density vector and the differential operator vector.The indices and take the four values 0,1, 2, 3 .
The seeming limitation of Maxwell's equations to invariance only under Lorentz transformation arises entirely from the differential operator being written as a covariant vector.In the extended tensor algebra, this operator is identified as transcovariant, and then Maxwell's equations look like: Written this way, Maxwell's equations are manifestly form invariant, not only under Lorentz transformation, but also under any arbitrary (just well-behaved) transformation, including Galilean transformation.
Conclusions
About Maxwell's equations and photons: Photons have a life history that begins with emission as an electromagnetic pulse pulse, proceeds with development into a waveform, then changes into regression back to a pulse, and ends with absorption by a receiver.This life history of the photon can be modeled by imagining some mirrors that apply boundary conditions corresponding to the desired scenario, feeding a Gaussian pulse at the source to Maxwell's equations, watching Hermite polynomials then emerge, and then finally pile up at the receiver.
About EM signals and photons:
The life history of the photon suggests that the assumption upon which Einstein's SRT is founded is over-simplified.If we will make the founding assumption more realistic, then we will get more believable results.The more believable results can help us reconcile SRT with the QM of atoms.We can understand why Planck's constant occurs.It represents the balance between competing phenomena: on the one hand, energy loss due to radiation from accelerating charges; on the other hand, energy gain due to internal torquing within the atomic system due to finite speed of signal propagation.About Atoms: Viewed in the right way, chemical and spectroscopic data reveal a tremendous amount of regularity.So we are well enabled to interpolate and extrapolate for situations where actual data is not available.We can analyze scenarios where electrons are subtracted from or added to an atom, all at once, or one at a time; whatever we need.But take care: in the existing literature, the distinction between 'all-at-once' and 'one-at-a-time' is often obscure, so be careful.
About Maxwell and Newton:
There should have been no conflict between Maxwell's equations and Newton's equations over the issue of transformation invariance.Maxwell's equations are form invariant under Galilean transformations, just as they are form invariant under Lorentz transformations.Physics does not have conflicts.Only people have conflicts.
And people can resolve their conflicts.The conflict perceived in the case of Newton vs.
Maxwell is resolved with an extension of mathematical formalism.About Physics in General: This work has shown that SRT deserves a moment of caution, and the reader may reasonably worry that GRT deserves some caution too.So it may be premature to develop a theory of quantum gravity.Placing the QG capstone onto the RT and QM pillars of 20 th century physics may produce something that resembles the ancient constructions at Stonehenge, but not the Gothic cathedrals of Europe, much less anything modern.
Appendix 1. Numerical data on ionization potentials for all elements
Charge
Fig. 1 .
Fig. 1.A wavelet develops when an EM pulse is acted upon by Maxwell's equations.
fields are Coulomb-Ampère fields, and the Coulomb field does not lie along retarded n as one might naively expect; instead, the Coulomb field and the radiation are arriving to the observer from different directions.
to the electron is torquing ee PT , where e is the electron orbit frequency, and e Fig. 2. Ionization potentials, scaled by / M Z and modeled algebraically.With their / M Z scaling, all of the IP 's can be represented in terms of a baseline value equal to that of Hydrogen, 1,1 IP , and an increment is as if all factors of e changed to pe ZZe.Removal of one electron is then like removal of one pe ZZe charge.What is comparable to the ionization potential for removing a single electron from the ion is then
1 Standard formulae for scalar and vector potentials
So now, the Coulomb field and the Poynting vector are reconciled to the same direction.That is the first big gift from the photon model in terms of EM fields given in Sect. 2.
means the far field radiation power, if it really ever manifested itself in the far field, would be even stronger than classically predicted.The classical Larmor formula for radiation power from a charge e (e in electrostatic units) is That means the concept of torque vs. radiation does a fairly good job predicting the ground state of Hydrogen.
Table details the behavior fractional rises in First-order IP 's over all sub- The older PT-based model suggests shielding of the nucleus by the filled inner shells of electrons.But the occurrence of a 2 Z in R , even for large 1 RT .Applied to X , the reverse transformation R takes X back to X : The prefix 'contra' means reverse to the prefix 'co'.The covariant transformation goes the same way the basis unit vectors change.So the covariant transformation XC X This is because C operates on a covariant object, whereas, in its original definition, R operated on a contravariant object.The index switching makes no difference if we limit attention to transformations that are space-time symmetric, i.e.Lorentz transformations.But if we wish to investigate any other type of transformation, we have to investigate whether the switch makes a difference.
Table is organized for user convenience, with the position of information corresponding to the index position: upper right for contravariant, lower right for covariant, lower left for transcovariant, and upper left for transcontravariant.The index position assigned to an object determines the transformation law that it follows.Now let two arbitrary numbers with magnitude less than unity be represented by the letters A and B (chosen from the word 'arbitrary'!).Let the arbitrary numbers represent in turn the off-diagonal elements of transformation matrices.The following table shows the corresponding matrix notation: Further additional index assignments on g create entities that can serve to convert a regular index into a trans one, or a trans one into a regular one.None of these entities are number invariant, but in practice, that does not matter.The user does not convert just a single object; the user converts a whole tensor equation.The index-converting g entities typically occur in pairs, and the pairs contract to number invariant objects.When they don't occur in pairs, they do occur on both sides of an equation, and cannot affect the issue of equation form invariance. Another two of these of g 's are g and g Better Unification for Physics in General Through Quantum Mechanics in Particular 157 Better Unification for Physics in General Through Quantum Mechanics in Particular 159 www.intechopen.comwww.intechopen.com | 14,512.4 | 2012-02-24T00:00:00.000 | [
"Physics"
] |
Homogeneous Riemannian structures in dimension three
In this note, we determine all the homogeneous structures on non-symmetric three-dimensional Riemannian Lie groups. We show that a non-symmetric three-dimensional Riemannian Lie group admits a non-canonical homogeneous structure if and only if its isometry group has dimension four.
if there exists a (1, 2)-tensor field T on M such that where ∇ is the Ambrose-Singer connection given by ∇ = ∇ − T , ∇ is the Levi-Civita connection of the metric g, and R denotes the Riemannian curvature tensor for which we adopt the sign convention R(X , The difference tensor field T is said to be a homogeneous structure on M. T will also denote the associated tensor field of type (0, 3) given by T (X , Y , Z ) = g(T (X , Y ), Z ). Conditions (1) were further investigated by Tricerri and Vanhecke [11], who considered the space T (V) of such tensor fields on a vector space (V, , ) and decomposed it into three irreducible components under the action of the orthogonal group as T The subspaces of such decomposition are given as follows Homogeneous manifolds admitting a homogeneous structure in one of the eight different classes induced by the above decomposition have been extensively studied in the literature. It was shown in [11] that naturally reductive spaces correspond to non-vanishing homogeneous structures of type T 3 and that a Riemannian manifold admits a non-vanishing structure of type T 1 if and only if it is locally isometric to the real hyperbolic space. The later also holds true for homogeneous structures of type T 1 ⊕ T 3 , T / ∈ T 1 and T / ∈ T 3 , in dimension greater than three, as shown in [8]. Riemannian manifolds of dimension less or equal to four admitting a homogeneous structure of type T 2 were described in [5] (see also [2]). Homogeneous structures in the class T 1 ⊕ T 2 in dimension less or equal to four were described in [3], and those in this class whose fundamental 1-form is closed were investigated in [9]. It was shown in [5] that a three-dimensional non-symmetric space admitting a homogeneous structure of type T 3 also admits a T 2 -structure.
In dimension two T (V) = T 1 (V), and hence a surface admits a non-zero homogeneous structure if and only if it is isometric to the hyperbolic plane. Dimension three is particularly relevant in the study of homogeneous spaces. First of all, it is the lowest possible dimension admitting locally homogeneous metrics which are not locally symmetric and, secondly, any three-dimensional homogeneous manifold is either symmetric or locally isometric to a Lie group endowed with a left-invariant metric [10].
The special case when (M, g) is a Lie group G equipped with a left-invariant metric , is of special interest for our purposes. Let T ∇ be the canonical homogeneous structure defined by for left-invariant vector fields X , Y and Z . Then the corresponding Ambrose-Singer connection ∇ = ∇ − T ∇ satisfies ∇ X Y = 0 for left-invariant vector fields. This structure is equivalent to the description G = G/{e}, which corresponds to the action G × G → G.
On the basis of the above, the aim of this work is to clarify the classification of the homogeneous Riemannian structures in dimension three, giving all the possible ones in the non-symmetric case. The following result characterizes the non-symmetric Lie groups admitting more than one homogeneous structure. The explicit description of all homogeneous structures on non-symmetric Lie groups is given in Theorems 1.2 and 1.3 by considering separately the unimodular and non-unimodular cases.
We recall that a three-dimensional complete and simply connected manifold is naturally reductive if and only if it admits a non-vanishing homogeneous structure of type T 3 . In this case (M, g) is a real space form R 3 , S 3 or H 3 , or it is isometric either to the special unitary group SU (2), or to the universal cover of SL(2, R) or to the 3-dimensional Heisenberg group H 3 , endowed with a suitable left-invariant metric described in terms of the Lie algebra (up to rotations) by where {e 1 , e 2 , e 3 } is an orthonormal basis (see [11]). In this way, (M, g) is naturally reductive if and only if it is isometric to a Lie group endowed with a left-invariant metric whose isometry group is at least four-dimensional. Theorem 1.1 is thus connected to the following theorem by Meeks and Perez (see [6]): a simply connected, 3-dimensional Lie group with a left-invariant metric (G 1 , , 1 ) is isometric to a second Lie group (G 2 , , 2 ) such that is not isomorphic to G 1 if and only if its isometry group has dimension at least 4.
Summary of results
We study the unimodular and non-unimodular cases separately. The unimodular case is dealt with in Sect. 2, and the non-unimodular case is considered in Sect. 3. We show that the homogeneous Riemannian structures on a non-symmetric three-dimensional Lie group G equipped with a left-invariant metric are given as follows, from where the proof of Theorem 1.1 is obtained at once.
Unimodular Lie groups
Left-invariant Riemannian metrics , on unimodular Lie groups G were described by Milnor (see [7]) in terms of parameters (λ 1 , λ 2 , λ 3 ), so that the Lie algebra becomes (i) The three structure constants λ 1 , λ 2 , λ 3 are different and the only homogeneous structure is the canonical one, given by The canonical homogeneous structure is of type T 2 if λ 1 + λ 2 + λ 3 = 0 (see also [3]) and it is of type T 2 ⊕ T 3 otherwise. (ii) Up to a rotation, the structure constants λ 1 = λ 2 = λ 3 , λ 3 = 0 and there exists a one-parameter family of homogeneous structures which corresponds to the canonical structure for κ = 1 Unimodular Lie groups in Theorem 1.2-(ii) correspond to SU (2), SL(2, R) and H 3 with left-invariant metric as in (3), which contains the case of the homogeneous structures on Berger spheres previously considered in [4].
Non-unimodular Lie groups
Non-unimodular Riemannian Lie groups (G, , ) are semi-direct extensions R R 2 of the Abelian group. It was shown in [7] that there exist an orthonormal basis {e 1 , e 2 , e 3 } so that In this case the homogeneous structure is of type which is of the generic type T 1 ⊕ T 2 ⊕ T 3 .
(ii) If δα = 0, β = − αγ δ and α = δ, then the only homogeneous structure is the canonical one, given by Non-unimodular Lie groups in Theorem 1.3 are semi-direct extensions R R 2 of the Abelian Lie group determined by an endomorphism − ad(e 1 ). Assertion (i) in Theorem 1.3 corresponds to the special situation det ad(e 1 ) = 0, and they are isometric (although not isomorphically isometric) to a left-invariant metric on SL(2, R) as in (3) corresponding to Theorem 1.2-(ii) (cf. [6,11]). We emphasize that isometries between Riemannian Lie groups need not preserve the Lie group structure, since they are not necessarily realized by group isomorphisms, as evidenced in the above-mentioned situation. On the contrary, Lie groups in Theorem 1.3-(ii) correspond to the generic situation, where one may always specialize the orthonormal basis {e 2 , e 3 } to be given by eigenvectors of the self-adjoint part of ad(e 1 ) (cf. [7]).
Non-symmetric simply connected homogeneous three-dimensional Riemannian manifolds with four-dimensional isometry group are isometric to the unitary group SU (2), the universal cover of SL(2, R), or the Heisenberg group with the special metrics (3). It follows from the description of homogeneous structures in Theorems 1.2 and 1.3 that (see also [11]):
A non-symmetric three-dimensional Riemannian Lie group admits a homogeneous structure different from the canonical one if and only if the isometry group is fourdimensional.
Remark 1.4 A more conceptual proof of this last statement can be summarized as follows. For any three-dimensional Lie groups (G 1 , , 1 ) and (G 2 , , 2 ) equipped with a left-invariant Riemannian metric, it follows from Theorems 1.2 and 1.3 that the infinitesimal models associated to their canonical homogeneous structures are isomorphic if and only if (G 1 , , 1 ) and (G 2 , , 2 ) are isomorphically isometric (see [2]). Besides, any non-symmetric homogeneous three-manifold with four-dimensional isometry group admits more than one homogeneous structure. It follows from the work in [6, 10] that a homogeneous three-manifold with threedimensional isometry group is isometric to a unique Riemannian Lie group, in which case any homogeneous structure is isomorphic to the canonical one. A unimodular Lie group corresponding to a Lie algebra as above is locally symmetric if and only if the eigenvalues of the structure operator satisfy λ 1 = λ 2 = λ 3 = 0 (in which case the sectional curvature is constant and positive) or, up to a rotation, one has λ 1 = 0 and λ 2 = λ 3 (in which case the metric is flat).
Homogeneous structures on non-symmetric unimodular Lie groups
Let T be a (0, 3)-tensor field so that the connection ∇ = ∇ − T makes the metric tensor parallel, i.e., T xyz + T xzy = 0 for x, y, z ∈ g. Denoting by {e 1 , e 2 , e 3 } the dual basis of {e 1 , e 2 , e 3 }, then the tensor field T can be written as T = 2 i j<k T i jk e i ⊗ (e j ∧ e k ).
Therefore, the non-zero components of the connection ∇ = ∇ − T are given by while the (0, 4)-curvature tensor field is determined by Let R ik j ;r = ( ∇ e r R)(e i , e j , e k , e ). A straightforward calculation using Eqs. (4) and (5) shows that the condition ∇ R = 0 in Eq. (1) is given by Next, depending on the eigenvalues λ i , we are led to the following two possibilities.
Case of two different eigenvalues
In this case, without loss of generality, we can assume λ 1 = λ 2 = λ 3 . Moreover, λ 3 = 0 since the space would be locally symmetric otherwise. Thus, Eq. (6) implies Let T i jk;r = ( ∇ e r T )(e i , e j , e k ). A straightforward calculation using Eqs. (4) and (9) In the particular case where κ = 1 2 (2λ 1 −λ 3 ) it corresponds to the canonical structure. Finally, a direct calculation shows that the projections of these structures are such that p 1 (T ) = 0 and
Homogeneous structures on non-symmetric non-unimodular Lie groups
If g is non-unimodular then there exists an orthonormal basis {e 1 , e 2 , e 3 } of g such that (see [7]) where α + δ = 0 and αγ + βδ = 0. A straightforward calculation shows that a non-unimodular Lie group corresponding to a Lie algebra above is locally symmetric if and only if it is of constant negative sectional curvature (which corresponds to the cases when ad(e 1 ) is a multiple of the identity or it has complex eigenvalues), or it is locally isometric to a product R × N (c), where N (c) is a surface of constant negative sectional curvature (if ad(e 1 ) is of rank-one and {e 2 , e 3 } is an orthonormal basis of eigenvectors). | 2,773.4 | 2023-02-19T00:00:00.000 | [
"Mathematics"
] |
Dynamics and Development of the COVID-19 Epidemic in the United States: A Compartmental Model Enhanced With Deep Learning Techniques
Background: Compartmental models dominate epidemic modeling. Transmission parameters between compartments are typically estimated through stochastic parameterization processes that depends on detailed statistics of transmission characteristics, which are economically and resource-wise expensive to collect. Objective: We aim to apply deep learning techniques as a lower data dependency alternative to estimate transmission parameters of a customized compartmental model, for the purpose of simulating the dynamics of the US coronavirus disease (COVID-19) epidemic and projecting its further development. Methods: We constructed a compartmental model and developed a multistep deep learning methodology to estimate the model’s transmission parameters. We then fed the estimated transmission parameters to the model to predict development of the US COVID-19 epidemic for 35 and 42 days. Epidemics are considered suppressed when the basic reproduction number (R0) is less than 1. Results: The deep learning–enhanced compartmental model predicts that R0 will fall to <1 around August 17-19, 2020, at which point the epidemic will effectively start to die out, and that the US “infected” population will peak around August 16-18, 2020, at 3,228,574 to 3,308,911 individual cases. The model also predicted that the number of accumulative confirmed cases will cross the 5 million mark around August 7, 2020. Conclusions: Current compartmental models require stochastic parameterization to estimate the transmission parameters. These models’ effectiveness depends upon detailed statistics on transmission characteristics. As an alternative, deep learning techniques are effective in estimating these stochastic parameters with greatly reduced dependency on data particularity. (J Med Internet Res 2020;22(8):e21173) doi: 10.2196/21173
The COVID-19 pandemic is still in progress, and most of the noticeable early research is descriptive in nature, focusing on reported cases to establish the baseline demographic parameters for the disease such as age, gender, health, and medical conditions in addition to the disease's clinical manifestations, in a Chinese context. These studies include reports on demographic characteristics, epidemiological and clinical characteristics, exposure and travel history to the epicenter, and illness timelines of laboratory-confirmed cases [1][2][3][4][5] as well as epidemiological information on patients from social networks and local, national, and international health authorities [6]. The spread of SARS-CoV-2 outside China (eg, Iceland) is also analyzed [7], albeit to a limited extent. Concerned about the worsening situation in New York City, researchers have characterized information on the first 393 consecutive patients with COVID-19 admitted to 2 hospitals in the city [8].
Some stage-specific studies on patients with COVID-19 have also been carried out, including a single-centered, retrospective study on critically ill adult patients in Wuhan, China [9] and a retrospective, multicenter study on adult laboratory-confirmed inpatients (≥18 years of age) from 2 Wuhan hospitals, who have been discharged or have died [10].
The aim of this paper is to establish a class of extended COVID-19 compartmental models, for which the transmission parameters are estimated by a multistep, multivariate deep learning methodology.
COVID-19 Epidemic Modeling
There have been attempts to model the COVID-19 epidemic dynamics. These studies add a worldwide mobile dimension, reflecting a higher level of mobility and globalization in 2020 than in 2003 (SARS) and even 2013 (MERS). The SEIR (Susceptible-Exposed-Infectious-Recovered) model is used to infer the basic reproduction ratio and simulate the Wuhan epidemic [11]; it considers domestic and international air travel to and from Wuhan to other cities to forecast the national and global spread of the virus. More sophisticated models have also been developed to correlate risk levels of foreign countries with their travel exposure to China [12,13], including a stochastic dual-SEIR approach on both the Wuhan population and international travelers, to estimate how transmission varied over time from Wuhan to international destinations [13]. Simulations on the international spread of the COVID-19 after the start of the travel ban from Wuhan on January 23, 2020, have also been conducted [14], which apply the Global Epidemic and Mobility Model to a multitude of Chinese and international cities, and a SEIR variety (SLIR, Susceptible-Latent-Infectious-Recovered) to project the impact of human-to-human transmissions. To simulate the transmission mechanism itself, a Bats-Hosts-Reservoir-People network is developed to simulate potential transmission from the infection sources (ie, bats) to humans [15].
Since March 2020, with the COVID-19 outbreak winding down in China, researchers have dedicated more efforts to analyzing the effectiveness of containment measures. Mobility and travel history data from Wuhan are used to ascertain the impact of the drastic control measures implemented in China [16]. A study investigated the spread and control of COVID-19 among Chinese cities, using data on human movements and public health interventions [17]. Using contact data for Wuhan and Shanghai and contact tracing information from Hunan Province, a group of researchers built a transmission model to study the impact of social distancing and school closure [18].
Theoretical Foundation
Compartmental models dominate epidemic modeling on COVID-19 epidemics (and previous coronavirus outbreaks), and they require detailed statistics on transmission characteristics to estimate the stochastic transmission parameters between compartments. Essentially, these models correlate factors such as geographic distances and contact intensities among heterogeneous subpopulations with gradient probability decay. Technically, transmission parameterization applies Bayesian inference methods such as Marcov Chain Monte Carlo or Gillespie algorithm [19] simulations to form probability density functions on a cross-section in order to estimate parameters for each timestep of a multivariate time series construct. These detailed statistics on transmission characteristics are economically and resource-wise expensive to collect.
We are particularly interested in extended compartmental models that cover multiple interconnected and heterogeneous subpopulations [10,15,20]. There are also some pure time series analyses on epidemic dynamics outside of mainstream compartmental modeling, for example, the AutoRegressive Integrated Moving Average approach [21] that is typically found in financial applications. Such analyses provide another perspective.
We developed a multistep, multivariate deep learning methodology to estimate the transmission parameters. We then fed these estimated transmission parameters to a customized compartmental model to predict the development of the US COVID-19 epidemic.
We established a SEIR-variety discrete time series on a daily interval as the theoretical foundation for a deep learning-enhanced compartment model. We started with the construction of a so-called SEIRQJD (SEIR-Quarantined-Isolated-Deceased) model ( Figure 1). (S) to Exposed (E) if Exposed (E) is reported directly, or Susceptible (S) to Infectious (I) if Exposed (E) is not reported directly; σ I , σ Q : from Exposed (E) to Infectious (I) and Quarantined (Q), respectively; κ I : from Quarantined (Q) to Infectious (I); γ J , γ R , γ D : from Infectious (I) to Isolated (J), Recovered (R) and Deceased (D), respectively; υ R , υ D : from Isolated (J) to Recovered (R) and Deceased (D), respectively.
We used the US COVID-19 epidemic datasets from John Hopkins University Center for Systems Science and Engineering (JHU CSSE) Github COVID-19 data depository, which does not include directly Exposed (E) and Quarantined (Q) data, and therefore, we set all transmission parameters to and from the "E" and "Q" compartments (σ I , σ Q , κ I ) to 0. Furthermore, the datasets assume that all deaths arise from the isolated population (J); thus, we also set the transmission parameter from Infectious (I) to Deceased (D), γ D , to 0. We then simplified the SEIRJD model to a SIRJD (Susceptible-Infectious-Recovered-Isolated-Deceased) construct, in which a population is grouped into 5 compartments: The SIRJD model has a daily (Δt=1) multivariate time series construct given by the follow matrix form: or The Greek letters in the time series are transmission parameters defined in the state diagram in Figure 1. Essentially, all these parameters are stochastic.
Since we need to estimate the transmission parameters, we can rewrite and rearrange Equations (1) and (2) The JHU CSSE dataset has an almost precise period of 7 days (±1 day), indicating that a majority of the reporting agencies in the country choose to update their respective statistics on a weekly, fixed-calendar interval. We ran a 7-day moving average on the dataset to smooth out this "unnatural" data seasonality.
Methodology
We then conducted the following step-by-step operations to model the US epidemic: 1. We constructed an in-sample SIRJD time series starting from April 12, 2020, with Dataset 1. 2. We used the in-sample SIRJD time series constructed in Step 1 to come up with an in-sample time series for the 2 most critical daily transmission parameters (β and γ R ). 3. We constructed a confirmed/dead-case time series starting from January 22, 2020 (in-sample time series), with Dataset 2. 4. We applied 2 deep learning approaches-the standard deep neural networks (DNN) and the advanced recurrent neural networks-long short-term memory (RNN-LSTM)-to fit the confirmed/dead in-sample time series from Step 3 and predict the further development of confirmed/dead cases for 35 and 42 days (out-of-sample time series). 5. We use the confirmed/dead in-sample time series from Step 3 as training data and the in-sample β and γ R time series from Step 2 as training label. We then applied the DNN and RNN-LSTM techniques to predict β and γ R for 35 and 42 days (out-of-sample time series). 6. Finally, we used the predicted (out-of-sample) transmission parameters (β and γ R ) from Step 5 to simulate 35-and 42-day progressions (out-of-sample time series) of the SIRJD model (particularly the SIR portion) in a recursive manner, starting with the data point of the last timestep from the in-sample SIRJD time series from Step 1.
Results
The results based on data up to July 31, 2020, are illustrated in Figures 3-6 for the 35-day forecast and Figures 7-10 for the 42-day forecast.
In Figure 3 (35-day forecast), the DNN method predicts that on August 19, 2020, the "Infected-to-Recovered" transmission parameter γ R will rise and stay above the "Susceptible-to-Infected" transmission parameter β. This means that the value of the basic reproduction rate, R 0 , will fall to <1 and that the spread of COVID-19 in the United States will effectively end on that day. In Figure 4 (35-day forecast), the RNN-LSTM method gives a slightly more aggressive prediction that γ R will overtake β on August 17, 2020. Thus, with the 35-day forecast, we predict that the tide of the US epidemic will turn around the August 17-19, 2020, timeframe. and Gamma_R is the "Infected-to-Recovered" transmission parameter (γ R ) for the in-sample (observed) data. Beta_fo is the forecasted β and Gamma_R_fo is the forecasted γ R for the out-of-sample (forecasted) data.
Figure 4.
Transmission parameter estimations (recurrent neural networks-long short-term memory) for 35 days. Beta is the "Susceptible-to-Infected" transmission parameter (β) and Gamma_R is the "Infected-to-Recovered" transmission parameter (γ R ) for the in-sample (observed) data. Beta_fo is the forecasted β and Gamma_R_fo is the forecasted γ R for the out-of-sample (forecasted) data.
In Figure 5 (35-day forecast), the DNN method predicts that the US "Infected" population will peak on August 18, 2020, at 3,267,907 individual cases. In Figure 6 (35-day forecast), the RNN-LSTM method predicts that the US "Infected" population will peak on August 16, 2020, at 3,228,574 individual cases.
For the 35-day forecast, the deep learning methods predict that the number of accumulative confirmed cases will cross the 5 million mark on August 7, 2020, at 5,007,479 cases by DNN ( Figure 5) and at 5,002,100 cases by RNN-LSTM ( Figure 6). In Figure 7 (42-day forecast), the DNN method also predicts (same as 35-day forecast) that γ R will overtake β on August 19, 2020. In Figure 8 (42-day forecast), the RNN-LSTM method gives exactly the same prediction, that R 0 will fall to <1 on August 19, 2020. and Gamma_R is the "Infected-to-Recovered" transmission parameter (γ R ) for the in-sample (observed) data. Beta_fo is the forecasted β and Gamma_R_fo is the forecasted γ R for the out-of-sample (forecasted) data.
Figure 8.
Transmission parameter estimations (recurrent neural networks-long short-term memory) for 42 days. Beta is the "Susceptible-to-Infected" transmission parameter (β) and Gamma_R is the "Infected-to-Recovered" transmission parameter (γ R ) for the in-sample (observed) data. Beta_fo is the forecasted β and Gamma_R_fo is the forecasted γ R for the out-of-sample (forecasted) data.
In Figure 9 (42-day forecast), the DNN method predicts that the US "Infected" population will peak on August 18, 2020, at 3,275,304 individual cases. In Figure 10 (42-day forecast), the RNN-LSTM method predicts that the US "Infected" population will peak on August 18, 2020, at 3,308,911 individual cases.
For the 42-day forecast, the deep learning methods predict that the number of accumulative confirmed cases will cross the 5 million mark on August 7, 2020, at 5,008,504 individual cases by DNN ( Figure 9) and 5,014,608 individual cases by RNN-LSTM (Figure 10), which are consistent with the 35-day forecasts.
Discussion
In this study, we applied DNN and RNN-LSTM techniques to estimate the stochastic transmission parameters for an SIRJD model with a discrete time series construct. We then used the SIRJD model to forecast further development of the US COVID-19 epidemic.
We used two US COVID-19 datasets from the JHU CSSE data depository. The first dataset includes detailed daily records (confirmed, active, dead, recovered, hospitalized, etc) starting from April 12, 2020, from which we constructed the SIRJD model. The second dataset includes time series tracked confirmed and dead cases starting from January 22, 2020, which we used to construct training data for deep learning. The JHU CSSE data have an almost precise period of 7 days (±1 day) that masks the true epidemic dynamics; thus, we ran a 7-day moving average on the dataset to smooth out this data seasonality.
We then applied DNN and RNN-LSTM deep learning techniques to fit the confirmed/dead series to predict the further development of confirmed/dead cases as well as to predict the "Susceptible-to-Infected" and "Infected-to-Recovered" transmission parameters (β and γ R ) for 35 and 42 days. Finally, we used the predicted transmission parameters (β and γ R ) to simulate the epidemic progression for 35 and 42 days.
With data up to July 31, 2020, the deep learning implementations predicted that the basic reproduction rate (R 0 ) will fall to <1 around August 17-19, 2020, for the 35-day forecast and around August 19, 2020, for the 42-day forecast, at which point the spread of the coronavirus will effectively start to die out.
Implementations for the 35-day forecast predict that the US "Infected" population will peak around August 16-18, 2020, at 3,228,574 to 3,267,907 individual cases. The implementations for the 42-day forecast predict that the peak will occur on August 18, 2020, at 3,275,304 to 3,308,911 individual cases. All implementations indicate that the number of accumulative confirmed cases will cross the 5 million mark around August 7, 2020.
The 42-day forecasts provide a wider range of time and numbers than the 35-day forecasts, because for the same training data size, a longer forecast produces wider probability distributions.
With the introduction of the deep learning-enhanced compartmental model, we provide an effective and easy-to-implement alternative to prevailing stochastic parameterization, which estimates transmission parameters through probability likelihood maximization or Marcov Chain Monte Carlo simulation. The effectiveness of the prevalent approach depends upon detailed statistics on transmission characteristics among heterogeneous subpopulations, and such statistics are economically and resource-wise expensive. On the other hand, deep learning techniques uncover hidden interconnections among seemly less-related data, reducing the prediction's dependency on data particularity. Future research on the usefulness of deep learning in epidemic modeling can further enhance its forecasting power. | 3,563 | 2020-06-07T00:00:00.000 | [
"Medicine",
"Computer Science",
"Mathematics"
] |
Speaking Skill’s Language Anxiety Experienced by Freshers of English Language Education Department in Islamic Private University
The aims of this study is to find out the language anxiety levels encountered by the freshmen of English Language Education Department, the reasons of the language anxiety, and how the students cope with the language anxiety. It is a mixed-method study conducted in an Islamic private university in Malang. The population included 128 English Language Education Department freshmen in the academic year 2019/2020. Through convenience sampling, 32 students from six speaking classes were obtained. A survey using Foreign Language Classroom Anxiety (FLCAS) questionnaire and interview were applied as the techniques to gather the data. The findings revealed that 91% freshmen are identified to experience a medium level of anxiety (76-119). Besides, the reasons of the language anxiety included communication apprehension, fear of negative evaluation, and fear of making mistakes in the test. Several ways to cope with the language anxiety comprised practicing before class and keeping the up with the positive mind.
INTRODUCTION
In the last three decades, the biggest concern of second and foreign language learning is language anxiety 1 . According to , the difficulties of Indonesian students in speaking English are lack of confidence, fear of making mistakes, limited ideas, and nervousness. 2 Besides, Aeni, Jabu, Rahman, & Strid state that most of the students feel anxious because they are afraid of negative evaluations. 3 It is hard for them to speak because English is not their first language. The students rarely use English in their daily activities. According to Keong et al., the difficulties in speaking English include the lack of English speaking practice and the inclination of mixing the foreign and native languages. 4 In fact, speaking skill is one of the major skills that the students have to be mastered. A person is considered successful in learning a foreign language when they can speak the language well 5 . It reflects that speaking skill is significant as a whole life aspect as it helps people to communicate with other people from other countries easily. In this globalization era, the students are required to have competent English-speaking skills. Nonetheless, many students face problems when they learn to speak English.
One of the problems is anxiety-an emotional tension characterized by increased blood pressure, heart rate or breathing rate, sweating, indigestion, or even muscular pain 6 . Language background variables such as self-reported speaking proficiency and frequency of language use contribute to the occurrence of language anxiety. Anxiety will affect the student's speaking skills 7 . Anxiety may also contain harms on learner's performance and academic achievement for foreign language learners 8 . It causes individual apprehension or fear of something that influences the process or the achievement of learning a foreign language.
A study conducted by Rahmawati analyzed student's anxiety in speaking activities of junior high school students. 9 The study found three main causes of students' anxiety, such as communication apprehension, fear of test, and fear of negative evaluation. Among these causes of anxiety, communication apprehension became the most dominant factor. Another study was conducted by Mardiansyah. This study analyzed the second-year students' speaking anxiety. 10 The findings showed six factors of anxiety, namely personal & interpersonal anxieties, student beliefs about language learning, lecturers' beliefs about language teaching, lecturer-student interaction, classroom tasks, and language tests. Among these factors, lecturer's beliefs and lecturer-student interaction serve as the most principal factors. Although some studies have discussed about the students' speaking anxiety, none of them barely discussed about the freshmen's speaking anxiety and how it may affect the speaking skills of the students. Therefore, the current study is to be conducted to analyze the language anxiety levels encountered by the freshmen of English Language Education Department, the reasons of the language anxiety, and how the students cope with the language anxiety.
RESEARCH METHOD
This study was conducted between January to February 2020. It used mixed design by collecting both qualitative data and quantitative data. The population of this research was 128 freshmen of English Language Education Department of a private Islamic university in Malang in the academic year 2019/2020. Sample random sampling was employed to select the respondents; as a result, 32 freshmen were chosen. FLCAS Questionnaire introduced by Horwitz was employed to measure the level of students' anxiety. 11 In gathering the data, the FLCAS questionnaire was first distributed to all of the respondents. After that, two students who received the highest scores in the FLCAS questionnaire were interviewed. All of the collected data were then classified and analyzed. Eventually, the result of the study was generalized and became the representative of the whole population.
FINDING AND DISCUSSION The Language Anxiety Level of Freshmen Students
The FLCAS scores show the student's level of language anxiety in forms of low, medium, and high anxiety with the range from 33 to 165. In this study, the scores of the participants range from 74 to 129. It shows that the lowest score is 74 (low anxiety) and the highest score is 129 (high anxiety). It can be seen in the following table: High Anxiety (120-165) 2 6% Total 32 100% Table 1 shows the total percentage of FLCAS score of 2019 freshmen in English Language Education Department. It displays that 3% of the students are diagnosed to experience low anxiety levels (33-75). Besides, 91% of the students are identified to have medium anxiety levels (76-119). 6% of the students are identified to experience a high anxiety level (120-165). According to the result, the majority of English Language Education Department freshmen have a medium anxiety level in their speaking skill. This finding is similar to the finding of a study conducted by Verawati 12 . She found that 88% of the students are identified to experience medium level of anxiety (87-107). Furthermore, Mardiansyah also revealed that 74% of the second year students of an English department are classified to experience medium level of anxiety (76-119). 13 According to the findings, language anxiety level of the majority of the English department students over the last few years is a medium level of anxiety.
The Reasons of Freshmen's Language Anxiety
From the finding, there are three main reasons triggering the language anxiety, namely communication apprehension, fear of negative evaluation, and test anxiety.
Communication Apprehension
44% of the participants agree that the students start to panic when they have to speak without any preparation in a language class. The reason is attached in following interview transcripts: Based on Almas, she finds a similar factor that makes students are anxiety. 14 She finds that 53% of the students are panic if they do not have any preparation before the speaking class. It occurs due to their lack of ability to speak in front of people. In fact, the students feel anxious because of their grammar, pronunciation, and vocabulary are also lacking. Additionally, Ala, Oda, Ali, & A Khammat point out in their study that the deficiency of competence also leads the students to experience anxiety in the classroom. 15 It is proven that 49,15% of the students indicate to get anxious when they are called to speak without having any preparation in advance. Those two studies believe that the students feel anxiety when they do not have enough time to prepare for the performance.
Fear of Negative Evaluation
The students are reported to feel not confident in their ability. It makes them afraid of being judged by their lecturers or friends. Point 19 shows that 22% of the participant students agree that the students are afraid that their lecturer is ready to correct every mistake they make. The reason is depicted in following interview transcripts: Student 13: "Yes, maybe. For example, my examination in last semester. One of my teacher said, "Hurry up girl or I will give you low score". Moreover, when your friends get a compliment but you are not, it gets my nerve. It makes me down and breaks my heart so much."
Students 88: "Yes, I am. I am typically person who think too much of what people say about my performance. From lecturer point of view, I am afraid when the lecturer correct me in the middle of presentation. It makes my confident drop in front of my friends."
Then, point 31 shows that 31% of the participant students agree that they are afraid that the other students will laugh at them when they speak the foreign language. The reason is depicted in following interview transcripts: It goes without saying that fear of negative evaluation has a big impact on students' performance. They are already nervous because they have to speak English. Then, the students have to face their friends' judgment about the performance. The students worry that their performance will get negative evaluation because their ability is poor compared to other students.
The finding is in line with Horwitz et al. who state that fear of negative evaluation may occur in any social, evaluative situation, such as work interviewing or speaking in foreign language class. 16 In addition, according to Aftat language anxiety has something to do with the issue of negative evaluation and correction; thus, many the students are afraid of being mocked by other students. As a result, the students decide to stop participating in speaking activity due to the negative evaluation that they may get.
Test Anxiety
Test anxiety is a fear that comes in the assessment situation. The finding shows that 13% of the participant students agree that even if the students are well prepared for a language class, they feel anxious about it. The reason that the student participants agree with the statement is given in the interview data: Students who learn a foreign language will face shyness. It becomes a problem, especially in speaking class. Furthermore, speaking in front of many people-while being assessed-is one of the common phobias that students are going through and the shyness feeling makes the their mind blank.
Ways to Cope with Language Anxiety
The students report the strategies related to reduce their anxiety during the learning process, especially English. The students find the suitable strategies to reduce all of their anxiety. They are carefully thinking about the way to escape from language anxiety. The answer is depicted from the interviews in the following examples: In line with this study, Abdul finds that students use relaxation strategy to reduce their anxiety. 17 The students try to take a deep breath and try to be calm. It can minimize students' anxiety even though it is not 100% successful. The other strategies are preparation strategy and positive thinking strategy. Preparation strategy means that the students study hard before they speak English in front of the class, such as frequently studying English and make it as a habit. Besides, positive thinking strategy makes the students be more confident. It gives the students an imagination that the students can give the best performance when the students speak English in front of the class.
CONCLUSION
Based on the findings and discussion, the researcher finds that 91% of the students are identified to experience a medium level of anxiety (76-119). Then, 6% of students are diagnosed with a high level of anxiety (120-165), while only 3% of the students are reported as a low level of anxiety (33-75). It is concluded that the majority of 2019 freshmen in English Language Education Department are reported to experience a medium level of anxiety on speaking skills. There are three factors that make students experience language anxiety, namely; 1) Communication Apprehension; 2) Fear of Negative Evaluation; and 3) Test Anxiety.
Lastly, the students claim some way to reduce their anxiety during their speaking class. Both of the students, state that the students will practice hard before the class started or during the examination days. Also, the students always think about positive thinking and try to calm down themselves by taking a deep breath. It works, even though it is not 100% successful. | 2,788.8 | 2020-12-31T00:00:00.000 | [
"Education",
"Linguistics"
] |
Evidence of entropy cascade in collisionless magnetized plasma turbulence
The turbulence of collisionless magnetized plasmas, as observed in space, astrophysical, and magnetically confined fusion plasmas, has attracted considerable interest for a long-time. The entropy cascade in collisionless magnetized plasmas is a theoretically proposed dynamics comparable to the Kolmogorov energy cascade in fluid turbulence. Here, we present evidence of an entropy cascade in laboratory plasmas by direct visualization of the entropy distribution in the phase space of turbulence in laboratory experiments. This measurement confirms the scaling laws predicted by the gyrokinetic theory with the dual self-similarity hypothesis, which reflects the interplay between the position and velocity of ions by perpendicular nonlinear phase mixing. This verification contributes to our understanding of turbulent heating in the solar corona, accretion disks, and magnetically confined fusion plasmas. Turbulence of collisionless magnetized plasmas is ubiquitous in space as well as laboratory plasmas, and as such is subject to intense study. The authors present experimental evidence of the existence of entropy cascade by direct visualization of entropy distribution in the phase-space of turbulence in laboratory experiments.
T he spectral universality in seemingly case-dependent fluid turbulence, which reflects self-similar dynamics in the inertial range of an energy cascade, is one of the most surprising findings in modern physics [1][2][3] . The presence or absence of universality in collisionless magnetized plasma turbulence exemplified by space, astrophysical, and magnetically confined fusion plasmas has been explored out of scientific interest. This question not only comes out of pure scientific curiosity but is also strongly associated with important practical problems, so-called turbulent heating in the solar wind 4,5 , solar corona 6,7 , accretion disks [8][9][10] , and energy transport in magnetically confined fusion plasmas [11][12][13] . These problems raise the question: at which scales are ions accelerated and thermalized? Some examples of turbulent heating include the coronal heating problem and the nonadiabatic temperature evolution of the solar wind 6 . One of the major models for explaining the heating mechanisms of the high-temperature corona/solar wind is the wave turbulence heating model (one is the microflare/nanoflare theory). The energy flux of the Alfvén waves/kinetic Alfvén waves propagating from the solar photosphere and chromosphere into the corona is considered to be sufficient to heat the corona temperature up to the observed temperature of~100 eV. However, this model encounters a complicated problem of what mechanisms (exemplified by ion cyclotron resonance, Alfvén resonance, linear phase mixing, and shock dissipation, among many others) are responsible for dissipating (partitioning) the wave energy of the Alfvén wave/kinetic Alfvén wave turbulence. The entropy cascade attributed to nonlinear phase mixing is a compelling hypothesis 4 for the mechanism. This hypothesis motivates us to experimentally study the validity of the entropy cascade via nonlinear phase mixing.
According to Boltzmann's H-theorem, entropy production, in other words, ion heating, is realized only by collisions in weakly collisional (collisionless) plasmas at the microscopic scale 14 much smaller than the ion gyro-scales (the inner scale) with a significant ∂f/∂v or ∂ 2 f/∂v 2 , where f and v are the ion velocity distribution function and the velocity vector of ions, respectively. However, macroscopic scales are typical energy inputs to the system (the outer scale), which are considerably separated from the dissipation scales (the inner scale). This fact strongly indicates that the injected energy is nonlinearly transferred as free energy (≈ negative signed entropy) from the outer scale to the inner scale in collisionless magnetized plasmas. This process is called an entropy cascade [14][15][16] . The gyrokinetic theory 15,17,18 predicts that the nonlinear phase-mixing 19 is responsible for the transfer of entropy in the inertial subrange 14,20 , and has been confirmed in a number of gyrokinetic numerical simulations regardless of twodimensional (2D) electrostatic 16 or three-dimensional (3D) electrostatic 21 or electromagnetic turbulence 4,22,23 . In addition, in a real plasma, an indication of a free energy cascade was observed in electromagnetic turbulence in the Earth's magnetosheath as fine-scale structures in the ion velocity distribution functions 24 . Regardless of the fact that the original concept of the entropy cascade by the nonlinear phase mixing considers only 2D electrostatic fluctuations 14,19 , signatures of the entropy cascade have been witnessed in magnetized plasma turbulence in various situations. This broad applicability of the entropy cascade picture to a wide range of collisionless magnetized plasma turbulence is attributed to the fact that turbulence of collisionless magnetized plasmas universally consists of highly anisotropic fluctuations with frequencies much lower than the ion cyclotron frequency in addition to the intrinsic electrostatic nature of perpendicular fluctuations.
Nonlinear phase mixing is a phase-randomizing mechanism of electrostatic fluctuations of quasi-2D magnetized plasmas by a finite-Larmor radius effect 19 . It couples ion dynamics in the position and the velocity spaces, resulting in entropy cascades in the phase space 14,25 .
Although the visualization of the entropy distribution in the phase space of ions has been implemented in some simulations 25,26 , no measurements have been conducted in real plasmas, including space and laboratory plasma experiments.
The gyrokinetic theory for treating gyroscale plasma phenomena considers kinetics of 'charged rings' of gyrating ions, whose statistics are represented by ring-averaged ion velocity distribution functions at a fixed guiding center. The gyrokinetic system is invariant under the scaling transformation; (g, ϕ, r, v ⊥ ) → (g, μ 2 ϕ, μr, μv ⊥ ), where g, ϕ, r, v ⊥ , and μ are fluctuation components of the ring-averaged ion velocity distribution function, the electrostatic potential, the space coordinate, the perpendicular velocity of ions, and a scaling factor, respectively 20 .
which is the perturbed distribution function, where F 0 is the background equilibrium distribution function that is steady on the timescale of turbulent fluctuations (a Maxwellian is assumed in the standard gyrokinetic theory), and R is the fixed guiding center position.
The dual self-similarity hypothesis for the position and velocity spaces based on the above scale invariance predicts the power laws of spectra of the free energy W g1 ¼ RR gðR;v ? Þ 2 2 dv ? dR and energy E g ¼ 1 2 Rφ ðrÞ 2 dr with the use of g(R, v ⊥ ) for the 2D electrostatic turbulence. The dual self-similar dynamics in the phase-space are expected to be accompanied by a dual cascade of two kinds of turbulence energy in 2D electrostatic turbulence: the forward cascade of free energy and an inverse cascade of electrostatic energy 25 . This dual self-similarity hypothesis extends the renowned Kolmogorov self-similarity hypothesis in fluid turbulence 27 to the phase space of ions in gyrokinetic turbulence. It argues that the turbulent behavior of ions at the sub-Larmor scales is independent of scale in both their position and velocity spaces. These are strongly coupled in the phase space by nonlinear phase mixing.
Therefore, in this experiment, we employed diagnostic instruments named Ring-averaged ion velocity distribution function probes (RIDFPs) 28 to measure g(R, v ⊥ ) for evaluation of the theoretically predicted power laws. Although our previous paper 29 showed agreement between measurements and the theoretical prediction on the power spectrum of E g as a function of the fluctuation wavenumber perpendicular to the background magnetic field k ⊥ , we still face a lack of information on the velocity space to conclude the validity of the dual-cascade theory of gyrokinetic turbulence.
Here, we show the direct visualization of the entropy distribution of ions in the phase space of laboratory-magnetized plasma turbulence. These results provide the evidence of the existence of dual self-similarity and the dual cascade of entropy and field energy in the phase space of turbulence.
Results and discussion
Experimental setup. In this experiment ("Methods": Magnetized plasma experiment (MPX) device, ring-averaged ion velocity distribution function probes, other measurement tools, and the plasma parameters), we prepared four states of electrostatic 2D turbulence driven by resistive drift-waves having varied driving perpendicular wavenumbers k drive ρ thi between~0 and 10 with control of the density of the background neutral particles, where ρ thi is the Larmor radius of ions at the thermal velocity v thi . While this control scheme of k drive ρ thi is not a well-established technique, we prepared the turbulent states with the control of the neutral particle density with reference to the numerical work 30 , which describes the numerical investigation results of an energy partition of turbulence in a cylindrical plasma. We use Fourier-Hankel components of the free energy: W g1 ðk ? ; pÞ p∑ jk ? j¼k ? jgðk ? ; pÞj 2 ¼ πk ? pjgðk ? ; pÞj 2 , where g(k ⊥ , p) is the Fourier-Hankel transform of g(R, v ⊥ ) concerning the guiding center position and the ion velocity 20 , and the parameter p indicates the reciprocal of the fluctuation scale of g(R, v ⊥ ) in the velocity direction corresponding to the wavenumber in the velocity space.
The gyrokinetic approximation requires ω ≪ Ω ci , where ω and Ω ci are the wave frequencies and the ion cyclotron frequency, respectively. The higher the axial magnetic field strength is, the more improved the gyrokinetic condition. However, our experiment does not completely satisfy ω ≪ Ω ci (ω/2π~0.1-4 kHz, Ω ci / 2π = 8.4 kHz), which is a consequence of the two following adverse impacts of the strong field on our plasma states: (i) the suppression of the excitation of the drift waves; in our plasmas, the high magnetic field stabilizes the drift waves because of a change in the radial profile of the density; and (ii) the reduction of the ion gyro-radius, which limits the performance of the diagnostic. In other words, the axial magnetic field strength is set at a weak value to fully use all the velocity channels of the RIDFPs by expanding the ion gyro radii. This improves the resolution of the RIDFP measurement in the velocity space. In the third paragraph from the end of this section, we explain the influence of this incomplete satisfaction of the gyrokinetic ordering on the interpretation of the experimental results.
Spectra of free energy in the k-v space. Figure 1 shows timeaveraged free energy spectra k ⊥ |g(k ⊥ , v ⊥ )| 2 as functions of k x ρ thi and v ⊥ up to~2v thi for ( Fig. 1a) k drive ρ thi~1 (W g1 injection at large scales) and (Fig. 1b) k drive ρ thi~1 0 (W g1 injection at small scales), respectively. We regard k x ≈ k ⊥ in evaluating k ⊥ |g(k ⊥ , v ⊥ )| 2 based on the assumption of isotropy and fast decay of |g(k ⊥ , v ⊥ )| 2 for k ⊥ . The factor k ⊥ indicates the circumferential length in the k ⊥ -space.
k ⊥ |g(k ⊥ , v ⊥ )| 2 for (A) k drive ρ thi~1 exhibits, in the entire range of v ⊥ , the large amplitude at k x ρ thi~1 −2 consistent with jφ f ð f ; k y Þj 2 measured by a fine-scale Langmuir probe (FSLP) for k drive ρ thi~1 (Fig. 2a), which shows excitation of k x ρ thi~1 components at f~1.0−1.3 kHz. Accordingly, the low k ⊥ components at k x ρ thi~1 -2 show variation in the v ⊥ -direction at the scale of~v thi in Fig. 1a. The amplitude of components for |k x ρ thi | > 2 decays in large k x with finer-scale variation in the v ⊥direction. On the other hand, k ⊥ |g(k ⊥ , v ⊥ )| 2 for (B) k drive ρ thi~1 0 exhibits significant power at |k x ρ thi | > 10. These |k x ρ thi | > 10 components exhibit structures in the v ⊥ -direction at sub-v thi scales. This indicates strong coupling between the position and velocity spaces. See the next subsection for a quantitative assessment of scales in v ⊥ space using spectra.
Comparison with theory. In the second-fourth rows of Fig. 2, we show variation in the spectra of the collisionless invariants of 2D electrostatic gyrokinetics, W g1 (k ⊥ , p) and E g (k ⊥ ), for varied k drive ρ thi approximately between 0 and 10, (the first column) k drive ρ thi~1 , (the second column) k drive ρ thi~3 −4, (the third column) k drive ρ thi~0 -4, and (the fourth column) k drive ρ thi~1 0. These values of k drive ρ thi are evaluated from jφ f ð f ; k y Þj 2 measured by FSLP as shown in the first row of Fig. 2a-d. In the respective cases of different k drive ρ thi , the following two distinct frequency bands can be identified in jφ f ð f ; k y Þj 2 : one showing significant power with nonstatistical/deterministic distribution corresponding to the drive, for example, k y ρ thi~1 component at f~1.3 kHz in Fig. 2a (k y ρ thi~3 -4 component at f~1.7 kHz in Fig. 2b, and k y ρ thi~1 0 component at f~3-4 kHz in Fig. 2d), and the other bands showing scattered, statistical distribution in the k y -direction corresponding to turbulent cascade. Nonlinear dynamics exhibited in these shots are local because no nonlocal resonant wave-wave interactions occurred except for the k drive ρ thi~0 -4 state (the vertical array of Fig. 2c, g, k and o), which exhibits a continuous driving spectrum in the f-k y ρ thi diagram and is a turbulent state originating from a nonlinear coherent state of drift waves called solitary drift waves 31 .
The plots shown in the second row ( Fig. 2e-h) are W g1 (k ⊥ , p) (negative signed entropy) in the k ⊥ -p space, namely, position-velocity space (see "Evaluation of 1D spectrum of free energy W g1 1D (k x , p) and relationship with W g1 (k ⊥ ) and W g1 (p)" in Methods). In the following results of varied k drive ρ thi , a position of the drive moves along the diagonal in the k ⊥ -p space, as shown in Fig. 2e-h.
When W g1 is injected at large scales (Fig. 2e), in which a significant power of W g1 can be seen at the left bottom of the diagram at k ⊥ ρ thi~p v thi~1 -4 corresponding to k drive ρ thi , W g1 broadly develops along the diagonal from the driving scale toward the upper-right direction, reaching the top right corner around k ⊥ ρ thi~p v thi~2 0. (A similar profile can be seen in Fig. 6 in the article by Tatsuno et al. 26 ). According to the gyrokinetic Poisson Eq., the potential fluctuationφðk ? Þ is generated solely by nonlinear phase mixing, that is, gðk ? ; p ¼ k ? Þ (Eq. (2.11) in the article by Plunk et al. 20 ). This provides a Fjørtoft-type relationship W g1 (k ⊥ , p = k ⊥ ) = k ⊥ E g (k ⊥ ) (Eq. (7.14) in the article by Plunk et al. 20 ). Therefore, diagonal transport of W g1 in the k ⊥ -p space is inevitable when a dual-cascade of W g1 and E g occurs. Fig. 1 Spectra of free energy in the wavenumber-velocity space. Time-averaged power spectra k ⊥ |g(k ⊥ , v ⊥ )| 2 measured by RIDFPs as functions of the wavenumber k x normalized by the ion Larmor radius ρ thi at the thermal velocity v thi and the perpendicular ion velocity v ⊥ up to~2v thi for a driving perpendicular wavenumbers k drive ρ thi~1 and b k drive ρ thi~1 0, respectively. This W g1 (k ⊥ , p) spectrum exhibits the generation of W g1 at finer scales than the drive. This indicates that the nonlinear phase mixing works, resulting in a forward cascade of W g1 . This cascading nature will be examined below by comparing their power laws obtained from the measurement and the theory.
As k drive ρ thi increased to ≈10, as shown in Fig. 2f-h, the significant W g1 part moved in the upper-right direction along the diagonal line toward higher k ⊥ ρ thi~p v thi locations corresponding to the increase in k drive ρ thi . In all the cases of k drive ρ thi (Fig. 2e-h), the spread of W g1 (k ⊥ , p) along with the diagonal directions (between the bottom left and the upper right) is obvious. In these cases, the Fjørtoft-type energetic transition 25 , namely, a transition involving only diagonal components, can be realized.
In the third row of Fig. 2i-l), (crosses) one-dimensional (1D) spectra W g1 1D of the free energy as functions of k x ρ thi and (open squares) p-spectra of W g1 (p), respectively, are shown. Note that when W g1 (k ⊥ ) ∝ k ⊥ −α , W g1 1D (k x ) ∝ k x −α (see "Evaluation of 1D spectrum of free energy W g1 1D (k x , p) and relationship with W g1 (k ⊥ ) and W g1 (p)" in Methods). Respective k drive ρ thi ranges are shown by purple bars. The blue and red bars represent the power laws predicted by the gyrokinetic theory for (blue) the inverse-cascade range k ⊥ < k drive and (red) the forward cascade range k ⊥ > k drive , respectively 20 . The respective power indices of W g1 1D (k x ) and W g1 (p) evaluated from the least-square fitting to the measured data points are indicated by numbers with the standard errors (SE). The noise levels of W g1 1D (k x ) and W g1 (p) estimated from a vacuum shot are included in Fig. 2i. W g1 (p) in Fig. 2i (injection at a large scale) shows power-law decay starting at k x ρ thi~kdrive ρ thi~1 up to the detection limit of k x ρ thi~p v thi~2 0, clearly indicating the existence of an inertial subrange of the entropy (free energy). The evaluated exponent for the measured W g1 (p), −1.0, approximately agrees with the theoretical value of −4/3 within 5 times SE. For smaller scales k x ρ thi > 3, W g1 1D (k x ) in Fig. 2i shows a similar decaying tendency to W g1 (p), which is a strong indication of the dual self-similarity dynamics, although the discrepancy of W g1 1D (k x ) from the theoretical exponent is larger than 25 times SE. Larger discrepancies between the theoretical exponents and the Fig. 2 Variation in spectra of the invariants of gyro-kinetics. The free energy W g1 (k ⊥ , p) and the electrostatic energy E g (k ⊥ ) for varied driving perpendicular wavenumbers k drive ρ thi between~0 and 10, (the 1st column) k drive ρ thi~1 , (the 2nd column) k drive ρ thi~3 −4, (the 3rd column) k drive ρ thi~0 −4, and (the 4th column) k drive ρ thi~1 0, respectively. The plots in the 1st row (a-d) are the power spectra of potential fluctuation jφ f ðf; k x Þj 2 measured by FSLP.
The plots shown in the 2nd row (e−h) are W g1 (k ⊥ , p) in the k ⊥ -p-space, namely, position-velocity-space. The 3rd row (i−l) are (cross) 1D spectra W g1 1D of the free energy as functions of k x ρ thi and (open square) p-spectra of W g1 (p), respectively. E g (k ⊥ ) spectra are shown in the 4th row (m−p). Respective k drive ρ thi ranges are shown by purple color bars. The blue and red bars represent power laws predicted by the gyrokinetic theory 20 for (blue) k ⊥ < k drive and (red) k ⊥ > k drive , respectively. measured ones in W g1 1D (k x ) than those in W g1 (p) are seen in all cases of k drive . As k drive ρ thi increases to 3-4 (Fig. 2j), W g1 (p) shows an inflection point at k x ρ thi~kdrive ρ thi~3 -4. Correspondingly, W g1 1D (k x ) follows this change in the spectrum. For an injection at small scales k drive ρ thi~1 0 (Fig. 2l), both W g1 (p) and W g1 1D (k x ) become independent of p and k x , indicating good agreement with the theory 20 . It should be noted that the decaying exponents of both W g1 1D (k x ) and W g1 (p) at k x ρ thi ≫ 1 exhibit similar values in the respective cases of k drive ρ thi and similar variation for varied k drive ρ thi in Fig. 2i-l. This indicates the formation of inertial subranges in both the position and velocity spaces and strong coupling between them. A similar result is obtained in the gyrokinetic simulation 16,26 .
In the case of k drive ρ thi~0 -4 (Fig. 2k), despite the driving source in the target k-range (i.e., noninertial range), strong k-p coupling occurs, indicating the universality of nonlinear phase mixing in magnetized plasma turbulence.
The abovementioned approximate agreement between the measurement and the theoretical prediction of W g1 (p) and W g1 (k ⊥ ) within~1 − 25 times SE is supported by the E g (k ⊥ ) spectra measured by FSLP shown in the fourth row of Fig. 2 (Fig. 2m-p). Note that when E g (k ⊥ ) ∝ k ⊥ −α , E g1 1D (k x ) ∝ k x −α ("Methods": Evaluation of the 1D spectrum of the electrostatic field energy E g 1D (k y ) and its relationship with E g (k ⊥ )). The blue and red bars represent the power laws predicted by kinetic theory for (blue) k ⊥ < k drive and (red) k ⊥ > k drive , respectively. The respective power indices of E g1 1D (k x ) evaluated from the leastsquare fitting to the measured data points are indicated aside by numbers with the standard errors. The noise levels of E g1 1D (k x ) estimated from a vacuum shot are included in Fig. 2m-p. The evaluated scaling for E g1 1D (k x ) in Fig. 2m is k x −3.0 , close to the theoretical power law k ⊥ −10/3 . The theoretical prediction k ⊥ −2 for the inertial range in the larger scale than the driving scale becomes dominant as k drive ρ thi increases. The exponent evaluated for the measured E g1 1D (k x ) in Fig. 2p is k x −1.8 . The observed behavior of these power laws in W g1 and E g is consistent with the theory based on the hypothesis of dual self-similarity and the dual cascade of the entropy and field energy of the gyrokinetic system 20 . Our result strongly supports the validity of the dual-self similar hypothesis of gyrokinetic turbulence.
Note that the nonlinear decorrelation time 16,26 for these states is evaluated as τ ρ~1 0 × 10 −5 s; hence, the dimensionless parameter 16,26 , which represents the scale separation analogous to Reynolds number, D~30-40. Accordingly, the cutoff wavenumber, above which the collisional dissipation dominates the cascade, k cut ρ thi~2 D 3/5~2 0. This guarantees that the observed power-law spectral range corresponds to the inertial subrange.
In what follows, we discuss the applicability of the gyrokinetic theory and its impact on the interpretation of the experimental results. The theoretical aspects of the applicability of gyro kinetics to space and astrophysical plasmas are discussed in previous works 15,18,23 . In brief, strong magnetization, anisotropy, small amplitude, low fluctuation frequencies, equilibrium Maxwellian distribution, and nonrelativistic effects are assumed.
As described in Experimental setup, our experiment does not completely satisfy the strong magnetization condition ω ≪ Ω ci in consideration of the two adverse impacts of the strong field on our plasma states. One possible influence of this incomplete satisfaction of the gyrokinetic ordering is the possibility of stochastic ion heating 32,33 . According to ref. 34 , the amplitude threshold for strong stochastic heating when β < 1 can be expressed in terms of the quantity ε i ∼ q i δΦ i /mv 2 , where β, q i , and δΦ i are the thermal pressure normalized by the magnetic field pressure, electric charge of the ions, and root mean square amplitude of the electrostatic potential fluctuation at k ⊥ ρ thi ∼ 1, respectively. In our case, ε i ∼ 0.2; therefore, the influence of stochastic ion heating is considered to be small. Ion cyclotron resonance heating is negligible because ω ⋡ Ω ci .
One of the weakest points of the gyrokinetic theory is the use of a Maxwellian as F 0 15 . Therefore, highly nonequilibrium turbulent states are not subjects of gyrokinetic theory. Nevertheless, the gyrokinetic theory is in effect in a wide range of space and turbulent astrophysical plasmas, as shown in numerous numerical simulations and theoretical considerations. Although our measurement has not had sufficient accuracy to be able to discuss a degree of deviation of F 0 from a Maxwellian distribution (Fig. 3d in "Methods" shows an example of the velocity distribution F 0 ), we believe that F 0 of our plasmas is not that different from a Maxwellian because of the following reasons: (i) no mechanisms that heat preferentially ions with specific velocity components exist; the collisional energy transfer caused by electron-ion collisions is the only possible heating source of ions; and (ii) ions are weak collisional, but not too weak. The meanfree path of ions for ion-ion collision is~0.5 m < 1.6 m~L, which is the length of the plasma column. For the same reasons, pressure anisotropy is not considered.
The influence of the electron behavior on the entropy cascade in the ion phase space is considered negligible according to gyrokinetic numerical simulations 4,16,23 . The work done by Tatsuno et al. showed that no essential difference was observed between the cases of applying Boltzmann-response (3D) and noresponse (2D) electrons in their simulations 4 . For more detailed electron energetics, please see, the work by Kawazura et al. 23 , which studied the partition of irreversible heating between ions and electrons in terms of a compressive drive using hybrid gyrokinetic simulations.
Conclusions.
In laboratory experiments, we present the measurement results of the Gibbs entropy distribution in the phase space of ions in electrostatic gyrokinetic turbulence. We confirm good agreement between the measurement and the theoretical prediction with a dual self-similar hypothesis in the scaling laws of the spectra of the entropy and the electric field energy. This result indicates an interplay between the position and velocity spaces of ions by perpendicular nonlinear phase mixing accompanied by a cascade of entropy in the phase space. Excitation of spectral components of the free energy W g1 with k ⊥ ∼ p in the phase space gives evidence of nonlinear phase mixing at sub-Larmor scales. This observation corroborates the evidence of the existence of dual self-similarity and the dual-cascade of entropy and field energy.
An entropy cascade via nonlinear phase mixing is considered universal in magnetized plasma turbulence because it has been witnessed in various numerical simulations in different magnetized turbulence setups, including 2D 16 and 3D electrostatic 21 , 3D electromagnetic turbulence, including the Alfvenic solar wind 4,22 , and a simulation targeting an Alfvenic hot accretion disk 23 . The essential physical components in entropy cascades via nonlinear phase mixing include the gyro motion of the particles at the sub-Larmor scales and the interaction between the particles and the electrostatic fluctuations in addition to the strong anisotropy (k ⊥ ≫ k || ). Our experiment prepares turbulent states with these essential components in a simplified setup. Therefore, although our turbulence setup is in a narrow range (electrostatic turbulence in a drift-kinetic regime), our result is crucial for verifying universality. We believe that verifying the entropy cascades via nonlinear phase mixing contributes to understanding turbulent heating in the solar corona, solar wind, accretion disks, and magnetically confined fusion plasmas.
Methods
Magnetized plasma experiment (MPX) device: experimental device. The experiment was conducted in the MPX device 35 (Fig. 3a), which can prepare qualified plasma configurations for our purposes, namely, quasi-2D configurations with the magnetic field (the strength is denoted by B 0 ), the density, and temperatures within the target ranges. The hot cathode generated plasmas with the introduction of argon gas as the working gas. g(R, v ⊥ ) was measured by two RIDFPs separated by 3 mm and 230 mm in the x-and the z-directions, respectively (Fig. 3a), to obtain perpendicular wavenumbers k ⊥ of g(R, v ⊥ ) with the use of a two-point correlation technique 36 . RIDFPs were positioned at the center axis of the target plasmas to minimize the influence of steady E × B rotation of the plasmas. Figure 3 shows the equilibrium ring-averaged ion velocity distribution functions F 0 for B 0 = 0.022 T and B 0 = 0.033 T, respectively. The red solid curves indicate Maxwellian with a temperature of 0.1 eV. It can be observed that the orbits of the ions (Larmor radii) shrink as B 0 change from 0.022 T to 0.033 T, indicating the validity of the RIDFP measurement.
Ring-averaged ion velocity distribution function probes 28 . The RIDFP is a set of ion collectors that detect different velocity components and is immersed into magnetized plasmas. The RIDFP achieves momentum selection of incoming ions by selection of the ion Larmor radii by the orbit filter. To nullify the influence of the sheath potential surrounding the RIDFP on the incoming ions' orbits, the RIDFP body's electrostatic potential is automatically adjusted to coincide with the space potential of the target plasma with the use of an emissive probe and a voltage follower 28 .
For precise measurement of the fluctuation g(R, v ⊥ ) in time, the ground potential of the current detection circuits is adjusted to that of the RIDFP body in order to eliminate capacitive coupling between the ion collectors and the RIDFP body. The length of RIDFP L = 79 mm satisfies the condition of v || f ci −1 > L, where v || is the parallel component of the thermal velocity of ions. This inequation imposes a condition for the plasma (ions) residing in the magnetic flux tube, in which an RIDFP is allocated, not to being severed by the RIDFP.
In the experiments, the resolution of the RIDFP measurement in the p-space Δ(pv thi ) can be evaluated as follows: Δpv upper_bound~Δ p(2v thi ) = j 0 ≒ 2.4, ∴Δp ≒ 1.2/ v thi ∴Δ(pv thi )~1.2, where v upper_bound and j 0 are the upper bounds of the measurable ion velocity by RIDFP and the first zero of the Bessel function of the first kind, respectively. The maximum (pv thi ) in the RIDFP measurement is obtained as: (pv thi ) max~j0 v thi /Δv~20.
The other measurement tools and the plasma parameters. In addition to RIDFPs, we employed a few sets of Langmuir probes (LPs) for different purposes. An LP measured the plasma density in addition to a microwave interferometer 37 .
The LP also measured the electron temperature and the space potential of the plasmas. A poloidal array of LPs named LPA diagnosed the macroscopic poloidal structures of fluctuations of ion saturation current and their floating potential. Another set of LPs named fine-scale LP (FSLP) was applied to measure the fluctuation of floating potentialφ f %φ as functions of frequencies f and k y (k x ), whose upper bound of measurable k ⊥ is~8 × 10 2 m −1 .
The hot cathode generated plasmas with the introduction of argon gas as the working gas. The typical plasma density and temperature are n e~0 .5-5 × 10 16 m −3 and T e~1 -5 eV, respectively, with a 15-20 cm diameter. Accordingly, the characteristic frequencies of the ion cyclotron f ci , drift-wave f DW , ion-ion Coulomb collisions f ii , and ion-neutral collisions f in have the following numbers: where Ω ci is the ion cyclotron angular frequency of singly ionized argon ion.
Iso
Evaluation of the 1D spectrum of the electrostatic field energy E g 1D (k y ) and its relationship with E g (k ⊥ ). From the FSLP measurement, the 1D spectrum of the electrostatic field energy E g 1D ðk y Þ R 1 À1 jφðk ? Þj 2 dk x is evaluated as follows: If turbulence is isotropic, E g 1D ðk y Þ ¼ R 1 À1 jφð ffiffiffiffiffiffiffiffiffi k 2 x þk 2 y p Þj 2 dk x : Applying a variable change tan θ ¼ k y k x and a cutoff θ cut for the upper bound of the integration, one can obtain When E g (k ⊥ ) ∝ k ⊥ −α , E g 1D (k y ) = ∫E g (k ⊥ )dk x ∝ k y −α .
Data availability
The data supporting this study's findings are available from the corresponding author upon reasonable request.
Received: 16 April 2022; Accepted: 9 December 2022; Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/ licenses/by/4.0/. | 7,933.8 | 2022-12-01T00:00:00.000 | [
"Physics"
] |
Case report: one case of coronavirus disease 2019 (COVID-19) in a patient co-infected by HIV with a normal CD4+ T cell count
Background The COVID-19 has been a severe pandemic all around the world. Nowadays the patient with co-infection of HIV and SARS-CoV-2 was rarely reported. Here we reported a special case with HIV and SARS-CoV-2 co-infection, which showed a prolonged viral shedding duration. Case presentation The patient was infected with HIV 8 years ago through sexual transmission and had the normal CD4+T cell count. She was found SARS-CoV-2 positive using real-time Polymerase Chain Reaction (RT-PCR) during the epidemic. Most importantly, the patient had a prolonged viral shedding duration of SARS-CoV-2 about 28 days. Conclusion The viral shedding duration may be prolonged in people living with HIV. The 14 days isolation strategy might not be long enough for them. The isolation or discharge of these patients needs further confirmation for preventing epidemics.
Background
COVID-19 is a novel virus disease with over 7250,000 confirmed cases worldwide [1]. And the knowledge regarding epidemiology and clinical presentation has been evolving gradually in the past months since the initial identification. In the general population, the reported case fatality rate ranged from 1.2 to 11.9% in different countries [2,3]. Xu et al. [4] described that 113 patients had persistently positive PCRs results for at least 21 days. And Lu et al. [5] also reported a maximum 20 days of prolonged viral clearance period.
Here we reported a case of HIV and SARS-CoV-2 coinfection who had a prolonged viral shedding duration about 28 days.
Case report
A 49-years old female diagnosed with HIV infection 8 years ago under regular ART (anti-retroviral therapy) went to our clinic for fatigue (day 1 of illness). He got a fever (day 4) with a maximum temperature of 38 ℃, accompanied by pharyngeal pain. The patient showed chills on day 5. Considering the clinical symptoms, the sputum sample was collected for RT-PCR assay of SARS-CoV-2 and the chest computed tomography (CT) was performed.
Previous medical history included syphilis, which was cured. The ART is Efavirenz 600 mg, Zidovudine 300 mg, and Lamivudine 150 mg. After that, she continued the ART regularly. Although the nadir CD4 + T cell count was 224, a recent test was normal. The HIV viral load remained undetectable from 2013 (Figs. 1, 2).
The CT result showed ground glass dense shadow and cord shadow under the pleura of the lateral segment of the middle lobe and dorsal-base segment of the lower lobe of the right lung (Fig. 3). Meantime, he was treated with cefuroxime and traditional Chinese medicine (Lianqin oral solution and Lianhua Qingwen capsule). At that time, the result of RT-PCR for SARS-CoV-2 was negative. But the symptoms were not relieved. We considered the possibility of false-negative to the RT-PCR result [6]. So, we had a re-check of RT-PCR for SARS-CoV-2 on day 7. The test result on day 7 turned positive, and the patient was diagnosed with COVID-19 (moderate type).
According to the Chinese COVID-19 treatment guideline at that time [7], on Day 8, we changed the cefuroxime and traditional Chinese medicine to interferon atomization (5 million bid), ribavirin (150 mg TID), and abidol (200 mg TID) for antiviral treatment. Meanwhile, the moxifloxacin (400 mg QD) was given to the patient for preventing bacterial infection.
On day 12, the temperature of the patient returned to normal. The symptoms of the patient alleviated completely, and the result of the CT scan on day 15 was also back to normal (Fig. 2). We consistently tested the RT-PCR for COVID-19 on day 19, day 25, and day 31 to 34, but all the results remained positive. The RT-PCR for COVID-19 turned negative for the first time on the day 35. Meantime, the IgM antibody for SARS-CoV-2 on day 35 was positive. Then we tested the RT-PCR and IgM for SARS-CoV-2 every 3 days. The RT-PCR for SARS-CoV-2 remained negative, while the IgM antibody for
Discussion
Nowadays, the COVID-19 has been a worldwide epidemic disease. As an epidemic disease, viral shedding duration is the key to disease control. Some studies found asymptomatic people who were still carrying the virus after isolation for 14 days [8].
The prolonged viral shedding duration in the general population has been reported by several studies and the prolonged viral shedding duration reported ranges from 21 to 45 days [4,9].
But there are few studies about the viral shedding duration in suspicious immunocompromised patients. At present, there are several cases of patients in immune suppressive status after organ transplantation. Huang reported two patients with COVID-19 who had undergone transplantation, one of whom had bone marrow transplantation, and the other had kidney transplantation. These two patients finally transferred to ARDS (Acute respiratory distress syndrome), and eventually died after [10]. Among the immunocompromised patients, Zhang et al. [11] reported a patient with kidney transplantation who had a prolonged viral shedding duration for 63 days. This is the first report of a patient co-infected with HIV and SARS-CoV-2 who showed a prolonged viral shedding duration. Even though not all people living with HIV are immunocompromised, especially those under ART with an undetectable HIV viral and normal CD4 count, these people may still be vulnerable to viral infection or subsequent bacterial pneumonia than the general population. Further studies and data collection are needed for this.
In our case, the patient had a history of fever and had CT findings of viral pneumonia. COVID-19 was diagnosed by the positive result of RT-PCR. And the viral shedding duration lasted about 28 days.
Xu et al. [4] concluded the risk factors of prolonged viral RNA shedding in COVID-19 patients: male sex, delayed admission to hospital after illness onset, and invasive mechanical ventilation. These risk factors cannot explain the prolonged duration of the patient in our report.
Qin et al. [12] reported that the total number of B cells, T cells, and NK cells decreased significantly in patients with COVID-19. And the sum of lymphocytes of the severe group dropped more significantly than the moderate group. So, the infection of SARS-CoV-2 might be dramatically for the people living with HIV. On the one hand, the immune system might be impaired after the infection of SARS-CoV-2 by the depletion of T lymphocytes [12]. On the other hand, during the chronic phase of HIV infection, generalized immune activation, and systemic CD4 + T lymphocyte depletion occur. Fortunately, the CD4 + T cell count of our case was normal from 2016 to now, which might be the reason for not causing severe pneumonia. But the prolonged viral shedding duration.
The paradox between the prolonged viral shedding duration and moderate clinical course might be due to the impaired cellular function despite normal CD4 + T cell count in people living with HIV [13].
Lu et al. [5] revealed that prolonged viral RNA shedding in children was associated with symptomatic infection, fever, pneumonia, and lymphocyte count less than 2.0 × 10 9 /L. The lymphocyte count of our case was also less than 2.0 × 10 9 /L, which might be a co-factor for the prolonged viral shedding duration. At last, there are no specific antiviral drugs for SARS-CoV-2. This patient was treated with ribavirin and abidol, which may not inhibit the replication of SARS-CoV-2 effectively.
Conclusion
The viral shedding duration may be prolonged in people living with HIV. The 14 days isolation strategy might not be long enough for them. The isolation or discharge of these patients needs further confirmation for preventing epidemics. | 1,744.4 | 2020-07-23T00:00:00.000 | [
"Medicine",
"Biology"
] |
Factors Influencing the Cooperative Relationship between Enterprises in the Supply Chain of China’s Marine Engineering Equipment Manufacturing Industry-An study based on GRNN-DEMATEL method
Based on the data of China’s Marine engineering equipment industry, in this Paper, the key influencing factors are identified by using Grounded theory and GRNN-DEMATEL method. The study results show the key influencing factors include enterprise’s operational, technical capabilities, enterprise’s social recognition, enterprise’s willingness to cooperate, trust between enterprises, communication and collaboration, opportunism and external environment. Second, enterprise’s operational and technical capabilities are the most important and critical factors, external environment is an irresistible factor. This study enriches and develops the study of supply chain management, and provides theoretical guidance and reference for improving the industry competitiveness.
Introduction
Marine engineering equipment manufacturing industry (hereinafter referred to as "marine industry") is the important prerequisite and foundation for the development of marine economy, and has great strategic significance for promoting the transformation and upgrading of marine manufacturing industry and accelerating the pace of building a maritime power [1]. Since 2010, China has successively formulated multiple plans, including Innovation and Development Strategy for Marine Engineering Equipment Industry, Medium-and Long-term Development Plan for Marine Engineering Equipment Manufacturing Industry (2011 2020), and Made in China 2025. At present, China's marine engineering equipment manufacturing industry has made great progress, but its development is still in at the middle and end of the world's marine industry development chain, and technology, products, etc. need to be improved. Along with the increasingly fierce global competition, the increasingly shortened product life cycle, and the enhancement of market demand drive function, one of the main problems to be solved for China's marine industry enterprises is to improve their own competitive advantages and the core competitiveness of the entire supply chain.
Supply chain is based on the premise of meeting customer demands, and centers on the core enterprises to win the market with the lowest cost, the fastest speed, the best quality, the best service through the control over information flow, material flow and capital flow throughout the process from the purchase of raw materials to completion of intermediate products and final products [2]. At present, the cooperation between enterprises in supply chain has changed from one-to-one cooperation to multi-enterprise cooperation, with strategic cooperation alliance among enterprises in supply chain formed finally [3]. Ma Shihua [3] pointed out that, interenterprise competition is no longer the competition launched by a single enterprise in a certain time and space to compete for market share of certain terminal markets, but the overall competition across time and space and based on product design, manufacturing, delivery and distribution, sales and services, and has transformed into supply chain efficiency competition. The supply chain mainly reflects the enterprise orientation based on market demand. In the processes of technology research and development, processing and production, the modularization and standardization degree of products are increasingly improved, and the integrated utilization of internal and external resources as well as the flexibility and agility in response to the market are enhanced [5]. Selective cooperation between nodal enterprises in the supply chain is the only way for enterprises to grow cooperatively. Supply chain cooperative relationship refers to the cooperative relationship in which both parties in the cooperation undertake a series of exchange activities under the mode of sharing risks and benefits, with a complete set of monitoring mechanism established and implemented [6,7]. Therefore, based on the characteristics of marine engineering equipment manufacturing industry, this Paper proposes that the relationship between enterprises in the supply chain of marine engineering equipment manufacturing industry refers to the close connection between the upstream and downstream enterprises of the marine industry in a certain form of cooperation, and a development system to enhance the core competitiveness of enterprises and achieve the overall strategic objectives of China's marine industry shall be established. The building of cooperative relationship between enterprises in the supply chain of marine industry is of great theoretical and practical guidance significance to China's marine industry in terms of improving the overall competitiveness, and enterprise's technological and management ability and comprehensive strength.
Currently, the studies on the marine industry are mostly studies on the strategic countermeasures of industrial development, on evaluations for industrial development potential, and on industrial mechanism. Based on the indepth study on the development status of China's marine engineering equipment manufacturing industry, Zhao Jinlou has explored the problems in the marine industry development and put forward relevant strategies [1]. With SWOT-AHP analysis method, Zhang Wei has proposed the development strategy and policy for China's marine engineering Marine engineering equipment manufacturing industry (hereinafter referred to as "marine industry") is the important prerequisite and foundation for the development of marine economy, and has great strategic significance for promoting the transformation and upgrading of marine manufacturing industry and accelerating the pace of building a maritime power [1]. Since 2010, China has successively formulated multiple plans, including Innovation and Development Strategy for Marine Engineering Equipment Industry, Mediumand Long-term Development Plan for Marine Engineering Equipment Manufacturing Industry (2011 2020), and Made in China 2025. At present, China's marine engineering equipment manufacturing industry has made great progress, but its development is still in at the middle and end of the world's marine industry development chain, and technology, products, etc. need to be improved. Along with the increasingly fierce global competition, the increasingly shortened product life cycle, and the enhancement of market demand drive function, one of the main problems to be solved for China's marine industry enterprises is to improve their own competitive advantages and the core competitiveness of the entire supply chain. Supply chain is based on the premise of meeting customer demands, and centers on the core enterprises to win the market with the lowest cost, the fastest speed, the best quality, the best service through the control over information flow, material flow and capital flow throughout the process from the purchase of raw materials to completion of intermediate products and final products [2]. At present, the cooperation between enterprises in supply chain has changed from one-to-one cooperation to multienterprise cooperation, with strategic cooperation alliance among enterprises in supply chain formed finally [3]. Ma Shihua [3] pointed out that, inter-enterprise competition is no longer the competition launched by a single enterprise in a certain time and space to compete for market share of certain terminal markets, but the overall competition across time and space and based on product design, manufacturing, delivery and distribution, sales and services, and has transformed into supply chain efficiency competition. The supply chain mainly reflects the enterprise orientation based on market demand. In the processes of technology research and development, processing and production, the modularization and standardization degree of products are increasingly improved, and the integrated utilization of internal and external resources as well as the flexibility and agility in response to the market are enhanced [5]. Selective cooperation between nodal enterprises in the supply chain is the only way for enterprises to grow cooperatively. Supply chain cooperative relationship refers to the cooperative relationship in which both parties in the cooperation undertake a series of exchange activities under the mode of sharing risks and benefits, with a complete set of monitoring mechanism established and implemented [6,7]. Therefore, based on the characteristics of marine engineering equipment manufacturing industry, this Paper proposes that the relationship between enterprises in the supply chain of marine engineering equipment manufacturing industry refers to the close connection between the upstream and downstream enterprises of the marine industry in a certain form of cooperation, and a development system to enhance the core competitiveness of enterprises and achieve the overall strategic objectives of China's marine industry shall be established. The building of cooperative relationship between enterprises in the supply chain of marine industry is of great theoretical and practical guidance significance to China's marine industry in terms of improving the overall competitiveness, and enterprise's technological and management ability and comprehensive strength.
Currently, the studies on the marine industry are mostly studies on the strategic countermeasures of industrial development, on evaluations for industrial development potential, and on industrial mechanism. Based on the in-depth study on the development status of China's marine engineering equipment manufacturing industry, Zhao Jinlou has explored the problems in the marine industry development and put forward relevant strategies [1]. With SWOT-AHP analysis method, Zhang Wei has proposed the development strategy and policy for China's marine engineering equipment manufacturing industry [8]. Hong wen, Chen Liang, et al. have studied the overall competitive environment of marine engineering equipment industry from the perspective of industrial division of labor and competitors, and pointed out the development trend of China's marine engineering equipment [9]. With the integrated DEMATEL/SIM method, Wu Xiaodong et al. have established the multilevel hierarchical system structure model that reflects the interaction between the development problem systems of marine engineering equipment industry, found the core problems in inter-enterprise development, and put forward the industrial development countermeasures from both the enterprise and the government levels [10]. In view of the pulling demand characteristics of China's ship and marine engineering equipment, Liu Xianquan performed a series analysis for the whole supply chain of the marine industry, and on this basis, put forward the strategy on how to avoid the risk of delivery [11]. Taking Fujian marine engineering equipment manufacturing industry as the study object, Zhang Zhe et al. have proposed countermeasures and suggestions on the development of marine engineering equipment manufacturing industry chain in key areas of Fujian Province through field investigation and information inquiry [12]. With DEA study method and statistical indicators of China Shipbuilding Industry Yearbook, Wu Xiaodong, Zhao Jingying, et al. have constructed an evaluation index system for provincial marine engineering equipment industry, and such system can be used to evaluate the relative efficiency in production of marine oil and gas resources platform products, the relative efficiency of scientific and technological research and development, and the influence of relative effect of related industries on marine engineering equipment manufacturing industry [13]. From the aspects of R&D, design and manufacturing technology capabilities, Pan Wei and Zhang Jijun have constructed an technical innovation capability evaluation index system applicable to marine oil platform manufacturing enterprises and consisting of 7 first-level indica-tors and 34 second-level indicators [14]. Cheng Yifei and Jia Xiangfeng have studied the exit mechanism of marine engineering equipment enterprises under environmental control from the perspective of public security interests and on the basis of analyzing the characteristics and policy institution of marine engineering equipment manufacturing industry [15]. With the structural equation model, Jia Xiaoxia and Xiahou Shuqin have concluded the influencing mechanism of network embedding on enterprise's technological innovation ability by taking 105 marine equipment manufacturing enterprises as the study objects [16,17]. With non-parametric Malmquist production efficiency method,Hong Xinyang has explored the reasons for the changes in enterprise's technological innovation efficiency from the perspective of technological progress and technological efficiency and by taking 10 listed companies in marine engineering equipment manufacturing industry as the study objects [18].
At present, scholars have studied the development strategy and industrial evaluation of China's marine industry. However, there are few studies on the cooperative relationship between enterprises in the supply chain of marine industry. Under such background of study, in this Paper, China's marine engineering equipment manufacturing enterprises are selected as the study objects, and the Grounded Theory qualitative study method is used to identify the factors influencing the cooperative relationship between enterprises in the supply chain of China's marine industry. Meanwhile, based on traditional DEMATEL method, GRNN (Generalized Regression Neural Network) is used in this Paper [19]. GRNN can effectively improve the feasibility of the direct correlation matrix analysis results. Besides, G-M method inherits and retains the "D-R" and "D+R" in traditional DEMATEL method to judge the importance of indicators, which has certain reference and expansion value for the relevant decision-making in the management for cooperation between enterprises in the supply chain of China's marine engineering equipment manufacturing industry.
Literature Review
The study on the factors influencing the cooperative relationship between enterprises in the supply chain is mainly divided into two perspectives: theoretical study and empirical study.
In terms of theoretical study, Zhang Cuihua et al. have proposed that the factors influencing the collaborative relationship between enterprises in the supply chain include inter-alliance-partner strategic factor and technical implementation factor [20], and based on B-S relationship, Ling Hong et al. [21] have proposed that organizational factor, environmental factor and technical factor are important factors influencing the cooperative relationship in the supply chain. Meanwhile, based on the above studies, it is pointed out that the degree of trust, the degree of information sharing and the quality of information sharing are important factors for the sustainable development of inter-enterprise relationship. Myhr has pointed out that the cooperative relationship between enterprises in the supply chain is affected by internal and external factors, where the external influencing factors include trust between enterprises, supply chain reliability, high-level support, common interests, information sharing, etc., and internal influencing factors include inter-enterprise commitments, enterprise cognition, internal management, etc. [22]. Zeng Wenjie and Ma Shihua have studied the factors influencing the collaborative relationship between node enterprises in the supply chain from the perspective of relationship in the supply chain, mainly including four measuring angles, i.e. communication, trust, commitment and cooperation [23]. Besides, product quality, delivery cycle, cost and inter-enterprise effective communication and service are important factors influencing the cooperative relationship between node enterprises in the supply chain. In addition, the supplier's product development and production, external environment of supply chain and other factors [24,25] also shall be included. Based on a friendship cooperation model between enterprises in the supply chain, Drake has pointed out that the inter-enterprise communication, trust mechanism and performance are the key links for the orderly maintenance of the friendship inter-enterprise cooperative relationship [26].
In terms of empirical study of specific industries or enterprises in the supply chain, basing on the empirical study on inter-enterprise cooperative relationship, AKkermans et al. have pointed out that trust, commitment and rights are also important factors affecting inter-enterprise cooperation [27]. Through studying the performance of inter-enterprise cooperation, Pan Wen'an [28] has proposed that inter-enterprise partnership is affected by organizational trust, relationship commitment and interdependence. Based on the study on manufacturing enterprises in the supply chain in Pearl River Delta of China, Ye Fei proposed that trust and commitment in supply chain partnership have a positive impact on the performance of inter-enterprise cooperation [29]. Based on the study on the manufacturing industry, Song Hua et al. have pointed out that the quality of inter-enterprise cooperation is an important indicator to ensure the maintenance of cooperation, and in addition, inter-enterprise cooperation conflicts are inevitable and must be solved in cooperation, and can point out the direction for future cooperation [30]. Through studying the manufacturing industry, service industry, information technology industry, real estate industry, etc, Li Yi believed that environmental dynamics, supplier dependence, willingness to commit and trust were important considerations affecting the selective cooperation among enterprises, and also affected the time dimension of cooperation among enterprises [31]. Dang Xinghua [32], based on the study on influencing factors under supply chain collaborative alliance mode, proposed that environmental factor, technological factor and internal organization are the important factors affecting the cooperative relationship, and refined these three factors into 11 second-level factors. Qiao Yanfen [33], based on the study on the factors influencing relationship between node enterprises in the supply chain from the perspective of taking manufacturer as the core, proposed three categories: product factor, technical factor and human factor.
There are few studies on the factors influencing the cooperative relationship between enterprises in the supply chain of China's marine industry, and the confidentiality of marine industry itself leads to the lack of relevant materials and historical data. Grounded Theory is a kind of inductive study on phenomena, and its essence lies in a series of spiral cycle progressive lifting processes of induction, comparison and analysis based on scientific logic [34], which ultimately form outline concept and theory; Grounded Theory has systematic and procedural characteristics, and its collection of relevant study data does not need to rely on historical data.
In view of the above studies, Grounded Theory analysis method has good tacit agreement with the study on the factors influencing the cooperative relationship between enterprises in the supply chain of China's marine engineering equipment manufacturing industry. First, most of the existing literatures directly determine the factors influencing the cooperative relationship between China's marine engineering equipment manufacturing enterprises on the basis of static analysis and scenario hypothesis, and hereby propose the strategies for improving management level for supply chain of marine engineering equipment manufacturing industry, lacking effective identification and analysis for the influencing factors. Because there are many factors influencing the cooperative relationship between enterprises in China's marine engineering equipment manufacturing industry, different factor analysis methods can bring diverse study conclusions. Second, based on the technological confidentiality, dynamics and complexity of marine engineering equipment manufacturing industry, Grounded Theory is very suitable for extracting the factors influencing the cooperative relationship between enterprises of China's marine engineering equipment manufacturing industry, identify the key influencing factors, and hereby build the corresponding theoretical model. Third, through the case analysis for China's marine engineering equipment manufacturing enterprises, it is easier to explain the role of the factors affecting the cooperative relationship between enterprises in the supply chain. Therefore, in this Paper, China National Offshore Oil Corp (CNOOC), Shanghai Waigaoqiao Free Trade Zone Group Co., Ltd., CIMC Raffles Offshore Co., Ltd., Dalian Shipbuilding Industry Group Co., Ltd., COSCO (Nantong) Shipyard Co., Ltd. and the subsidiaries of these corporations are taken as the main study objects, the Grounded Theory is used to collect and analyze data, and explore and construct the model study on the factors influencing the cooperative relationship between enterprises of China's marine engineering equipment manufacturing industry, and meanwhile G-D method is adopted to judge the identified key influencing factors.
Study method
Grounded Theory was first proposed by Glaser and Strauss [34,35]. It is a process of transforming data into concepts by inductive method after systematic data collection and mining and hereby establishing theory, and a more scientific qualitative study method. Grounded Theory emphasizes the collection and collation of data, and starts with ensuring the correctness and credibility of study conclusions. Its main purpose is to describe the properties and significance of the phenomenon from the theoretical level, and hereby establish a theory to collate, summarize, deduce and normalize various documents [36,37].
Sources and collection of data
Based on the theoretical sampling principle, in this Paper, the data is collected from multiple channels to improve the reliability, credibility and validity of study conclusions. The main sources of data selected are as follows: (1) enterprise's official website [data collation covers the development history, profile, annual report, major news, organizational structure, and core technologies (including submersible drilling platform, 981 drilling platform, jack-up drilling platform, deep-water pipe-laying crane vessel) of enterprises, as well as R&D team building, infrastructure supporting, etc.]; (2) TV, network and other media: to collect character interviews about marine engineering equipment manufacturing enterprises, to read/watch relevant articles and videos; (3) Network and TV media: to collect the development trend information, statistical yearbooks, news reports, industrial policies, regional policies and industrial development reports of marine engineering equipment manufacturing industry; (4) Phone call or face-to-face interviews with middle and senior enterprise managers: to collect relevant information about inter-enterprise cooperation. In order to ensure the heterogeneity and reliability of data collected, there are four main stages in data collection [38], as shown in the Figure 1 below. In the above steps, the work on collection and collation of relevant data lasted 12 months. In the early stage, the data on development background, growth process, major adjustment, etc. of upstream and downstream enterprises including 6 marine engineering final assembly enterprises and 18 final assembly enterprises were collected and collated. Besides, based on the company profile, rules and regulations, and important development strategies on the enterprise websites and brochures, data totaling 20,000 words was collated. In-depth interviews with senior and middle managers of four cooperative upstream and downstream enterprises were conducted, based on which interview memorandum (including outline, notes, summary, etc.) totaling 60,000 words was formed. Major corporations for whom the relevant data is collated are as shown in the following Table 1.
1982
CIMC Raffles Offshore Co., Ltd. ("CIMC Raffles") is a wholly-owned subsidiary of CIMC Group. It has four marine research institutes (which are respectively located in Yantai, Shanghai, Norway and Sweden) and three construction bases (which are respectively located in Yantai, Haiyang and Longkou) to form the overall industrial structure of "four institutes and three bases", and has nearly 10,000 employees. Its main businesses include the design, construction, maintenance and renovation of different marine equipment such as drilling platforms, production platforms, marine engineering vessels, offshore support vessels, marine ranch platforms, offshore wind turbine vessels, luxury yachts and high-end cruise ships, and offshore complexes, the operation and leasing of equipment, and "turnkey" general contracting services for customers. Shanghai Waigaoqiao Shipbuilding Co., Ltd.
Identification of the Factors Influencing the Cooperative Relationship Between Enterprises in the Supply Chain of China's Marine Engineering Equipment Manufacturing Industry
In this Paper, the Grounded Theory study method is used to collate and analyze the collected data and to refine the concepts, categories and their internal relationships from a large number of surveys and collected network self-intersections [38] to relatively, comprehensively and objectively identify the factors influencing the cooperative relationship between enterprises in the supply chain of China's marine engineering equipment manufacturing industry. At present, the most widely used Grounded Theory study method is procedural grounded theory study method.
Open coding
Open coding refers to the process of gradually conceptualizing and categorizing the acquired data records, and then correctly reflecting the data content with the concepts and categories, and breaking, crushing and re-integrating the data records and the abstracted concepts. The main purpose of open coding is to identify phenomena, define concepts and discover categories, i.e., to deal with the problem of data convergence [18]. Defining concepts refers to the process of summarizing different original data, establishing different free nodes and finally naming them unifiedly. Discovering categories refers to the process of converging and naming similar concepts. Based on above related original data, in this Paper, the data is coded and modeled, and meanwhile, the reserved part of the original data is used for theoretical saturation test. In order to ensure the correctness of understanding, through collating and classifying the original data and reading and analyzing the interview data of marine engineering equipment manufacturing industry and the related industry news trends word by word with the help of NVIVO 10.0 program, 316 original sentences are sorted out and more than 600 nodes are abstracted from the original sentences, based on which 100 concepts are synthesized. Category is the re-classification and re-integration for many concepts, i.e. category is the subsequent analysis focus [19].
Axial coding
Axial coding is a better development category based on the property and dimension of category. In this Paper, the relevance of different categories is obtained through studying the open coding, and further summarization and integration is performed to form a more conceptual fundamental category. Based on the analysis for the current situation of technological innovation and development and inter-enterprise cooperative relationship in China's marine engineering equipment manufacturing industry, 34 categories were summarized into 7 fundamental categories.
Selective coding
Selective coding is to systematically link the core category with other categories by logical relations, and to complete the categories that are not fully developed. The main task of this process is to identify the core category [40] which can dominate other categories. All concepts are explained concisely by developing story lines, canonical relation structure and developed categories. In this Paper, the canonical relation structure is used to determine the core category, i.e. cooperative relationship between enterprises in the supply chain of marine engineering equipment manufacturing industry, and three fundamental categories, i.e. selection of partners for cooperation between enterprises in the supply chain, behavior for cooperation between enterprises in the supply chain, and external environment, based on which the story line of the core category is described. The behavior for cooperation between enterprises in the supply chain of marine engineering equipment manufacturing industry determines the development of the cooperative relationship between enterprises. The performance of the core enterprises in the supply chain is used to check the quality of the cooperative relationship. Some uncontrollable external factors are also important influencing factors for the development of enterprises. Selection of partners for cooperation between enterprises in the supply chain factor influencing the cooperative relationship between enterprises in the supply chain of marine engineering equipment manufacturing industry The technical capability and operation situation of marine engineering equipment manufacturing enterprises are the important prerequisites and primary considerations for choosing partners for cooperation between enterprises in the supply chain of marine engineering equipment manufacturing industry. Enterprise's social recognition and willingness to cooperate are the necessary and sufficient conditions for the final determination of the cooperative relationship between enterprises. Behavior for cooperation between enterprises in the supply chain factor influencing the cooperative relationship between enterprises in the supply chain of marine engineering equipment manufacturing industry Trust, communication and collaboration, and opportunism between enterprises in the supply chain are important behaviors for cooperation between enterprises in the supply chain, and they are also important means to affect the maintenance and development of cooperation between enterprises in China's marine engineering equipment manufacturing industry. External environment factor influencing the cooperative relationship between enterprises in the supply chain of marine engineering equipment manufacturing industry External environment mainly refers to the policy environment and market environment, etc. faced by the industry. The guidance from the government and the support from financial institutions are the basic guarantees for the technological innovation of marine engineering equipment manufacturing enterprises. The constant changes in market demand play an important guiding role in the technological innovation of marine engineering equipment manufacturing industry.
Theoretical saturation test
The so-called saturation means that the data collection can be stopped if data on the characteristics of a certain category cannot be further developed, that is, theory tends to be saturated. In order to ensure the creditability of the study, in this Paper, theoretical saturation test is performed for above conclusions. In this study, open coding, axial coding and selective coding were performed for the reserved 1/3 of original materials, and no frequent new concepts and categories were found in the testing process, so above theoretical model is saturated.
Determination of influencing factors and model interpretation
Through open coding, axial coding, selective coding and analysis and study on the canonical relationship structure, the core category (i.e. cooperation between enterprises in the supply chain of marine engineering equipment manufacturing industry) is determined, and on this basis, model of the factors influencing the cooperative relationship between enterprises of China's marine engineering equipment manufacturing industry is constructed (as shown in Fig. 2). The study indicates that the 7 major influencing factors (i.e. fundamental categories) are respectively enterprise's operational and technical capabilities, corporate reputation, enterprise's willingness to cooperate, trust between enterprises in the supply chain, communication and collaboration between enterprises in the supply chain, opportunism and external environment.
1) Enterprise's operational and technical capabilities
Enterprise's operational capability is the comprehensive embodiment of the enterprise's own capability in its daily business activities. Especially when the operation objectives of high-tech enterprises are consistent with those of other enterprises, the enterprises will express friendly willingness to cooperate. Enterprise's operational capability reflects the timeliness, management capability, product capability and ability to react to market conditions of the enterprises for operating the cooperation in the management of cooperation. The operation cost reflects the enterprise's operational capability. Enterprise's operation management runs through the whole process of production, manufacturing and cooperation of the enterprise. Enterprises acquire advanced technology and information from the outside world, and then create new technology and information by combining such Fig. 2 Conceptual model of the factors influencing the cooperative relationship between enterprises in the supply chain of china's marine engineering equipment manufacturing industry acquired advanced technology and information with internal knowledge to realize technological innovation and diffusion and achieve technological knowledge reserve and accumulation. This kind of technological knowledge contains lots of tacit knowledge and exists in the process of organization, so technical capability can only be acquired through learning, which is a long-term cumulative process. The effectiveness of the cumulative learning depends on the recipient's preparatory technical knowledge and effort intensity. In this sense, it is consistent with An Tongliang's enterprise's technological capability concept: An Tongliang believes that enterprise's technological capability is cumulative learning in which the enterprise chooses, acquires, digests, absorbs, improves and creates technology and integrates such technology with other resources to produce products and provide service [41]. That is to say, enterprise's technological capability is the collection of enterprise's ability to acquire information and other resources, and the technician's ability to integrate, reserve, and organize and coordinate resources. From the perspective of science and technology, enterprise's technological capability is a system integration function that is supported by enterprise's financial ability, centered on and determined by product innovation ability and process innovation ability, and serves for realization of technological innovation strategy. Technological innovation always takes place in specific economic environment, factor background, cultural background and organizational structure. Economic environment and other factors determine the technological innovation capability of different enterprises, and meanwhile determine the primary factor for enterprises in the supply chain to choose partners.
2) Corporate reputation Corporate reputation: the company's behavior and norms have been highly recognized or convinced in the society, so the company can obtain higher social status and greater support in the economic market, and acquire the necessary resources and opportunities or the ability to withstand various uncertainties in the future. In the cooperation between node enterprises in the supply chain, corporate reputation refers to the comprehensive evaluation on the enterprise by internal and external actors, including raw material suppliers, manufacturers, equipment enterprises, governments, research institutions, media and end users. Such evaluation is based on the information transmission and interaction in the company's social network. Corporate reputation is an important source of sustainable competitive advantage, and also comprehensive evaluation on the business activities of the enterprise in the market. Its value comes from the asymmetry of information. Firstly, enterprises with positive reputation can obtain more trust from their partners and can easily acquire more opportunities to cooperate closely with other enterprises, and vice versa. Secondly, corporate reputation can be used as a restraint and incentive mechanism between enterprises, and can reasonably reduce costs. Besides, from the perspective of enterprises themselves, in the reputation value itself, the incentive effect of corporate reputation has characteristics of perennity and complexity, far higher than the short-term interests of enterprises. Thirdly, good corporate reputation can help enterprises consolidate and promote the establishment and maintenance of transaction relationship with node enterprises in the supply chain.
3) Enterprise's willingness to cooperate Willingness to cooperate: whether the member enterprises of cooperation organization are willing to coordinate and cooperate with the other members of the organization, whether they are willing to take a series of activities beneficial to the development of the organization, and whether their behaviors can bring benefits to the member enterprises and achieve the anticipated goal of cooperation. Competition, efficiency, information and learning demands are all external manifestations of enterprises to achieve their survival goals fundamentally, while the technology, R&D and market entry demands of enterprises are classified according to their strategic intentions, which is the way to expand their survival space. For enterprises in the supply chain of China's marine engineering equipment manufacturing industry, technological upgrading and expansion for their survival space are the essential needs to expand their cooperation. Therefore, clarifying the enterprise's willingness to cooperate is conducive to achieving an effective cooperation system between enterprises, reducing the risk of research and development for both sides, reducing the cost of opportunism, and acquiring accurate cooperation information, and is an important precondition for establishing an efficient cooperative strategic alliance between enterprises 4) Trust between enterprises in the supply chain Trust between enterprises in the supply chain: Node enterprises in the supply chain, including suppliers, manufacturers, customers, intermediaries and other organizations, believe that partners have the ability to abide by the rules and fulfill their commitments during the cooperation process and firmly believe that the partners will not betray to gain more personal benefits. Trust between enterprises is a key and core factor for enterprises to maintain and develop cooperation, which facilitates information sharing between enterprises, reduces transaction costs and opportunism, and enhances the stability of mutual cooperation and cooperation ability to respond to uncertain external environment.
5) Communication and collaboration between enterprises in the supply chain
When node enterprises in the supply chain choose to cooperate, problems such as uneven profit distribution, unsmooth information flow and asymmetric information sharing are likely to occur in the process of cooperation. Therefore, the communication and collaboration mechanism between enterprises in the supply chain is an operation mechanism that is based on the sharing of resources, technology and business strategy, brings the upstream and downstream enterprises of the node enterprises in the supply chain together, and can realize inter-enterprise sharing of information and technology, absorption and transfer of knowledge, conflict resolution, rational reduction of R&D risks, etc., and it aims to maintain the cooperation between enterprises in the supply chain and ensure the enterprises to obtain the expected benefits as stipulated in the contract and improve the overall competitive advantages.
6) Opportunism
Opportunism refers to a kind of speculative behavior that damages the interests of partners due to a cunning means like deception, concealment or distortion performed by the node enterprise in the supply chain to maximize its own benefits in the face of asymmetric information transmission in cooperation.
These fundamental categories and their corresponding categories affect the cooperative relationship between enterprises in China's marine engineering equipment manufacturing industry in varying degrees, and the fundamental categories are interrelated and interact with each other. If one of the factors is unbalanced or missing, it will lead to the decline of the cooperative relationship between enterprises, and ultimately result in the decline of the performance of cooperation between enterprises, affecting the competitiveness of the entire supply chain. Therefore, only by identifying the factors influencing the cooperation between enterprises in marine engineering equipment manufacturing industry, can we better realize the technological innovation of enterprises and maintain the development of core competitiveness of enterprises.
GRNN-DEMATEL Based Empirical Analysis on Influencing Factors
In this paper, with qualitative study method, factors in seven levels influencing the cooperative relationship between enterprises in the supply chain of marine engineering equipment manufacturing industry are qualitatively identified, including enterprise's operational and technical capabilities, corporate reputation, enterprise's willingness to cooperate, trust, communication and collaboration, opportunism and external environment. On the basis of qualitative study results, in order to enhance the validity, operability and feasibility of qualitative study results, DEMATEL (Decision Making Trial and Evaluation Laboratory) has constructed a direct impact matrix that can reflect the logical relationship among different factors by using graph theory and matrix tools. This matrix can improve the understanding for specific interrelated problem groups and complex cluster problems and achieve sorting and causal quantitative analysis for the degree of mutual influence among different factors. However, with DEMATEL method, it is difficult to solve the realistic problem in the relationship among the factors influencing the cooperative relationship between enterprises in the complex supply chain, and besides, the subjective judgment process of experts may affect the credibility of the final result. Therefore, in this Paper, GRNN-DEMATEL empirical analysis method is used to empirically analyze the factors influencing the cooperative relationship between enterprises in the supply chain of marine engineering equipment manufacturing industry.
GRNN (Generalized Regression Neural Network)
GRNN was proposed by American scholar Donald F. Specht in 1991, which is a radial basis neural network suitable for solving nonlinear problems, with strong nonlinear mapping ability and high degree of robustness, flexibility and fault tolerance. Compared with RBF and BP neural networks, GRNN has a strong advantage in learning speed and approximation ability in processing unstable data, especially in the case of a small number of corresponding samples, it can achieve good prediction effect [13,14]. The structure of GRNN is composed of four layers: input layer, pattern layer, summation layer, and output layer. Where, network input is: Input layer [13,14] After simple distribution, each neuron is transmitted to the pattern layer as an input variable, where: Dimension of input vector = number of neurons. The number of neurons is set to Pattern layer In the pattern layer, the neuron transfer function is set to: n -Number of learning samples, used to represent the number of neurons; X -Network input variable; Xi-Learning sample corresponding to the ith neuron; σ -Smoothing factor; i-neurons.
I output is the Euler distance function between the input variable and its corresponding sample X.
Summation layer
The summation layer is to sum the outputs of two types of neurons in the pattern layer, and the transfer function is radial basis function. 1 st type: It arithmetically sums the outputs of all neurons in the pattern layer, where the connection weight between the pattern layer and each neuron is 1, and the transfer function is: It sums the outputs of all the neurons in the pattern layer, i.e. the summation of the i th neuron in the pattern layer and the i th molecule in the summation layer. The connection weight between neurons is the j th element in the i th output sample Yi. The transfer function is: (4) Output layer [13,14] Y j refers to dividing each neuron by the output of summation layer, and it is a linear function, i.e.
Where, k represents the number of neurons in the output layer, k = dimension of output vector of learning sample.
In this Paper, the weight w is obtained by using the target output and input values in GRNN, based on which the influence degree of each index on the target output is measured, and hereby the influence degree of each influencing factor on the final result is obtained [13].
GRNN-DEMATEL model
GRNN-DEMATEL algorithm inherits and retains the values of "D-R" and "D+R" obtained by traditional DEMATEL method, and uses "D-R" index to distinguish the result group and cause group in the factor group, and uses "D+R" value to judge the importance of each index. The specific steps are as follows: (1) Use the target index value of the tth study object as the target output vector of GRNN to obtain the weight vector: ω = (ω t j ) = S × P Where, w t j is the weight of the j th influencing factor of the t th study object on target index, t = 1, 2, · · · , m.
(2) Obtain the average value wj* of the influence degree of the j th influencing factor on the target index: Where, m is total number of study objects, and ω t j is the absolute value of ω t j .
(3) Calculate the direct correlation matrix of each influencing factor index: Where, b ii = 0,b i j = ωi * ω j * , if ω j * =0, then b i j =0, the importance of the i th influencing factor index relative to the j th influencing factor index. (4) Normalize the direct correlation matrix: (5) Calculate the full association matrix: where, (1-X)-1 is the inverse of, and I-X is unit matrix. (6) Establish a causal relationship diagram. Define D as the sum of all rows of T , and R as the sum of all columns of T . "D i + R i " is defined as the prominence of index i. The greater the prominence is, the greater the importance of this index will be. "D i − R i " is defined as the correlation degree of index i, which can be used to distinguish the cause group and the result group. If the "D i − R i " of index i is greater than 0, the index belongs to the cause group; if the "D i − R i " of index i is less than 0, the index belongs to the result group. Among so many influencing factors, the influencing factors in the result group are the affecting results of the influencing factors in the cause group.
Empirical analysis
Selection of data for empirical analysis In foregoing paragraphs, with qualitative study method, factors in seven levels influencing the cooperative relationship between enterprises in the supply chain of marine engineering equipment manufacturing industry are qualitatively identified, including enterprise's operational and technical capabilities, enterprise's social recognition, enterprise's willingness to cooperate, trust, communication and collaboration, opportunism and external environment. On the basis of qualitative study results, in order to enhance the validity, operability and feasibility of qualitative study results, in this Paper, GRNN-DEMATEL empirical analysis method is used to empirically analyze the factors influencing the cooperative relationship between enterprises in the supply chain of marine engineering equipment manufacturing industry. Besides, in this Paper, Likert 1-7 subscale is used prepare questionnaires, empirical analysis data is collected through on-site distribution of questionnaires, and 120 senior and middle managers of marine engineering equipment manufacturing enterprises are invited to respectively grade the influence degrees of "enterprise operational and technical capabilities, corporate reputation, enterprise's willingness to cooperate, trust, communication and collaboration, opportunism, and external environment on the cooperative relationship between enterprises in the supply chain of marine engineering equipment manufacturing industry. Finally, 120 study samples are collected and 120 study objects are formed. These 120 marine engineering equipment manufacturing enterprises all have over 15 years of history, and they are representative and typical large and medium-sized enterprises in eastern China. The middle and senior managers of these enterprises are familiar with the operation mode of supply chain and know well the knowledge related to the supply chain of marine engineering equipment manufacturing industry.
Empirical analysis process and results
In this Paper, on the basis of collecting the sample data of study objects, matlab programming software is used to obtain GRNN-DEMATEL method based empirical analysis results on the factors influencing the cooperative relationship between enterprises in the supply chain of marine engineering equipment manufacturing industry, as detailed in Table 3. The empirical analysis results in Table 3 show that: (1) D+R values corresponding to the seven factors are all greater than zero; enterprise's operational and technical capabilities, corporate reputation, enterprise's willingness to cooperate, trust, communication and collaboration, opportunism and external environment are all the factors influencing the cooperative relationship between enterprises in the supply chain of marine engineering equipment manufacturing industry, where enterprise's operational and technical capabilities are the most important and critical factors affecting the cooperative relationship between enterprises in the supply chain of marine engineering equipment manufacturing industry; According to the degree and importance of the influence on the cooperative relationship between enterprises in the supply chain of marine engineering equipment manufacturing industry, in descending order, these influencing factors are ranked as follows: enterprise's operational and technical capabilities, corporate reputation, enterprise's willingness to cooperate, trust, communication and collaboration, opportunism and external environment. (2) D-R values corresponding to enterprise's operational and technical capabilities and external environment are greater than zero, while D-R values corresponding to the other influencing factors are smaller than zero; such results further reveal that in the seven factors influencing the cooperative relationship between enterprises in the supply chain of marine engineering equipment manufacturing industry, the cause-type influencing factors include enterprise's operational and technical capabilities and external environment, and the other five factors, the influencing results from the two cause-type influencing factors (i.e. enterprise's operational and technical capabilities and external environment), are result-type influencing factors. In order to better form and promote the cooperative relationship between enterprises in the supply chain of marine engineering equipment manufacturing industry, we should focus on taking these two cause-type influencing factors (i.e. enterprise's operational and technical capabilities and external environment) as the entry point and the fundamental starting point.
Operational and technical capabilities of the enterprises in the supply chain are the necessary conditions for enterprises to choose partners. Corporate reputation and enterprise's willingness to cooperate are the sufficient and necessary conditions for the final construction of the partnership. These three factors are the pre-influencing factors for the selection of partners for cooperation between enterprises in the supply chain of China's marine engineering equipment manufacturing industry. Trust, and communication and collaboration between enterprises in the supply chain are the necessary conditions for inter-enterprise cooperation behavior to keep stable and develop in a good direction. Opportunism is an inevitable negative factor in inter-enterprise cooperation and a key factor for enterprises to choose to continue or terminate the cooperation. Therefore, trust, and communication and collaboration between enterprises, and opportunism are the built-in driving forces for alliance cooperation of enterprises in China's marine engineering equipment manufacturing industry. The external factors affecting the cooperation between enterprises in the supply chain have typical uncertainties in their external environment, and because of such uncertainties, the changes in external environment become important links that must be considered and grasped at all times for the maintenance and development of inter-enterprise cooperation.
Study Conclusion and Inspiration
Study conclusion Because of the important strategic position of the marine engineering equipment manufacturing industry to China's marine economic development, and the technology confidentiality and complexity of the marine industry itself, it is difficult to analyze the factors influencing the cooperative relationship between enterprises in the supply chain of marine industry through quantitative indicators. Therefore, Grounded Theory qualitative study method is adopted. Meanwhile, the Grounded Theory based data coding qualitative study method shows that the main factors influencing the cooperative relationship between enterprises in the supply chain of China's marine engineering equipment manufacturing industry are respectively enterprise's operational and technical capabilities, trust between enterprises, communication and collaboration between enterprises, opportunism and external environment, corporate reputation, and enterprise's willingness to cooperate. In the process of enterprise cooperation, these influencing factors are presented as follows: first, in the process of establishing the cooperative relationship between enterprises in the supply chain of marine engineering equipment manufacturing industry, the three factors including enterprise's operational and technical capabilities, corporate reputation, and enterprise's willingness to cooperate are the important preconditions (i.e. pre-influencing factors); second, trust, and communication and collaboration mechanism between enterprises in the supply chain are important guarantee factors for the sustainable and efficient development of inter-enterprise cooperation; meanwhile, opportunistic behavior is inevitable in the cooperation process, but opportunism is controllable in the cooperation process; third, external environment (such as the policies on the development of enterprises in the supply chain of marine industry, and market economy, etc.) is an uncontrollable factor influencing the enterprise cooperation; when discussing its impact, quantitative study is impossible, but it is an important entry point for the study.
In this Paper, we use GRNN-DEMATEL method to empirically analyze the factors influencing the cooperative relationship between enterprises in the supply chain of marine engineering equipment manufacturing industry while studying the factors influencing the cooperation between enterprises in the supply chain of marine engineering equipment manufacturing industry. The study shows that these major influencing factors are mainly divided into two major categories: cause-type influencing factors (enterprise's operational and technical capabilities and external environment) and result-type influencing factors (corporate reputation, enterprise's willingness to cooperate, trust between enterprises, communication and collaboration between enterprises, opportunism and external environment). Cause-type influencing factors are the important foundation for study on inter-enterprise cooperation and the cornerstone of inter-enterprise synthesis. Result-type influencing factors have a guiding effect on the coordinated development between enterprises. The operational and technical capabilities of the enterprises in the supply chain are the necessary conditions for enterprises to choose their partners. The corporate reputation and enterprise's willingness to cooperate are the necessary and sufficient conditions for the enterprise partnership to be finally constructed. Trust, and communication and collaboration between enterprises in the supply chain are the necessary conditions for inter-enterprise cooperation behavior to keep stable and develop in a good direction. Opportunism is an inevitable negative factor in inter-enterprise cooperation and a key factor for enterprises to choose to continue or terminate the cooperation. The external factors affecting the cooperation between enterprises in the supply chain have typical uncertainties in their external environment, and because of such uncertainties, the changes in external environment become important links that must be considered and grasped at all times for the maintenance and development of inter-enterprise cooperation.
Inspiration
First, in this study, we take China's marine engineering equipment manufacturing industry as the study object to perform in-depth study on China's currently typical factors influencing the cooperative relationship between enterprises in the supply chain of china's marine engineering equipment manufacturing industry, and identify the important factors influencing the cooperative relationship between enterprises in the supply chain of China's marine engineering equipment manufacturing industry by systematic materials and empirical data and through Grounded Theory, long-term research data collection, tracking and study -enterprise's operational and technical capabilities, corporate reputation, enterprise's willingness to cooperate, trust between enterprises, communication and collaboration between enterprises, opportunism and external environment, etc.
Second, in this Paper, relevant data are coded and cases are studied by Grounded Theory study method, through which the unique and indispensable situational influencing factors are identified -external environment. Besides, GRNN-DEMATEL study method is used to further identify the influencing factors. The study results enrich the theoretical study on the cooperative relationship between enterprises in China's marine engineering equipment manufacturing industry, and can provide important guidance for the selection of cooperation alliance mode between enterprises in marine industry.
Thirdly, from the practical point of view, in view of the fact that the development of China's marine engineering equipment manufacturing industry is still in the middle and late stages, in this Paper, we identify and analyze the key factors affecting the cooperative relationship between enterprises based on typical enterprise practice situation. The study shows that only by scientifically and systematically identifying the influencing factors, can we accurately choose the cooperative mode and ensure the smooth development of cooperative relationship. | 11,648 | 2020-01-01T00:00:00.000 | [
"Business",
"Engineering"
] |
Fabrication of Isolated Iron Nanowires
Nanoscale interconnects are an important component of molecular electronics. Here we use X-ray spectromicroscopy techniques as well as scanning probe methods to explore the self-assembled growth of insulated iron nanowires as a potential means of supplying an earth abundant solution. The intrinsic anisotropy of a TiO2(110) substrate directs the growth of micron length iron wires at elevated temperatures, with a strong metal–support interaction giving rise to ilmenite (FeTiO3) encapsulation. Iron nanoparticles that decorate the nanowires display magnetic properties that suggest other possible applications.
T he potential of single molecule transistors to further the miniaturization of electronics remains an attractive goal. 1 A key challenge lies in the fabrication of interconnects, with self-assembled nanostructures showing considerable promise. 2,3In this work we make use of the remarkable properties of TiO 2 to construct oriented encapsulated metallic wires of nanometer dimensions.The surface properties of TiO 2 have been studied extensively for more than five decades following the discovery of its photocatalytic properties. 4,5Since then tremendous progress has been made in this field, and the applications of TiO 2 have expanded into a variety of technological areas including gas sensing, heterogeneous catalysis, corrosion protection, and electrical devices. 6etal nanoparticles on metal oxide supports have been studied extensively due to their wide-ranging technological applications.This is especially the case for rutile TiO 2 (110), which is the prototypical metal-oxide surface for fundamental research.Moreover, the TiO 2 (110)-(1 × 1) surface is anisotropic (see Figure S1), which facilitates the directed growth of nanostructures, 7,8 and the 3 eV band gap ensures electrical isolation of the conducting nanostructures from the substrate.Iron wires are investigated here, as the element is earth abundant and the wires offer potential in magnetic applications.As well as promoting self-assembly of metallic wires, the TiO 2 (110) substrate is also known to encapsulate metal nanostructures with oxides at elevated temperatures. 9,10his so-called strong metal support interaction (SMSI) 8,10−12 provides a potential means to insulate the metallic wires.
In this Letter, we investigate the magnetic, chemical, and topographic properties of Fe nanowires grown on rutile TiO 2 (110)(1 × 1) using X-ray spectromicroscopy techniques and scanning probe methods.The results suggest a fabrication strategy for insulated metal nanowires with potentially useful magnetic properties.
Scanning tunneling microscopy (STM) in London was used to determine the optimum growth conditions for the Fe nanowires.X-ray photoemission electron microscopy (XPEEM) and spin-polarized low energy electron microscopy (SPLEEM) experiments were conducted on the I06 beamline at Diamond Light Source 13 and at Osaka Electro-Communication University, 14 respectively (see the Experimental Methods in the Supporting Information).Rutile TiO 2 (110) crystals were prepared via multiple cycles of argon ion sputtering and annealing in UHV (∼1000 K) until a sharp (1 × 1) low energy electron diffraction (LEED) pattern was obtained and contamination was below the detection level of Auger electron spectroscopy (AES).Fe metal was deposited via physical vapor deposition in UHV from an electron-beam evaporator, while the TiO 2 (110) crystal was held at an elevated temperature (∼1070 K).LEED and AES results from Fe/ TiO 2 (110) are shown in Figure S2.
The deposition of Fe at elevated temperatures results in the formation of two types of nanostructures, namely, nanowires oriented along the [001] direction of the substrate (height ∼1 nm) and flat-topped pseudohexagonal islands (height ∼8 nm), as seen in Figure 1A and Figure 1B, respectively.This is a similar behavior to that observed for Pd/TiO 2 (110), 9 with the size and morphology of the resulting structures being tuned by variations to the substrate temperature and deposition amount.The elongation of the nanowires along the [001] direction is driven by the strain 15 induced by the anisotropy of the TiO 2 (110) substrate.This gives rise to a lattice mismatch between the substrate and an Fe(110) (bcc) overlayer of about 3% in the [001] direction and 12% in the [11̅ 0] direction. 16lso visible in Figure 1A are regions of reconstructed TiO 2 (110)-(1 × 2), formed as the surface becomes oxygendeficient during the high-temperature deposition of Fe.
An atomically resolved image of the surface of the pseudohexagonal island in Figure 1B is displayed in Figure 1C.The surface is composed of regular parallel rows of bright atomic-scale features aligned in the [001] direction of TiO 2 (110) and parallel to the long growth direction of the nanowires and resembles a modified Fe(110)-O "A" surface formed by O 2 adsorption on Fe(110), as described by Freindl et al. 17 The atomic-scale surface structure of the nanowires was observed in STM to be identical to that of the pseudohexagonal islands (see Figure S3).The presence of O on the surface of the nanostructures is expected due to facile migration/spillover of oxygen from the TiO 2 (110) substrate promoted by the elevated temperature during deposition, a clear indication of a strong metal support interaction (SMSI). 18o grow wires in preference to pseudohexagonal islands, a greater amount of iron was deposited than in the STM experiment (∼10 monolayer equivalents (MLE) vs ∼1 MLE).This also had the side effect of a 10× longer time period at high temperature (the dosing rate was the same), which promoted encapsulation with a metal oxide.Figure 1D−F
The Journal of Physical Chemistry Letters
shows Fe L 3 -edge XPEEM images (hν = 708 eV) of nanowires deposited onto TiO 2 (110) at ∼1070 K.The images show the presence of several Fe-containing nanowires with lengths of 5− 10 μm and widths up to ∼500 nm.Postanalysis with atomic force microscopy (AFM) showed that these nanowires had heights of <20 nm (Figure S4).The secondary-electron XPEEM measurements collect electrons with kinetic energies lower than 4 eV and as such will give a sampling depth in the range 5−10 nm, 19 so that the core of the nanowires will be sampled.The average height of the nanowires was about 14 nm.Small dot-like features decorate the surface of some of the nanowires as seen in Figure 1D and F. Additionally, large micrometer-sized irregularly shaped clusters were occasionally observed on the surface, an example of which is displayed in Figure 1E, which acted as a nucleation point for several nanowires.This feature was identified through X-ray absorption spectroscopy (XAS) and X-ray photoelectron spectroscopy (XPS) as calcium, a common bulk contaminant of rutile TiO 2 (110) samples. 5However, Ca was absent from most of the nanowires investigated.
X-ray absorption spectroscopy (XAS) at the Ti L edge (Figure 2) is used to compare the titanium species of the TiO 2 (110) substrate (A) and within the encapsulation nanowires (B).The spectrum of the substrate matches that expected from the TiO 2 (110) literature; 20 however, the spectrum obtained from the nanowires is rather different: in particular, we note the lack of splitting of the e g band at the L 3 edge and the differing intensity at the L 2 edge (substrate, t 2g band > e g band; wires, e g band > t 2g band).−23 Ordered ilmenite structures have been previously reported for low coverages of iron deposited onto the TiO 2 (011) surface under slightly oxidizing conditions, although these proved to be unstable at high annealing temperatures in contrast to the encapsulation layers here. 24hotoemission is used to probe the near surface of the nanowires, with Ti 2p (hν = 650 eV) and Fe 2p spectra (hν = 820 eV) probing to a depth of 4−5 nm. 25 The Ti 2p XPS spectrum (obtained via the micro-XPS mode of the XPEEM instrument, which sampled the bare substrate as well as a number of nanowires) reveals the presence of three types of titanium species, namely, Ti 2+ , Ti 3+ , and Ti 4+ , as displayed in Figure 2C.A Shirley type background was subtracted from the data, and each Ti 2p doublet was fitted to three contributions with Voigt lineshapes (30:70 Gaussian−Lorentzian ratio), corresponding to Ti 2+ , Ti 3+ , and Ti 4+ species.The fitting of these overlapping features requires the imposition of certain restraints such as the peak area and position; the area of the peaks in the Ti 2p 1/2 region was constrained to half that of the Ti 2p 3/2 region, the spin−orbit separation of each oxidized Ti species was held constant at 5.7 eV, and the Ti 2+ −Ti 3+ and Ti 3+ −Ti 4+ energy separation for each multiplet peak was set to 1.7 and 1.8 eV, respectively. 26The presence of reduced Ti species is partially indicative of photon-induced reduction of the TiO 2 , as has been reported previously from similar microfocused undulator beamlines, 27 in addition to the thermally induced surface reduction during the Fe deposition process.As micro-XPS also sampled some of the nanowires, the reduced Ti species may also originate from the encapsulation layer.From XPEEM imaging we estimate that approximately 5% of the surface region sampled for the data in Figure 2 was covered by nanowires.
The XPS spectrum of the Fe 2p region of the nanowires (also obtained in the micro-XPS mode of the XPEEM instrument, which sampled a region containing a few nanowires as well as the bare substrate) is displayed in Figure 2D.The interpretation of Fe 2p XPS is challenging, especially in the case of mixed-oxide systems.Nevertheless, the low binding energy feature at 706.6 eV matches well with that reported for metallic Fe 0 , and the main peak at 709.7 eV is likely to be related to oxidized Fe 2+ and Fe 3+ species along with their complex multiplet structure. 28An Fe 2+ contribution is expected for an ilmenite layer, with Fe 3+ possibly arising from Fe 2 O 3 at the interface with the iron nanowires.The faint metallic iron component (<5% of the total peak area) suggests that the encapsulation layer has a thickness of around 0.5 nm, given the probing depth at a photoelectron kinetic energy of ∼100 eV.Given the total wire thickness of ∼14 nm (see Figure S4) and assuming a uniform encapsulation layer, this reflects a metallic iron contribution of ∼85% of the total wire volume.
X-ray magnetic circular dichroism (XMCD) XPEEM measurements were used to probe the magnetic behavior of the iron nanowires.Figure 3A shows an XAS image obtained at the maximum of the Fe L 3 edge (hν = 708 eV).The nanowires (elongated stripes) and bright nanodots are clearly visible on the darker TiO 2 (110) substrate.An XMCD (magnetic contrast) image was recorded at the L 3 edge and is displayed in Figure 3B.The XMCD image was calculated from two sets of images recorded at the Fe L 3 peak, normalized with the offresonance image, with right (μ + ) and left (μ − ) circularly polarized light, as (μ + − μ -)/(μ − + μ + ).Domains magnetized
The Journal of Physical Chemistry Letters
parallel or antiparallel to the polarization vector will appear black or white in the XMCD image, while domains with a magnetization perpendicular to the polarization vector will have a gray contrast (corresponding to zero XMCD asymmetry). 29In the Figure 3C data, there is evidence that the nanodots are well magnetized as they display a pronounced contrast in the XMCD image.The nanowires, however, do not display any sizable contrast in the XMCD images in Figure 3B.Further XMCD images of nanodots from other regions of the sample are displayed in Figure S5.Parts C and D of Figure 3 show an XMCD image and an XAS image, respectively, where the nanodots display opposite contrast in XMCD at the L 3 edge (see line profiles in Figure 3E), indicating their opposite magnetization directions.
The Fe L 2,3 -edge X-ray absorption spectra acquired from the nanodots and the nanowires imaged in Figure 3A are displayed in Figure 4. Figure 4A shows the integrated XAS spectra (normalized to the pre-edge region) calculated by sampling stacks of XPEEM images to acquire spatially resolved XAS as well as right (μ + ) and left (μ − ) circularly polarized spectra.The green and orange curves were collected from the nanodots and the nanowires, respectively.As expected from the intensity of the two species observed in the image in Figure 3A, the dots display a higher overall intensity, as well as a slightly different line shape.The Fe L 2,3 -edge absorption spectra of the nanowires very closely match that of FeTiO 3 , primarily composed of octahedral Fe 2+ with the main L 3 peak at 708 eV accompanied by a shoulder characteristic of Fe 3+ at 710 eV and the L 2 peak at 720.8 eV; 21 the results are consistent with the mixed-oxide view from our XPS data in Figure 2. The lower panel of Figure 4A displays the calculated (using CRISPY) 30 XAS spectrum of Fe 2+ in an octahedral geometry (pink dashed line) showing particularly good agreement with the fine structure of the L 2 edge for the nanowires.−12 The nanodots display a less pronounced L 3 shoulder at 710 eV and a quite different L 2 edge, where the feature at 719.4 eV is no longer present, indicating a lower amount of Fe 3+ and more metallic character.Figure 4B shows separate XAS spectra from the nanodots acquired with right (blue) and left (red) circularly polarized light, as well as the XMCD difference between the two (black, dashed line) and the calculated (using CRISPY) 30 XMCD for octahedral Fe 2+ (dashed pink line).Figure 4C shows the same set of spectra as those acquired from the nanowires.There is a clear XMCD signal from the nanodots compared with a very minor signal from the nanowires, in line with the results seen in the imaging experiments in Figure 3.−23 The system here contains a mixture of iron species as well as a nanosized object that has unknown band structures.Hence, rather than extracting the absolute values of the magnetic parameters m l and m s for the nanodots and wires from the spectra we use the ratio m l /m s , which only depends on the p and q values. 31,32The measurement of these from the XMCD spectra is shown in Figure S6 and Table ST1.−33,36−40 Overall, our XAS and XPS results present a complex picture that suggests that the nanowires and nanodots are composed of a metallic iron core with an encapsulation layer consisting of mixed Fe−Ti oxides, possibly a mixture of FeTiO 3 and α-Fe 2 O 3 , which would explain the presence of the mixed valence state of Fe The Journal of Physical Chemistry Letters (Fe 0 , Fe 2+ , and Fe 3+ ) and the existence of an XMCD signal.Moreover, the nanodots display a more metallic character, with a subsequent significantly higher XMCD signal.
In order to probe the magnetic behavior of the nanowires and nanodots in a more surface-sensitive manner, spinpolarized LEEM (SPLEEM) images were acquired on a different Fe/TiO 2 (110) sample prepared in the same way.At the starting voltages used for the images in Figure 5, the typical probe depth of the SPLEEM is around 0.4−0.5 nm.This compares with the secondary electron XPEEM results shown above, where the probe depth is up to a few nm.Despite the identical growth conditions, nanodots were not observed on these samples, and the only Fe-related structures formed were nanowires which displayed the same general morphology as those prepared for the synchrotron experiments.SPLEEM images of a typical wire are displayed in Figure 5, where parts A and B were acquired with the polarization vector of the incident beam (P 0 = 90%) parallel to the [110] direction of the surface, along with the asymmetry image (Figure 5C).No magnetic contrast was observed in this asymmetry image.In order to examine possible orientation dependence, SPLEEM images were also acquired with P parallel to the [11̅ 0] and [001] crystallographic directions of the substrate, and the results also showed no magnetic contrast.The discrepancy of these results with the slight XMCD signal detected by the XMCD measurements shown in Figure 4 is due to the greater surface sensitivity of the electron-based probe compared to the soft X-rays, which do not probe the metallic iron in the core of the nanowires.
In summary, insulated nanowires of metallic iron were grown on a rutile TiO 2 (110) support.These nanowires, insulated by encapsulating in a mixture of FeTiO 3 and Fe 2 O 3 , are decorated with magnetic nanodots.This type of selfassembled wire, fabricated from earth-abundant materials, suggests its application as an interconnect in nanoscale electronics.
Additional details of the experimental and theoretical methods and further characterization of the nanowire system (AFM, STM, low energy electron diffraction, and XMCD spectro-microscopy) (PDF) Transparent Peer Review report available (PDF) ■ AUTHOR INFORMATION
Figure 1 .
Figure 1.Structural characterization of iron nanostructures prepared on TiO 2 (110) at 1070 K. (A) STM image of an Fe nanowire (V s = +1.0V, I t = 0.2 nA) recorded after deposition of 1 MLE Fe. (B) STM image of a pseudohexagonal Fe nanoisland (V s = +2.9V, I t = 0.07 nA) recorded after deposition of 1 MLE Fe. (C) High-resolution image of the top surface of the Fe islands (V s = +3.0V, I t = 0.14 nA).(D−F) XPEEM images of Fe nanowires recorded after deposition of 10 MLE Fe at 1070 K (hν = 708 eV, KE = 4 eV).All images have the same orientation with respect to the TiO 2 (110) substrate.
Figure 2 .
Figure 2. The nature of the Ti species on the encapsulated nanowires and oxidation states of Ti and Fe associated with the nanowires and substrate.Ti L-edge XAS spectra of the Fe/TiO 2 (110) system acquired from XPEEM images (KE = 4 eV), with sampling of areas corresponding to the bare substrate (A, red curve) and the Fe nanowires (B, blue curve).(C) Ti 2p XPS spectrum (hν = 650 eV) and (D) Fe 2p XPS spectrum (hν = 820 eV), obtained from the Fe nanowires supported on TiO 2 (110) with bare substrate in-between.
Figure 3 .
Figure 3. Magnetic behavior of the nanowires and dots.XMCD-XPEEM (KE = 4 eV) images of Fe nanowires and nanodots (green circles in parts A and B) supported on TiO 2 (110) at the Fe L 3 edge (hν = 708 eV).(A) XAS image and (B) XMCD-XPEEM image of the same 10 μm FOV.(C) XMCD image highlighting a few of the nanodots.(D) XAS image of the same area as part C, showing the morphology of the dots and wire (2 × 2 μm 2 ).(E) Line profiles across two of the nanodots from the XMCD image in part C.
but close to values recorded for Fe 2 O 3 −FeTiO 3 by Hojo et al. (m l /m s : 0.21 in plane, 0.14 out of plane; H = 10 T, T = 150 K)
Figure 4 .
Figure 4. Fe L-edge XAS and XMCD spectra (KE = 4 eV) obtained from the Fe structures on TiO 2 (110).(A) Integrated XAS (average of rightcircular and left-circular spectra) taken from regions of the images in Figure3Acorresponding to the nanodots (green) and nanowires (orange).Spectra are normalized to the pre-edge region.The calculated Fe 2+ XAS spectrum is shown in the lower panel as a dashed pink line.(B) Circularly polarized XAS (blue, red lines) and XMCD (dashed black line) spectra from the nanodots.Spectra are normalized to the edge step.The lower panel shows the calculated XMCD spectrum for Fe 2+ in octahedral geometry (dashed pink line).(C) Circularly polarized XAS (blue, red lines) and XMCD (dashed black line) spectra from the nanowires.Spectra are normalized to the edge step.The lower panel shows the calculated XMCD spectrum for Fe 2+ in octahedral geometry (dashed pink line).
Figure 5 .
Figure 5. Spin-polarized LEEM images of a typical Fe nanowire on TiO 2 (110).The wire was prepared with the sample held at ∼1100 K. Parts A and B were acquired at room temperature with the electron beam polarization vector P // [110] with spin up and spin down, respectively.The resulting asymmetry image is displayed in part C. FOV = 10 μm, SV = 4.1 V. | 4,627 | 2023-09-18T00:00:00.000 | [
"Materials Science",
"Physics"
] |
Neuroprotective Effect of Danhong Injection on Cerebral Ischemia-Reperfusion Injury in Rats by Activation of the PI3K-Akt Pathway
Many traditional Chinese medicines, including Danhong injection (DHI), can be used to treat cerebral ischemia-reperfusion injury and have neuroprotective effects on the brain; however, few studies have explored the mechanism by which this effect is generated. In this study, we investigated the neuroprotective effect of DHI against cerebral ischemia-reperfusion injury mediated via the PI3K-Akt signaling pathway. After establishing the model of middle cerebral artery occlusion (MCAO), 60 male Sprague–Dawley rats were allocated to six groups as follows: sham, MCAO, DHI (MCAO + DHI), LY294002 (MCAO + LY294002 [PI3K-Akt pathway specific inhibitor]), DHI + LY294002 (MCAO + DHI + LY294002), and NMDP + LY294002 (MCAO + NMDP [nimodipine] + LY294002). Hematoxylin and eosin (HE) and terminal deoxynucleotidyl transferase dUTP nick-end labeling (TUNEL) staining were used to evaluate the pathological changes of brain tissue and the degree of neuronal apoptosis. Real-time quantitative polymerase chain reaction (qRT-PCR), western blot analysis and enzyme-linked immunosorbent assays were used to measure the expression of Bad, Bax, Bcl-2, Bim, P53, MDM2, Akt, PI3K, p-Akt, p-PI3K, and Cyt-C. Compared with the MCAO group, brain tissue cell apoptosis was significantly reduced in the DHI group, and the brain function score was significantly improved. In addition, the expression of pro-apoptotic factors (Bad, Bax, and Bim) was significantly downregulated in the DHI group, while expression of the anti-apoptotic factor Bcl-2 was significantly upregulated, and expression of the apoptotic gene p53 was also significantly attenuated. Moreover, this neuroprotective effect was attenuated by the PI3K-Akt signaling pathway inhibitor (LY294002). Thus, our results confirmed the neuroprotective effects of DHI in rats with ischemia-reperfusion injury and indicate that these effects on the brain are partly generated by activation of the PI3K-Akt signaling pathway.
INTRODUCTION
Of the many types of cerebrovascular diseases, ischemic cerebrovascular disease is the most harmful (Catanese et al., 2017). Ischemic cerebrovascular disease is characterized by high morbidity and mortality (Dong et al., 2016); however, acute ischemic stroke is the main cause of many disabilities related to brain tissue damage in adults (Boers et al., 2013), Furthermore, acute ischemic stroke accounts for 30% of deaths worldwide. Within a few minutes after the onset of ischemic stroke, brain tissue cells begin to undergo necrosis; therefore, early thrombolytic therapy can restore blood flow in necrotic areas and reduce mortality in patients with ischemic stroke (Christophe et al., 2017). When the blood flow is restored, oxygen is returned to the ischemic area of the brain to rescue and re-establish neurons (Sanderson et al., 2013). In vivo and in vitro studies have shown that the structure of mitochondria changes during brain ischemia, thereby reducing the supply of energy and the occurrence of acidosis (Verdin et al., 2010). In addition, the process of cerebral ischemia is associated with the release of large amounts of oxygen-free radicals combined with calcium overload and inflammatory reactions (Pinton et al., 2008;Raha and Robinson, 2010).
Numerous studies in recent years have shown that apoptosis plays an important role in ischemic brain damage, especially in reperfusion damage (Chen et al., 2011). The mechanism of apoptosis in the brain ischemia is very complex, and its occurrence is regulated by a variety of genes, including the caspase, the Bcl-2, and p53 gene families (Green and Reed, 1998;Martinou and Youle, 2011). These genes are associated with the PI3K-Akt pathway, which is involved in the regulation of various other cellular functions such as cell proliferation, cell differentiation, and glucose transport (Brazil et al., 2004). Studies have also shown that the PI3K-Akt signaling pathway is involved in neuroprotection against cerebral ischemic injury (Janelidze et al., 2001;Noshita et al., 2001).
To date, many drugs have been used to treat cerebral ischemiareperfusion injury, but these are associated with problems such as a short therapeutic time window (Lee et al., 2018). Traditional Chinese medicine (TCM) has been practiced for thousands of years (Cheung, 2011) and has made a significant difference in the treatment of certain diseases, including cerebrovascular disease. Traditional Chinese herbal medicine is widely used to treat stroke (Bu et al., 2013;Fu et al., 2014). Since its launch in 2002, Danhong Injection (DHI) has been widely used to prevent and treat a variety of cardiovascular diseases, such as blood reperfusion damage, atherosclerosis, acute coronary artery syndrome and hepatic venous blocking disease (Yao et al., 2011). DHI is formulated from two well-known traditional Chinese medicines, Salvia miltiorrhiza Bunge (Danshen in Chinese) and Carthamus tinctorius L. (Honghua in Chinese). From the perspective of TCM, these compounds are often used in combination to achieve synergistic effects and reduce side-effects in the treatment of cerebrovascular diseases Li et al., 2015). According to previous studies in cerebral ischemia model mice, DHI significantly improves the survival rate and improves neurological symptoms and brain tissue damage after cerebral ischemic injury (Yu et al., 2012;Feng et al., 2018). DHI prevents the development of cerebrovascular thrombosis by promoting the growth of nerve cells and endothelial cells, alleviating local ischemia and hypoxia in the brain, and dilating cerebrovascular vessels and increasing vascular elasticity (Man et al., 2006). Thus, DHI has been shown to exhibit unique advantages in the treatment of cardiovascular and cerebrovascular diseases, although the specific mechanism of action remains to be clarified.
In this study, we evaluated the neuroprotective effect of DHI in a model of ischemia-reperfusion injury established in rats and investigate the potential mechanism by analyzing the expression of important genes and proteins in the PI3K-Akt signaling pathway. Our results provide experimental evidence based on modern pharmacology for the treatment of cerebral ischemic diseases and provides a scientific basis for the clinical use of DHI to treat cardiovascular and cerebrovascular ischemic diseases.
Reagents and Experiment Animals
DHI (10 mL/ampoules, China Food and Drug Administration Permission Number: Z20026866) was provided by Heze Buchang Pharmaceutical Co., Ltd., China. 1000 ml of DHI is prepared from 250 g of Carthamus tinctorius L. and 750 g of Salvia miltiorrhiza Bunge. China's State Food and Drug Administration has set clear and strict drug quality control requirements for DHI [The file number is WS-11220(ZD-11220)-2002-2017Z]. According to this standard, the main active substances of DHI are sodium danshensu (C 9 H 9 O 5 Na, not less than 0.80 mg per 1 ml DHI), protocatechuic aldehyde (C 7 H 6 O 3 , not less than 0.10 mg per 1 ml DHI), rosmarinic acid (C 18 H 16 O 8 , not less than 0.10 mg per 1 ml DHI), salvianolic acid B (C 36 H 30 O 16 , not less than 0.16 mg per 1 ml DHI), p-coumaric acid (C 9 H 8 O 3 , not less than 20 ug per 1 ml DHI), their chemical structures are shown in Figure 1.
Middle Cerebral Artery Occlusion (MCAO) Models Establishment
Rats were first anesthetized by intraperitoneal injection of chlorine hydrate (10%, 400 mg/kg). The rat was fixed and then cut along the midline of the neck to reveal the left common carrot artery (CCA), external carrot artery (ECA), and internal carotid artery (ICA). The proximal ends of the ICA, CCA, and ECA were clamped with a micro-arterial clamp. A small portion (4 mm in length) was cut in the CCA and a wire plug was inserted into the ICA. The plug was then inserted gently until a slight resistance was felt. Finally, the distal end of the CCA was ligated and the wound was sutured (Longa et al., 1989;Belayev et al., 1996). A successful model was judged by Horner syndrome in the right eye when the rats awoke up, with its left forelimb bent after lifting the tail, and moved left in a circle as they moved autonomously on the ground. Rats with massive bleeding, subarachnoid hemorrhage, and premature death were excluded after cerebral ischemiareperfusion injury. Finally, sixty male Sprague-Dawley rats were used in the experiment.
Animal Grouping
Sixty male Sprague-Dawley rats were allocated to six groups (n = 10 per group) as follows: sham, MCAO, DHI (MCAO + DHI), LY294002 [MCAO + LY294002 (PI3K-Akt pathway specific inhibitor)], DHI + LY294002 (MCAO + DHI + LY294002), and NMDP + LY294002 (MCAO + NMDP [nimodipine] + LY294002). The MCAO was established as described in section "Middle Cerebral Artery Occlusion (MCAO) Models Establishment". In the sham group, the artery was not ligated (only the threading process was performed), and the equivalent volume of physiological saline was administered. LY294002 (specific PI3K/Akt signaling pathway inhibitor) was diluted to 0.5 mg/mL in DMSO to prepare a stock solution. And 10 µL of the stock LY294002 was then injected 30 min prior to modeling. Animals were administered DHI at 0.84 mL/kg, which is equivalent to the human dosage of 8 mL. The conversion formula was as follows: The dose of rats (mL/kg) = 6.3 × the dose of human (mL)/60 kg. The dihydropyridine calcium antagonist NMDP (molecular formula: C 21 H 26 N 2 O 7 ) was used as a positive control drug in this experiment, and the dosages of NMDP for rats were 10 mL/kg according to a paper (Ai et al., 2016). DHI, DHI + LY294002 and NMDP + LY294002 groups were administered daily via the tail vein for 3 days. Sham and MCAO groups were given the same amount of physiological saline undergoing the same procedures.
Behavioral Observation
The degree of ischemia-reperfusion injury in rat brain tissue needs to be evaluated after modeling. According to the Zea-Longa neurological deficit scoring criteria, the neurological function of the rats was recorded based on behavioral changes (Ramya et al., 2010). Using this system, higher scores indicate more severe cerebral ischemia-reperfusion injury. The specific scoring criteria were as follows: 0 points, no symptoms of nerve damage; 1 point, the rat cannot fully extend the contralateral forepaw, indicating a minor neurological defect; 2 points, the rat turns to the temporal side, indicating a moderate neurological deficit; 3points, The rats were slumped to the contralateral side at rest, indicating serious neurological impairment; and 4 points, the rats could not be revived and consciousness was lost, indicating a very serious neurological deficit.
Measurement of Cerebral Infarction
The brain samples were collected at 72 h after cerebral ischemia and frozen at −20 • C for 12 min. Then the brain samples were sliced into 2-mm-thick coronal slices and immediately stained with 2% TTC solution at 37 • C for 12 min. Infarct volume was calculated the Image J, which expressed as a percentage of the total volume of slices.
Cyt-C and MDM2 ELISAs
Serum levels of rat Cyt-C and rat MDM2 were determined using commercial ELISA kits according to the manufacturer's instructions. All samples were analyzed in triplicate and the absorbance (OD value) of each well of the 96-well plate was measured at a wavelength of 450 nm. Concentrations of rat Cyt-C and rat MDM2 were then calculated with reference to relevant standards.
HE Staining
Rats were deeply anesthetized with 10% chloral hydrate (300 mg/kg) and fixed on a surgical board placed on a dissection table. The thoracic cavity was exposed and the heart was freed, the perfusion needle was inserted from the left ventricle until reaching the aortic level and fixed, and then frozen sterile saline (4 • C) was perfused. The rats were then decapitated and the brain tissue was removed by reperfusion of frozen 4% paraformaldehyde (4 • C). Immediately after sacrifice, rat brain tissue was removed and partially dewaxed with xylene (5 mm rat brain tissue). After dewaxed, the samples were washed (5×) using a graded ethanol series (100%, 95%, 80%, and 75% diluted with distilled water). After washing, the tissue was stained with hematoxylin (2 g/L) for 5 min and then rinsed again with distilled water. The sample was then immersed in hydrochloric acid/ethanol (1 ml of concentrated hydrochloric acid mixed with 99 ml of 70% alcohol) for 30 s and then in distilled water for 15 min. Samples were then immersed in eosin solution (1%) for 2 min before rinsing with distilled water. Finally, dehydration was carried out with absolute ethanol, and the tissue was sealed with a neutral resin. Images of the sample were collected by microscopic (NIKON ECLIPSE TI-SR and NIKON DS-U3) photographing (200 × and 400 × microscopic observation).
TUNEL Staining
Apoptosis-positive cells in the rat brain group were detected using TUNEL staining kits according to the manufacturer's instructions. Paraffin-embedded sections of rat brain tissue were deparaffinized and washed (3 × for 5 min) with phosphate buffered saline (PBS). Then, 2% proteinase K was added and digested for 30 min before washing (3 × for 5 min) with PBS. The TUNEL mixture was then added, and sections were incubated at 37 • C for 30 min before washing (3 × for 5 min) with PBS. Sections were then incubated with POD peroxidase labeling reagent for 30 min at 37 • C before washing (3 × for 5 min) with PBS. Thereafter, freshly prepared DAB solution was added. observed under a microscope for 2-6 min, rinsed with water, counterstained, and mounted. After TUNEL staining, sections were observed under an optical microscope. The number of TUNEL-positive (apoptotic) cells in three fields of non-overlapping brain tissue were counted for analysis.
Western Blotting
Brain tissue samples (100 mg) were placed in Petri dishes containing 1 mL of pre-cooled Lysis Buffer, and homogenized. The homogenate was centrifuged at 12,000 × g rpm for 5 min at 4 • C. The supernatant was transferred to a pre-cooled centrifuge tube and protein denaturation was carried out by the addition of loading buffer (containing β-mercaptoethanol at a ratio of 50:3) at a sample: loading buffer ratio of 1:4). Samples were boiled for 5 min at room temperature. The total protein concentration of the sample was determined using a BCA protein concentration assay kit. Proteins were then separated by SDS-PAGE concentrated glue and transferred to a PVDF membrane. After washing (3 × for 10 min) with Tris buffered salinetween (TBST), the PVDF membrane blocked in 5% skimmed milk powder for 2 h. After washing (3 × for 10 min) with TBST, the membrane was incubated (with shaking) overnight at 4 • C and with primary detection antibodies (rabbit anti-mouse monoclonal antibodies of Bim, Bax, Bcl-2, p-Akt, p-PI3K, PI3K, and AKT; dilution factors shown in section "Reagents and Experiment Animals "). The next day, membranes were shaken at room temperature for 30 min and then washed (3 × for 10 min) with TBST. Membranes were then incubated with the secondary detection antibody diluted in blocking solution and shaken for 1 to 2 h at room temperature. Subsequently, membranes were washed (3 × for 10 min) with TBST and protein bands were detected using a chemiluminescent reagent (A and B mixed 1:1). Each experiment was repeated three times using the same procedure to obtain an average value.
qRT-PCR Assay
Total RNA was isolated from rat brain tissue by incubation with TRIzol reagent (1000 µl TRIzol per 200 mg of rat tissue) for 5-10 min. After centrifugation at 12,000 × g for 10 min, the supernatant (1.5 mL) was mixed with 200 µL chloroform in a centrifuge tube and centrifuged at 12,000 × g rpm for 10 min at 4 • C. The supernatant was then mixed with 600 µL of isopropyl alcohol in a new 1.5 mL centrifuge tube and centrifuged at 12,000 × g rpm for 10 min at 4 • C. After discarding the supernatant, the precipitate was rinsed with 1 mL of 75% absolute ethanol (750 µL absolute ethanol and 250 µL of DEPC water) and then, 1 mL of absolute ethanol. After centrifugation at 12,000 × g rpm for 5 min at 4 • C, the supernatant was discarded and the RNA was resuspended in 40 µL of DEPC water for storage at −80 • C prior to analysis. cDNA was generated by reverse transcription at 42 • C for 15 min and 85 • C for 5 min. In preparation for qRT-PCR analysis, the samples were thoroughly mixed by vortexing and briefly centrifuged at 4000 × g rpm. The reaction system was prepared with 10 µL of UltraSYBR Mixture, 1 µL of PCR Forward Primer (10 µM), 1 µL of PCR Reverse Primer (10 µM), 2 µL of cDNA template and 6 µL of ddH 2 O. The qRT-PCR conditions were as follows: 95 • C for 10 min denaturation, followed by 40 cycles of 95 • C for 15 s, and 60 • C for 60 s. The primer sequences used for qRT-PCR are shown in Table 1.
Statistical Analysis
Data analysis was performed using SPSS 24.0 statistical software (SPSS Inc., Chicago, IL, United States). All data were expressed as mean ± standard deviation (x ± s), and P < 0.05 was be used as the criterion for statistical significance. In pairwise comparisons between groups, t-tests were used for two independent samples with homogeneity of variance, and Kruskal-Wallis H tests were used for those with heterogeneity of variance.
Nerve Function Assessment
Neurological function scores of each group were shown in Figure 2. No prominent changes were observed in the scores (all 0 points) of the sham group at 2, 24, 48, and 72 h after brain ischemia-reperfusion injury. Different degrees of nerve function damage were observed in the other five groups, with all scores significantly higher than those in the sham group (P < 0.05). Excluding the sham group, the scores in the other groups decreased over time, reaching their lowest at 72 h. In comparison with the MCAO group, the scores in the DHI, LY294002, DHI + LY294002, and NMDP + LY294002 groups were significantly lower at 72 h (P < 0.05). Furthermore, the score in the NMDP + LY294002 group was significantly lower than that in the LY294002 group at 72 h (P < 0.05), while there was no significant difference compared with the score in the DHI + LY294002 group (P > 0.05).
Cerebral Infarct Volume Assessment
As shown in Figure 3, TTC (2,3,5-triphenyltetrazolium chloride) staining showed deep red in the viable tissue and white color in the right infarcted hemisphere. There was no significantly cerebral infarction in the sham group. Compared with the sham group, the infarct volume was increased in the MCAO group (P < 0.01). Moreover, the infarct volume was significantly decreased in the DHI, LY294002, DHI + LY294002, and NMDP + LY294002 groups in comparison to the MCAO group (P < 0.01). Compared with the LY294002 group, the infarct volume was decreased in the DHI + LY294002 and NMDP + LY294002 groups (P < 0.05).
Histopathological Changes in the Hippocampus
As shown in Figure 4, hippocampal neurons and glial cells in the sham group were neatly arranged, with normal structures. The hippocampal nerve cells in the MCAO and LY294002 groups were disorganized, with disrupted cell membrane and swollen cell morphology, loss and death of a large number of neurons, and partial nuclear dissolution and condensation. In comparison to the MCAO group, neuronal and glial cell necrosis, nuclear condensation, cell membrane and cell structure destruction were improved in the DHI group. Compared with the LY294002 group, neuronal necrosis was reduced in the DHI + LY294002 and NMDP + LY294002 groups, with obvious pathological improvement.
Degree of Apoptosis in Brain Tissue Cells
As shown in Figure 5, no apoptotic cells (brown-yellow stained) were found in the brain tissue in the sham group. A large number of apoptotic cells were observed in the hippocampus of the MCAO and LY294002 groups. In comparison to the MCAO group, fewer apoptotic of neurons were observed in the DHI group. Furthermore, neuronal apoptosis in the DHI + LY294002 and NMDP + LY294002 groups was reduced compared to that in the LY294002 group. These findings indicated that DHI has an anti-apoptotic effect after ischemia-reperfusion injury, and this effect is blocked by the PI3K-Akt pathway inhibitor.
Serum Levels of Cytochrome-C and MDM2
As shown in Figure 6, serum levels of Cyt-C and MDM2 of rats in the MCAO group were significantly increased compared with Compared with the sham operation group, p < 0.05; compared with the MCAO group, *p < 0.05, **p < 0.01; compared with the LY294002 group, # p < 0.05, ## p < 0.01. Sham, sham operation group; MCAO, middle cerebral artery occlusion; LY294002, 2-(4-morpholinyl)-8-phenyl-chromone; DHI, Danhong Injection; NMDP, nimodipine. those in the sham group (P < 0.05). In comparison to the MCAO group, Cyt-C expression levels were significantly decreased in the DHI (P < 0.01) and NMDP + LY294002 groups (P < 0.05), and MDM2 expression levels were also significantly decreased in both groups (P < 0.01). In contrast, there was no significant differences in Cyt-C and MDM2 expression levels between the LY294002 and DHI + LY294002 groups (P > 0.05). In comparison with the LY294002 group, significantly decreased expression levels of Cyt-C (P < 0.05) and MDM2 (P < 0.0) were detected in the NMDP + LY294002 group, while there was no significant differences compared with the other groups (P > 0.05). These results indicated that DHI inhibits apoptosis and neuronal activity by reducing the level of Cyt-C and inhibiting MDM2 expression in brain tissue.
The Protein Expressions of PI3K-Akt Pathway Related Proteins in Each Group
As shown in Figure 7, p-Akt protein expression was significantly downregulated in the MCAO group compared with that in the sham group (P < 0.01), while there were no significant differences in the expression of p-PI3K, PI3K, and Akt proteins (P > 0.05). Furthermore, p-Akt protein expression in the DHI group was significantly higher than that in the MCAO group (P < 0.05). Compared with the DHI group, a significant decrease of the expression levels of p-PI3K, PI3K, and Akt proteins were observed in brain tissues of the DHI + LY294002 group (P < 0.01). The expression levels of p-Akt, p-PI3K, PI3K, and Akt proteins were all significantly decreased in brain tissues of the NMDP + LY294002 group compared with the MCAO group (P < 0.01). The expression of p-Akt protein in brain tissue in the DHI + LY294002 group was significantly upregulated in comparison to that in the LY294002 group (P < 0.01), while there were no significant differences compared with the other groups (P > 0.05). The expression of p-PI3K and PI3K proteins in the brain tissues of the NMDP + LY294002 group were significantly enhanced compared with the LY294002 group (P < 0.05), while no significant changes were observed in the other groups (P > 0.05). These findings indicated that DHI protects against brain ischemia-reperfusion injury by activating the PI3K-Akt signaling pathway in a rat model.
Expression of Apoptosis-Related Factors
As shown in Figure 8, expression levels of Bad, Bim, and Bax proteins in the brain tissue in the MCAO group were significantly upregulated compared with those in the sham group (P < 0.01), while Bcl-2 protein expression levels were significantly downregulated (P < 0.01). In comparison to the MCAO group, only Bim protein expression in the brain of the DHI group was significantly decreased (P < 0.01). A significant decrease of Bax and Bcl-2 protein expression in the brain tissues of the LY294002 group was observed (P < 0.05), while Bcl-2 protein expression was significantly decreased (P < 0.01). In the brain tissues of the NMDP + LY294002 group, Bcl-2 protein expression levels were significantly upregulated (P < 0.05), while the expression levels of Bad and Bim proteins were significantly downregulated (P < 0.01). Bcl-2 protein expression in brain tissue of the DHI + LY294002 group was significantly increased in comparison with the LY294002 group (P < 0.01), while no significant changes were observed in the other groups (P > 0.05). A significant decrease in Bad, Bim, and Bax protein expression was observed in the brain tissues of the NMDP + LY294002 group (P < 0.01), whereas a significant increase in Bcl-2 protein expression was observed (P < 0.01). These findings suggested that the expression of anti-apoptosis-related factors was promoted by DHI, while the expression of pro-apoptoticrelated factors was inhibited. Furthermore, the anti-apoptotic effect of DHI was inhibited by LY294002.
p53 mRNA Expression
As shown in Table 2 and Figure 9, the expression of p53 mRNA in the brain tissues of the MCAO group was significantly increased compared with that in the sham group (P < 0.01). In comparison with the MCAO group, decreased p53 expression The expression of Bax in brain tissue of each group rats determined by western blot. (E) The expression of Bcl-2 in brain tissue of each group rats determined by western blot (n = 4). Compared with the sham operation group, p < 0.01; compared with the MCAO group, *p < 0.05, **p < 0.01; compared with the LY294002 group, ## p < 0.01. Sham, sham operation group; MCAO, middle cerebral artery occlusion; LY294002, 2-(4-morpholinyl)-8-phenyl-chromone; DHI, Danhong Injection; NMDP, nimodipine.
was detected in the DHI (P < 0.05) and NMDP + LY294002 groups (P > 0.05). Expression of p53 in LY294002 group and DHI + LY294002 groups was increased significantly (P < 0.01 or P < 0.05). Compared with the LY294002 group, the expression of p53 mRNA was significantly decreased in both the DHI + LY294002 group (P < 0.05) and the NMDP + LY294002 group (P < 0.01). These results suggested that DHI inhibited apoptosis by downregulation of p53 gene expression, and LY294002 attenuated this effect.
In this study, we confirmed the neuroprotective effect of DHI on brain ischemia-reperfusion damage and provided evidence that this effect is mediated via the PI3K-Akt pathway, since inhibiting the PI3K-Akt signaling pathway weaken the neuroprotective effect of DHI on brain ischemic reperfusion damage in a rat MCAO model.
Ischemia-reperfusion damage is caused by many factors including the production of oxygen free radicals (Watson and Ginsberg, 2010), which play a crucial role in neuronal apoptosis. Free radicals also alter the response of blood vessels by damaging endothelial cells and disrupt the blood-brain barrier. Nitric oxide FIGURE 9 | The p53 mRNA expression level in each group determined by qRT-PCR (n = 4). Compared with the sham operation group, p < 0.01; compared with the MCAO group, *p < 0.05, **p < 0.01; compared with the LY294002 group, ## p < 0.01. Sham, sham operation group; MCAO, middle cerebral artery occlusion; LY294002, 2-(4-morpholinyl)-8-phenyl-chromone; DHI, Danhong Injection; NMDP, nimodipine.
is also involved in acute brain injury and induce apoptosis of nerve cells (Liu et al., 2006). In addition, studies have shown that excitatory amino acids (EAA), which is toxic to brain cells, play an important role of ischemia (Choi et al., 2014). Studies have also shown that the presence of energy metabolism disorders in the brain ischemia leads to a lack of ATP in cells and a decrease in pH, which seriously inhibits the activity of the Na + /Ca 2+− exchange protein, causing an ion imbalance in the cells, which eventually leads to the destruction of the cellular defense system in the brain (Liu et al., 1991). The local inflammatory reactions associated with brain ischemia reperfusion are a major cause of reperfusion damage (Mu et al., 2011), although apoptosis is the main cause of cell death under these conditions (Lipton, 1999). Apoptosis is a gene-regulated active death process, in which caspase-3, Bcl-2, and Bax genes play important regulatory roles.
Activation of Akt plays an important role in neuronal survival following cerebral ischemia-reperfusion injury. Studies have shown that Akt1 overexpression reduces the infarct size after cerebral ischemia by 35% in MCAO model rats (Ohba et al., 2004). Recent studies have also shown that Aktl has an important protective effect on ischemia-reperfusion injury in rats, with Akt overexpression shown to reduce the volume of infarcted brain tissue by 50% (Giuseppe et al., 2008). Therefore, the activation of Akt-mediated neuroprotection has been confirmed in a large number of studies of many agents, such as GDNF, VEGF and erythropoietin, which mediate their neuroprotective effects via the PI3K-Akt signaling pathway (Jin et al., 2003;Dilaver et al., 2005;Kilic et al., 2005). In accordance with these studies, our study provides evidence that the neuroprotective effects of DHI are also mediated via the PI3K-Akt pathway.
Both the p53 and MDM2 genes are associated with apoptosis (Polyak et al., 1997;Ray et al., 2011), and are also important in signaling downstream of Akt (Seger, 2002). These genes have been shown to play important roles in neuronal apoptosis, senescence and cell cycle arrest. It has been reported that p53 negatively regulates the PI3K-Akt pathway; therefore, the Akt-MDM2-p53 axis forms a negative feedback loop to regulate p53 expression and block p53-mediated pro-apoptotic gene transcription (Kim et al., 2001). In our study, we found that p53 and MDM2 gene expression was significantly increased in the MCAO group compared with that in the sham group, while the levels were significantly reduced in the DHI group. When the activation of PI3K-Atk pathway was inhibited, the effects of DHI were greatly attenuated, indicating that the mechanism underlying the neuroprotective effects of DHI involves regulation of p53 gene expression via PI3K-Atk signaling pathway.
Mitochondria are organelles that play a key regulatory role in neuronal apoptosis signaling pathways (Green and Reed, 1998). Phosphorylation of PI3K-Akt leads to upregulation of mitochondrial transcription factors and cytochrome c oxidase, resulting in decreased ATP production and cell death (Zhou et al., 2000). Cyt-C is a water-soluble protein encoded by a nuclear gene located outside the mitochondrial body. Cyt-C functions as an electron carrier in the mitochondrial respiratory chain, which plays an important role in the mitochondrial energy metabolism (Song et al., 2017). During apoptosis, Cyt-C is released into the cytoplasm, where it binds to apoptosis activation factor 1 (Apaf-1), and spontaneously activates caspase-9 to form a Cyt-C/Apaf-1/caspase-9 complex (Jiang et al., 2017). This further activates the caspase family, causing cell necrosis and DNA fragmentation which results in apoptosis (Jiang and Wang, 2000). Studies have shown that in the early stages of apoptosis, Cyt-C is released from the mitochondrial membrane to initiate the process of cellular apoptosis. Furthermore, Cyt-C release is induced by expression of the pro-apoptosis gene Bax, the anti-apoptosis gene Bcl-2 blocks the release of Cyt-C and activation of caspases (Jürgensmeier et al., 1998). Both Bax and Bcl-2 are downstream proteins in the PI3K-Akt signaling pathway that regulate the release of Cyt-C in mitochondria and the activation of caspase.
The components of TCM are very complicated and can contain dozens of compounds. There are also many precious compounds in the extracts of Rhizoma Salviae Miltiorrhizae and Flos Carthami contain many other important compounds including Tanshinone, Salvianic acid A, Hydroxysafflor Yellow A, and Safflower Yellow B, which have significant effects in the treatment or prevention of cardiovascular and cerebrovascular diseases.
Sodium danshensu is one of the important ingredients in Danshen and one of the quality control standards of DHI. Shao et al. found that sodium danshensu has a neuroprotective effect on the brain of rats with cerebral ischemia-reperfusion injury, and the related mechanism may be by activating the PI3K/Akt pathway to inhibit apoptosis (Guo et al., 2015). Zhang et al. (2017) discovered through research that rosmarinic acid protects rat hippocampal neurons from cerebral ischemia-reperfusion injury through the Akt/JNK3/caspase-3 pathway. And rosmarinic acid is also an important component in DHI, and its content is also one of the quality inspection standards of DHI. There are also two main components of DHI: salvianolic acid B and p-coumaric acid. Fan et al. found that salvianolic acid B has neuroprotective effect on brain injury induced by ischemia-reperfusion injury in rats by reducing the generation of free radicals, and which may be an effective clinical candidate treatment (Fan et al., 2018). During the research, Sakamula et al. found that pretreatment with p-coumaric acid can significantly reduce malondialdehyde levels, whole cerebral infarct volume, and hippocampal neuron death, and increase catalase and superoxide dismutase activities, eventually producing neuroprotective effect (Sakamula and Thong-asa, 2018). Xu et al. showed that Tanshinone IIA exerts a significant cardioprotective effect by improving heart function and reducing the infarct size (Wei et al., 2009). Liu et al. found that Salvianic acid A inhibited cerebrovascular endothelial apoptosis induced in mice by hydrogen peroxide via the PI3K/Akt/Raf/MEK/ERK pathway (Chen-Li et al., 2007). Zhong et al. demonstrated that Salvianic acid A reduced the number of apoptotic nerve cells after ischemia in rats through the restoration of movement (Jing et al., 2007). Lin et al. demonstrated that Hydroxysafflor Yellow A can prevent brain ischemic reperfusion damage By reducing the expression of genes involved in brain cell apoptosis via the PI3K/Akt/GSK3 beta signaling pathway (Lin et al., 2013). In a study of the protective effect of Danshensu and Hydroxysafflor Yellow on ischemic reperfusion injury in mice, Xu et al. showed that the drug combination had a better protective effect on nerve cells in mice than the individual drugs alone (Xu et al., 2017). Du et al. found that Safflower Yellow B protected the brain ischemic reperfusion damage by inhibiting AMPK-mediated NF-κB activation and reducing the expression of inflammatory cytokines (Du et al., 2019). The evidence provided in this study confirm the reliable neuroprotection against ischemiareperfusion injury provided by DHI, which is a combination of two TCM active components.
It has been reported that The Jak2-STAT3 signaling pathway also plays an important role in the protection of the brain against ischemia-reperfusion damage (Irawan et al., 2010) via a mechanism that involves the PI3K-Akt signaling pathway (Hou et al., 2018). Further studies are required to explore the relationship between the neuroprotective effect of DHI on brain ischemia-reperfusion injury and Jak2-STAT3 signaling pathways, as well as the interaction effect between the Jak2-STAT3 and PI3K-Akt signaling pathways.
CONCLUSION
In summary, our results demonstrate that DHI can protect brain tissue from ischemia-reperfusion injury in rats by reducing the inflammatory response and apoptosis of brain tissue cells. And we found that DHI produces this neuroprotective effect by regulating the expression of important proteins and genes in the PI3K-Akt pathway, indicating that this signaling pathway may be the mechanism behind this protective effect. The findings of this study provide a reference for the clinical anti-apoptosis and neuroprotection of DHI.
DATA AVAILABILITY STATEMENT
The datasets generated for this study are available on request to the corresponding author.
ETHICS STATEMENT
The animal study was reviewed and approved by the Institutional Animal Care and Use Committee at Zhejiang Chinese Medical University.
AUTHOR CONTRIBUTIONS
WJ and HW conceived and designed the study. CF, HW, and YZ were tested and analyzed the data. CF and HW wrote this manuscript. LY, YH, and CS coordinated the research and provided the technical assistance. WJ, HW, and LY modified the file. All authors reviewed the results and approved the final version of the manuscript. | 8,023.4 | 2020-03-11T00:00:00.000 | [
"Biology"
] |